TSTP Solution File: SEU912^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU912^5 : 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 : n025.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 14:10:48 EDT 2022

% Result   : Theorem 50.03s 50.21s
% Output   : Proof 50.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  171
% Syntax   : Number of formulae    :  186 (  20 unt;  16 typ;   8 def)
%            Number of atoms       :  781 (  46 equ;   0 cnn)
%            Maximal formula atoms :   33 (   4 avg)
%            Number of connectives : 2135 ( 574   ~;  95   |;   0   &; 781   @)
%                                         (  75 <=>; 610  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (   7 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  249 ( 249   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   94 (  92 usr;  81 con; 0-2 aty)
%            Number of variables   :  439 (  84   ^ 355   !;   0   ?; 439   :)

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

thf(ty_b,type,
    b: $tType ).

thf(ty_c,type,
    c: $tType ).

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

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

thf(ty_cC,type,
    cC: ( c > $o ) > $o ).

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

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

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

thf(ty_eigen__3,type,
    eigen__3: a > $o ).

thf(ty_eigen__10,type,
    eigen__10: b ).

thf(ty_cB,type,
    cB: ( b > $o ) > $o ).

thf(ty_cA,type,
    cA: ( a > $o ) > $o ).

thf(ty_eigen__22,type,
    eigen__22: a > $o ).

thf(ty_g,type,
    g: ( b > $o ) > c > $o ).

thf(ty_f,type,
    f: ( a > $o ) > b > $o ).

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

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ( cA @ X1 )
           => ( cC @ ( g @ ( f @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

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

thf(eigendef_eigen__6,definition,
    ( eigen__6
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ( cA @ X1 )
               => ~ ! [X2: c] :
                      ( ( eigen__0 @ X2 )
                     => ( g @ ( f @ X1 ) @ X2 ) ) )
           => ~ ! [X2: a > $o] :
                  ( ~ ( ! [X3: ( a > $o ) > $o] :
                          ( ~ ( ( X3
                                @ ^ [X4: a] : $false )
                             => ~ ! [X4: a > $o] :
                                    ( ( X3 @ X4 )
                                   => ! [X5: a] :
                                        ( ( X2 @ X5 )
                                       => ( X3
                                          @ ^ [X6: a] :
                                              ( ~ ( X4 @ X6 )
                                             => ( X5 = X6 ) ) ) ) ) )
                         => ( X3 @ X2 ) )
                     => ~ ! [X3: a] :
                            ( ( X2 @ X3 )
                           => ( X1 @ X3 ) ) )
                 => ~ ! [X3: a > $o] :
                        ( ~ ( ( cA @ X3 )
                           => ~ ! [X4: a] :
                                  ( ( X2 @ X4 )
                                 => ( X3 @ X4 ) ) )
                       => ~ ( ( cA @ X3 )
                           => ~ ! [X4: c] :
                                  ( ( eigen__0 @ X4 )
                                 => ( g @ ( f @ X3 ) @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__6])]) ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__1
      @ ^ [X1: c > $o] :
          ~ ( ~ ( ! [X2: ( c > $o ) > $o] :
                    ( ~ ( ( X2
                          @ ^ [X3: c] : $false )
                       => ~ ! [X3: c > $o] :
                              ( ( X2 @ X3 )
                             => ! [X4: c] :
                                  ( ( X1 @ X4 )
                                 => ( X2
                                    @ ^ [X5: c] :
                                        ( ~ ( X3 @ X5 )
                                       => ( X4 = X5 ) ) ) ) ) )
                   => ( X2 @ X1 ) )
               => ~ ! [X2: c] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: c > $o] :
                            ( ( cC @ X3 )
                           => ~ ( X3 @ X2 ) ) ) )
           => ~ ( ! [X2: a > $o] :
                    ( ~ ( ( cA @ X2 )
                       => ~ ! [X3: c] :
                              ( ( X1 @ X3 )
                             => ( g @ ( f @ X2 ) @ X3 ) ) )
                   => ( cA @ X2 ) )
               => ~ ! [X2: a > $o] :
                      ( ~ ( ( cA @ X2 )
                         => ~ ! [X3: c] :
                                ( ( X1 @ X3 )
                               => ( g @ ( f @ X2 ) @ X3 ) ) )
                     => ~ ! [X3: a > $o] :
                            ( ~ ( ! [X4: ( a > $o ) > $o] :
                                    ( ~ ( ( X4
                                          @ ^ [X5: a] : $false )
                                       => ~ ! [X5: a > $o] :
                                              ( ( X4 @ X5 )
                                             => ! [X6: a] :
                                                  ( ( X3 @ X6 )
                                                 => ( X4
                                                    @ ^ [X7: a] :
                                                        ( ~ ( X5 @ X7 )
                                                       => ( X6 = X7 ) ) ) ) ) )
                                   => ( X4 @ X3 ) )
                               => ~ ! [X4: a] :
                                      ( ( X3 @ X4 )
                                     => ( X2 @ X4 ) ) )
                           => ~ ! [X4: a > $o] :
                                  ( ~ ( ( cA @ X4 )
                                     => ~ ! [X5: a] :
                                            ( ( X3 @ X5 )
                                           => ( X4 @ X5 ) ) )
                                 => ~ ( ( cA @ X4 )
                                     => ~ ! [X5: c] :
                                            ( ( X1 @ X5 )
                                           => ( g @ ( f @ X4 ) @ X5 ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

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

thf(eigendef_eigen__10,definition,
    ( eigen__10
    = ( eps__2
      @ ^ [X1: b] :
          ~ ( ( eigen__7 @ X1 )
           => ~ ! [X2: b > $o] :
                  ( ( cB @ X2 )
                 => ~ ( X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__10])]) ).

thf(eigendef_eigen__22,definition,
    ( eigen__22
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ! [X2: ( a > $o ) > $o] :
                    ( ~ ( ( X2
                          @ ^ [X3: a] : $false )
                       => ~ ! [X3: a > $o] :
                              ( ( X2 @ X3 )
                             => ! [X4: a] :
                                  ( ( X1 @ X4 )
                                 => ( X2
                                    @ ^ [X5: a] :
                                        ( ~ ( X3 @ X5 )
                                       => ( X4 = X5 ) ) ) ) ) )
                   => ( X2 @ X1 ) )
               => ~ ! [X2: a] :
                      ( ( X1 @ X2 )
                     => ( eigen__6 @ X2 ) ) )
           => ~ ! [X2: a > $o] :
                  ( ~ ( ( cA @ X2 )
                     => ~ ! [X3: a] :
                            ( ( X1 @ X3 )
                           => ( X2 @ X3 ) ) )
                 => ~ ( ( cA @ X2 )
                     => ~ ! [X3: b] :
                            ( ( eigen__7 @ X3 )
                           => ( f @ X2 @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__22])]) ).

thf(eigendef_eigen__26,definition,
    ( eigen__26
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ( cA @ X1 )
               => ~ ! [X2: a] :
                      ( ( eigen__22 @ X2 )
                     => ( X1 @ X2 ) ) )
           => ~ ( ( cA @ X1 )
               => ~ ! [X2: c] :
                      ( ( eigen__0 @ X2 )
                     => ( g @ ( f @ X1 ) @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__26])]) ).

thf(h3,assumption,
    ! [X1: ( b > $o ) > $o,X2: b > $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__3 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__7,definition,
    ( eigen__7
    = ( eps__3
      @ ^ [X1: b > $o] :
          ~ ( ~ ( ! [X2: ( b > $o ) > $o] :
                    ( ~ ( ( X2
                          @ ^ [X3: b] : $false )
                       => ~ ! [X3: b > $o] :
                              ( ( X2 @ X3 )
                             => ! [X4: b] :
                                  ( ( X1 @ X4 )
                                 => ( X2
                                    @ ^ [X5: b] :
                                        ( ~ ( X3 @ X5 )
                                       => ( X4 = X5 ) ) ) ) ) )
                   => ( X2 @ X1 ) )
               => ~ ! [X2: b] :
                      ( ( X1 @ X2 )
                     => ( f @ eigen__6 @ X2 ) ) )
           => ~ ! [X2: b > $o] :
                  ( ~ ( ( cB @ X2 )
                     => ~ ! [X3: b] :
                            ( ( X1 @ X3 )
                           => ( X2 @ X3 ) ) )
                 => ~ ( ( cB @ X2 )
                     => ~ ! [X3: c] :
                            ( ( eigen__0 @ X3 )
                           => ( g @ X2 @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__7])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( ~ ( ! [X1: a > $o] :
                  ( ( cA @ X1 )
                 => ( cB @ ( f @ X1 ) ) )
             => ~ ! [X1: b > $o] :
                    ( ~ ( ! [X2: ( b > $o ) > $o] :
                            ( ~ ( ( X2
                                  @ ^ [X3: b] : $false )
                               => ~ ! [X3: b > $o] :
                                      ( ( X2 @ X3 )
                                     => ! [X4: b] :
                                          ( ( X1 @ X4 )
                                         => ( X2
                                            @ ^ [X5: b] :
                                                ( ~ ( X3 @ X5 )
                                               => ( X4 = X5 ) ) ) ) ) )
                           => ( X2 @ X1 ) )
                       => ~ ! [X2: b] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: b > $o] :
                                    ( ( cB @ X3 )
                                   => ~ ( X3 @ X2 ) ) ) )
                   => ~ ( ! [X2: a > $o] :
                            ( ~ ( ( cA @ X2 )
                               => ~ ! [X3: b] :
                                      ( ( X1 @ X3 )
                                     => ( f @ X2 @ X3 ) ) )
                           => ( cA @ X2 ) )
                       => ~ ! [X2: a > $o] :
                              ( ~ ( ( cA @ X2 )
                                 => ~ ! [X3: b] :
                                        ( ( X1 @ X3 )
                                       => ( f @ X2 @ X3 ) ) )
                             => ~ ! [X3: a > $o] :
                                    ( ~ ( ! [X4: ( a > $o ) > $o] :
                                            ( ~ ( ( X4
                                                  @ ^ [X5: a] : $false )
                                               => ~ ! [X5: a > $o] :
                                                      ( ( X4 @ X5 )
                                                     => ! [X6: a] :
                                                          ( ( X3 @ X6 )
                                                         => ( X4
                                                            @ ^ [X7: a] :
                                                                ( ~ ( X5 @ X7 )
                                                               => ( X6 = X7 ) ) ) ) ) )
                                           => ( X4 @ X3 ) )
                                       => ~ ! [X4: a] :
                                              ( ( X3 @ X4 )
                                             => ( X2 @ X4 ) ) )
                                   => ~ ! [X4: a > $o] :
                                          ( ~ ( ( cA @ X4 )
                                             => ~ ! [X5: a] :
                                                    ( ( X3 @ X5 )
                                                   => ( X4 @ X5 ) ) )
                                         => ~ ( ( cA @ X4 )
                                             => ~ ! [X5: b] :
                                                    ( ( X1 @ X5 )
                                                   => ( f @ X4 @ X5 ) ) ) ) ) ) ) ) )
         => ~ ! [X1: b > $o] :
                ( ( cB @ X1 )
               => ( cC @ ( g @ X1 ) ) ) )
     => ~ ! [X1: c > $o] :
            ( ~ ( ! [X2: ( c > $o ) > $o] :
                    ( ~ ( ( X2
                          @ ^ [X3: c] : $false )
                       => ~ ! [X3: c > $o] :
                              ( ( X2 @ X3 )
                             => ! [X4: c] :
                                  ( ( X1 @ X4 )
                                 => ( X2
                                    @ ^ [X5: c] :
                                        ( ~ ( X3 @ X5 )
                                       => ( X4 = X5 ) ) ) ) ) )
                   => ( X2 @ X1 ) )
               => ~ ! [X2: c] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: c > $o] :
                            ( ( cC @ X3 )
                           => ~ ( X3 @ X2 ) ) ) )
           => ~ ( ! [X2: b > $o] :
                    ( ~ ( ( cB @ X2 )
                       => ~ ! [X3: c] :
                              ( ( X1 @ X3 )
                             => ( g @ X2 @ X3 ) ) )
                   => ( cB @ X2 ) )
               => ~ ! [X2: b > $o] :
                      ( ~ ( ( cB @ X2 )
                         => ~ ! [X3: c] :
                                ( ( X1 @ X3 )
                               => ( g @ X2 @ X3 ) ) )
                     => ~ ! [X3: b > $o] :
                            ( ~ ( ! [X4: ( b > $o ) > $o] :
                                    ( ~ ( ( X4
                                          @ ^ [X5: b] : $false )
                                       => ~ ! [X5: b > $o] :
                                              ( ( X4 @ X5 )
                                             => ! [X6: b] :
                                                  ( ( X3 @ X6 )
                                                 => ( X4
                                                    @ ^ [X7: b] :
                                                        ( ~ ( X5 @ X7 )
                                                       => ( X6 = X7 ) ) ) ) ) )
                                   => ( X4 @ X3 ) )
                               => ~ ! [X4: b] :
                                      ( ( X3 @ X4 )
                                     => ( X2 @ X4 ) ) )
                           => ~ ! [X4: b > $o] :
                                  ( ~ ( ( cB @ X4 )
                                     => ~ ! [X5: b] :
                                            ( ( X3 @ X5 )
                                           => ( X4 @ X5 ) ) )
                                 => ~ ( ( cB @ X4 )
                                     => ~ ! [X5: c] :
                                            ( ( X1 @ X5 )
                                           => ( g @ X4 @ X5 ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( ! [X1: ( c > $o ) > $o] :
              ( ~ ( ( X1
                    @ ^ [X2: c] : $false )
                 => ~ ! [X2: c > $o] :
                        ( ( X1 @ X2 )
                       => ! [X3: c] :
                            ( ( eigen__0 @ X3 )
                           => ( X1
                              @ ^ [X4: c] :
                                  ( ~ ( X2 @ X4 )
                                 => ( X3 = X4 ) ) ) ) ) )
             => ( X1 @ eigen__0 ) )
         => ~ ! [X1: c] :
                ( ( eigen__0 @ X1 )
               => ~ ! [X2: c > $o] :
                      ( ( cC @ X2 )
                     => ~ ( X2 @ X1 ) ) ) )
     => ~ ( ! [X1: b > $o] :
              ( ~ ( ( cB @ X1 )
                 => ~ ! [X2: c] :
                        ( ( eigen__0 @ X2 )
                       => ( g @ X1 @ X2 ) ) )
             => ( cB @ X1 ) )
         => ~ ! [X1: b > $o] :
                ( ~ ( ( cB @ X1 )
                   => ~ ! [X2: c] :
                          ( ( eigen__0 @ X2 )
                         => ( g @ X1 @ X2 ) ) )
               => ~ ! [X2: b > $o] :
                      ( ~ ( ! [X3: ( b > $o ) > $o] :
                              ( ~ ( ( X3
                                    @ ^ [X4: b] : $false )
                                 => ~ ! [X4: b > $o] :
                                        ( ( X3 @ X4 )
                                       => ! [X5: b] :
                                            ( ( X2 @ X5 )
                                           => ( X3
                                              @ ^ [X6: b] :
                                                  ( ~ ( X4 @ X6 )
                                                 => ( X5 = X6 ) ) ) ) ) )
                             => ( X3 @ X2 ) )
                         => ~ ! [X3: b] :
                                ( ( X2 @ X3 )
                               => ( X1 @ X3 ) ) )
                     => ~ ! [X3: b > $o] :
                            ( ~ ( ( cB @ X3 )
                               => ~ ! [X4: b] :
                                      ( ( X2 @ X4 )
                                     => ( X3 @ X4 ) ) )
                           => ~ ( ( cB @ X3 )
                               => ~ ! [X4: c] :
                                      ( ( eigen__0 @ X4 )
                                     => ( g @ X3 @ X4 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( cC @ ( g @ ( f @ eigen__3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( cB @ ( f @ eigen__26 ) )
     => ~ ! [X1: b] :
            ( ( eigen__7 @ X1 )
           => ( f @ eigen__26 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: c > $o] :
        ( ~ ( ! [X2: ( c > $o ) > $o] :
                ( ~ ( ( X2
                      @ ^ [X3: c] : $false )
                   => ~ ! [X3: c > $o] :
                          ( ( X2 @ X3 )
                         => ! [X4: c] :
                              ( ( X1 @ X4 )
                             => ( X2
                                @ ^ [X5: c] :
                                    ( ~ ( X3 @ X5 )
                                   => ( X4 = X5 ) ) ) ) ) )
               => ( X2 @ X1 ) )
           => ~ ! [X2: c] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: c > $o] :
                        ( ( cC @ X3 )
                       => ~ ( X3 @ X2 ) ) ) )
       => ~ ( ! [X2: a > $o] :
                ( ~ ( ( cA @ X2 )
                   => ~ ! [X3: c] :
                          ( ( X1 @ X3 )
                         => ( g @ ( f @ X2 ) @ X3 ) ) )
               => ( cA @ X2 ) )
           => ~ ! [X2: a > $o] :
                  ( ~ ( ( cA @ X2 )
                     => ~ ! [X3: c] :
                            ( ( X1 @ X3 )
                           => ( g @ ( f @ X2 ) @ X3 ) ) )
                 => ~ ! [X3: a > $o] :
                        ( ~ ( ! [X4: ( a > $o ) > $o] :
                                ( ~ ( ( X4
                                      @ ^ [X5: a] : $false )
                                   => ~ ! [X5: a > $o] :
                                          ( ( X4 @ X5 )
                                         => ! [X6: a] :
                                              ( ( X3 @ X6 )
                                             => ( X4
                                                @ ^ [X7: a] :
                                                    ( ~ ( X5 @ X7 )
                                                   => ( X6 = X7 ) ) ) ) ) )
                               => ( X4 @ X3 ) )
                           => ~ ! [X4: a] :
                                  ( ( X3 @ X4 )
                                 => ( X2 @ X4 ) ) )
                       => ~ ! [X4: a > $o] :
                              ( ~ ( ( cA @ X4 )
                                 => ~ ! [X5: a] :
                                        ( ( X3 @ X5 )
                                       => ( X4 @ X5 ) ) )
                             => ~ ( ( cA @ X4 )
                                 => ~ ! [X5: c] :
                                        ( ( X1 @ X5 )
                                       => ( g @ ( f @ X4 ) @ X5 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( cB @ ( f @ eigen__6 ) )
     => ~ ! [X1: c] :
            ( ( eigen__0 @ X1 )
           => ( g @ ( f @ eigen__6 ) @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( eigen__7 @ eigen__10 )
     => ( f @ eigen__6 @ eigen__10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ ( ! [X1: ( c > $o ) > $o] :
              ( ~ ( ( X1
                    @ ^ [X2: c] : $false )
                 => ~ ! [X2: c > $o] :
                        ( ( X1 @ X2 )
                       => ! [X3: c] :
                            ( ( eigen__0 @ X3 )
                           => ( X1
                              @ ^ [X4: c] :
                                  ( ~ ( X2 @ X4 )
                                 => ( X3 = X4 ) ) ) ) ) )
             => ( X1 @ eigen__0 ) )
         => ~ ! [X1: c] :
                ( ( eigen__0 @ X1 )
               => ~ ! [X2: c > $o] :
                      ( ( cC @ X2 )
                     => ~ ( X2 @ X1 ) ) ) )
     => ~ ( ! [X1: a > $o] :
              ( ~ ( ( cA @ X1 )
                 => ~ ! [X2: c] :
                        ( ( eigen__0 @ X2 )
                       => ( g @ ( f @ X1 ) @ X2 ) ) )
             => ( cA @ X1 ) )
         => ~ ! [X1: a > $o] :
                ( ~ ( ( cA @ X1 )
                   => ~ ! [X2: c] :
                          ( ( eigen__0 @ X2 )
                         => ( g @ ( f @ X1 ) @ X2 ) ) )
               => ~ ! [X2: a > $o] :
                      ( ~ ( ! [X3: ( a > $o ) > $o] :
                              ( ~ ( ( X3
                                    @ ^ [X4: a] : $false )
                                 => ~ ! [X4: a > $o] :
                                        ( ( X3 @ X4 )
                                       => ! [X5: a] :
                                            ( ( X2 @ X5 )
                                           => ( X3
                                              @ ^ [X6: a] :
                                                  ( ~ ( X4 @ X6 )
                                                 => ( X5 = X6 ) ) ) ) ) )
                             => ( X3 @ X2 ) )
                         => ~ ! [X3: a] :
                                ( ( X2 @ X3 )
                               => ( X1 @ X3 ) ) )
                     => ~ ! [X3: a > $o] :
                            ( ~ ( ( cA @ X3 )
                               => ~ ! [X4: a] :
                                      ( ( X2 @ X4 )
                                     => ( X3 @ X4 ) ) )
                           => ~ ( ( cA @ X3 )
                               => ~ ! [X4: c] :
                                      ( ( eigen__0 @ X4 )
                                     => ( g @ ( f @ X3 ) @ X4 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ! [X1: a > $o] :
          ( ~ ( ( cA @ X1 )
             => ~ ! [X2: b] :
                    ( ( eigen__7 @ X2 )
                   => ( f @ X1 @ X2 ) ) )
         => ( cA @ X1 ) )
     => ~ ! [X1: a > $o] :
            ( ~ ( ( cA @ X1 )
               => ~ ! [X2: b] :
                      ( ( eigen__7 @ X2 )
                     => ( f @ X1 @ X2 ) ) )
           => ~ ! [X2: a > $o] :
                  ( ~ ( ! [X3: ( a > $o ) > $o] :
                          ( ~ ( ( X3
                                @ ^ [X4: a] : $false )
                             => ~ ! [X4: a > $o] :
                                    ( ( X3 @ X4 )
                                   => ! [X5: a] :
                                        ( ( X2 @ X5 )
                                       => ( X3
                                          @ ^ [X6: a] :
                                              ( ~ ( X4 @ X6 )
                                             => ( X5 = X6 ) ) ) ) ) )
                         => ( X3 @ X2 ) )
                     => ~ ! [X3: a] :
                            ( ( X2 @ X3 )
                           => ( X1 @ X3 ) ) )
                 => ~ ! [X3: a > $o] :
                        ( ~ ( ( cA @ X3 )
                           => ~ ! [X4: a] :
                                  ( ( X2 @ X4 )
                                 => ( X3 @ X4 ) ) )
                       => ~ ( ( cA @ X3 )
                           => ~ ! [X4: b] :
                                  ( ( eigen__7 @ X4 )
                                 => ( f @ X3 @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ~ ( ! [X1: ( a > $o ) > $o] :
              ( ~ ( ( X1
                    @ ^ [X2: a] : $false )
                 => ~ ! [X2: a > $o] :
                        ( ( X1 @ X2 )
                       => ! [X3: a] :
                            ( ( eigen__22 @ X3 )
                           => ( X1
                              @ ^ [X4: a] :
                                  ( ~ ( X2 @ X4 )
                                 => ( X3 = X4 ) ) ) ) ) )
             => ( X1 @ eigen__22 ) )
         => ~ ! [X1: a] :
                ( ( eigen__22 @ X1 )
               => ( eigen__6 @ X1 ) ) )
     => ~ ! [X1: a > $o] :
            ( ~ ( ( cA @ X1 )
               => ~ ! [X2: a] :
                      ( ( eigen__22 @ X2 )
                     => ( X1 @ X2 ) ) )
           => ~ ( ( cA @ X1 )
               => ~ ! [X2: c] :
                      ( ( eigen__0 @ X2 )
                     => ( g @ ( f @ X1 ) @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( cB @ ( f @ eigen__3 ) )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: ( a > $o ) > $o] :
                ( ~ ( ( X2
                      @ ^ [X3: a] : $false )
                   => ~ ! [X3: a > $o] :
                          ( ( X2 @ X3 )
                         => ! [X4: a] :
                              ( ( X1 @ X4 )
                             => ( X2
                                @ ^ [X5: a] :
                                    ( ~ ( X3 @ X5 )
                                   => ( X4 = X5 ) ) ) ) ) )
               => ( X2 @ X1 ) )
           => ~ ! [X2: a] :
                  ( ( X1 @ X2 )
                 => ( eigen__6 @ X2 ) ) )
       => ~ ! [X2: a > $o] :
              ( ~ ( ( cA @ X2 )
                 => ~ ! [X3: a] :
                        ( ( X1 @ X3 )
                       => ( X2 @ X3 ) ) )
             => ~ ( ( cA @ X2 )
                 => ~ ! [X3: b] :
                        ( ( eigen__7 @ X3 )
                       => ( f @ X2 @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ! [X1: ( b > $o ) > $o] :
          ( ~ ( ( X1
                @ ^ [X2: b] : $false )
             => ~ ! [X2: b > $o] :
                    ( ( X1 @ X2 )
                   => ! [X3: b] :
                        ( ( eigen__7 @ X3 )
                       => ( X1
                          @ ^ [X4: b] :
                              ( ~ ( X2 @ X4 )
                             => ( X3 = X4 ) ) ) ) ) )
         => ( X1 @ eigen__7 ) )
     => ~ ! [X1: b] :
            ( ( eigen__7 @ X1 )
           => ~ ! [X2: b > $o] :
                  ( ( cB @ X2 )
                 => ~ ( X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: c > $o] :
        ( ~ ( ! [X2: ( c > $o ) > $o] :
                ( ~ ( ( X2
                      @ ^ [X3: c] : $false )
                   => ~ ! [X3: c > $o] :
                          ( ( X2 @ X3 )
                         => ! [X4: c] :
                              ( ( X1 @ X4 )
                             => ( X2
                                @ ^ [X5: c] :
                                    ( ~ ( X3 @ X5 )
                                   => ( X4 = X5 ) ) ) ) ) )
               => ( X2 @ X1 ) )
           => ~ ! [X2: c] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: c > $o] :
                        ( ( cC @ X3 )
                       => ~ ( X3 @ X2 ) ) ) )
       => ~ ( ! [X2: b > $o] :
                ( ~ ( ( cB @ X2 )
                   => ~ ! [X3: c] :
                          ( ( X1 @ X3 )
                         => ( g @ X2 @ X3 ) ) )
               => ( cB @ X2 ) )
           => ~ ! [X2: b > $o] :
                  ( ~ ( ( cB @ X2 )
                     => ~ ! [X3: c] :
                            ( ( X1 @ X3 )
                           => ( g @ X2 @ X3 ) ) )
                 => ~ ! [X3: b > $o] :
                        ( ~ ( ! [X4: ( b > $o ) > $o] :
                                ( ~ ( ( X4
                                      @ ^ [X5: b] : $false )
                                   => ~ ! [X5: b > $o] :
                                          ( ( X4 @ X5 )
                                         => ! [X6: b] :
                                              ( ( X3 @ X6 )
                                             => ( X4
                                                @ ^ [X7: b] :
                                                    ( ~ ( X5 @ X7 )
                                                   => ( X6 = X7 ) ) ) ) ) )
                               => ( X4 @ X3 ) )
                           => ~ ! [X4: b] :
                                  ( ( X3 @ X4 )
                                 => ( X2 @ X4 ) ) )
                       => ~ ! [X4: b > $o] :
                              ( ~ ( ( cB @ X4 )
                                 => ~ ! [X5: b] :
                                        ( ( X3 @ X5 )
                                       => ( X4 @ X5 ) ) )
                             => ~ ( ( cB @ X4 )
                                 => ~ ! [X5: c] :
                                        ( ( X1 @ X5 )
                                       => ( g @ X4 @ X5 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( eigen__7 @ eigen__10 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ! [X1: ( a > $o ) > $o] :
          ( ~ ( ( X1
                @ ^ [X2: a] : $false )
             => ~ ! [X2: a > $o] :
                    ( ( X1 @ X2 )
                   => ! [X3: a] :
                        ( ( eigen__22 @ X3 )
                       => ( X1
                          @ ^ [X4: a] :
                              ( ~ ( X2 @ X4 )
                             => ( X3 = X4 ) ) ) ) ) )
         => ( X1 @ eigen__22 ) )
     => ~ ! [X1: a] :
            ( ( eigen__22 @ X1 )
           => ( eigen__6 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: b > $o] :
        ( ~ ( ! [X2: ( b > $o ) > $o] :
                ( ~ ( ( X2
                      @ ^ [X3: b] : $false )
                   => ~ ! [X3: b > $o] :
                          ( ( X2 @ X3 )
                         => ! [X4: b] :
                              ( ( X1 @ X4 )
                             => ( X2
                                @ ^ [X5: b] :
                                    ( ~ ( X3 @ X5 )
                                   => ( X4 = X5 ) ) ) ) ) )
               => ( X2 @ X1 ) )
           => ~ ! [X2: b] :
                  ( ( X1 @ X2 )
                 => ( f @ eigen__6 @ X2 ) ) )
       => ~ ! [X2: b > $o] :
              ( ~ ( ( cB @ X2 )
                 => ~ ! [X3: b] :
                        ( ( X1 @ X3 )
                       => ( X2 @ X3 ) ) )
             => ~ ( ( cB @ X2 )
                 => ~ ! [X3: c] :
                        ( ( eigen__0 @ X3 )
                       => ( g @ X2 @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( cA @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( cA @ eigen__26 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ~ ( ! [X1: ( b > $o ) > $o] :
              ( ~ ( ( X1
                    @ ^ [X2: b] : $false )
                 => ~ ! [X2: b > $o] :
                        ( ( X1 @ X2 )
                       => ! [X3: b] :
                            ( ( eigen__7 @ X3 )
                           => ( X1
                              @ ^ [X4: b] :
                                  ( ~ ( X2 @ X4 )
                                 => ( X3 = X4 ) ) ) ) ) )
             => ( X1 @ eigen__7 ) )
         => ~ ! [X1: b] :
                ( ( eigen__7 @ X1 )
               => ( f @ eigen__6 @ X1 ) ) )
     => ~ ! [X1: b > $o] :
            ( ~ ( ( cB @ X1 )
               => ~ ! [X2: b] :
                      ( ( eigen__7 @ X2 )
                     => ( X1 @ X2 ) ) )
           => ~ ( ( cB @ X1 )
               => ~ ! [X2: c] :
                      ( ( eigen__0 @ X2 )
                     => ( g @ X1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( cA @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( cB @ ( f @ eigen__6 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( sP18
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( sP22
     => ~ ( f @ eigen__6 @ eigen__10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: a > $o] :
        ( ( cA @ X1 )
       => ( cC @ ( g @ ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP19
     => ~ ! [X1: a] :
            ( ( eigen__22 @ X1 )
           => ( eigen__26 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: c] :
        ( ( eigen__0 @ X1 )
       => ( g @ ( f @ eigen__6 ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ! [X1: a > $o] :
        ( ~ ( ( cA @ X1 )
           => ~ ! [X2: b] :
                  ( ( eigen__7 @ X2 )
                 => ( f @ X1 @ X2 ) ) )
       => ~ ! [X2: a > $o] :
              ( ~ ( ! [X3: ( a > $o ) > $o] :
                      ( ~ ( ( X3
                            @ ^ [X4: a] : $false )
                         => ~ ! [X4: a > $o] :
                                ( ( X3 @ X4 )
                               => ! [X5: a] :
                                    ( ( X2 @ X5 )
                                   => ( X3
                                      @ ^ [X6: a] :
                                          ( ~ ( X4 @ X6 )
                                         => ( X5 = X6 ) ) ) ) ) )
                     => ( X3 @ X2 ) )
                 => ~ ! [X3: a] :
                        ( ( X2 @ X3 )
                       => ( X1 @ X3 ) ) )
             => ~ ! [X3: a > $o] :
                    ( ~ ( ( cA @ X3 )
                       => ~ ! [X4: a] :
                              ( ( X2 @ X4 )
                             => ( X3 @ X4 ) ) )
                   => ~ ( ( cA @ X3 )
                       => ~ ! [X4: b] :
                              ( ( eigen__7 @ X4 )
                             => ( f @ X3 @ X4 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( ~ ( sP21
         => ~ sP27 )
     => ~ ! [X1: a > $o] :
            ( ~ ( ! [X2: ( a > $o ) > $o] :
                    ( ~ ( ( X2
                          @ ^ [X3: a] : $false )
                       => ~ ! [X3: a > $o] :
                              ( ( X2 @ X3 )
                             => ! [X4: a] :
                                  ( ( X1 @ X4 )
                                 => ( X2
                                    @ ^ [X5: a] :
                                        ( ~ ( X3 @ X5 )
                                       => ( X4 = X5 ) ) ) ) ) )
                   => ( X2 @ X1 ) )
               => ~ ! [X2: a] :
                      ( ( X1 @ X2 )
                     => ( eigen__6 @ X2 ) ) )
           => ~ ! [X2: a > $o] :
                  ( ~ ( ( cA @ X2 )
                     => ~ ! [X3: a] :
                            ( ( X1 @ X3 )
                           => ( X2 @ X3 ) ) )
                 => ~ ( ( cA @ X2 )
                     => ~ ! [X3: c] :
                            ( ( eigen__0 @ X3 )
                           => ( g @ ( f @ X2 ) @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( ~ sP6
     => ~ sP17 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ( cB @ ( f @ eigen__26 ) )
     => ~ ! [X1: c] :
            ( ( eigen__0 @ X1 )
           => ( g @ ( f @ eigen__26 ) @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ! [X1: a > $o] :
        ( ~ ( ( cA @ X1 )
           => ~ ! [X2: c] :
                  ( ( eigen__0 @ X2 )
                 => ( g @ ( f @ X1 ) @ X2 ) ) )
       => ( cA @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( ! [X1: b > $o] :
          ( ~ ( ( cB @ X1 )
             => ~ ! [X2: c] :
                    ( ( eigen__0 @ X2 )
                   => ( g @ X1 @ X2 ) ) )
         => ( cB @ X1 ) )
     => ~ ! [X1: b > $o] :
            ( ~ ( ( cB @ X1 )
               => ~ ! [X2: c] :
                      ( ( eigen__0 @ X2 )
                     => ( g @ X1 @ X2 ) ) )
           => ~ ! [X2: b > $o] :
                  ( ~ ( ! [X3: ( b > $o ) > $o] :
                          ( ~ ( ( X3
                                @ ^ [X4: b] : $false )
                             => ~ ! [X4: b > $o] :
                                    ( ( X3 @ X4 )
                                   => ! [X5: b] :
                                        ( ( X2 @ X5 )
                                       => ( X3
                                          @ ^ [X6: b] :
                                              ( ~ ( X4 @ X6 )
                                             => ( X5 = X6 ) ) ) ) ) )
                         => ( X3 @ X2 ) )
                     => ~ ! [X3: b] :
                            ( ( X2 @ X3 )
                           => ( X1 @ X3 ) ) )
                 => ~ ! [X3: b > $o] :
                        ( ~ ( ( cB @ X3 )
                           => ~ ! [X4: b] :
                                  ( ( X2 @ X4 )
                                 => ( X3 @ X4 ) ) )
                       => ~ ( ( cB @ X3 )
                           => ~ ! [X4: c] :
                                  ( ( eigen__0 @ X4 )
                                 => ( g @ X3 @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: c] :
        ( ( eigen__0 @ X1 )
       => ( g @ ( f @ eigen__26 ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: a > $o] :
        ( ~ ( ( cA @ X1 )
           => ~ ! [X2: a] :
                  ( ( eigen__22 @ X2 )
                 => ( X1 @ X2 ) ) )
       => ~ ( ( cA @ X1 )
           => ~ ! [X2: b] :
                  ( ( eigen__7 @ X2 )
                 => ( f @ X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( ! [X1: ( c > $o ) > $o] :
          ( ~ ( ( X1
                @ ^ [X2: c] : $false )
             => ~ ! [X2: c > $o] :
                    ( ( X1 @ X2 )
                   => ! [X3: c] :
                        ( ( eigen__0 @ X3 )
                       => ( X1
                          @ ^ [X4: c] :
                              ( ~ ( X2 @ X4 )
                             => ( X3 = X4 ) ) ) ) ) )
         => ( X1 @ eigen__0 ) )
     => ~ ! [X1: c] :
            ( ( eigen__0 @ X1 )
           => ~ ! [X2: c > $o] :
                  ( ( cC @ X2 )
                 => ~ ( X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( f @ eigen__6 @ eigen__10 ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ! [X1: b > $o] :
        ( ( cB @ X1 )
       => ( cC @ ( g @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ! [X1: a > $o] :
        ( ~ ( ( cA @ X1 )
           => ~ ! [X2: a] :
                  ( ( eigen__22 @ X2 )
                 => ( X1 @ X2 ) ) )
       => ~ ( ( cA @ X1 )
           => ~ ! [X2: c] :
                  ( ( eigen__0 @ X2 )
                 => ( g @ ( f @ X1 ) @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ! [X1: a > $o] :
        ( ( cA @ X1 )
       => ( cB @ ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( cB @ ( f @ eigen__26 ) ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ( ~ sP13
     => ~ sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ( cA @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: ( a > $o ) > $o] :
                ( ~ ( ( X2
                      @ ^ [X3: a] : $false )
                   => ~ ! [X3: a > $o] :
                          ( ( X2 @ X3 )
                         => ! [X4: a] :
                              ( ( X1 @ X4 )
                             => ( X2
                                @ ^ [X5: a] :
                                    ( ~ ( X3 @ X5 )
                                   => ( X4 = X5 ) ) ) ) ) )
               => ( X2 @ X1 ) )
           => ~ ! [X2: a] :
                  ( ( X1 @ X2 )
                 => ( eigen__6 @ X2 ) ) )
       => ~ ! [X2: a > $o] :
              ( ~ ( ( cA @ X2 )
                 => ~ ! [X3: a] :
                        ( ( X1 @ X3 )
                       => ( X2 @ X3 ) ) )
             => ~ ( ( cA @ X2 )
                 => ~ ! [X3: c] :
                        ( ( eigen__0 @ X3 )
                       => ( g @ ( f @ X2 ) @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ! [X1: b] :
        ( ( eigen__7 @ X1 )
       => ( f @ eigen__26 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( ! [X1: ( b > $o ) > $o] :
          ( ~ ( ( X1
                @ ^ [X2: b] : $false )
             => ~ ! [X2: b > $o] :
                    ( ( X1 @ X2 )
                   => ! [X3: b] :
                        ( ( eigen__7 @ X3 )
                       => ( X1
                          @ ^ [X4: b] :
                              ( ~ ( X2 @ X4 )
                             => ( X3 = X4 ) ) ) ) ) )
         => ( X1 @ eigen__7 ) )
     => ~ ! [X1: b] :
            ( ( eigen__7 @ X1 )
           => ( f @ eigen__6 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ( sP19
     => sP41 ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( ~ ( sP43
         => ~ ! [X1: c] :
                ( ( eigen__0 @ X1 )
               => ( g @ ( f @ eigen__1 ) @ X1 ) ) )
     => sP43 ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ( sP25
     => ~ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ( sP21
     => ~ ! [X1: b] :
            ( ( eigen__7 @ X1 )
           => ( f @ eigen__6 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ! [X1: b > $o] :
        ( ~ ( ( cB @ X1 )
           => ~ ! [X2: c] :
                  ( ( eigen__0 @ X2 )
                 => ( g @ X1 @ X2 ) ) )
       => ~ ! [X2: b > $o] :
              ( ~ ( ! [X3: ( b > $o ) > $o] :
                      ( ~ ( ( X3
                            @ ^ [X4: b] : $false )
                         => ~ ! [X4: b > $o] :
                                ( ( X3 @ X4 )
                               => ! [X5: b] :
                                    ( ( X2 @ X5 )
                                   => ( X3
                                      @ ^ [X6: b] :
                                          ( ~ ( X4 @ X6 )
                                         => ( X5 = X6 ) ) ) ) ) )
                     => ( X3 @ X2 ) )
                 => ~ ! [X3: b] :
                        ( ( X2 @ X3 )
                       => ( X1 @ X3 ) ) )
             => ~ ! [X3: b > $o] :
                    ( ~ ( ( cB @ X3 )
                       => ~ ! [X4: b] :
                              ( ( X2 @ X4 )
                             => ( X3 @ X4 ) ) )
                   => ~ ( ( cB @ X3 )
                       => ~ ! [X4: c] :
                              ( ( eigen__0 @ X4 )
                             => ( g @ X3 @ X4 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ! [X1: b > $o] :
        ( ~ ( ( cB @ X1 )
           => ~ ! [X2: b] :
                  ( ( eigen__7 @ X2 )
                 => ( X1 @ X2 ) ) )
       => ~ ( ( cB @ X1 )
           => ~ ! [X2: c] :
                  ( ( eigen__0 @ X2 )
                 => ( g @ X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( ~ sP1
     => ~ sP49 ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ! [X1: ( b > $o ) > $o] :
        ( ~ ( ( X1
              @ ^ [X2: b] : $false )
           => ~ ! [X2: b > $o] :
                  ( ( X1 @ X2 )
                 => ! [X3: b] :
                      ( ( eigen__7 @ X3 )
                     => ( X1
                        @ ^ [X4: b] :
                            ( ~ ( X2 @ X4 )
                           => ( X3 = X4 ) ) ) ) ) )
       => ( X1 @ eigen__7 ) ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ( ~ sP26
     => ~ ( sP19
         => ~ sP34 ) ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ( ~ sP50
     => ~ sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ! [X1: b] :
        ( ( eigen__7 @ X1 )
       => ~ ! [X2: b > $o] :
              ( ( cB @ X2 )
             => ~ ( X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ( sP40
     => ~ ! [X1: b > $o] :
            ( ~ ( ! [X2: ( b > $o ) > $o] :
                    ( ~ ( ( X2
                          @ ^ [X3: b] : $false )
                       => ~ ! [X3: b > $o] :
                              ( ( X2 @ X3 )
                             => ! [X4: b] :
                                  ( ( X1 @ X4 )
                                 => ( X2
                                    @ ^ [X5: b] :
                                        ( ~ ( X3 @ X5 )
                                       => ( X4 = X5 ) ) ) ) ) )
                   => ( X2 @ X1 ) )
               => ~ ! [X2: b] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: b > $o] :
                            ( ( cB @ X3 )
                           => ~ ( X3 @ X2 ) ) ) )
           => ~ ( ! [X2: a > $o] :
                    ( ~ ( ( cA @ X2 )
                       => ~ ! [X3: b] :
                              ( ( X1 @ X3 )
                             => ( f @ X2 @ X3 ) ) )
                   => ( cA @ X2 ) )
               => ~ ! [X2: a > $o] :
                      ( ~ ( ( cA @ X2 )
                         => ~ ! [X3: b] :
                                ( ( X1 @ X3 )
                               => ( f @ X2 @ X3 ) ) )
                     => ~ ! [X3: a > $o] :
                            ( ~ ( ! [X4: ( a > $o ) > $o] :
                                    ( ~ ( ( X4
                                          @ ^ [X5: a] : $false )
                                       => ~ ! [X5: a > $o] :
                                              ( ( X4 @ X5 )
                                             => ! [X6: a] :
                                                  ( ( X3 @ X6 )
                                                 => ( X4
                                                    @ ^ [X7: a] :
                                                        ( ~ ( X5 @ X7 )
                                                       => ( X6 = X7 ) ) ) ) ) )
                                   => ( X4 @ X3 ) )
                               => ~ ! [X4: a] :
                                      ( ( X3 @ X4 )
                                     => ( X2 @ X4 ) ) )
                           => ~ ! [X4: a > $o] :
                                  ( ~ ( ( cA @ X4 )
                                     => ~ ! [X5: a] :
                                            ( ( X3 @ X5 )
                                           => ( X4 @ X5 ) ) )
                                 => ~ ( ( cA @ X4 )
                                     => ~ ! [X5: b] :
                                            ( ( X1 @ X5 )
                                           => ( f @ X4 @ X5 ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
    ( sP59
  <=> ( ~ sP16
     => ~ sP35 ) ),
    introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
    ( sP60
  <=> ( ~ sP4
     => ~ sP31 ) ),
    introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
    ( sP61
  <=> ! [X1: b > $o] :
        ( ~ ( ! [X2: ( b > $o ) > $o] :
                ( ~ ( ( X2
                      @ ^ [X3: b] : $false )
                   => ~ ! [X3: b > $o] :
                          ( ( X2 @ X3 )
                         => ! [X4: b] :
                              ( ( X1 @ X4 )
                             => ( X2
                                @ ^ [X5: b] :
                                    ( ~ ( X3 @ X5 )
                                   => ( X4 = X5 ) ) ) ) ) )
               => ( X2 @ X1 ) )
           => ~ ! [X2: b] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: b > $o] :
                        ( ( cB @ X3 )
                       => ~ ( X3 @ X2 ) ) ) )
       => ~ ( ! [X2: a > $o] :
                ( ~ ( ( cA @ X2 )
                   => ~ ! [X3: b] :
                          ( ( X1 @ X3 )
                         => ( f @ X2 @ X3 ) ) )
               => ( cA @ X2 ) )
           => ~ ! [X2: a > $o] :
                  ( ~ ( ( cA @ X2 )
                     => ~ ! [X3: b] :
                            ( ( X1 @ X3 )
                           => ( f @ X2 @ X3 ) ) )
                 => ~ ! [X3: a > $o] :
                        ( ~ ( ! [X4: ( a > $o ) > $o] :
                                ( ~ ( ( X4
                                      @ ^ [X5: a] : $false )
                                   => ~ ! [X5: a > $o] :
                                          ( ( X4 @ X5 )
                                         => ! [X6: a] :
                                              ( ( X3 @ X6 )
                                             => ( X4
                                                @ ^ [X7: a] :
                                                    ( ~ ( X5 @ X7 )
                                                   => ( X6 = X7 ) ) ) ) ) )
                               => ( X4 @ X3 ) )
                           => ~ ! [X4: a] :
                                  ( ( X3 @ X4 )
                                 => ( X2 @ X4 ) ) )
                       => ~ ! [X4: a > $o] :
                              ( ~ ( ( cA @ X4 )
                                 => ~ ! [X5: a] :
                                        ( ( X3 @ X5 )
                                       => ( X4 @ X5 ) ) )
                             => ~ ( ( cA @ X4 )
                                 => ~ ! [X5: b] :
                                        ( ( X1 @ X5 )
                                       => ( f @ X4 @ X5 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
    ( sP62
  <=> ( ~ sP26
     => ~ ( sP19
         => ~ sP45 ) ) ),
    introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
    ( sP63
  <=> ( sP18
     => ( cB @ ( f @ eigen__3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
    ( sP64
  <=> ! [X1: b > $o] :
        ( ( cB @ X1 )
       => ~ ( X1 @ eigen__10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
    ( sP65
  <=> ( sP21
     => ~ sP27 ) ),
    introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
    ( sP66
  <=> ( sP19
     => ~ sP45 ) ),
    introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
    ( sP67
  <=> ! [X1: b] :
        ( ( eigen__7 @ X1 )
       => ( f @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
    ( sP68
  <=> ( sP19
     => ~ sP34 ) ),
    introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
    ( sP69
  <=> ( sP32
     => ~ ! [X1: a > $o] :
            ( ~ ( ( cA @ X1 )
               => ~ ! [X2: c] :
                      ( ( eigen__0 @ X2 )
                     => ( g @ ( f @ X1 ) @ X2 ) ) )
           => ~ ! [X2: a > $o] :
                  ( ~ ( ! [X3: ( a > $o ) > $o] :
                          ( ~ ( ( X3
                                @ ^ [X4: a] : $false )
                             => ~ ! [X4: a > $o] :
                                    ( ( X3 @ X4 )
                                   => ! [X5: a] :
                                        ( ( X2 @ X5 )
                                       => ( X3
                                          @ ^ [X6: a] :
                                              ( ~ ( X4 @ X6 )
                                             => ( X5 = X6 ) ) ) ) ) )
                         => ( X3 @ X2 ) )
                     => ~ ! [X3: a] :
                            ( ( X2 @ X3 )
                           => ( X1 @ X3 ) ) )
                 => ~ ! [X3: a > $o] :
                        ( ~ ( ( cA @ X3 )
                           => ~ ! [X4: a] :
                                  ( ( X2 @ X4 )
                                 => ( X3 @ X4 ) ) )
                       => ~ ( ( cA @ X3 )
                           => ~ ! [X4: c] :
                                  ( ( eigen__0 @ X4 )
                                 => ( g @ ( f @ X3 ) @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
    ( sP70
  <=> ( cB @ ( f @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
    ( sP71
  <=> ( sP21
     => sP22 ) ),
    introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
    ( sP72
  <=> ( ~ sP58
     => ~ sP38 ) ),
    introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
    ( sP73
  <=> ( sP43
     => ~ ! [X1: c] :
            ( ( eigen__0 @ X1 )
           => ( g @ ( f @ eigen__1 ) @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
    ( sP74
  <=> ( sP15
     => ~ sP64 ) ),
    introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
    ( sP75
  <=> ! [X1: a > $o] :
        ( ~ ( ( cA @ X1 )
           => ~ ! [X2: c] :
                  ( ( eigen__0 @ X2 )
                 => ( g @ ( f @ X1 ) @ X2 ) ) )
       => ~ ! [X2: a > $o] :
              ( ~ ( ! [X3: ( a > $o ) > $o] :
                      ( ~ ( ( X3
                            @ ^ [X4: a] : $false )
                         => ~ ! [X4: a > $o] :
                                ( ( X3 @ X4 )
                               => ! [X5: a] :
                                    ( ( X2 @ X5 )
                                   => ( X3
                                      @ ^ [X6: a] :
                                          ( ~ ( X4 @ X6 )
                                         => ( X5 = X6 ) ) ) ) ) )
                     => ( X3 @ X2 ) )
                 => ~ ! [X3: a] :
                        ( ( X2 @ X3 )
                       => ( X1 @ X3 ) ) )
             => ~ ! [X3: a > $o] :
                    ( ~ ( ( cA @ X3 )
                       => ~ ! [X4: a] :
                              ( ( X2 @ X4 )
                             => ( X3 @ X4 ) ) )
                   => ~ ( ( cA @ X3 )
                       => ~ ! [X4: c] :
                              ( ( eigen__0 @ X4 )
                             => ( g @ ( f @ X3 ) @ X4 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(cDOMTHM9_pme,conjecture,
    sP53 ).

thf(h4,negated_conjecture,
    ~ sP53,
    inference(assume_negation,[status(cth)],[cDOMTHM9_pme]) ).

thf(1,plain,
    ( sP31
    | sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP52
    | sP60 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP60
    | sP4
    | ~ sP31 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | ~ sP41
    | ~ sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP66
    | sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP40
    | sP47 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP47
    | ~ sP19
    | sP41 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP35
    | sP62 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP62
    | sP26
    | ~ sP66 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP68
    | ~ sP19
    | ~ sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP26
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP55
    | sP68 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP55
    | ~ sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP39
    | ~ sP55 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__26]) ).

thf(15,plain,
    ( ~ sP44
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP10
    | sP16
    | ~ sP39 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( sP59
    | sP35 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( sP59
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP12
    | ~ sP59 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__22]) ).

thf(20,plain,
    ( ~ sP28
    | sP56 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP56
    | sP50
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP50
    | ~ sP21
    | ~ sP67 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP9
    | sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( sP73
    | sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP64
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP24
    | ~ sP22
    | ~ sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP67
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP7
    | ~ sP15
    | sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( sP74
    | sP64 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    ( sP74
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( sP57
    | ~ sP74 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__10]) ).

thf(32,plain,
    ( ~ sP61
    | sP42 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP42
    | sP13
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP13
    | ~ sP54
    | ~ sP57 ),
    inference(prop_rule,[status(thm)],]) ).

thf(35,plain,
    ( sP46
    | sP67 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( sP46
    | sP54 ),
    inference(prop_rule,[status(thm)],]) ).

thf(37,plain,
    ( sP20
    | sP52 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( sP20
    | ~ sP46 ),
    inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
    ( sP17
    | ~ sP20 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__7]) ).

thf(40,plain,
    ( ~ sP51
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP30
    | sP6
    | ~ sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( ~ sP6
    | ~ sP22
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( ~ sP40
    | sP71 ),
    inference(all_rule,[status(thm)],]) ).

thf(44,plain,
    ( ~ sP71
    | ~ sP21
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( sP65
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(46,plain,
    ( sP65
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( sP29
    | sP44 ),
    inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
    ( sP29
    | ~ sP65 ),
    inference(prop_rule,[status(thm)],]) ).

thf(49,plain,
    ( sP75
    | ~ sP29 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(50,plain,
    ( ~ sP38
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(51,plain,
    ( ~ sP11
    | ~ sP70
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
    ( ~ sP40
    | sP63 ),
    inference(all_rule,[status(thm)],]) ).

thf(53,plain,
    ( ~ sP63
    | ~ sP18
    | sP70 ),
    inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
    ( sP23
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(55,plain,
    ( sP23
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
    ( sP25
    | ~ sP23 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(57,plain,
    ( sP48
    | ~ sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(58,plain,
    ( sP48
    | ~ sP73 ),
    inference(prop_rule,[status(thm)],]) ).

thf(59,plain,
    ( sP33
    | sP51 ),
    inference(prop_rule,[status(thm)],]) ).

thf(60,plain,
    ( sP32
    | ~ sP48 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(61,plain,
    ( ~ sP14
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(62,plain,
    ( ~ sP2
    | sP36
    | ~ sP33 ),
    inference(prop_rule,[status(thm)],]) ).

thf(63,plain,
    ( ~ sP69
    | ~ sP32
    | ~ sP75 ),
    inference(prop_rule,[status(thm)],]) ).

thf(64,plain,
    ( sP8
    | sP69 ),
    inference(prop_rule,[status(thm)],]) ).

thf(65,plain,
    ( sP8
    | ~ sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(66,plain,
    ( sP58
    | sP61 ),
    inference(prop_rule,[status(thm)],]) ).

thf(67,plain,
    ( sP58
    | sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(68,plain,
    ( sP5
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).

thf(69,plain,
    ( sP72
    | sP38 ),
    inference(prop_rule,[status(thm)],]) ).

thf(70,plain,
    ( sP72
    | ~ sP58 ),
    inference(prop_rule,[status(thm)],]) ).

thf(71,plain,
    ( ~ sP49
    | ~ sP25
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(72,plain,
    ( sP1
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(73,plain,
    ( sP1
    | ~ sP72 ),
    inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
    ( sP53
    | sP49 ),
    inference(prop_rule,[status(thm)],]) ).

thf(75,plain,
    ( sP53
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(76,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,h4]) ).

thf(77,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h4,h2,h1,h0]),eigenvar_choice(discharge,[h3])],[76,h3]) ).

thf(78,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h4,h1,h0]),eigenvar_choice(discharge,[h2])],[77,h2]) ).

thf(79,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h4,h0]),eigenvar_choice(discharge,[h1])],[78,h1]) ).

thf(80,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h4]),eigenvar_choice(discharge,[h0])],[79,h0]) ).

thf(0,theorem,
    sP53,
    inference(contra,[status(thm),contra(discharge,[h4])],[76,h4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU912^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n025.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 : Mon Jun 20 11:09:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 50.03/50.21  % SZS status Theorem
% 50.03/50.21  % Mode: mode371
% 50.03/50.21  % Inferences: 597
% 50.03/50.21  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------