TSTP Solution File: SYO069^4.003 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO069^4.003 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Thu Jul 21 19:30:04 EDT 2022

% Result   : Theorem 252.84s 253.00s
% Output   : Proof 252.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  231
% Syntax   : Number of formulae    :  244 (  34 unt;  19 typ;  28 def)
%            Number of atoms       : 1153 (  28 equ;   0 cnn)
%            Maximal formula atoms :   71 (   5 avg)
%            Number of connectives : 2313 ( 291   ~; 118   |;   0   &;1148   @)
%                                         (  93 <=>; 661  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  34   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  135 ( 132 usr; 124 con; 0-2 aty)
%                                         (   2  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  411 (  36   ^ 375   !;   0   ?; 411   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
    eigen__6: $i ).

thf(ty_a0,type,
    a0: $i > $o ).

thf(ty_a3,type,
    a3: $i > $o ).

thf(ty_eigen__16,type,
    eigen__16: $i ).

thf(ty_a1,type,
    a1: $i > $o ).

thf(ty_eigen__35,type,
    eigen__35: $i ).

thf(ty_a2,type,
    a2: $i > $o ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

thf(ty_eigen__15,type,
    eigen__15: $i ).

thf(ty_b3,type,
    b3: $i > $o ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_b2,type,
    b2: $i > $o ).

thf(ty_eigen__55,type,
    eigen__55: $i ).

thf(ty_eigen__11,type,
    eigen__11: $i ).

thf(ty_b1,type,
    b1: $i > $o ).

thf(ty_irel,type,
    irel: $i > $i > $o ).

thf(ty_b0,type,
    b0: $i > $o ).

thf(ty_eigen__50,type,
    eigen__50: $i ).

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

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

thf(eigendef_eigen__11,definition,
    ( eigen__11
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( irel @ eigen__6 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b2 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a3 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__11])]) ).

thf(eigendef_eigen__55,definition,
    ( eigen__55
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( irel @ eigen__16 @ X1 )
           => ( a2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__55])]) ).

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( irel @ eigen__0 @ X1 )
           => ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__15,definition,
    ( eigen__15
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( irel @ eigen__6 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b3 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__15])]) ).

thf(eigendef_eigen__6,definition,
    ( eigen__6
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( irel @ eigen__1 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__6])]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ~ ( ( ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( a0 @ X3 ) )
                         => ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( f @ X3 ) ) )
                       => ( ( ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( ! [X4: $i] :
                                      ( ( irel @ X3 @ X4 )
                                     => ( b3 @ X4 ) )
                                 => ! [X4: $i] :
                                      ( ( irel @ X3 @ X4 )
                                     => ( b0 @ X4 ) ) ) )
                           => ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( a3 @ X3 ) ) )
                         => ( ( ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( b0 @ X4 ) )
                                   => ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( a1 @ X4 ) ) ) )
                             => ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( a0 @ X3 ) ) )
                           => ( ( ! [X3: $i] :
                                    ( ( irel @ X2 @ X3 )
                                   => ( ! [X4: $i] :
                                          ( ( irel @ X3 @ X4 )
                                         => ( b1 @ X4 ) )
                                     => ! [X4: $i] :
                                          ( ( irel @ X3 @ X4 )
                                         => ( a2 @ X4 ) ) ) )
                               => ! [X3: $i] :
                                    ( ( irel @ X2 @ X3 )
                                   => ( a1 @ X3 ) ) )
                             => ~ ( ! [X3: $i] :
                                      ( ( irel @ X2 @ X3 )
                                     => ( ! [X4: $i] :
                                            ( ( irel @ X3 @ X4 )
                                           => ( b2 @ X4 ) )
                                       => ! [X4: $i] :
                                            ( ( irel @ X3 @ X4 )
                                           => ( a3 @ X4 ) ) ) )
                                 => ! [X3: $i] :
                                      ( ( irel @ X2 @ X3 )
                                     => ( a2 @ X3 ) ) ) ) ) ) ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( f @ X2 ) ) )
             => ~ ( ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ~ ( ( ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( ! [X4: $i] :
                                      ( ( irel @ X3 @ X4 )
                                     => ( b2 @ X4 ) )
                                 => ! [X4: $i] :
                                      ( ( irel @ X3 @ X4 )
                                     => ( a3 @ X4 ) ) ) )
                           => ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( a2 @ X3 ) ) )
                         => ( ( ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( b1 @ X4 ) )
                                   => ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( a2 @ X4 ) ) ) )
                             => ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( a1 @ X3 ) ) )
                           => ( ( ! [X3: $i] :
                                    ( ( irel @ X2 @ X3 )
                                   => ( ! [X4: $i] :
                                          ( ( irel @ X3 @ X4 )
                                         => ( b0 @ X4 ) )
                                     => ! [X4: $i] :
                                          ( ( irel @ X3 @ X4 )
                                         => ( a1 @ X4 ) ) ) )
                               => ! [X3: $i] :
                                    ( ( irel @ X2 @ X3 )
                                   => ( a0 @ X3 ) ) )
                             => ( ( ! [X3: $i] :
                                      ( ( irel @ X2 @ X3 )
                                     => ( ! [X4: $i] :
                                            ( ( irel @ X3 @ X4 )
                                           => ( b3 @ X4 ) )
                                       => ! [X4: $i] :
                                            ( ( irel @ X3 @ X4 )
                                           => ( b0 @ X4 ) ) ) )
                                 => ! [X3: $i] :
                                      ( ( irel @ X2 @ X3 )
                                     => ( a3 @ X3 ) ) )
                               => ~ ( ! [X3: $i] :
                                        ( ( irel @ X2 @ X3 )
                                       => ( a0 @ X3 ) )
                                   => ! [X3: $i] :
                                        ( ( irel @ X2 @ X3 )
                                       => ( f @ X3 ) ) ) ) ) ) ) )
                 => ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( f @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(eigendef_eigen__50,definition,
    ( eigen__50
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( irel @ eigen__15 @ X1 )
           => ( b0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__50])]) ).

thf(eigendef_eigen__16,definition,
    ( eigen__16
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( irel @ eigen__6 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b1 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a2 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__16])]) ).

thf(eigendef_eigen__35,definition,
    ( eigen__35
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( irel @ eigen__11 @ X1 )
           => ( a3 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__35])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a1 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( a0 @ X1 ) ) )
     => ( ( ! [X1: $i] :
              ( ( irel @ eigen__1 @ X1 )
             => ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( b1 @ X2 ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( a2 @ X2 ) ) ) )
         => ! [X1: $i] :
              ( ( irel @ eigen__1 @ X1 )
             => ( a1 @ X1 ) ) )
       => ~ ( ! [X1: $i] :
                ( ( irel @ eigen__1 @ X1 )
               => ( ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( b2 @ X2 ) )
                 => ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( a3 @ X2 ) ) ) )
           => ! [X1: $i] :
                ( ( irel @ eigen__1 @ X1 )
               => ( a2 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ~ ( ( irel @ eigen__6 @ eigen__11 )
           => ~ ( irel @ eigen__11 @ X1 ) )
       => ( irel @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ( ( irel @ eigen__0 @ X1 )
       => ~ ( ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( ! [X3: $i] :
                        ( ( irel @ X2 @ X3 )
                       => ( b2 @ X3 ) )
                   => ! [X3: $i] :
                        ( ( irel @ X2 @ X3 )
                       => ( a3 @ X3 ) ) ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a2 @ X2 ) ) )
           => ( ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( ! [X3: $i] :
                          ( ( irel @ X2 @ X3 )
                         => ( b1 @ X3 ) )
                     => ! [X3: $i] :
                          ( ( irel @ X2 @ X3 )
                         => ( a2 @ X3 ) ) ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( a1 @ X2 ) ) )
             => ( ( ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( b0 @ X3 ) )
                       => ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( a1 @ X3 ) ) ) )
                 => ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( a0 @ X2 ) ) )
               => ( ( ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( b3 @ X3 ) )
                         => ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( b0 @ X3 ) ) ) )
                   => ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( a3 @ X2 ) ) )
                 => ~ ( ! [X2: $i] :
                          ( ( irel @ X1 @ X2 )
                         => ( a0 @ X2 ) )
                     => ! [X2: $i] :
                          ( ( irel @ X1 @ X2 )
                         => ( f @ X2 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( irel @ eigen__16 @ eigen__55 )
     => ( a2 @ eigen__55 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a1 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( a0 @ X1 ) ) )
     => ( ( ! [X1: $i] :
              ( ( irel @ eigen__1 @ X1 )
             => ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( b3 @ X2 ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( b0 @ X2 ) ) ) )
         => ! [X1: $i] :
              ( ( irel @ eigen__1 @ X1 )
             => ( a3 @ X1 ) ) )
       => ~ ( ! [X1: $i] :
                ( ( irel @ eigen__1 @ X1 )
               => ( a0 @ X1 ) )
           => ! [X1: $i] :
                ( ( irel @ eigen__1 @ X1 )
               => ( f @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ! [X1: $i] :
          ( ( irel @ eigen__6 @ X1 )
         => ( ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( b2 @ X2 ) )
           => ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( a3 @ X2 ) ) ) )
     => ! [X1: $i] :
          ( ( irel @ eigen__6 @ X1 )
         => ( a2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( irel @ eigen__11 @ X1 )
       => ( a3 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( irel @ eigen__0 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i] :
        ( ( irel @ eigen__6 @ X1 )
       => ( a1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( irel @ eigen__6 @ X1 )
           => ~ ( irel @ X1 @ X2 ) )
       => ( irel @ eigen__6 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ( irel @ eigen__6 @ X1 )
       => ( b0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i] :
        ( ~ ( ( irel @ eigen__6 @ eigen__16 )
           => ~ ( irel @ eigen__16 @ X1 ) )
       => ( irel @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( irel @ eigen__6 @ eigen__16 )
     => ( ! [X1: $i] :
            ( ( irel @ eigen__16 @ X1 )
           => ( b1 @ X1 ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__16 @ X1 )
           => ( a2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ! [X1: $i] :
          ( ( irel @ eigen__15 @ X1 )
         => ( b3 @ X1 ) )
     => ! [X1: $i] :
          ( ( irel @ eigen__15 @ X1 )
         => ( b0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ! [X1: $i] :
          ( ( irel @ eigen__0 @ X1 )
         => ~ ( ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( a0 @ X2 ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( f @ X2 ) ) )
             => ( ( ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( b3 @ X3 ) )
                       => ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( b0 @ X3 ) ) ) )
                 => ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( a3 @ X2 ) ) )
               => ( ( ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( b0 @ X3 ) )
                         => ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( a1 @ X3 ) ) ) )
                   => ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( a0 @ X2 ) ) )
                 => ( ( ! [X2: $i] :
                          ( ( irel @ X1 @ X2 )
                         => ( ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( b1 @ X3 ) )
                           => ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( a2 @ X3 ) ) ) )
                     => ! [X2: $i] :
                          ( ( irel @ X1 @ X2 )
                         => ( a1 @ X2 ) ) )
                   => ~ ( ! [X2: $i] :
                            ( ( irel @ X1 @ X2 )
                           => ( ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( b2 @ X3 ) )
                             => ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( a3 @ X3 ) ) ) )
                       => ! [X2: $i] :
                            ( ( irel @ X1 @ X2 )
                           => ( a2 @ X2 ) ) ) ) ) ) ) )
     => ! [X1: $i] :
          ( ( irel @ eigen__0 @ X1 )
         => ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( irel @ eigen__1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( ( irel @ eigen__1 @ eigen__6 )
     => ( sP12
       => sP10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b1 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a2 @ X2 ) ) ) )
       => sP10 )
     => ( ( ! [X1: $i] :
              ( ( irel @ eigen__6 @ X1 )
             => ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( b0 @ X2 ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( a1 @ X2 ) ) ) )
         => ! [X1: $i] :
              ( ( irel @ eigen__6 @ X1 )
             => ( a0 @ X1 ) ) )
       => ( ( ! [X1: $i] :
                ( ( irel @ eigen__6 @ X1 )
               => ( ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( b3 @ X2 ) )
                 => ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( b0 @ X2 ) ) ) )
           => ! [X1: $i] :
                ( ( irel @ eigen__6 @ X1 )
               => ( a3 @ X1 ) ) )
         => ~ ( ! [X1: $i] :
                  ( ( irel @ eigen__6 @ X1 )
                 => ( a0 @ X1 ) )
             => ! [X1: $i] :
                  ( ( irel @ eigen__6 @ X1 )
                 => ( f @ X1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b3 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( a3 @ X1 ) ) )
     => ~ ( ! [X1: $i] :
              ( ( irel @ eigen__6 @ X1 )
             => ( a0 @ X1 ) )
         => ! [X1: $i] :
              ( ( irel @ eigen__6 @ X1 )
             => ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i] :
        ( ~ ( sP9
           => ~ ( irel @ eigen__1 @ X1 ) )
       => ( irel @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: $i] :
        ( ( irel @ eigen__6 @ X1 )
       => ( a3 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( irel @ eigen__6 @ eigen__16 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( irel @ eigen__11 @ eigen__35 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ~ ( sP23
         => ~ ( irel @ eigen__16 @ eigen__55 ) )
     => ( irel @ eigen__6 @ eigen__55 ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( ! [X1: $i] :
          ( ( irel @ eigen__6 @ X1 )
         => ( ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( b1 @ X2 ) )
           => ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( a2 @ X2 ) ) ) )
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( irel @ eigen__6 @ eigen__11 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( sP17
     => ( f @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( irel @ eigen__1 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( sP26
     => ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( irel @ eigen__6 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( sP12
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( irel @ eigen__0 @ X1 )
           => ~ ( irel @ X1 @ X2 ) )
       => ( irel @ eigen__0 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( ( irel @ eigen__0 @ eigen__6 )
     => ~ ( sP7
         => sP19 ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( irel @ eigen__0 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b3 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( a3 @ X1 ) ) )
     => ~ ( ! [X1: $i] :
              ( ( irel @ eigen__1 @ X1 )
             => ( a0 @ X1 ) )
         => ! [X1: $i] :
              ( ( irel @ eigen__1 @ X1 )
             => ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a1 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( a0 @ X1 ) ) )
     => sP30 ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( sP4
     => ! [X1: $i] :
          ( ( irel @ eigen__0 @ X1 )
         => ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( ~ ( sP27
         => ~ sP24 )
     => ( irel @ eigen__6 @ eigen__35 ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( a0 @ X1 ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( f @ X1 ) ) )
     => ( ( ! [X1: $i] :
              ( ( irel @ eigen__6 @ X1 )
             => ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( b3 @ X2 ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( b0 @ X2 ) ) ) )
         => sP22 )
       => sP37 ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( ~ ( sP31
         => ~ ( irel @ eigen__15 @ eigen__50 ) )
     => ( irel @ eigen__6 @ eigen__50 ) ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ( ! [X1: $i] :
          ( ( irel @ eigen__6 @ X1 )
         => ( ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( b3 @ X2 ) )
           => ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( b0 @ X2 ) ) ) )
     => sP22 ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ! [X1: $i] :
        ( ( irel @ eigen__1 @ X1 )
       => ( ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( b0 @ X2 ) )
         => ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( a1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ! [X1: $i] :
        ( ( irel @ eigen__1 @ X1 )
       => ( a0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( sP35
     => ~ sP40 ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( ( irel @ eigen__15 @ eigen__50 )
     => ( b0 @ eigen__50 ) ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ( irel @ eigen__6 @ eigen__55 ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( sP47
     => ( a2 @ eigen__55 ) ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ( ~ ( sP9
         => ~ sP29 )
     => sP35 ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ( sP27
     => ( ! [X1: $i] :
            ( ( irel @ eigen__11 @ X1 )
           => ( b2 @ X1 ) )
       => sP8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ( sP44
     => ! [X1: $i] :
          ( ( irel @ eigen__1 @ X1 )
         => ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ! [X1: $i] :
        ( ( irel @ eigen__6 @ X1 )
       => ( ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( b1 @ X2 ) )
         => ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( a2 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( a3 @ eigen__35 ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ( sP27
     => ~ sP24 ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ( ! [X1: $i] :
          ( ( irel @ eigen__11 @ X1 )
         => ( b2 @ X1 ) )
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a1 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__6 @ X1 )
           => ( a0 @ X1 ) ) )
     => sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ( sP9
     => ~ ( ( ! [X1: $i] :
                ( ( irel @ eigen__1 @ X1 )
               => ( ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( b2 @ X2 ) )
                 => ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( a3 @ X2 ) ) ) )
           => ! [X1: $i] :
                ( ( irel @ eigen__1 @ X1 )
               => ( a2 @ X1 ) ) )
         => ( ( ! [X1: $i] :
                  ( ( irel @ eigen__1 @ X1 )
                 => ( ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( b1 @ X2 ) )
                   => ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( a2 @ X2 ) ) ) )
             => ! [X1: $i] :
                  ( ( irel @ eigen__1 @ X1 )
                 => ( a1 @ X1 ) ) )
           => sP6 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b1 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a2 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( a1 @ X1 ) ) )
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
    ( sP59
  <=> ! [X1: $i] :
        ( ~ ( sP31
           => ~ ( irel @ eigen__15 @ X1 ) )
       => ( irel @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
    ( sP60
  <=> ( sP9
     => ( f @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
    ( sP61
  <=> ( f @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
    ( sP62
  <=> ( a2 @ eigen__55 ) ),
    introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
    ( sP63
  <=> ( irel @ eigen__6 @ eigen__50 ) ),
    introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
    ( sP64
  <=> ! [X1: $i] :
        ( ( irel @ eigen__1 @ X1 )
       => ( f @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
    ( sP65
  <=> ( sP42
     => sP37 ) ),
    introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
    ( sP66
  <=> ( sP43
     => sP44 ) ),
    introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
    ( sP67
  <=> ( sP9
     => ~ ( sP51
         => ( ( ! [X1: $i] :
                  ( ( irel @ eigen__1 @ X1 )
                 => ( ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( b3 @ X2 ) )
                   => ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( b0 @ X2 ) ) ) )
             => ! [X1: $i] :
                  ( ( irel @ eigen__1 @ X1 )
                 => ( a3 @ X1 ) ) )
           => sP1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
    ( sP68
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( irel @ X1 @ X2 )
           => ~ ( irel @ X2 @ X3 ) )
       => ( irel @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
    ( sP69
  <=> ! [X1: $i] :
        ( ( irel @ eigen__16 @ X1 )
       => ( a2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
    ( sP70
  <=> ( ! [X1: $i] :
          ( ( irel @ eigen__16 @ X1 )
         => ( b1 @ X1 ) )
     => sP69 ) ),
    introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
    ( sP71
  <=> ! [X1: $i] :
        ~ ( ( ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ~ ( ( ! [X3: $i] :
                          ( ( irel @ X2 @ X3 )
                         => ( a0 @ X3 ) )
                     => ! [X3: $i] :
                          ( ( irel @ X2 @ X3 )
                         => ( f @ X3 ) ) )
                   => ( ( ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( ! [X4: $i] :
                                  ( ( irel @ X3 @ X4 )
                                 => ( b3 @ X4 ) )
                             => ! [X4: $i] :
                                  ( ( irel @ X3 @ X4 )
                                 => ( b0 @ X4 ) ) ) )
                       => ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( a3 @ X3 ) ) )
                     => ( ( ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( ! [X4: $i] :
                                    ( ( irel @ X3 @ X4 )
                                   => ( b0 @ X4 ) )
                               => ! [X4: $i] :
                                    ( ( irel @ X3 @ X4 )
                                   => ( a1 @ X4 ) ) ) )
                         => ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( a0 @ X3 ) ) )
                       => ( ( ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( ! [X4: $i] :
                                      ( ( irel @ X3 @ X4 )
                                     => ( b1 @ X4 ) )
                                 => ! [X4: $i] :
                                      ( ( irel @ X3 @ X4 )
                                     => ( a2 @ X4 ) ) ) )
                           => ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( a1 @ X3 ) ) )
                         => ~ ( ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( b2 @ X4 ) )
                                   => ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( a3 @ X4 ) ) ) )
                             => ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( a2 @ X3 ) ) ) ) ) ) ) )
           => ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( f @ X2 ) ) )
         => ~ ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ~ ( ( ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( ! [X4: $i] :
                                  ( ( irel @ X3 @ X4 )
                                 => ( b2 @ X4 ) )
                             => ! [X4: $i] :
                                  ( ( irel @ X3 @ X4 )
                                 => ( a3 @ X4 ) ) ) )
                       => ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( a2 @ X3 ) ) )
                     => ( ( ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( ! [X4: $i] :
                                    ( ( irel @ X3 @ X4 )
                                   => ( b1 @ X4 ) )
                               => ! [X4: $i] :
                                    ( ( irel @ X3 @ X4 )
                                   => ( a2 @ X4 ) ) ) )
                         => ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( a1 @ X3 ) ) )
                       => ( ( ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( ! [X4: $i] :
                                      ( ( irel @ X3 @ X4 )
                                     => ( b0 @ X4 ) )
                                 => ! [X4: $i] :
                                      ( ( irel @ X3 @ X4 )
                                     => ( a1 @ X4 ) ) ) )
                           => ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( a0 @ X3 ) ) )
                         => ( ( ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( b3 @ X4 ) )
                                   => ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( b0 @ X4 ) ) ) )
                             => ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( a3 @ X3 ) ) )
                           => ~ ( ! [X3: $i] :
                                    ( ( irel @ X2 @ X3 )
                                   => ( a0 @ X3 ) )
                               => ! [X3: $i] :
                                    ( ( irel @ X2 @ X3 )
                                   => ( f @ X3 ) ) ) ) ) ) ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( f @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
    ( sP72
  <=> ( sP9
     => ~ sP29 ) ),
    introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
    ( sP73
  <=> ( sP7
     => sP19 ) ),
    introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
    ( sP74
  <=> ! [X1: $i] :
        ( ( irel @ eigen__15 @ X1 )
       => ( b0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
    ( sP75
  <=> ( irel @ eigen__6 @ eigen__35 ) ),
    introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(sP76,plain,
    ( sP76
  <=> ! [X1: $i] :
        ( ( irel @ eigen__0 @ X1 )
       => ( f @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP76])]) ).

thf(sP77,plain,
    ( sP77
  <=> ( sP23
     => ~ ( irel @ eigen__16 @ eigen__55 ) ) ),
    introduced(definition,[new_symbols(definition,[sP77])]) ).

thf(sP78,plain,
    ( sP78
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b2 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a3 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( a2 @ X1 ) ) )
     => sP58 ) ),
    introduced(definition,[new_symbols(definition,[sP78])]) ).

thf(sP79,plain,
    ( sP79
  <=> ( sP75
     => sP53 ) ),
    introduced(definition,[new_symbols(definition,[sP79])]) ).

thf(sP80,plain,
    ( sP80
  <=> ( sP63
     => ( b0 @ eigen__50 ) ) ),
    introduced(definition,[new_symbols(definition,[sP80])]) ).

thf(sP81,plain,
    ( sP81
  <=> ! [X1: $i] :
        ( ( irel @ eigen__6 @ X1 )
       => ( a2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP81])]) ).

thf(sP82,plain,
    ( sP82
  <=> ( sP51
     => ( ( ! [X1: $i] :
              ( ( irel @ eigen__1 @ X1 )
             => ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( b3 @ X2 ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( b0 @ X2 ) ) ) )
         => ! [X1: $i] :
              ( ( irel @ eigen__1 @ X1 )
             => ( a3 @ X1 ) ) )
       => sP1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP82])]) ).

thf(sP83,plain,
    ( sP83
  <=> ! [X1: $i] :
        ( ( irel @ eigen__6 @ X1 )
       => ( ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( b3 @ X2 ) )
         => ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( b0 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP83])]) ).

thf(sP84,plain,
    ( sP84
  <=> ( irel @ eigen__15 @ eigen__50 ) ),
    introduced(definition,[new_symbols(definition,[sP84])]) ).

thf(sP85,plain,
    ( sP85
  <=> ( b0 @ eigen__50 ) ),
    introduced(definition,[new_symbols(definition,[sP85])]) ).

thf(sP86,plain,
    ( sP86
  <=> ! [X1: $i] :
        ( ( irel @ eigen__0 @ X1 )
       => ~ ( ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( a0 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( f @ X2 ) ) )
           => ( ( ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( ! [X3: $i] :
                          ( ( irel @ X2 @ X3 )
                         => ( b3 @ X3 ) )
                     => ! [X3: $i] :
                          ( ( irel @ X2 @ X3 )
                         => ( b0 @ X3 ) ) ) )
               => ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ( a3 @ X2 ) ) )
             => ( ( ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( b0 @ X3 ) )
                       => ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( a1 @ X3 ) ) ) )
                 => ! [X2: $i] :
                      ( ( irel @ X1 @ X2 )
                     => ( a0 @ X2 ) ) )
               => ( ( ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( b1 @ X3 ) )
                         => ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( a2 @ X3 ) ) ) )
                   => ! [X2: $i] :
                        ( ( irel @ X1 @ X2 )
                       => ( a1 @ X2 ) ) )
                 => ~ ( ! [X2: $i] :
                          ( ( irel @ X1 @ X2 )
                         => ( ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( b2 @ X3 ) )
                           => ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( a3 @ X3 ) ) ) )
                     => ! [X2: $i] :
                          ( ( irel @ X1 @ X2 )
                         => ( a2 @ X2 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP86])]) ).

thf(sP87,plain,
    ( sP87
  <=> ( irel @ eigen__16 @ eigen__55 ) ),
    introduced(definition,[new_symbols(definition,[sP87])]) ).

thf(sP88,plain,
    ( sP88
  <=> ( sP16
     => ~ sP38 ) ),
    introduced(definition,[new_symbols(definition,[sP88])]) ).

thf(sP89,plain,
    ( sP89
  <=> ( sP31
     => sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP89])]) ).

thf(sP90,plain,
    ( sP90
  <=> ( sP31
     => ~ sP84 ) ),
    introduced(definition,[new_symbols(definition,[sP90])]) ).

thf(sP91,plain,
    ( sP91
  <=> ( sP24
     => sP53 ) ),
    introduced(definition,[new_symbols(definition,[sP91])]) ).

thf(sP92,plain,
    ( sP92
  <=> ( ( ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b3 @ X2 ) )
             => ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ( b0 @ X2 ) ) ) )
       => ! [X1: $i] :
            ( ( irel @ eigen__1 @ X1 )
           => ( a3 @ X1 ) ) )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP92])]) ).

thf(sP93,plain,
    ( sP93
  <=> ! [X1: $i] :
        ( ( irel @ eigen__6 @ X1 )
       => ( ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( b2 @ X2 ) )
         => ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( a3 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP93])]) ).

thf(def_mnot,definition,
    ( mnot
    = ( ^ [X1: $i > $o,X2: $i] :
          ~ ( X1 @ X2 ) ) ) ).

thf(def_mor,definition,
    ( mor
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ~ ( X1 @ X3 )
         => ( X2 @ X3 ) ) ) ) ).

thf(def_mand,definition,
    ( mand
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ~ ( ( X1 @ X3 )
           => ~ ( X2 @ X3 ) ) ) ) ).

thf(def_mimplies,definition,
    ( mimplies
    = ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).

thf(def_mbox_s4,definition,
    ( mbox_s4
    = ( ^ [X1: $i > $o,X2: $i] :
        ! [X3: $i] :
          ( ( irel @ X2 @ X3 )
         => ( X1 @ X3 ) ) ) ) ).

thf(def_iatom,definition,
    ( iatom
    = ( ^ [X1: $i > $o] : X1 ) ) ).

thf(def_inot,definition,
    ( inot
    = ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).

thf(def_itrue,definition,
    ( itrue
    = ( ^ [X1: $i] : ~ $false ) ) ).

thf(def_ifalse,definition,
    ( ifalse
    = ( inot @ itrue ) ) ).

thf(def_iand,definition,
    iand = mand ).

thf(def_ior,definition,
    ( ior
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).

thf(def_iimplies,definition,
    ( iimplies
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).

thf(def_iimplied,definition,
    ( iimplied
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).

thf(def_iequiv,definition,
    ( iequiv
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).

thf(def_ixor,definition,
    ( ixor
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).

thf(def_ivalid,definition,
    ivalid = !! ).

thf(def_isatisfiable,definition,
    ( isatisfiable
    = ( ^ [X1: $i > $o] :
          ~ ! [X2: $i] :
              ~ ( X1 @ X2 ) ) ) ).

thf(def_icountersatisfiable,definition,
    ( icountersatisfiable
    = ( ^ [X1: $i > $o] :
          ~ ( !! @ X1 ) ) ) ).

thf(def_iinvalid,definition,
    ( iinvalid
    = ( ^ [X1: $i > $o] :
        ! [X2: $i] :
          ~ ( X1 @ X2 ) ) ) ).

thf(con,conjecture,
    ! [X1: $i] :
      ~ ( ( ~ ~ ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ~ ( ( ~ ~ ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( a0 @ X3 ) )
                       => ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( f @ X3 ) ) )
                     => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                      ( ( irel @ X2 @ X3 )
                                     => ( ~ ~ ! [X4: $i] :
                                                ( ( irel @ X3 @ X4 )
                                               => ( b3 @ X4 ) )
                                       => ! [X4: $i] :
                                            ( ( irel @ X3 @ X4 )
                                           => ( b0 @ X4 ) ) ) )
                             => ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( a3 @ X3 ) ) )
                           => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                            ( ( irel @ X2 @ X3 )
                                           => ( ~ ~ ! [X4: $i] :
                                                      ( ( irel @ X3 @ X4 )
                                                     => ( b0 @ X4 ) )
                                             => ! [X4: $i] :
                                                  ( ( irel @ X3 @ X4 )
                                                 => ( a1 @ X4 ) ) ) )
                                   => ! [X3: $i] :
                                        ( ( irel @ X2 @ X3 )
                                       => ( a0 @ X3 ) ) )
                                 => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                                  ( ( irel @ X2 @ X3 )
                                                 => ( ~ ~ ! [X4: $i] :
                                                            ( ( irel @ X3 @ X4 )
                                                           => ( b1 @ X4 ) )
                                                   => ! [X4: $i] :
                                                        ( ( irel @ X3 @ X4 )
                                                       => ( a2 @ X4 ) ) ) )
                                         => ! [X3: $i] :
                                              ( ( irel @ X2 @ X3 )
                                             => ( a1 @ X3 ) ) )
                                       => ~ ( ~ ~ ! [X3: $i] :
                                                    ( ( irel @ X2 @ X3 )
                                                   => ( ~ ~ ! [X4: $i] :
                                                              ( ( irel @ X3 @ X4 )
                                                             => ( b2 @ X4 ) )
                                                     => ! [X4: $i] :
                                                          ( ( irel @ X3 @ X4 )
                                                         => ( a3 @ X4 ) ) ) )
                                           => ! [X3: $i] :
                                                ( ( irel @ X2 @ X3 )
                                               => ( a2 @ X3 ) ) ) ) ) ) ) )
         => ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( f @ X2 ) ) )
       => ~ ( ~ ~ ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ~ ( ( ~ ~ ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( ~ ~ ! [X4: $i] :
                                            ( ( irel @ X3 @ X4 )
                                           => ( b2 @ X4 ) )
                                   => ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( a3 @ X4 ) ) ) )
                         => ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( a2 @ X3 ) ) )
                       => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                        ( ( irel @ X2 @ X3 )
                                       => ( ~ ~ ! [X4: $i] :
                                                  ( ( irel @ X3 @ X4 )
                                                 => ( b1 @ X4 ) )
                                         => ! [X4: $i] :
                                              ( ( irel @ X3 @ X4 )
                                             => ( a2 @ X4 ) ) ) )
                               => ! [X3: $i] :
                                    ( ( irel @ X2 @ X3 )
                                   => ( a1 @ X3 ) ) )
                             => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                              ( ( irel @ X2 @ X3 )
                                             => ( ~ ~ ! [X4: $i] :
                                                        ( ( irel @ X3 @ X4 )
                                                       => ( b0 @ X4 ) )
                                               => ! [X4: $i] :
                                                    ( ( irel @ X3 @ X4 )
                                                   => ( a1 @ X4 ) ) ) )
                                     => ! [X3: $i] :
                                          ( ( irel @ X2 @ X3 )
                                         => ( a0 @ X3 ) ) )
                                   => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                                    ( ( irel @ X2 @ X3 )
                                                   => ( ~ ~ ! [X4: $i] :
                                                              ( ( irel @ X3 @ X4 )
                                                             => ( b3 @ X4 ) )
                                                     => ! [X4: $i] :
                                                          ( ( irel @ X3 @ X4 )
                                                         => ( b0 @ X4 ) ) ) )
                                           => ! [X3: $i] :
                                                ( ( irel @ X2 @ X3 )
                                               => ( a3 @ X3 ) ) )
                                         => ~ ( ~ ~ ! [X3: $i] :
                                                      ( ( irel @ X2 @ X3 )
                                                     => ( a0 @ X3 ) )
                                             => ! [X3: $i] :
                                                  ( ( irel @ X2 @ X3 )
                                                 => ( f @ X3 ) ) ) ) ) ) ) )
           => ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( f @ X2 ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ sP71,
    inference(assume_negation,[status(cth)],[con]) ).

thf(1,plain,
    ( ~ sP11
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP39 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP39
    | sP54
    | sP75 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP54
    | ~ sP27
    | ~ sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP11
    | sP59 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP59
    | sP41 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP41
    | sP90
    | sP63 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP90
    | ~ sP31
    | ~ sP84 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP11
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP13
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP25
    | sP77
    | sP47 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP77
    | ~ sP23
    | ~ sP87 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP33
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP21
    | sP49 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP49
    | sP72
    | sP35 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP72
    | ~ sP9
    | ~ sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP81
    | sP48 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP48
    | ~ sP47
    | sP62 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP12
    | sP80 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP80
    | ~ sP63
    | sP85 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP2
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP68
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP68
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( sP5
    | ~ sP62 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( sP5
    | sP87 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP22
    | sP79 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP79
    | ~ sP75
    | sP53 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( sP46
    | ~ sP85 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( sP46
    | sP84 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    ( sP69
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__55]) ).

thf(31,plain,
    ( sP91
    | ~ sP53 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( sP91
    | sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
    ( sP74
    | ~ sP46 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__50]) ).

thf(34,plain,
    ( sP70
    | ~ sP69 ),
    inference(prop_rule,[status(thm)],]) ).

thf(35,plain,
    ( sP8
    | ~ sP91 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__35]) ).

thf(36,plain,
    ( sP15
    | ~ sP74 ),
    inference(prop_rule,[status(thm)],]) ).

thf(37,plain,
    ( sP14
    | ~ sP70 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( sP14
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
    ( sP55
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( sP89
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( sP89
    | sP31 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( sP50
    | ~ sP55 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( sP50
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( sP20
    | sP42 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( sP52
    | ~ sP14 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).

thf(46,plain,
    ( sP30
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( sP30
    | sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
    ( sP83
    | ~ sP89 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).

thf(49,plain,
    ( ~ sP26
    | ~ sP52
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(50,plain,
    ( sP56
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
    ( sP93
    | ~ sP50 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).

thf(52,plain,
    ( ~ sP42
    | ~ sP83
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(53,plain,
    ( sP37
    | ~ sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
    ( sP65
    | ~ sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(55,plain,
    ( sP65
    | sP42 ),
    inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
    ( ~ sP7
    | ~ sP93
    | sP81 ),
    inference(prop_rule,[status(thm)],]) ).

thf(57,plain,
    ( sP19
    | ~ sP56 ),
    inference(prop_rule,[status(thm)],]) ).

thf(58,plain,
    ( sP19
    | sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(59,plain,
    ( sP73
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(60,plain,
    ( sP73
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(61,plain,
    ( sP40
    | ~ sP65 ),
    inference(prop_rule,[status(thm)],]) ).

thf(62,plain,
    ( ~ sP45
    | ~ sP35
    | ~ sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(63,plain,
    ( ~ sP34
    | ~ sP35
    | ~ sP73 ),
    inference(prop_rule,[status(thm)],]) ).

thf(64,plain,
    ( ~ sP4
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(65,plain,
    ( ~ sP86
    | sP45 ),
    inference(all_rule,[status(thm)],]) ).

thf(66,plain,
    ( sP36
    | sP51 ),
    inference(prop_rule,[status(thm)],]) ).

thf(67,plain,
    ( sP6
    | ~ sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(68,plain,
    ( sP6
    | sP66 ),
    inference(prop_rule,[status(thm)],]) ).

thf(69,plain,
    ( sP58
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(70,plain,
    ( sP78
    | ~ sP58 ),
    inference(prop_rule,[status(thm)],]) ).

thf(71,plain,
    ( sP32
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(72,plain,
    ( sP32
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(73,plain,
    ( sP18
    | ~ sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
    ( sP18
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(75,plain,
    ( ~ sP64
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(76,plain,
    ( ~ sP28
    | ~ sP17
    | sP61 ),
    inference(prop_rule,[status(thm)],]) ).

thf(77,plain,
    ( ~ sP51
    | ~ sP44
    | sP64 ),
    inference(prop_rule,[status(thm)],]) ).

thf(78,plain,
    ( sP43
    | ~ sP18 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(79,plain,
    ( ~ sP66
    | ~ sP43
    | sP44 ),
    inference(prop_rule,[status(thm)],]) ).

thf(80,plain,
    ( sP1
    | sP66 ),
    inference(prop_rule,[status(thm)],]) ).

thf(81,plain,
    ( sP92
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(82,plain,
    ( sP82
    | ~ sP92 ),
    inference(prop_rule,[status(thm)],]) ).

thf(83,plain,
    ( sP82
    | sP51 ),
    inference(prop_rule,[status(thm)],]) ).

thf(84,plain,
    ( ~ sP86
    | sP67 ),
    inference(all_rule,[status(thm)],]) ).

thf(85,plain,
    ( ~ sP67
    | ~ sP9
    | ~ sP82 ),
    inference(prop_rule,[status(thm)],]) ).

thf(86,plain,
    ( sP16
    | ~ sP76 ),
    inference(prop_rule,[status(thm)],]) ).

thf(87,plain,
    ( sP16
    | sP86 ),
    inference(prop_rule,[status(thm)],]) ).

thf(88,plain,
    ( ~ sP4
    | sP57 ),
    inference(all_rule,[status(thm)],]) ).

thf(89,plain,
    ( ~ sP57
    | ~ sP9
    | ~ sP78 ),
    inference(prop_rule,[status(thm)],]) ).

thf(90,plain,
    ( sP60
    | ~ sP61 ),
    inference(prop_rule,[status(thm)],]) ).

thf(91,plain,
    ( sP60
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(92,plain,
    ( sP76
    | ~ sP60 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(93,plain,
    ( sP38
    | ~ sP76 ),
    inference(prop_rule,[status(thm)],]) ).

thf(94,plain,
    ( sP38
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(95,plain,
    ( ~ sP88
    | ~ sP16
    | ~ sP38 ),
    inference(prop_rule,[status(thm)],]) ).

thf(96,plain,
    ( sP71
    | sP88 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(trans_axiom,axiom,
    sP68 ).

thf(refl_axiom,axiom,
    sP2 ).

thf(97,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,trans_axiom,refl_axiom,h1]) ).

thf(98,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[97,h0]) ).

thf(0,theorem,
    ! [X1: $i] :
      ~ ( ( ~ ~ ! [X2: $i] :
                  ( ( irel @ X1 @ X2 )
                 => ~ ( ( ~ ~ ! [X3: $i] :
                                ( ( irel @ X2 @ X3 )
                               => ( a0 @ X3 ) )
                       => ! [X3: $i] :
                            ( ( irel @ X2 @ X3 )
                           => ( f @ X3 ) ) )
                     => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                      ( ( irel @ X2 @ X3 )
                                     => ( ~ ~ ! [X4: $i] :
                                                ( ( irel @ X3 @ X4 )
                                               => ( b3 @ X4 ) )
                                       => ! [X4: $i] :
                                            ( ( irel @ X3 @ X4 )
                                           => ( b0 @ X4 ) ) ) )
                             => ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( a3 @ X3 ) ) )
                           => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                            ( ( irel @ X2 @ X3 )
                                           => ( ~ ~ ! [X4: $i] :
                                                      ( ( irel @ X3 @ X4 )
                                                     => ( b0 @ X4 ) )
                                             => ! [X4: $i] :
                                                  ( ( irel @ X3 @ X4 )
                                                 => ( a1 @ X4 ) ) ) )
                                   => ! [X3: $i] :
                                        ( ( irel @ X2 @ X3 )
                                       => ( a0 @ X3 ) ) )
                                 => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                                  ( ( irel @ X2 @ X3 )
                                                 => ( ~ ~ ! [X4: $i] :
                                                            ( ( irel @ X3 @ X4 )
                                                           => ( b1 @ X4 ) )
                                                   => ! [X4: $i] :
                                                        ( ( irel @ X3 @ X4 )
                                                       => ( a2 @ X4 ) ) ) )
                                         => ! [X3: $i] :
                                              ( ( irel @ X2 @ X3 )
                                             => ( a1 @ X3 ) ) )
                                       => ~ ( ~ ~ ! [X3: $i] :
                                                    ( ( irel @ X2 @ X3 )
                                                   => ( ~ ~ ! [X4: $i] :
                                                              ( ( irel @ X3 @ X4 )
                                                             => ( b2 @ X4 ) )
                                                     => ! [X4: $i] :
                                                          ( ( irel @ X3 @ X4 )
                                                         => ( a3 @ X4 ) ) ) )
                                           => ! [X3: $i] :
                                                ( ( irel @ X2 @ X3 )
                                               => ( a2 @ X3 ) ) ) ) ) ) ) )
         => ! [X2: $i] :
              ( ( irel @ X1 @ X2 )
             => ( f @ X2 ) ) )
       => ~ ( ~ ~ ! [X2: $i] :
                    ( ( irel @ X1 @ X2 )
                   => ~ ( ( ~ ~ ! [X3: $i] :
                                  ( ( irel @ X2 @ X3 )
                                 => ( ~ ~ ! [X4: $i] :
                                            ( ( irel @ X3 @ X4 )
                                           => ( b2 @ X4 ) )
                                   => ! [X4: $i] :
                                        ( ( irel @ X3 @ X4 )
                                       => ( a3 @ X4 ) ) ) )
                         => ! [X3: $i] :
                              ( ( irel @ X2 @ X3 )
                             => ( a2 @ X3 ) ) )
                       => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                        ( ( irel @ X2 @ X3 )
                                       => ( ~ ~ ! [X4: $i] :
                                                  ( ( irel @ X3 @ X4 )
                                                 => ( b1 @ X4 ) )
                                         => ! [X4: $i] :
                                              ( ( irel @ X3 @ X4 )
                                             => ( a2 @ X4 ) ) ) )
                               => ! [X3: $i] :
                                    ( ( irel @ X2 @ X3 )
                                   => ( a1 @ X3 ) ) )
                             => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                              ( ( irel @ X2 @ X3 )
                                             => ( ~ ~ ! [X4: $i] :
                                                        ( ( irel @ X3 @ X4 )
                                                       => ( b0 @ X4 ) )
                                               => ! [X4: $i] :
                                                    ( ( irel @ X3 @ X4 )
                                                   => ( a1 @ X4 ) ) ) )
                                     => ! [X3: $i] :
                                          ( ( irel @ X2 @ X3 )
                                         => ( a0 @ X3 ) ) )
                                   => ~ ~ ( ( ~ ~ ! [X3: $i] :
                                                    ( ( irel @ X2 @ X3 )
                                                   => ( ~ ~ ! [X4: $i] :
                                                              ( ( irel @ X3 @ X4 )
                                                             => ( b3 @ X4 ) )
                                                     => ! [X4: $i] :
                                                          ( ( irel @ X3 @ X4 )
                                                         => ( b0 @ X4 ) ) ) )
                                           => ! [X3: $i] :
                                                ( ( irel @ X2 @ X3 )
                                               => ( a3 @ X3 ) ) )
                                         => ~ ( ~ ~ ! [X3: $i] :
                                                      ( ( irel @ X2 @ X3 )
                                                     => ( a0 @ X3 ) )
                                             => ! [X3: $i] :
                                                  ( ( irel @ X2 @ X3 )
                                                 => ( f @ X3 ) ) ) ) ) ) ) )
           => ! [X2: $i] :
                ( ( irel @ X1 @ X2 )
               => ( f @ X2 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[97,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SYO069^4.003 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.08/0.29  % Computer : n006.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit : 300
% 0.08/0.29  % WCLimit  : 600
% 0.08/0.29  % DateTime : Sat Jul  9 15:37:51 EDT 2022
% 0.08/0.29  % CPUTime  : 
% 252.84/253.00  % SZS status Theorem
% 252.84/253.00  % Mode: mode519
% 252.84/253.00  % Inferences: 12408
% 252.84/253.00  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------