TSTP Solution File: SEU466^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU466^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n032.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 13:52:19 EDT 2022

% Result   : Theorem 0.14s 0.32s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  107 (  65 unt;   7 typ;  31 def)
%            Number of atoms       :  248 (  43 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 1078 ( 225   ~;  18   |;   0   &; 583   @)
%                                         (  18 <=>; 233  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  160 ( 160   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   58 (  55 usr;  54 con; 0-2 aty)
%                                         (   1  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  346 (  65   ^ 281   !;   0   ?; 346   :)

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

thf(ty_eigen__2,type,
    eigen__2: $i ).

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

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

thf(ty_eigen__4,type,
    eigen__4: $i ).

thf(ty_eigen__5,type,
    eigen__5: $i ).

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

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

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ! [X2: $i] :
              ( ! [X3: $i > $i > $o] :
                  ( ~ ( ! [X4: $i,X5: $i,X6: $i] :
                          ( ~ ( ( X3 @ X4 @ X5 )
                             => ~ ( X3 @ X5 @ X6 ) )
                         => ( X3 @ X4 @ X6 ) )
                     => ~ ! [X4: $i,X5: $i] :
                            ( ( eigen__0 @ X4 @ X5 )
                           => ( X3 @ X4 @ X5 ) ) )
                 => ( X3 @ X1 @ X2 ) )
             => ( eigen__3 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ! [X2: $i > $i > $o] :
                ( ~ ( ! [X3: $i,X4: $i,X5: $i] :
                        ( ~ ( ( X2 @ X3 @ X4 )
                           => ~ ( X2 @ X4 @ X5 ) )
                       => ( X2 @ X3 @ X5 ) )
                   => ~ ! [X3: $i,X4: $i] :
                          ( ( eigen__0 @ X3 @ X4 )
                         => ( X2 @ X3 @ X4 ) ) )
               => ( X2 @ eigen__4 @ X1 ) )
           => ( eigen__3 @ eigen__4 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i] :
        ( ( eigen__0 @ X1 @ X2 )
       => ( eigen__3 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
              ( ~ ( ( eigen__3 @ X1 @ X2 )
                 => ~ ( eigen__3 @ X2 @ X3 ) )
             => ( eigen__3 @ X1 @ X3 ) )
         => ~ ! [X1: $i,X2: $i] :
                ( ! [X3: $i > $i > $o] :
                    ( ~ ( ! [X4: $i,X5: $i,X6: $i] :
                            ( ~ ( ( X3 @ X4 @ X5 )
                               => ~ ( X3 @ X5 @ X6 ) )
                           => ( X3 @ X4 @ X6 ) )
                       => ~ ! [X4: $i,X5: $i] :
                              ( ( eigen__0 @ X4 @ X5 )
                             => ( X3 @ X4 @ X5 ) ) )
                   => ( X3 @ X1 @ X2 ) )
               => ( eigen__3 @ X1 @ X2 ) ) )
     => ( eigen__3 @ eigen__1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i > $i > $o] :
        ( ~ ( ! [X2: $i,X3: $i,X4: $i] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) )
           => ~ ! [X2: $i,X3: $i] :
                  ( ( eigen__0 @ X2 @ X3 )
                 => ( X1 @ X2 @ X3 ) ) )
       => ( X1 @ eigen__1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i > $i > $o] :
            ( ~ ( ! [X4: $i,X5: $i,X6: $i] :
                    ( ~ ( ( X3 @ X4 @ X5 )
                       => ~ ( X3 @ X5 @ X6 ) )
                   => ( X3 @ X4 @ X6 ) )
               => ~ ! [X4: $i,X5: $i] :
                      ( ( eigen__0 @ X4 @ X5 )
                     => ( X3 @ X4 @ X5 ) ) )
           => ( X3 @ X1 @ X2 ) )
       => ( eigen__6 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i > $i > $o] :
        ( ~ ( ! [X2: $i,X3: $i,X4: $i] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) )
           => ~ ! [X2: $i,X3: $i] :
                  ( ( eigen__0 @ X2 @ X3 )
                 => ( X1 @ X2 @ X3 ) ) )
       => ( X1 @ eigen__4 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( ( eigen__3 @ X1 @ X2 )
             => ~ ( eigen__3 @ X2 @ X3 ) )
         => ( eigen__3 @ X1 @ X3 ) )
     => ~ ! [X1: $i,X2: $i] :
            ( ! [X3: $i > $i > $o] :
                ( ~ ( ! [X4: $i,X5: $i,X6: $i] :
                        ( ~ ( ( X3 @ X4 @ X5 )
                           => ~ ( X3 @ X5 @ X6 ) )
                       => ( X3 @ X4 @ X6 ) )
                   => ~ ! [X4: $i,X5: $i] :
                          ( ( eigen__0 @ X4 @ X5 )
                         => ( X3 @ X4 @ X5 ) ) )
               => ( X3 @ X1 @ X2 ) )
           => ( eigen__3 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ! [X2: $i > $i > $o] :
            ( ~ ( ! [X3: $i,X4: $i,X5: $i] :
                    ( ~ ( ( X2 @ X3 @ X4 )
                       => ~ ( X2 @ X4 @ X5 ) )
                   => ( X2 @ X3 @ X5 ) )
               => ~ ! [X3: $i,X4: $i] :
                      ( ( eigen__0 @ X3 @ X4 )
                     => ( X2 @ X3 @ X4 ) ) )
           => ( X2 @ eigen__4 @ X1 ) )
       => ( eigen__3 @ eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP3
     => ( eigen__6 @ eigen__1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
              ( ~ ( ( eigen__3 @ X1 @ X2 )
                 => ~ ( eigen__3 @ X2 @ X3 ) )
             => ( eigen__3 @ X1 @ X3 ) )
         => ~ sP1 )
     => ( eigen__3 @ eigen__4 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( eigen__3 @ X1 @ X2 )
           => ~ ( eigen__3 @ X2 @ X3 ) )
       => ( eigen__3 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( eigen__3 @ eigen__1 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i > $i > $o] :
            ( ~ ( ! [X4: $i,X5: $i,X6: $i] :
                    ( ~ ( ( X3 @ X4 @ X5 )
                       => ~ ( X3 @ X5 @ X6 ) )
                   => ( X3 @ X4 @ X6 ) )
               => ~ ! [X4: $i,X5: $i] :
                      ( ( eigen__0 @ X4 @ X5 )
                     => ( X3 @ X4 @ X5 ) ) )
           => ( X3 @ X1 @ X2 ) )
       => ( eigen__3 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP5
     => ( eigen__3 @ eigen__4 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( sP10
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( eigen__3 @ eigen__4 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i > $i > $o] :
        ( ~ ( ! [X2: $i,X3: $i,X4: $i] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) )
           => ~ ! [X2: $i,X3: $i] :
                  ( ! [X4: $i > $i > $o] :
                      ( ~ ( ! [X5: $i,X6: $i,X7: $i] :
                              ( ~ ( ( X4 @ X5 @ X6 )
                                 => ~ ( X4 @ X6 @ X7 ) )
                             => ( X4 @ X5 @ X7 ) )
                         => ~ ! [X5: $i,X6: $i] :
                                ( ( eigen__0 @ X5 @ X6 )
                               => ( X4 @ X5 @ X6 ) ) )
                     => ( X4 @ X2 @ X3 ) )
                 => ( X1 @ X2 @ X3 ) ) )
       => ( X1 @ eigen__1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: $i] :
        ( ! [X2: $i > $i > $o] :
            ( ~ ( ! [X3: $i,X4: $i,X5: $i] :
                    ( ~ ( ( X2 @ X3 @ X4 )
                       => ~ ( X2 @ X4 @ X5 ) )
                   => ( X2 @ X3 @ X5 ) )
               => ~ ! [X3: $i,X4: $i] :
                      ( ( eigen__0 @ X3 @ X4 )
                     => ( X2 @ X3 @ X4 ) ) )
           => ( X2 @ eigen__1 @ X1 ) )
       => ( eigen__6 @ eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( eigen__6 @ eigen__1 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(def_subrel,definition,
    ( subrel
    = ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ( X1 @ X3 @ X4 )
         => ( X2 @ X3 @ X4 ) ) ) ) ).

thf(def_inv,definition,
    ( inv
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).

thf(def_idem,definition,
    ( idem
    = ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X2: $i > $i > $o] :
          ( ( X1 @ ( X1 @ X2 ) )
          = ( X1 @ X2 ) ) ) ) ).

thf(def_infl,definition,
    ( infl
    = ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).

thf(def_mono,definition,
    ( mono
    = ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X2: $i > $i > $o,X3: $i > $i > $o] :
          ( ( subrel @ X2 @ X3 )
         => ( subrel @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ).

thf(def_refl,definition,
    ( refl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).

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

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

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

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

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

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

thf(def_trans,definition,
    ( trans
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( X1 @ X2 @ X3 )
             => ~ ( X1 @ X3 @ X4 ) )
         => ( X1 @ X2 @ X4 ) ) ) ) ).

thf(def_tc,definition,
    ( tc
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
        ! [X4: $i > $i > $o] :
          ( ~ ( ( trans @ X4 )
             => ~ ( subrel @ X1 @ X4 ) )
         => ( X4 @ X2 @ X3 ) ) ) ) ).

thf(def_trc,definition,
    ( trc
    = ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).

thf(def_trsc,definition,
    ( trsc
    = ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).

thf(def_po,definition,
    ( po
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ~ ( ( refl @ X1 )
               => ~ ( antisymm @ X1 ) )
           => ~ ( trans @ X1 ) ) ) ) ).

thf(def_so,definition,
    ( so
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ( asymm @ X1 )
           => ~ ( trans @ X1 ) ) ) ) ).

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

thf(def_term,definition,
    ( term
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ~ ( X2 @ X3 )
         => ~ ! [X3: $i] :
                ( ( X2 @ X3 )
               => ~ ! [X4: $i] :
                      ( ( X2 @ X4 )
                     => ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ).

thf(def_ind,definition,
    ( ind
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i > $o] :
          ( ! [X3: $i] :
              ( ! [X4: $i] :
                  ( ( tc @ X1 @ X3 @ X4 )
                 => ( X2 @ X4 ) )
             => ( X2 @ X3 ) )
         => ( !! @ X2 ) ) ) ) ).

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

thf(def_nfof,definition,
    ( nfof
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ~ ( ( trc @ X1 @ X3 @ X2 )
           => ~ ( innf @ X1 @ X2 ) ) ) ) ).

thf(def_norm,definition,
    ( norm
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] :
          ~ ! [X3: $i] :
              ~ ( nfof @ X1 @ X3 @ X2 ) ) ) ).

thf(def_join,definition,
    ( join
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ~ ! [X4: $i] :
              ( ( trc @ X1 @ X2 @ X4 )
             => ~ ( trc @ X1 @ X3 @ X4 ) ) ) ) ).

thf(def_lconfl,definition,
    ( lconfl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( X1 @ X2 @ X4 )
             => ~ ( X1 @ X2 @ X3 ) )
         => ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_sconfl,definition,
    ( sconfl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( X1 @ X2 @ X4 )
             => ~ ( trc @ X1 @ X2 @ X3 ) )
         => ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_confl,definition,
    ( confl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( trc @ X1 @ X2 @ X4 )
             => ~ ( trc @ X1 @ X2 @ X3 ) )
         => ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_cr,definition,
    ( cr
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ( trsc @ X1 @ X2 @ X3 )
         => ( join @ X1 @ X2 @ X3 ) ) ) ) ).

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

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

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

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

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

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

thf(h6,assumption,
    sP16 != sP3,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP16,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP16,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( ~ sP14
     => sP11 ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP14,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ sP11,
    introduced(assumption,[]) ).

thf(h14,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP5
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | sP14
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP14
    | ~ sP10
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP13
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP13
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP7
    | ~ sP13 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).

thf(7,plain,
    ( sP12
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).

thf(8,plain,
    ( ~ sP16
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP2
    | sP6
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP6
    | ~ sP10
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,h11,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h7,h14,h15,h13]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,11,h14,h15]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,12,h12,h13]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h8,13,h11]) ).

thf(h16,assumption,
    ~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
              ( ~ ( ( eigen__6 @ X1 @ X2 )
                 => ~ ( eigen__6 @ X2 @ X3 ) )
             => ( eigen__6 @ X1 @ X3 ) )
         => ~ sP4 )
     => sP18 ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( ( eigen__6 @ X1 @ X2 )
             => ~ ( eigen__6 @ X2 @ X3 ) )
         => ( eigen__6 @ X1 @ X3 ) )
     => ~ sP4 ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ sP18,
    introduced(assumption,[]) ).

thf(h19,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( ( eigen__6 @ X1 @ X2 )
         => ~ ( eigen__6 @ X2 @ X3 ) )
     => ( eigen__6 @ X1 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(15,plain,
    ( ~ sP4
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP17
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP8
    | ~ sP3
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h19,h20,h17,h18,h16,h9,h10,h6,h5,h4,h3,h2,h1,h0])],[15,16,17,h20,h18,h10]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h9,h10,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,18,h19,h20]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h16,h9,h10,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,19,h17,h18]) ).

thf(21,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h10,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__6)],[h9,20,h16]) ).

thf(22,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h6,14,21,h7,h8,h9,h10]) ).

thf(23,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,22,h6]) ).

thf(24,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,23,h5]) ).

thf(25,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,24,h4]) ).

thf(26,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,25,h3]) ).

thf(27,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,26,h2]) ).

thf(28,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0]) ).

thf(0,theorem,
    ! [X1: $i > $i > $o] :
      ( ( ^ [X2: $i,X3: $i] :
          ! [X4: $i > $i > $o] :
            ( ~ ( ! [X5: $i,X6: $i,X7: $i] :
                    ( ~ ( ( X4 @ X5 @ X6 )
                       => ~ ( X4 @ X6 @ X7 ) )
                   => ( X4 @ X5 @ X7 ) )
               => ~ ! [X5: $i,X6: $i] :
                      ( ! [X7: $i > $i > $o] :
                          ( ~ ( ! [X8: $i,X9: $i,X10: $i] :
                                  ( ~ ( ( X7 @ X8 @ X9 )
                                     => ~ ( X7 @ X9 @ X10 ) )
                                 => ( X7 @ X8 @ X10 ) )
                             => ~ ! [X8: $i,X9: $i] :
                                    ( ( X1 @ X8 @ X9 )
                                   => ( X7 @ X8 @ X9 ) ) )
                         => ( X7 @ X5 @ X6 ) )
                     => ( X4 @ X5 @ X6 ) ) )
           => ( X4 @ X2 @ X3 ) ) )
      = ( ^ [X2: $i,X3: $i] :
          ! [X4: $i > $i > $o] :
            ( ~ ( ! [X5: $i,X6: $i,X7: $i] :
                    ( ~ ( ( X4 @ X5 @ X6 )
                       => ~ ( X4 @ X6 @ X7 ) )
                   => ( X4 @ X5 @ X7 ) )
               => ~ ! [X5: $i,X6: $i] :
                      ( ( X1 @ X5 @ X6 )
                     => ( X4 @ X5 @ X6 ) ) )
           => ( X4 @ X2 @ X3 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[27,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : SEU466^1 : TPTP v8.1.0. Released v3.6.0.
% 0.06/0.10  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 600
% 0.10/0.29  % DateTime : Sun Jun 19 15:09:48 EDT 2022
% 0.10/0.29  % CPUTime  : 
% 0.14/0.32  % SZS status Theorem
% 0.14/0.32  % Mode: mode213
% 0.14/0.32  % Inferences: 17
% 0.14/0.32  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------