TSTP Solution File: SEU781^2 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU781^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 14:05:01 EDT 2022

% Result   : Theorem 0.36s 0.59s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   82
% Syntax   : Number of formulae    :  100 (  28 unt;  12 typ;   4 def)
%            Number of atoms       :  300 (   4 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  940 (  87   ~;  27   |;   0   &; 620   @)
%                                         (  26 <=>; 180  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  42 usr;  38 con; 0-3 aty)
%            Number of variables   :  108 (   5   ^ 103   !;   0   ?; 108   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_subset,type,
    subset: $i > $i > $o ).

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

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

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

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

thf(ty_cartprod,type,
    cartprod: $i > $i > $i ).

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

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

thf(ty_kpair,type,
    kpair: $i > $i > $i ).

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

thf(ty_breln1compset,type,
    breln1compset: $i > $i > $i > $i ).

thf(ty_in,type,
    in: $i > $i > $o ).

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

thf(eigendef_eigen__16,definition,
    ( eigen__16
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ~ ( ( in @ X1 @ eigen__0 )
               => ~ ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 ) )
           => ~ ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__16])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ! [X3: $i] :
                  ( ( in @ X3 @ eigen__0 )
                 => ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ X1 ) )
                   => ~ ! [X4: $i] :
                          ( ~ ( ( in @ X4 @ eigen__0 )
                             => ~ ( in @ ( kpair @ X2 @ X4 ) @ eigen__1 ) )
                         => ~ ( in @ ( kpair @ X4 @ X3 ) @ X1 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 )
         => ( ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 )
           => eigen__5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
               => ~ ! [X3: $i] :
                      ( ~ ( ( in @ X3 @ eigen__0 )
                         => ~ ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 ) )
                     => ~ ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ~ ( ( in @ X1 @ eigen__0 )
           => ~ ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 ) )
       => ~ ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( in @ eigen__3 @ eigen__0 )
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
           => ~ ! [X2: $i] :
                  ( ~ ( ( in @ X2 @ eigen__0 )
                     => ~ ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 ) )
                 => ~ ( in @ ( kpair @ X2 @ X1 ) @ eigen__2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( in @ eigen__3 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
             => ~ ! [X3: $i] :
                    ( ~ ( ( in @ X3 @ eigen__0 )
                       => ~ ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 ) )
                   => ~ ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( in @ ( kpair @ eigen__3 @ eigen__16 ) @ eigen__1 )
     => ( ( in @ ( kpair @ eigen__16 @ eigen__4 ) @ eigen__2 )
       => eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( in @ eigen__16 @ eigen__0 )
     => ~ ( in @ ( kpair @ eigen__3 @ eigen__16 ) @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( in @ ( kpair @ eigen__16 @ eigen__4 ) @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( in @ eigen__16 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
         => ~ ! [X2: $i] :
                ( ~ ( ( in @ X2 @ eigen__0 )
                   => ~ ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 ) )
               => ~ ( in @ ( kpair @ X2 @ X1 ) @ eigen__2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ( in @ eigen__4 @ eigen__0 )
     => ( ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
       => ~ sP5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i] :
        ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ X1 ) )
                 => ~ ! [X4: $i] :
                        ( ~ ( ( in @ X4 @ eigen__0 )
                           => ~ ( in @ ( kpair @ X2 @ X4 ) @ eigen__1 ) )
                       => ~ ( in @ ( kpair @ X4 @ X3 ) @ X1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( sP11
     => eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( in @ ( kpair @ eigen__3 @ eigen__16 ) @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ eigen__0 )
                   => ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ eigen__0 @ X1 @ X2 ) )
                     => ~ ! [X5: $i] :
                            ( ~ ( ( in @ X5 @ eigen__0 )
                               => ~ ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
                           => ~ ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> eigen__5 ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: $i,X2: $i] :
        ( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
       => ! [X3: $i] :
            ( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ! [X5: $i] :
                    ( ( in @ X5 @ X1 )
                   => ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
                     => ~ ! [X6: $i] :
                            ( ~ ( ( in @ X6 @ X1 )
                               => ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
                           => ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( sP12
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ~ sP10
     => ~ sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( sP20
     => ~ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( in @ eigen__4 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(def_breln,definition,
    ( breln
    = ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).

thf(def_breln1,definition,
    ( breln1
    = ( ^ [X1: $i] : ( breln @ X1 @ X1 ) ) ) ).

thf(def_breln1compE,definition,
    ( breln1compE
    = ( ! [X1: $i,X2: $i] :
          ( ( breln1 @ X1 @ X2 )
         => ! [X3: $i] :
              ( ( breln1 @ X1 @ X3 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ! [X5: $i] :
                      ( ( in @ X5 @ X1 )
                     => ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
                       => ~ ! [X6: $i] :
                              ( ~ ( ( in @ X6 @ X1 )
                                 => ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
                             => ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) ) ) ) ) ) ) ) ).

thf(breln1compEex,conjecture,
    ( sP22
   => ! [X1: $i,X2: $i] :
        ( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
       => ! [X3: $i] :
            ( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ! [X5: $i] :
                    ( ( in @ X5 @ X1 )
                   => ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
                     => ! [X6: $o] :
                          ( ! [X7: $i] :
                              ( ( in @ X7 @ X1 )
                             => ( ( in @ ( kpair @ X4 @ X7 ) @ X2 )
                               => ( ( in @ ( kpair @ X7 @ X5 ) @ X3 )
                                 => X6 ) ) )
                         => X6 ) ) ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( sP22
     => ! [X1: $i,X2: $i] :
          ( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
         => ! [X3: $i] :
              ( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ! [X5: $i] :
                      ( ( in @ X5 @ X1 )
                     => ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
                       => ! [X6: $o] :
                            ( ! [X7: $i] :
                                ( ( in @ X7 @ X1 )
                               => ( ( in @ ( kpair @ X4 @ X7 ) @ X2 )
                                 => ( ( in @ ( kpair @ X7 @ X5 ) @ X3 )
                                   => X6 ) ) )
                           => X6 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[breln1compEex]) ).

thf(h2,assumption,
    sP22,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
       => ! [X3: $i] :
            ( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ! [X5: $i] :
                    ( ( in @ X5 @ X1 )
                   => ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
                     => ! [X6: $o] :
                          ( ! [X7: $i] :
                              ( ( in @ X7 @ X1 )
                             => ( ( in @ ( kpair @ X4 @ X7 ) @ X2 )
                               => ( ( in @ ( kpair @ X7 @ X5 ) @ X3 )
                                 => X6 ) ) )
                         => X6 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: $i] :
        ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ eigen__0 )
                   => ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ eigen__0 @ X1 @ X2 ) )
                     => ! [X5: $o] :
                          ( ! [X6: $i] :
                              ( ( in @ X6 @ eigen__0 )
                             => ( ( in @ ( kpair @ X3 @ X6 ) @ X1 )
                               => ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
                                 => X5 ) ) )
                         => X5 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP4
     => ! [X1: $i] :
          ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ! [X3: $i] :
                  ( ( in @ X3 @ eigen__0 )
                 => ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ X1 ) )
                   => ! [X4: $o] :
                        ( ! [X5: $i] :
                            ( ( in @ X5 @ eigen__0 )
                           => ( ( in @ ( kpair @ X2 @ X5 ) @ eigen__1 )
                             => ( ( in @ ( kpair @ X5 @ X3 ) @ X1 )
                               => X4 ) ) )
                       => X4 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: $i] :
        ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ X1 ) )
                 => ! [X4: $o] :
                      ( ! [X5: $i] :
                          ( ( in @ X5 @ eigen__0 )
                         => ( ( in @ ( kpair @ X2 @ X5 ) @ eigen__1 )
                           => ( ( in @ ( kpair @ X5 @ X3 ) @ X1 )
                             => X4 ) ) )
                     => X4 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( sP13
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
               => ! [X3: $o] :
                    ( ! [X4: $i] :
                        ( ( in @ X4 @ eigen__0 )
                       => ( ( in @ ( kpair @ X1 @ X4 ) @ eigen__1 )
                         => ( ( in @ ( kpair @ X4 @ X2 ) @ eigen__2 )
                           => X3 ) ) )
                   => X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
             => ! [X3: $o] :
                  ( ! [X4: $i] :
                      ( ( in @ X4 @ eigen__0 )
                     => ( ( in @ ( kpair @ X1 @ X4 ) @ eigen__1 )
                       => ( ( in @ ( kpair @ X4 @ X2 ) @ eigen__2 )
                         => X3 ) ) )
                 => X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( sP7
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
           => ! [X2: $o] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ eigen__0 )
                   => ( ( in @ ( kpair @ eigen__3 @ X3 ) @ eigen__1 )
                     => ( ( in @ ( kpair @ X3 @ X1 ) @ eigen__2 )
                       => X2 ) ) )
               => X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
         => ! [X2: $o] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ eigen__0 )
                 => ( ( in @ ( kpair @ eigen__3 @ X3 ) @ eigen__1 )
                   => ( ( in @ ( kpair @ X3 @ X1 ) @ eigen__2 )
                     => X2 ) ) )
             => X2 ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( sP26
     => ( sP20
       => ! [X1: $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ eigen__0 )
               => ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 )
                 => ( ( in @ ( kpair @ X2 @ eigen__4 ) @ eigen__2 )
                   => X1 ) ) )
           => X1 ) ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP26,
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ ( sP20
     => ! [X1: $o] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 )
               => ( ( in @ ( kpair @ X2 @ eigen__4 ) @ eigen__2 )
                 => X1 ) ) )
         => X1 ) ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP20,
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ ! [X1: $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 )
             => ( ( in @ ( kpair @ X2 @ eigen__4 ) @ eigen__2 )
               => X1 ) ) )
       => X1 ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ ( sP2
     => sP21 ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ sP21,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP23
    | ~ sP12
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP9
    | ~ sP18
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP17
    | ~ sP11
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP10
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP10
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP24
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP24
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP5
    | ~ sP24 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).

thf(10,plain,
    ( ~ sP14
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP15
    | ~ sP26
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP25
    | ~ sP20
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP8
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP6
    | ~ sP7
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP16
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP3
    | ~ sP13
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP22
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP19
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP1
    | ~ sP4
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h20,h21,h19,h17,h18,h15,h16,h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h2,h6,h9,h12,h15,h17,h20,h21]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h15,h16,h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,20,h20,h21]) ).

thf(22,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__5)],[h18,21,h19]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,22,h17,h18]) ).

thf(24,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,23,h15,h16]) ).

thf(25,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h13,24,h14]) ).

thf(26,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,25,h12,h13]) ).

thf(27,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h10,26,h11]) ).

thf(28,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,27,h9,h10]) ).

thf(29,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,28,h8]) ).

thf(30,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,29,h6,h7]) ).

thf(31,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,30,h5]) ).

thf(32,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,31,h4]) ).

thf(33,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,32,h2,h3]) ).

thf(34,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[33,h0]) ).

thf(0,theorem,
    ( sP22
   => ! [X1: $i,X2: $i] :
        ( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
       => ! [X3: $i] :
            ( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ! [X5: $i] :
                    ( ( in @ X5 @ X1 )
                   => ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
                     => ! [X6: $o] :
                          ( ! [X7: $i] :
                              ( ( in @ X7 @ X1 )
                             => ( ( in @ ( kpair @ X4 @ X7 ) @ X2 )
                               => ( ( in @ ( kpair @ X7 @ X5 ) @ X3 )
                                 => X6 ) ) )
                         => X6 ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[33,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU781^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 20 13:42:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.36/0.59  % SZS status Theorem
% 0.36/0.59  % Mode: mode213
% 0.36/0.59  % Inferences: 1413
% 0.36/0.59  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------