TSTP Solution File: SEU787^2 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU787^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 17:30:37 EDT 2023

% Result   : Theorem 0.68s 0.88s
% Output   : Proof 0.68s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_binunion,type,
    binunion: $i > $i > $i ).

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

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

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

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

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

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

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

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

thf(ty_breln1,type,
    breln1: $i > $i > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ eigen__2 )
     => eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( breln1 @ eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ eigen__1 )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( in @ eigen__4 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ ( binunion @ eigen__1 @ eigen__2 ) )
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ( breln1 @ eigen__0 @ X1 )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ( ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ eigen__1 @ X1 ) )
                 => ( ~ ( in @ ( kpair @ X2 @ X3 ) @ eigen__1 )
                   => ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( in @ eigen__3 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( binunion @ eigen__1 @ eigen__2 ) )
         => ( ~ ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 )
           => ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( breln1 @ eigen__0 @ eigen__1 )
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP2
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ ( kpair @ X1 @ X2 ) @ ( binunion @ eigen__1 @ eigen__2 ) )
               => ( ~ ( in @ ( kpair @ X1 @ X2 ) @ eigen__1 )
                 => ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( in @ ( kpair @ X1 @ X2 ) @ ( binunion @ eigen__1 @ eigen__2 ) )
             => ( ~ ( in @ ( kpair @ X1 @ X2 ) @ eigen__1 )
               => ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [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 ) @ ( binunion @ X2 @ X3 ) )
                     => ( ~ ( in @ ( kpair @ X4 @ X5 ) @ X2 )
                       => ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( sP14
     => eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP8
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

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

thf(sP18,plain,
    ( sP18
  <=> ( breln1 @ eigen__0 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( sP5
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

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

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i] :
        ( ( breln1 @ eigen__0 @ X1 )
       => ! [X2: $i] :
            ( ( breln1 @ eigen__0 @ X2 )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ eigen__0 )
                   => ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
                     => ( ~ ( in @ ( kpair @ X3 @ X4 ) @ X1 )
                       => ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(def_breln1unionE,definition,
    ( breln1unionE
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( breln1 @ X1 @ X2 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( breln1 @ X1 @ X3 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X4 @ X1 )
                  @ ! [X5: $i] :
                      ( ^ [X6: $o,X7: $o] :
                          ( X6
                         => X7 )
                      @ ( in @ X5 @ X1 )
                      @ ( ^ [X6: $o,X7: $o] :
                            ( X6
                           => X7 )
                        @ ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X2 @ X3 ) )
                        @ ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
                          | ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ) ) ) ) ).

thf(breln1unionEcases,conjecture,
    ( sP13
   => ! [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 ) @ ( binunion @ X2 @ X3 ) )
                     => ! [X6: $o] :
                          ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
                           => X6 )
                         => ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
                             => X6 )
                           => X6 ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP13
     => ! [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 ) @ ( binunion @ X2 @ X3 ) )
                       => ! [X6: $o] :
                            ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
                             => X6 )
                           => ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
                               => X6 )
                             => X6 ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[breln1unionEcases]) ).

thf(h1,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [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 ) @ ( binunion @ X2 @ X3 ) )
                     => ! [X6: $o] :
                          ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
                           => X6 )
                         => ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
                             => X6 )
                           => X6 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i] :
        ( ( breln1 @ eigen__0 @ X1 )
       => ! [X2: $i] :
            ( ( breln1 @ eigen__0 @ X2 )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ eigen__0 )
                   => ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
                     => ! [X5: $o] :
                          ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
                           => X5 )
                         => ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
                             => X5 )
                           => X5 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP18
     => ! [X1: $i] :
          ( ( breln1 @ eigen__0 @ X1 )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ! [X3: $i] :
                  ( ( in @ X3 @ eigen__0 )
                 => ( ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ eigen__1 @ X1 ) )
                   => ! [X4: $o] :
                        ( ( ( in @ ( kpair @ X2 @ X3 ) @ eigen__1 )
                         => X4 )
                       => ( ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
                           => X4 )
                         => X4 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ! [X1: $i] :
        ( ( breln1 @ eigen__0 @ X1 )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ( ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ eigen__1 @ X1 ) )
                 => ! [X4: $o] :
                      ( ( ( in @ ( kpair @ X2 @ X3 ) @ eigen__1 )
                       => X4 )
                     => ( ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
                         => X4 )
                       => X4 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( sP2
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ ( kpair @ X1 @ X2 ) @ ( binunion @ eigen__1 @ eigen__2 ) )
               => ! [X3: $o] :
                    ( ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__1 )
                     => X3 )
                   => ( ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 )
                       => X3 )
                     => X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( in @ ( kpair @ X1 @ X2 ) @ ( binunion @ eigen__1 @ eigen__2 ) )
             => ! [X3: $o] :
                  ( ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__1 )
                   => X3 )
                 => ( ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 )
                     => X3 )
                   => X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( sP8
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( binunion @ eigen__1 @ eigen__2 ) )
           => ! [X2: $o] :
                ( ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 )
                 => X2 )
               => ( ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 )
                   => X2 )
                 => X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( binunion @ eigen__1 @ eigen__2 ) )
         => ! [X2: $o] :
              ( ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 )
               => X2 )
             => ( ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 )
                 => X2 )
               => X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( sP5
     => ( sP20
       => ! [X1: $o] :
            ( ( sP14
             => X1 )
           => ( ( sP3
               => X1 )
             => X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ( sP20
     => ! [X1: $o] :
          ( ( sP14
           => X1 )
         => ( ( sP3
             => X1 )
           => X1 ) ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP20,
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ ! [X1: $o] :
        ( ( sP14
         => X1 )
       => ( ( sP3
           => X1 )
         => X1 ) ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ ( sP15
     => ( sP1
       => sP17 ) ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    sP15,
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ( sP1
     => sP17 ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h22,assumption,
    ~ sP17,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP19
    | ~ sP5
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP16
    | ~ sP8
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP12
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP11
    | ~ sP2
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP7
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP10
    | ~ sP18
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP21
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP13
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP4
    | sP14
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP6
    | ~ sP20
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP15
    | ~ sP14
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP1
    | ~ sP3
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h21,h22,h19,h20,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h1,h5,h8,h11,h14,h16,h19,h21,h22]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,14,h21,h22]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,15,h19,h20]) ).

thf(17,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h17,16,h18]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,17,h16,h17]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,18,h14,h15]) ).

thf(20,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,19,h13]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,20,h11,h12]) ).

thf(22,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,21,h10]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,22,h8,h9]) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,23,h7]) ).

thf(25,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,24,h5,h6]) ).

thf(26,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,25,h4]) ).

thf(27,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,26,h3]) ).

thf(28,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,27,h1,h2]) ).

thf(0,theorem,
    ( sP13
   => ! [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 ) @ ( binunion @ X2 @ X3 ) )
                     => ! [X6: $o] :
                          ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
                           => X6 )
                         => ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
                             => X6 )
                           => X6 ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[28,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEU787^2 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36  % Computer : n031.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Wed Aug 23 16:33:20 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.68/0.88  % SZS status Theorem
% 0.68/0.88  % Mode: cade22grackle2xfee4
% 0.68/0.88  % Steps: 8604
% 0.68/0.88  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------