TSTP Solution File: SEU611^2 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU611^2 : 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 : n018.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 13:54:17 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $i ).

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

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

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

thf(ty_dsetconstr,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

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

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

thf(sP1,plain,
    ( sP1
  <=> ( ( in @ eigen__2 @ ( binunion @ eigen__0 @ eigen__1 ) )
     => ( ~ ( in @ eigen__2 @ eigen__0 )
       => ( in @ eigen__2 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ ( dsetconstr @ ( binunion @ eigen__0 @ eigen__1 ) @ X1 ) )
       => ( X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
       => ( in @ X3 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
       => ( ~ ( in @ X3 @ X1 )
         => ( in @ X3 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ( ( in @ X1
          @ ( dsetconstr @ ( binunion @ eigen__0 @ eigen__1 )
            @ ^ [X2: $i] :
                ( ( in @ X2 @ eigen__0 )
               => ~ ( in @ X2 @ eigen__1 ) ) ) )
       => ( ( in @ X1 @ eigen__0 )
         => ~ ( in @ X1 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( in @ eigen__2
        @ ( dsetconstr @ ( binunion @ eigen__0 @ eigen__1 )
          @ ^ [X1: $i] :
              ( ( in @ X1 @ eigen__0 )
             => ~ ( in @ X1 @ eigen__1 ) ) ) )
     => ( sP2
       => ~ ( in @ eigen__2 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
       => ( X2 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ sP2
     => ( in @ eigen__2 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ ( dsetconstr @ ( binunion @ eigen__0 @ eigen__1 ) @ X1 ) )
       => ( in @ X2 @ ( binunion @ eigen__0 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP2
     => ~ ( in @ eigen__2 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

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

thf(sP13,plain,
    ( sP13
  <=> ( in @ eigen__2 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> eigen__3 ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( binunion @ eigen__0 @ X1 ) )
       => ( ~ ( in @ X2 @ eigen__0 )
         => ( in @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i] :
        ( ( in @ X1
          @ ( dsetconstr @ ( binunion @ eigen__0 @ eigen__1 )
            @ ^ [X2: $i] :
                ( ( in @ X2 @ eigen__0 )
               => ~ ( in @ X2 @ eigen__1 ) ) ) )
       => ( in @ X1 @ ( binunion @ eigen__0 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( in @ eigen__2
        @ ( dsetconstr @ ( binunion @ eigen__0 @ eigen__1 )
          @ ^ [X1: $i] :
              ( ( in @ X1 @ eigen__0 )
             => ~ ( in @ X1 @ eigen__1 ) ) ) )
     => ( in @ eigen__2 @ ( binunion @ eigen__0 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( in @ eigen__2
      @ ( dsetconstr @ ( binunion @ eigen__0 @ eigen__1 )
        @ ^ [X1: $i] :
            ( ( in @ X1 @ eigen__0 )
           => ~ ( in @ X1 @ eigen__1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( in @ eigen__2 @ ( binunion @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(def_dsetconstrEL,definition,
    dsetconstrEL = sP4 ).

thf(def_dsetconstrER,definition,
    dsetconstrER = sP8 ).

thf(def_binunionE,definition,
    binunionE = sP5 ).

thf(def_symdiff,definition,
    ( symdiff
    = ( ^ [X1: $i,X2: $i] :
          ( dsetconstr @ ( binunion @ X1 @ X2 )
          @ ^ [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( in @ X3 @ X2 ) ) ) ) ) ).

thf(symdiffE,conjecture,
    ( sP4
   => ( sP8
     => ( sP5
       => ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3
              @ ( dsetconstr @ ( binunion @ X1 @ X2 )
                @ ^ [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ~ ( in @ X4 @ X2 ) ) ) )
           => ! [X4: $o] :
                ( ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => X4 ) )
               => ( ( ~ ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ X2 )
                     => X4 ) )
                 => X4 ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP4
     => ( sP8
       => ( sP5
         => ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3
                @ ( dsetconstr @ ( binunion @ X1 @ X2 )
                  @ ^ [X4: $i] :
                      ( ( in @ X4 @ X1 )
                     => ~ ( in @ X4 @ X2 ) ) ) )
             => ! [X4: $o] :
                  ( ( ( in @ X3 @ X1 )
                   => ( ~ ( in @ X3 @ X2 )
                     => X4 ) )
                 => ( ( ~ ( in @ X3 @ X1 )
                     => ( ( in @ X3 @ X2 )
                       => X4 ) )
                   => X4 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[symdiffE]) ).

thf(h1,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP8
     => ( sP5
       => ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3
              @ ( dsetconstr @ ( binunion @ X1 @ X2 )
                @ ^ [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ~ ( in @ X4 @ X2 ) ) ) )
           => ! [X4: $o] :
                ( ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => X4 ) )
               => ( ( ~ ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ X2 )
                     => X4 ) )
                 => X4 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP5
     => ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3
            @ ( dsetconstr @ ( binunion @ X1 @ X2 )
              @ ^ [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ~ ( in @ X4 @ X2 ) ) ) )
         => ! [X4: $o] :
              ( ( ( in @ X3 @ X1 )
               => ( ~ ( in @ X3 @ X2 )
                 => X4 ) )
             => ( ( ~ ( in @ X3 @ X1 )
                 => ( ( in @ X3 @ X2 )
                   => X4 ) )
               => X4 ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP5,
    introduced(assumption,[]) ).

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

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

thf(h8,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1
          @ ( dsetconstr @ ( binunion @ eigen__0 @ eigen__1 )
            @ ^ [X2: $i] :
                ( ( in @ X2 @ eigen__0 )
               => ~ ( in @ X2 @ eigen__1 ) ) ) )
       => ! [X2: $o] :
            ( ( ( in @ X1 @ eigen__0 )
             => ( ~ ( in @ X1 @ eigen__1 )
               => X2 ) )
           => ( ( ~ ( in @ X1 @ eigen__0 )
               => ( ( in @ X1 @ eigen__1 )
                 => X2 ) )
             => X2 ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( sP18
     => ! [X1: $o] :
          ( ( sP2
           => ( ~ sP13
             => X1 ) )
         => ( ( ~ sP2
             => ( sP13
               => X1 ) )
           => X1 ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ! [X1: $o] :
        ( ( sP2
         => ( ~ sP13
           => X1 ) )
       => ( ( ~ sP2
           => ( sP13
             => X1 ) )
         => X1 ) ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ( ( sP2
       => ( ~ sP13
         => sP14 ) )
     => ( ( ~ sP2
         => ( sP13
           => sP14 ) )
       => sP14 ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ( sP2
   => ( ~ sP13
     => sP14 ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( ( ~ sP2
       => ( sP13
         => sP14 ) )
     => sP14 ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h16,assumption,
    ( ~ sP13
   => sP14 ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    ( ~ sP2
   => ( sP13
     => sP14 ) ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ sP14,
    introduced(assumption,[]) ).

thf(h19,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h20,assumption,
    ( sP13
   => sP14 ),
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h19,h17,h18,h15,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[h19,h15]) ).

thf(h21,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(h22,assumption,
    sP14,
    introduced(assumption,[]) ).

thf(2,plain,
    ( ~ sP4
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP10
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP16
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP17
    | ~ sP18
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP15
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP12
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP1
    | ~ sP19
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP9
    | sP2
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP5
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(12,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h22,h20,h17,h18,h15,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[h22,h18]) ).

thf(13,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h20,h17,h18,h15,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h20,11,12,h21,h22]) ).

thf(14,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h17,h18,h15,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,1,13,h19,h20]) ).

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

thf(h23,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(16,plain,
    ( ~ sP11
    | ~ sP2
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(18,plain,
    ( ~ sP3
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP6
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP7
    | ~ sP18
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h19,h17,h18,h23,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[16,17,18,19,20,h3,h10,h23,h19]) ).

thf(22,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h21,h20,h17,h18,h23,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[h23,h21]) ).

thf(23,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h22,h20,h17,h18,h23,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[h22,h18]) ).

thf(24,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h20,h17,h18,h23,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h20,22,23,h21,h22]) ).

thf(25,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h17,h18,h23,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,21,24,h19,h20]) ).

thf(26,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h23,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h14,25,h17,h18]) ).

thf(27,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h19,h17,h18,h22,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[h22,h18]) ).

thf(28,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h21,h20,h17,h18,h22,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[h22,h18]) ).

thf(29,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h22,h20,h17,h18,h22,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[h22,h18]) ).

thf(30,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h20,h17,h18,h22,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h20,28,29,h21,h22]) ).

thf(31,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h17,h18,h22,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,27,30,h19,h20]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h22,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h14,31,h17,h18]) ).

thf(33,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h22])],[h16,26,32,h23,h22]) ).

thf(34,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h13,15,33,h15,h16]) ).

thf(35,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,34,h13,h14]) ).

thf(36,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,35,h12]) ).

thf(37,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,36,h10,h11]) ).

thf(38,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,37,h9]) ).

thf(39,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,38,h8]) ).

thf(40,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,39,h7]) ).

thf(41,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,40,h5,h6]) ).

thf(42,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,41,h3,h4]) ).

thf(43,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,42,h1,h2]) ).

thf(0,theorem,
    ( sP4
   => ( sP8
     => ( sP5
       => ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3
              @ ( dsetconstr @ ( binunion @ X1 @ X2 )
                @ ^ [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ~ ( in @ X4 @ X2 ) ) ) )
           => ! [X4: $o] :
                ( ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => X4 ) )
               => ( ( ~ ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ X2 )
                     => X4 ) )
                 => X4 ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[43,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU611^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 19 08:21:19 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % Mode: mode213
% 0.13/0.38  % Inferences: 15
% 0.13/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------