TSTP Solution File: SEU651^2 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU651^2 : 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 : 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  : 300s
% DateTime : Thu Aug 31 17:20:40 EDT 2023

% Result   : Theorem 27.63s 28.00s
% Output   : Proof 27.63s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
    emptyset: $i ).

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

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

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

thf(ty_setadjoin,type,
    setadjoin: $i > $i > $i ).

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

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

thf(sP1,plain,
    ( sP1
  <=> ( eigen__2 = eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ X1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) )
     => ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
        = ( setadjoin @ eigen__2 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP1
     => ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( in @ eigen__1 @ ( setadjoin @ eigen__3 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
      = ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
      = ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i] :
        ( ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ X1 @ emptyset ) )
       => ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
      = ( setadjoin @ eigen__3 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

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

thf(sP13,plain,
    ( sP13
  <=> ( ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
      = ( setadjoin @ eigen__2 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( sP6
     => ( eigen__1 = eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
       => ( X1 = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( setadjoin @ eigen__3 @ emptyset )
      = ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i] :
        ( ( in @ eigen__1 @ ( setadjoin @ X1 @ emptyset ) )
       => ( eigen__1 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ( setadjoin @ eigen__2 @ emptyset )
      = ( setadjoin @ eigen__3 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ X1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( eigen__1 = eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
      = ( setadjoin @ eigen__2 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: $i] :
        ( ( eigen__2 = X1 )
       => ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( sP22
     => sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( ( setadjoin @ eigen__2 @ emptyset )
      = ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

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

thf(sP34,plain,
    ( sP34
  <=> ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset )
      = ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(def_uniqinunit,definition,
    ( uniqinunit
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
          @ ( X1 = X2 ) ) ) ) ).

thf(def_secondinupair,definition,
    secondinupair = sP9 ).

thf(def_setukpairinjR12,definition,
    ( setukpairinjR12
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) ) ) ) ).

thf(setukpairinjR1,conjecture,
    ( sP16
   => ( sP9
     => ( sP33
       => ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
           => ( ( X3 = X4 )
             => ( X2 = X4 ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP16
     => ( sP9
       => ( sP33
         => ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
             => ( ( X3 = X4 )
               => ( X2 = X4 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[setukpairinjR1]) ).

thf(h1,assumption,
    sP16,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP9
     => ( sP33
       => ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
           => ( ( X3 = X4 )
             => ( X2 = X4 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP33
     => ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
         => ( ( X3 = X4 )
           => ( X2 = X4 ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP33,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ! [X1: $i,X2: $i,X3: $i,X4: $i] :
        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
       => ( ( X3 = X4 )
         => ( X2 = X4 ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: $i,X2: $i,X3: $i] :
        ( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
       => ( ( X2 = X3 )
         => ( X1 = X3 ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
       => ( ( X1 = X2 )
         => ( eigen__1 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: $i] :
        ( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
       => ( ( eigen__2 = X1 )
         => ( eigen__1 = X1 ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( sP23
     => ( sP1
       => sP24 ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP23,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ( sP1
     => sP24 ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP24,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP35
    | sP30
    | ~ sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP38
    | sP22
    | ~ sP32
    | sP30 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP34
    | sP37
    | ~ sP36
    | sP30 ),
    inference(mating_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP25
    | sP17
    | ~ sP19
    | sP30 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP38
    | sP26
    | ~ sP32
    | ~ sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | sP6
    | ~ sP11
    | sP30 ),
    inference(mating_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP32
    | sP36
    | ~ sP20
    | ~ sP35 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP19
    | sP30
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP14
    | sP29 ),
    inference(symeq,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP17
    | sP11 ),
    inference(symeq,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP8
    | sP7 ),
    inference(symeq,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP28
    | ~ sP22
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP13
    | ~ sP37
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP3
    | ~ sP26
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP15
    | ~ sP6
    | sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP5
    | ~ sP1
    | sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ~ sP30,
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP10
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP12
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP12
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP18
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP21
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP31
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP2
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP27
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP16
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP16
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP16
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP9
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP9
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP9
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP33
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP23
    | sP20 ),
    inference(symeq,[status(thm)],]) ).

thf(34,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,h1,h3,h5,h11,h13,h14]) ).

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

thf(37,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,36,h10]) ).

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,
    ( sP16
   => ( sP9
     => ( sP33
       => ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
           => ( ( X3 = X4 )
             => ( X2 = X4 ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[43,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU651^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.35  % Computer : n032.cluster.edu
% 0.11/0.35  % Model    : x86_64 x86_64
% 0.11/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35  % Memory   : 8042.1875MB
% 0.11/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35  % CPULimit : 300
% 0.11/0.35  % WCLimit  : 300
% 0.11/0.35  % DateTime : Wed Aug 23 19:49:26 EDT 2023
% 0.11/0.35  % CPUTime  : 
% 27.63/28.00  % SZS status Theorem
% 27.63/28.00  % Mode: cade22grackle2x798d
% 27.63/28.00  % Steps: 4410
% 27.63/28.00  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------