TSTP Solution File: SEU649^2 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU649^2 : 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 : n019.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 13:55:12 EDT 2022

% Result   : Theorem 28.11s 28.23s
% Output   : Proof 28.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  118
% Syntax   : Number of formulae    :  126 (  19 unt;   7 typ;   9 def)
%            Number of atoms       :  306 (  65 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  485 (  64   ~;  62   |;   0   &; 251   @)
%                                         (  52 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   67 (  65 usr;  64 con; 0-2 aty)
%            Number of variables   :   51 (   4   ^  47   !;   0   ?;  51   :)

% 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_emptyset,type,
    emptyset: $i ).

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

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

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

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

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) )
           => ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( eigen__0 = X1 )
           => ( ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) )
              = ( setadjoin @ eigen__0 @ emptyset ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ! [X2: $i] :
              ( ( X1 = X2 )
             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                = ( setadjoin @ X1 @ emptyset ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) )
           => ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( in @ X3 @ X2 ) )
       => ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ X1 ) )
         => ( X1 = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

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

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

thf(sP5,plain,
    ( sP5
  <=> ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ( X3 != X1 )
         => ( X3 = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

thf(sP8,plain,
    ( sP8
  <=> ( ( in @ eigen__3 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) )
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( in @ eigen__3 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) )
     => ( ( eigen__3 != eigen__0 )
       => ( eigen__3 = eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( eigen__3 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ! [X1: $i,X2: $i] :
          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
         => ( X1 = X2 ) )
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( eigen__0 = eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) )
       => ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( in @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) )
       => ( eigen__2 = X1 ) ) ),
    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
  <=> ( ( eigen__3 = eigen__1 )
     => ( in @ eigen__3 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) )
       => ( ( X2 != eigen__0 )
         => ( X2 = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ( eigen__0 = eigen__1 )
     => ( eigen__1 = eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) )
           => ( in @ X2 @ X1 ) )
       => ( ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ X2 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) )
         => ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
            = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( eigen__3 = eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

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

thf(sP24,plain,
    ( sP24
  <=> ( ( eigen__2 = eigen__0 )
     => sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( sP6
     => ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
            = ( setadjoin @ X1 @ emptyset ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
          = ( setadjoin @ X1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ~ sP10
     => ( eigen__3 = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) )
       => ( ( X1 != eigen__0 )
         => ( X1 = eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( eigen__2 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( in @ eigen__3 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( eigen__1 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
     => sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: $i] :
        ( ( eigen__2 = X1 )
       => ( X1 = eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( sP1
     => sP33 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( eigen__3 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( sP10
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ! [X1: $i] :
        ( ( eigen__0 = X1 )
       => ( ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) )
          = ( setadjoin @ eigen__0 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( sP3
     => ( sP13
       => ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
          = ( setadjoin @ eigen__0 @ emptyset ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( emptyset = emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ! [X1: $i] : ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
      = ( setadjoin @ eigen__0 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( sP5
     => sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( eigen__0 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( ( setadjoin @ eigen__1 @ emptyset )
      = ( setadjoin @ eigen__0 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ! [X1: $i] :
        ( ( eigen__3 = X1 )
       => ( in @ eigen__3 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( sP13
     => sP43 ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
      = ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ! [X1: $i] :
        ( ( eigen__0 = X1 )
       => ( X1 = eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ( in @ eigen__3 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(def_setext,definition,
    setext = sP1 ).

thf(def_setadjoinIL,definition,
    setadjoinIL = sP49 ).

thf(def_uniqinunit,definition,
    uniqinunit = sP16 ).

thf(def_eqinunit,definition,
    eqinunit = sP37 ).

thf(def_upairset2E,definition,
    upairset2E = sP6 ).

thf(setukpairinjR11,conjecture,
    sP35 ).

thf(h1,negated_conjecture,
    ~ sP35,
    inference(assume_negation,[status(cth)],[setukpairinjR11]) ).

thf(1,plain,
    ( ~ sP52
    | sP7
    | ~ sP22
    | ~ sP46 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    sP41,
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP46
    | ~ sP32
    | ~ sP41 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    sP22,
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    sP50,
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP28
    | sP14
    | ~ sP12
    | ~ sP50 ),
    inference(mating_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP47
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP17
    | ~ sP36
    | sP52 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP24
    | ~ sP30
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP34
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP19
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP42
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP37
    | sP47 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP47
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP38
    | ~ sP10
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP18
    | sP29 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP29
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP9
    | ~ sP31
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP27
    | sP10
    | sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( sP8
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP8
    | sP31 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP3
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(23,plain,
    ( ~ sP16
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP15
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP2
    | ~ sP5
    | sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( sP44
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( sP44
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( sP13
    | ~ sP44 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(29,plain,
    ( ~ sP49
    | sP42 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP6
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP1
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP21
    | sP40 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP40
    | ~ sP3
    | sP48 ),
    inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP48
    | ~ sP13
    | sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP20
    | ~ sP45
    | sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP51
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP19
    | sP51 ),
    inference(all_rule,[status(thm)],]) ).

thf(38,plain,
    sP19,
    inference(eq_sym,[status(thm)],]) ).

thf(39,plain,
    ( sP23
    | ~ sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( sP23
    | sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( sP39
    | ~ sP23 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(42,plain,
    ( sP26
    | ~ sP39 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(43,plain,
    ( sP25
    | ~ sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( sP25
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( sP4
    | ~ sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(46,plain,
    ( sP4
    | sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( sP11
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
    ( sP11
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(49,plain,
    ( sP33
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(50,plain,
    ( sP33
    | sP49 ),
    inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
    ( sP35
    | ~ sP33 ),
    inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
    ( sP35
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(53,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,h1]) ).

thf(54,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[53,h0]) ).

thf(0,theorem,
    sP35,
    inference(contra,[status(thm),contra(discharge,[h1])],[53,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SEU649^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n019.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 13:09:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 28.11/28.23  % SZS status Theorem
% 28.11/28.23  % Mode: mode454
% 28.11/28.23  % Inferences: 1879
% 28.11/28.23  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------