TSTP Solution File: SEV019^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV019^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n007.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 18:04:28 EDT 2022

% Result   : Theorem 0.99s 1.34s
% Output   : Proof 0.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  109
% Syntax   : Number of formulae    :  130 (  28 unt;  11 typ;   3 def)
%            Number of atoms       :  309 (  26 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  512 ( 151   ~;  48   |;   0   &; 197   @)
%                                         (  41 <=>;  75  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   54 (  52 usr;  49 con; 0-2 aty)
%            Number of variables   :   86 (   3   ^  83   !;   0   ?;  86   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_eigen__25,type,
    eigen__25: a ).

thf(ty_eigen__24,type,
    eigen__24: a ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(ty_eigen__26,type,
    eigen__26: a ).

thf(ty_eigen__11,type,
    eigen__11: a ).

thf(ty_eigen__10,type,
    eigen__10: a ).

thf(ty_eigen__8,type,
    eigen__8: a > $o ).

thf(ty_eigen__41,type,
    eigen__41: a > $o ).

thf(ty_eigen__20,type,
    eigen__20: a > $o ).

thf(ty_cQ,type,
    cQ: a > a > $o ).

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

thf(eigendef_eigen__8,definition,
    ( eigen__8
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ~ ! [X2: a] :
                      ~ ( X1 @ X2 )
               => ~ ! [X2: a] :
                      ( ( X1 @ X2 )
                     => ! [X3: a] :
                          ( ( X1 @ X3 )
                          = ( cQ @ X2 @ X3 ) ) ) )
           => ~ ( X1 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__8])]) ).

thf(eigendef_eigen__41,definition,
    ( eigen__41
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ~ ! [X2: a] :
                      ~ ( X1 @ X2 )
               => ~ ! [X2: a] :
                      ( ( X1 @ X2 )
                     => ! [X3: a] :
                          ( ( X1 @ X3 )
                          = ( cQ @ X2 @ X3 ) ) ) )
           => ~ ( X1 @ eigen__24 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__41])]) ).

thf(eigendef_eigen__20,definition,
    ( eigen__20
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ~ ! [X2: a] :
                      ~ ( X1 @ X2 )
               => ~ ! [X2: a] :
                      ( ( X1 @ X2 )
                     => ! [X3: a] :
                          ( ( X1 @ X3 )
                          = ( cQ @ X2 @ X3 ) ) ) )
           => ~ ( X1 @ eigen__10 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__20])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a] :
        ~ ! [X2: a > $o] :
            ( ~ ( ~ ! [X3: a] :
                      ~ ( X2 @ X3 )
               => ~ ! [X3: a] :
                      ( ( X2 @ X3 )
                     => ! [X4: a] :
                          ( ( X2 @ X4 )
                          = ( cQ @ X3 @ X4 ) ) ) )
           => ~ ( X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( cQ @ eigen__10 @ eigen__11 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a] :
        ( ( eigen__20 @ X1 )
        = ( cQ @ eigen__11 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( eigen__41 @ eigen__25 )
      = ( cQ @ eigen__24 @ eigen__25 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: a] :
        ( ( eigen__20 @ X1 )
       => ! [X2: a] :
            ( ( eigen__20 @ X2 )
            = ( cQ @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a] :
        ( ( eigen__8 @ X1 )
       => ! [X2: a] :
            ( ( eigen__8 @ X2 )
            = ( cQ @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__20 @ eigen__11 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: a] :
        ( ( eigen__41 @ X1 )
       => ! [X2: a] :
            ( ( eigen__41 @ X2 )
            = ( cQ @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ ( ~ ! [X1: a] :
                ~ ( eigen__41 @ X1 )
         => ~ sP8 )
     => ~ ( eigen__41 @ eigen__24 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP7 = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: a] :
        ( ( eigen__8 @ X1 )
        = ( cQ @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: a] :
        ( ( eigen__20 @ X1 )
        = ( cQ @ eigen__10 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( cQ @ eigen__24 @ eigen__26 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( eigen__41 @ eigen__25 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( eigen__41 @ eigen__26 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ( eigen__20 @ eigen__10 )
      = ( cQ @ eigen__11 @ eigen__10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( sP7
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: a > $o] :
        ( ~ ( ~ ! [X2: a] :
                  ~ ( X1 @ X2 )
           => ~ ! [X2: a] :
                  ( ( X1 @ X2 )
                 => ! [X3: a] :
                      ( ( X1 @ X3 )
                      = ( cQ @ X2 @ X3 ) ) ) )
       => ~ ( X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ( eigen__41 @ eigen__24 )
     => ! [X1: a] :
          ( ( eigen__41 @ X1 )
          = ( cQ @ eigen__24 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( sP14
     => ! [X1: a] :
          ( ( eigen__41 @ X1 )
          = ( cQ @ eigen__25 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( sP15 = sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: a > $o] :
        ( ~ ( ~ ! [X2: a] :
                  ~ ( X1 @ X2 )
           => ~ ! [X2: a] :
                  ( ( X1 @ X2 )
                 => ! [X3: a] :
                      ( ( X1 @ X3 )
                      = ( cQ @ X2 @ X3 ) ) ) )
       => ~ ( X1 @ eigen__10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( ~ ! [X1: a] :
            ~ ( eigen__41 @ X1 )
     => ~ sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ( eigen__20 @ eigen__10 )
     => sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ( eigen__8 @ eigen__0 )
     => sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( eigen__8 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ~ ! [X1: a] :
            ~ ( eigen__8 @ X1 )
     => ~ sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( cQ @ eigen__24 @ eigen__25 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( eigen__41 @ eigen__24 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: a] :
        ( ( eigen__41 @ X1 )
        = ( cQ @ eigen__25 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ~ ( ~ ! [X1: a] :
                ~ ( eigen__20 @ X1 )
         => ~ sP5 )
     => ~ ( eigen__20 @ eigen__10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ~ ! [X1: a] :
            ~ ( eigen__20 @ X1 )
     => ~ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( cQ @ eigen__0 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: a] :
        ( ( eigen__41 @ X1 )
        = ( cQ @ eigen__24 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( ~ sP27
     => ~ sP26 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ! [X1: a > $o] :
        ( ~ ( ~ ! [X2: a] :
                  ~ ( X1 @ X2 )
           => ~ ! [X2: a] :
                  ( ( X1 @ X2 )
                 => ! [X3: a] :
                      ( ( X1 @ X3 )
                      = ( cQ @ X2 @ X3 ) ) ) )
       => ~ ( X1 @ eigen__24 ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( eigen__20 @ eigen__10 ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( sP15
      = ( cQ @ eigen__25 @ eigen__26 ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( cQ @ eigen__11 @ eigen__10 ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( cQ @ eigen__25 @ eigen__26 ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( sP26 = sP33 ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(cTHM559_pme,conjecture,
    ( sP1
   => ~ ( ~ ( ! [X1: a] : ( cQ @ X1 @ X1 )
           => ~ ! [X1: a,X2: a] :
                  ( ( cQ @ X1 @ X2 )
                 => ( cQ @ X2 @ X1 ) ) )
       => ~ ! [X1: a,X2: a,X3: a] :
              ( ~ ( ( cQ @ X1 @ X2 )
                 => ~ ( cQ @ X2 @ X3 ) )
             => ( cQ @ X1 @ X3 ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( sP1
     => ~ ( ~ ( ! [X1: a] : ( cQ @ X1 @ X1 )
             => ~ ! [X1: a,X2: a] :
                    ( ( cQ @ X1 @ X2 )
                   => ( cQ @ X2 @ X1 ) ) )
         => ~ ! [X1: a,X2: a,X3: a] :
                ( ~ ( ( cQ @ X1 @ X2 )
                   => ~ ( cQ @ X2 @ X3 ) )
               => ( cQ @ X1 @ X3 ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM559_pme]) ).

thf(h2,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( ~ ( ! [X1: a] : ( cQ @ X1 @ X1 )
       => ~ ! [X1: a,X2: a] :
              ( ( cQ @ X1 @ X2 )
             => ( cQ @ X2 @ X1 ) ) )
   => ~ ! [X1: a,X2: a,X3: a] :
          ( ~ ( ( cQ @ X1 @ X2 )
             => ~ ( cQ @ X2 @ X3 ) )
         => ( cQ @ X1 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ( ! [X1: a] : ( cQ @ X1 @ X1 )
   => ~ ! [X1: a,X2: a] :
          ( ( cQ @ X1 @ X2 )
         => ( cQ @ X2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: a,X2: a,X3: a] :
        ( ~ ( ( cQ @ X1 @ X2 )
           => ~ ( cQ @ X2 @ X3 ) )
       => ( cQ @ X1 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ! [X1: a] : ( cQ @ X1 @ X1 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: a,X2: a] :
        ( ( cQ @ X1 @ X2 )
       => ( cQ @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP33,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP41
    | ~ sP26
    | sP33 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP11
    | sP41 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP25
    | ~ sP26
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP27
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP35
    | sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP35
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP18
    | ~ sP35 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).

thf(9,plain,
    ( ~ sP1
    | ~ sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,h8]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h6,10,h8]) ).

thf(h9,assumption,
    ~ ! [X1: a] :
        ( ( cQ @ eigen__10 @ X1 )
       => ( cQ @ X1 @ eigen__10 ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( sP2
     => sP39 ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP39,
    introduced(assumption,[]) ).

thf(12,plain,
    ( ~ sP16
    | ~ sP37
    | sP39 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP10
    | sP7
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP3
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP17
    | ~ sP7
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP12
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP5
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP5
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP24
    | ~ sP37
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( sP32
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP31
    | sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP31
    | ~ sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP22
    | ~ sP31 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__20]) ).

thf(24,plain,
    ( ~ sP1
    | ~ sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h9,h7,h4,h2,h3,h1,h0])],[12,13,14,15,16,17,18,19,20,21,22,23,24,h2,h11,h12]) ).

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

thf(27,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__11)],[h9,26,h10]) ).

thf(28,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__10)],[h7,27,h9]) ).

thf(29,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h4,11,28,h6,h7]) ).

thf(h13,assumption,
    ~ ! [X1: a,X2: a] :
        ( ~ ( ( cQ @ eigen__24 @ X1 )
           => ~ ( cQ @ X1 @ X2 ) )
       => ( cQ @ eigen__24 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ! [X1: a] :
        ( ~ ( sP28
           => ~ ( cQ @ eigen__25 @ X1 ) )
       => ( cQ @ eigen__24 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ( ~ ( sP28
         => ~ sP40 )
     => sP13 ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ ( sP28
     => ~ sP40 ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(h18,assumption,
    sP28,
    introduced(assumption,[]) ).

thf(h19,assumption,
    sP40,
    introduced(assumption,[]) ).

thf(30,plain,
    ( ~ sP21
    | ~ sP15
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP38
    | sP15
    | ~ sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP34
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP30
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP4
    | sP14
    | ~ sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP20
    | ~ sP14
    | sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP34
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP8
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP8
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP19
    | ~ sP29
    | sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( sP23
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( sP9
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( sP9
    | ~ sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( sP36
    | ~ sP9 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__41]) ).

thf(44,plain,
    ( ~ sP1
    | ~ sP36 ),
    inference(all_rule,[status(thm)],]) ).

thf(45,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h18,h19,h16,h17,h15,h14,h13,h5,h2,h3,h1,h0])],[30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,h2,h18,h19,h17]) ).

thf(46,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h14,h13,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h16,45,h18,h19]) ).

thf(47,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h14,h13,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,46,h16,h17]) ).

thf(48,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h14,h13,h5,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__26)],[h14,47,h15]) ).

thf(49,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h13,h5,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__25)],[h13,48,h14]) ).

thf(50,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__24)],[h5,49,h13]) ).

thf(51,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,29,50,h4,h5]) ).

thf(52,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,51,h2,h3]) ).

thf(53,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[52,h0]) ).

thf(0,theorem,
    ( sP1
   => ~ ( ~ ( ! [X1: a] : ( cQ @ X1 @ X1 )
           => ~ ! [X1: a,X2: a] :
                  ( ( cQ @ X1 @ X2 )
                 => ( cQ @ X2 @ X1 ) ) )
       => ~ ! [X1: a,X2: a,X3: a] :
              ( ~ ( ( cQ @ X1 @ X2 )
                 => ~ ( cQ @ X2 @ X3 ) )
             => ( cQ @ X1 @ X3 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[52,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV019^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n007.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 : Tue Jun 28 14:49:37 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.99/1.34  % SZS status Theorem
% 0.99/1.34  % Mode: mode213
% 0.99/1.34  % Inferences: 1809
% 0.99/1.34  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------