TSTP Solution File: SEU902^5 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU902^5 : 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 : n021.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 14:10:45 EDT 2022

% Result   : Theorem 18.24s 18.64s
% Output   : Proof 18.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   49 (  10 unt;   3 typ;   2 def)
%            Number of atoms       :  140 (  30 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  183 (  54   ~;  22   |;   0   &;  66   @)
%                                         (  18 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  23 usr;  21 con; 0-2 aty)
%            Number of variables   :   28 (   6   ^  22   !;   0   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_d,type,
    d: $i > $o ).

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

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

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: ( $i > $o ) > $i] :
          ~ ( ~ ( ! [X2: $i > $o,X3: $i > $o] :
                    ( ( ( X1 @ X2 )
                      = ( X1 @ X3 ) )
                   => ( X2 = X3 ) )
               => ( d
                 != ( ^ [X2: $i] :
                        ~ ! [X3: $i > $o] :
                            ( ~ ( X3 @ ( X1 @ X3 ) )
                           => ( X2
                             != ( X1 @ X3 ) ) ) ) ) )
           => ~ ( d @ ( X1 @ d ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(h1,assumption,
    ! [X1: ( $i > $o ) > $o,X2: $i > $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__1
      @ ^ [X1: $i > $o] :
          ~ ( ~ ( X1 @ ( eigen__0 @ X1 ) )
           => ( ( eigen__0 @ d )
             != ( eigen__0 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( ! [X1: $i > $o,X2: $i > $o] :
              ( ( ( eigen__0 @ X1 )
                = ( eigen__0 @ X2 ) )
             => ( X1 = X2 ) )
         => ( d
           != ( ^ [X1: $i] :
                  ~ ! [X2: $i > $o] :
                      ( ~ ( X2 @ ( eigen__0 @ X2 ) )
                     => ( X1
                       != ( eigen__0 @ X2 ) ) ) ) ) )
     => ~ ( d @ ( eigen__0 @ d ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( eigen__4 @ ( eigen__0 @ d ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i > $o] :
        ( ~ ( X1 @ ( eigen__0 @ X1 ) )
       => ( ( eigen__0 @ d )
         != ( eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( eigen__4 @ ( eigen__0 @ eigen__4 ) )
     => ( ( eigen__0 @ d )
       != ( eigen__0 @ eigen__4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i > $o] :
        ( ( ( eigen__0 @ d )
          = ( eigen__0 @ X1 ) )
       => ( d = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( eigen__0 @ d )
      = ( eigen__0 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i > $o,X2: $i > $o] :
        ( ( ( eigen__0 @ X1 )
          = ( eigen__0 @ X2 ) )
       => ( X1 = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( d @ ( eigen__0 @ d ) )
      = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( d @ ( eigen__0 @ d ) )
      = ( ~ sP3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( d
      = ( ^ [X1: $i] :
            ~ ! [X2: $i > $o] :
                ( ~ ( X2 @ ( eigen__0 @ X2 ) )
               => ( X1
                 != ( eigen__0 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i] :
        ( ( d @ X1 )
        = ( ~ ! [X2: $i > $o] :
                ( ~ ( X2 @ ( eigen__0 @ X2 ) )
               => ( X1
                 != ( eigen__0 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP7
     => ~ sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: ( $i > $o ) > $i] :
        ( ~ ( ! [X2: $i > $o,X3: $i > $o] :
                ( ( ( X1 @ X2 )
                  = ( X1 @ X3 ) )
               => ( X2 = X3 ) )
           => ( d
             != ( ^ [X2: $i] :
                    ~ ! [X3: $i > $o] :
                        ( ~ ( X3 @ ( X1 @ X3 ) )
                       => ( X2
                         != ( X1 @ X3 ) ) ) ) ) )
       => ~ ( d @ ( X1 @ d ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( eigen__4 @ ( eigen__0 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( d @ X1 )
        = ( eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( d = eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( d @ ( eigen__0 @ d ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( sP6
     => sP16 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(cTHM143_pme,conjecture,
    sP13 ).

thf(h2,negated_conjecture,
    ~ sP13,
    inference(assume_negation,[status(cth)],[cTHM143_pme]) ).

thf(1,plain,
    ( ~ sP2
    | sP14
    | ~ sP6 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | ~ sP17
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP15
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP16
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP5
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP18
    | ~ sP6
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP4
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP4
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP3
    | ~ sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).

thf(10,plain,
    ( ~ sP9
    | ~ sP17
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP7
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP11
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP10
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP12
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( sP12
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP1
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( sP1
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( sP13
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(19,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h2]) ).

thf(20,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[19,h1]) ).

thf(21,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[20,h0]) ).

thf(0,theorem,
    sP13,
    inference(contra,[status(thm),contra(discharge,[h2])],[19,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU902^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n021.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 : Sun Jun 19 05:40:02 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 18.24/18.64  % SZS status Theorem
% 18.24/18.64  % Mode: mode454
% 18.24/18.64  % Inferences: 124
% 18.24/18.64  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------