TSTP Solution File: SEU930^5 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU930^5 : 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 : n016.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 14:10:54 EDT 2022

% Result   : Theorem 4.34s 4.54s
% Output   : Proof 4.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   47
% Syntax   : Number of formulae    :   52 (   9 unt;   3 typ;   1 def)
%            Number of atoms       :  114 (  37 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  159 (  28   ~;  23   |;   0   &;  63   @)
%                                         (  21 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  25 usr;  24 con; 0-2 aty)
%            Number of variables   :   21 (   3   ^  18   !;   0   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_g,type,
    g: $i > $i ).

thf(ty_f,type,
    f: $i > $i ).

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

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

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

thf(sP2,plain,
    ( sP2
  <=> ( ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) )
      = ( ^ [X1: $i] : ( g @ ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( ( f @ eigen__0 )
        = ( g @ ( f @ eigen__0 ) ) )
     => ( ( g @ ( f @ eigen__0 ) )
        = ( f @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ( ( f @ ( g @ X1 ) )
        = ( g @ ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( ( g @ ( f @ eigen__0 ) )
        = ( f @ eigen__0 ) )
     => ( ( f @ eigen__0 )
        = eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( ( g @ eigen__0 )
        = eigen__0 )
     => ~ ! [X1: $i] :
            ( ( ( g @ X1 )
              = X1 )
           => ( X1 = eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( f @ ( g @ eigen__0 ) )
      = ( g @ ( f @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(sP9,plain,
    ( sP9
  <=> ( sP7
     => ! [X1: $i] :
          ( ( ( g @ eigen__0 )
            = X1 )
         => ( ( f @ X1 )
            = ( g @ ( f @ eigen__0 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

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

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

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ( ( g @ eigen__0 )
          = X1 )
       => ( ( f @ X1 )
          = ( g @ ( f @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( g @ eigen__0 )
      = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ( ( f @ eigen__0 )
          = X1 )
       => ( X1
          = ( f @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ( g @ ( f @ eigen__0 ) )
      = ( f @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i] :
        ( ~ ( ( ( g @ X1 )
              = X1 )
           => ~ ! [X2: $i] :
                  ( ( ( g @ X2 )
                    = X2 )
                 => ( X2 = X1 ) ) )
       => ( ( f @ X1 )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( sP2
     => sP16 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

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

thf(sP19,plain,
    ( sP19
  <=> ( ( f @ eigen__0 )
      = ( g @ ( f @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ! [X1: $i] :
        ( ( ( g @ X1 )
          = X1 )
       => ( X1 = eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( ~ sP6
     => sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(cTHM171A_pme,conjecture,
    sP17 ).

thf(h1,negated_conjecture,
    ~ sP17,
    inference(assume_negation,[status(cth)],[cTHM171A_pme]) ).

thf(1,plain,
    ( ~ sP8
    | ~ sP13
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP12
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP9
    | ~ sP7
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP10
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP2
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP3
    | ~ sP19
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP14
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP20
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP5
    | ~ sP15
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP1
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    sP1,
    inference(eq_ind,[status(thm)],]) ).

thf(13,plain,
    ( sP6
    | sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP6
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP18
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    sP18,
    inference(eq_sym,[status(thm)],]) ).

thf(17,plain,
    ( sP21
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( sP21
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP16
    | ~ sP21 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(20,plain,
    ( sP17
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP17
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,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,h1]) ).

thf(23,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[22,h0]) ).

thf(0,theorem,
    sP17,
    inference(contra,[status(thm),contra(discharge,[h1])],[22,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU930^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n016.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 : Sat Jun 18 20:25:37 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 4.34/4.54  % SZS status Theorem
% 4.34/4.54  % Mode: mode506
% 4.34/4.54  % Inferences: 20474
% 4.34/4.54  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------