%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU929^5 : 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 : n015.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 36.74s 36.97s
% Output   : Proof 36.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   42 (  12 unt;   4 typ;   2 def)
%            Number of atoms       :   77 (  20 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  151 (  20   ~;  15   |;   0   &;  90   @)
%                                         (  14 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;  18 con; 0-2 aty)
%            Number of variables   :   14 (   5   ^   9   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
    eigen__1: $i > $i ).

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

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

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__1
      @ ^ [X1: $i] :
          ( ( f @ ( g @ X1 ) )
         != ( g @ ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

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

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

thf(sP3,plain,
    ( sP3
  <=> ( ( ( f @ ( eigen__1 @ eigen__0 ) )
        = ( eigen__1 @ ( f @ eigen__0 ) ) )
     => ( ( f @ ( f @ ( eigen__1 @ eigen__0 ) ) )
        = ( f @ ( eigen__1 @ ( 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
  <=> ( ( ( f @ ( f @ eigen__0 ) )
        = ( f @ ( f @ eigen__0 ) ) )
     => ~ ! [X1: $i > $i] :
            ( ( ( f @ ( X1 @ eigen__0 ) )
              = ( X1 @ ( f @ eigen__0 ) ) )
           => ( ( f @ ( f @ ( X1 @ eigen__0 ) ) )
              = ( f @ ( X1 @ ( f @ eigen__0 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( f @ ( f @ ( eigen__1 @ eigen__0 ) ) )
      = ( f @ ( eigen__1 @ ( f @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

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

thf(sP9,plain,
    ( sP9
  <=> ( ( f @ ( g @ eigen__0 ) )
      = ( g @ ( f @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( f @ ( eigen__1 @ eigen__0 ) )
      = ( eigen__1 @ ( f @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) )
      = ( ^ [X1: $i] : ( g @ ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP1
     => sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

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

thf(sP14,plain,
    ( sP14
  <=> ( ~ sP5
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(cTHM170_pme,conjecture,
    sP12 ).

thf(h2,negated_conjecture,
    ~ sP12,
    inference(assume_negation,[status(cth)],[cTHM170_pme]) ).

thf(1,plain,
    ( sP6
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    sP2,
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP3
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP3
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP7
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP13
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(7,plain,
    ( sP8
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP5
    | ~ sP8
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP14
    | sP5
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP1
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP4
    | ~ sP9 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).

thf(12,plain,
    ( sP11
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP12
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP12
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,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,h2]) ).

thf(16,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[15,h1]) ).

thf(17,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[16,h0]) ).

thf(0,theorem,
    sP12,
    inference(contra,[status(thm),contra(discharge,[h2])],[15,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SEU929^5 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36  % Computer : n015.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.37  % DateTime : Mon Jun 20 03:04:30 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 36.74/36.97  % SZS status Theorem
% 36.74/36.97  % Mode: mode485
% 36.74/36.97  % Inferences: 459
% 36.74/36.97  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------