%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU514^2 : 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 : 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 13:52:40 EDT 2022

% Result   : Theorem 1.98s 2.20s
% Output   : Proof 1.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   39 (  10 unt;   5 typ;   4 def)
%            Number of atoms       :   87 (  12 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  127 (  19   ~;  13   |;   0   &;  70   @)
%                                         (  12 <=>;  13  =>;   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     :   21 (  19 usr;  18 con; 0-2 aty)
%            Number of variables   :   20 (   3   ^  17   !;   0   ?;  20   :)

% 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_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__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ X2 @ ( setadjoin @ eigen__0 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

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

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

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

thf(sP2,plain,
    ( sP2
  <=> ( in @ eigen__2 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ( sP2
     => ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( eigen__2 != eigen__0 )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( setadjoin @ eigen__0 @ eigen__1 ) )
        = ( ( X1 != eigen__0 )
         => ( in @ X1 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ X2 )
       => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP1
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

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

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

thf(sP12,plain,
    ( sP12
  <=> ( sP9 = sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(def_setadjoinAx,definition,
    setadjoinAx = sP1 ).

thf(setadjoinIR,conjecture,
    sP8 ).

thf(h1,negated_conjecture,
    ~ sP8,
    inference(assume_negation,[status(cth)],[setadjoinIR]) ).

thf(1,plain,
    ( sP5
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP12
    | sP9
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP11
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP6
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP4
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP4
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP3
    | ~ sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(9,plain,
    ( sP10
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(10,plain,
    ( sP7
    | ~ sP10 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(11,plain,
    ( sP8
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP8
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(14,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).

thf(0,theorem,
    sP8,
    inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SEU514^2 : TPTP v8.1.0. Released v3.7.0.
% 0.04/0.14  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36  % Computer : n015.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sun Jun 19 07:20:14 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 1.98/2.20  % SZS status Theorem
% 1.98/2.20  % Mode: mode506
% 1.98/2.20  % Inferences: 13
% 1.98/2.20  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------