%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO513^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n002.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  : 300s
% DateTime : Fri Sep  1 04:47:20 EDT 2023

% Result   : Theorem 0.20s 0.42s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   30 (  11 unt;   2 typ;   2 def)
%            Number of atoms       :   64 (   3 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   85 (  31   ~;  13   |;   0   &;  26   @)
%                                         (   9 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;  13 con; 0-2 aty)
%            Number of variables   :   14 (   2   ^;  12   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__10,type,
    eigen__10: $o > $o ).

thf(ty_eigen__11,type,
    eigen__11: $o ).

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

thf(eigendef_eigen__11,definition,
    ( eigen__11
    = ( eps__0
      @ ^ [X1: $o] :
          ~ ~ ( eigen__10 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__11])]) ).

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

thf(eigendef_eigen__10,definition,
    ( eigen__10
    = ( eps__1
      @ ^ [X1: $o > $o] :
          ~ ( ~ ! [X2: $o] :
                  ~ ( X1 @ X2 )
           => ( X1
              @ ~ ( X1 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__10])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ! [X1: $o] :
            ~ ( eigen__10 @ X1 )
     => ( eigen__10
        @ ~ ( eigen__10 @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $o] :
        ~ ( eigen__10 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__10
      @ ~ ( eigen__10 @ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> eigen__11 ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: ( $o > $o ) > $o] :
        ~ ! [X2: $o > $o] :
            ( ~ ! [X3: $o] :
                  ~ ( X2 @ X3 )
           => ( X2 @ ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $o > $o] :
        ( ~ ! [X2: $o] :
              ~ ( X1 @ X2 )
       => ( X1
          @ ~ ( X1 @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__10 @ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__10 @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP4 = ~ sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(choiceo,conjecture,
    ~ sP5 ).

thf(h2,negated_conjecture,
    sP5,
    inference(assume_negation,[status(cth)],[choiceo]) ).

thf(1,plain,
    ( ~ sP8
    | sP3
    | ~ sP8 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP8
    | sP4 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP9
    | ~ sP4
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP7
    | sP3
    | ~ sP9 ),
    inference(mating_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP2
    | sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).

thf(6,plain,
    ( sP1
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP1
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP6
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__10]) ).

thf(9,plain,
    ( ~ sP5
    | ~ sP6 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(11,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[10,h1]) ).

thf(12,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[11,h0]) ).

thf(0,theorem,
    ~ sP5,
    inference(contra,[status(thm),contra(discharge,[h2])],[10,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SYO513^1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 04:31:18 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  % Mode: cade22grackle2xfee4
% 0.20/0.42  % Steps: 134
% 0.20/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------