%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO282^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -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  : 300s
% DateTime : Fri Sep  1 04:46:08 EDT 2023

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   23 (   6 unt;   4 typ;   1 def)
%            Number of atoms       :   31 (   1 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   63 (  28   ~;   5   |;   0   &;  18   @)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   9 con; 0-2 aty)
%            Number of variables   :   16 (   1   ^;  15   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_b,type,
    b: $tType ).

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

thf(ty_eigen__1,type,
    eigen__1: b ).

thf(ty_eigen__2,type,
    eigen__2: b ).

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

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: b] :
          ~ ~ ( eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ! [X1: b] :
            ~ ( eigen__0 @ X1 )
     => ( eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ! [X1: b] :
            ~ ( eigen__0 @ X1 )
     => ( eigen__0 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: b] :
        ~ ( eigen__0 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: b] :
        ~ ( ~ sP4
         => ( eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(cL51,conjecture,
    ! [X1: b > $o] :
      ~ ! [X2: b] :
          ~ ( ~ ! [X3: b] :
                  ~ ( X1 @ X3 )
           => ( X1 @ X2 ) ) ).

thf(h1,negated_conjecture,
    ~ ! [X1: b > $o] :
        ~ ! [X2: b] :
            ~ ( ~ ! [X3: b] :
                    ~ ( X1 @ X3 )
             => ( X1 @ X2 ) ),
    inference(assume_negation,[status(cth)],[cL51]) ).

thf(h2,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP2
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP4
    | sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(4,plain,
    ( sP1
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP5
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,6,h2]) ).

thf(8,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).

thf(0,theorem,
    ! [X1: b > $o] :
      ~ ! [X2: b] :
          ~ ( ~ ! [X3: b] :
                  ~ ( X1 @ X3 )
           => ( X1 @ X2 ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYO282^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n021.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  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 05:56:26 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % Mode: cade22grackle2xfee4
% 0.20/0.39  % Steps: 13
% 0.20/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------