%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : PUZ088^5 : 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 : n024.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 : Thu Aug 31 13:21:50 EDT 2023

% Result   : Theorem 0.19s 0.41s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   31 (   9 unt;   4 typ;   1 def)
%            Number of atoms       :   53 (   1 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   73 (  26   ~;   7   |;   0   &;  22   @)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;  13 con; 0-2 aty)
%            Number of variables   :   10 (   1   ^;   9   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cLYLE,type,
    cLYLE: $i ).

thf(ty_cBRUCE,type,
    cBRUCE: $i ).

thf(ty_cLIKES,type,
    cLIKES: $i > $i > $o ).

thf(ty_eigen__0,type,
    eigen__0: $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] :
          ~ ( cLIKES @ cLYLE @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] : ( cLIKES @ cLYLE @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ( cLIKES @ cLYLE @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( ~ sP3
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] : ( cLIKES @ X1 @ cBRUCE ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ~ ! [X2: $i] : ( cLIKES @ X1 @ X2 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cTHM68A,conjecture,
    ( ~ ( sP7
       => ~ sP1 )
   => ~ sP8 ) ).

thf(h1,negated_conjecture,
    ~ ( ~ ( sP7
         => ~ sP1 )
     => ~ sP8 ),
    inference(assume_negation,[status(cth)],[cTHM68A]) ).

thf(h2,assumption,
    ~ ( sP7
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP3
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | sP3
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP7
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP1
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP2
    | ~ sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(6,plain,
    ( ~ sP8
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,h4,h5,h3]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,7,h4,h5]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,8,h2,h3]) ).

thf(10,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0]) ).

thf(0,theorem,
    ( ~ ( sP7
       => ~ sP1 )
   => ~ sP8 ),
    inference(contra,[status(thm),contra(discharge,[h1])],[9,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : PUZ088^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n024.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 21:57:23 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  % Mode: cade22grackle2xfee4
% 0.19/0.41  % Steps: 44
% 0.19/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------