%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : PUZ146^1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n019.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 13:22:07 EDT 2023

% Result   : Theorem 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_hobby,type,
    hobby: $tType ).

thf(ty_weight_lifting,type,
    weight_lifting: hobby ).

thf(ty_beer_drinking,type,
    beer_drinking: hobby ).

thf(ty_belly_dancing,type,
    belly_dancing: hobby ).

thf(ty_peter,type,
    peter: earthling ).

thf(ty_has_hobby,type,
    has_hobby: earthling > hobby > $o ).

thf(ty_mary,type,
    mary: earthling ).

thf(sP1,plain,
    ( sP1
  <=> ( has_hobby @ peter @ beer_drinking ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: hobby] :
        ( ( has_hobby @ peter @ X1 )
        = ( has_hobby @ mary @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( has_hobby @ mary @ beer_drinking ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( has_hobby @ peter )
      = ( has_hobby @ mary ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP1 = sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(def_peters_hobbies,definition,
    ( peters_hobbies
    = ( has_hobby @ peter ) ) ).

thf(def_marys_hobbies,definition,
    ( marys_hobbies
    = ( has_hobby @ mary ) ) ).

thf(peter_and_mary_have_different_hobbies,conjecture,
    ~ sP4 ).

thf(h0,negated_conjecture,
    sP4,
    inference(assume_negation,[status(cth)],[peter_and_mary_have_different_hobbies]) ).

thf(h1,assumption,
    ~ ( ( beer_drinking != belly_dancing )
     => ( belly_dancing = weight_lifting ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    beer_drinking != weight_lifting,
    introduced(assumption,[]) ).

thf(h3,assumption,
    beer_drinking != belly_dancing,
    introduced(assumption,[]) ).

thf(h4,assumption,
    belly_dancing != weight_lifting,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP5
    | ~ sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(3,plain,
    ( ~ sP4
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(peter_does_beer_drinking,axiom,
    sP1 ).

thf(mary_does_not_do_beer_drinking,axiom,
    ~ sP3 ).

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

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,4,h3,h4]) ).

thf(not_the_same_2,axiom,
    ~ ( ~ ( ( beer_drinking != belly_dancing )
         => ( belly_dancing = weight_lifting ) )
     => ( beer_drinking = weight_lifting ) ) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[not_the_same_2,5,h1,h2]) ).

thf(0,theorem,
    ~ sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : PUZ146^1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.34  % Computer : n019.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Sat Aug 26 22:52:13 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.39  % SZS status Theorem
% 0.19/0.39  % Mode: cade22grackle2xfee4
% 0.19/0.39  % Steps: 19
% 0.19/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------