%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : PUZ140^1 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n031.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 13:22:01 EDT 2023

% Result   : Theorem 0.17s 0.43s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_beverage,type,
    beverage: $tType ).

thf(ty_syrup,type,
    syrup: $tType ).

thf(ty_hot,type,
    hot: beverage > $o ).

thf(ty_coffee,type,
    coffee: beverage ).

thf(ty_heat,type,
    heat: beverage > beverage ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: beverage > syrup > beverage] :
        ~ ! [X2: syrup] :
            ~ ! [X3: beverage] :
                ( ( ( X1 @ coffee @ X2 )
                  = X3 )
               => ~ ( hot @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( hot @ ( heat @ coffee ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: beverage] : ( hot @ ( heat @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: beverage] :
        ( ( ( heat @ coffee )
          = X1 )
       => ~ ( hot @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(def_cold_mixture,definition,
    ( cold_mixture
    = ( ^ [X1: beverage,X2: syrup] : ( mix @ X1 @ X2 ) ) ) ).

thf(def_hot_mixture,definition,
    ( hot_mixture
    = ( ^ [X1: beverage,X2: syrup] : ( heat @ ( mix @ X1 @ X2 ) ) ) ) ).

thf(hot_coffee,conjecture,
    ~ sP1 ).

thf(h0,negated_conjecture,
    sP1,
    inference(assume_negation,[status(cth)],[hot_coffee]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(its_hot,axiom,
    sP3 ).

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

thf(0,theorem,
    ~ sP1,
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.16  % Problem  : PUZ140^1 : TPTP v8.1.2. Released v6.1.0.
% 0.08/0.17  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.37  % Computer : n031.cluster.edu
% 0.12/0.37  % Model    : x86_64 x86_64
% 0.12/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37  % Memory   : 8042.1875MB
% 0.12/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37  % CPULimit : 300
% 0.12/0.37  % WCLimit  : 300
% 0.12/0.37  % DateTime : Sat Aug 26 23:19:08 EDT 2023
% 0.12/0.37  % CPUTime  : 
% 0.17/0.43  % SZS status Theorem
% 0.17/0.43  % Mode: cade22grackle2xfee4
% 0.17/0.43  % Steps: 394
% 0.17/0.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------