%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : PUZ140^2 : 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 : n011.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 0.12s 0.39s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   24 (   9 unt;   6 typ;   2 def)
%            Number of atoms       :   40 (  12 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   73 (  27   ~;   4   |;   0   &;  26   @)
%                                         (   5 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :   11 (   1   ^;  10   !;   0   ?;  11   :)

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

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

thf(ty_eigen__0,type,
    eigen__0: syrup ).

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

thf(ty_coffee,type,
    coffee: beverage ).

thf(ty_mix,type,
    mix: beverage > syrup > beverage ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: syrup] :
          ~ ~ ! [X2: beverage] :
                ( ~ ( ( X2
                      = ( mix @ coffee @ X1 ) )
                   => ( X2 != coffee ) )
               => ~ ( hot @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: syrup] :
        ~ ! [X2: beverage] :
            ( ~ ( ( X2
                  = ( mix @ coffee @ X1 ) )
               => ( X2 != coffee ) )
           => ~ ( hot @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: syrup] :
        ~ ( ( ( mix @ coffee @ X1 )
            = coffee )
         => ~ ( hot @ ( mix @ coffee @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( ( mix @ coffee @ eigen__0 )
        = coffee )
     => ~ ( hot @ ( mix @ coffee @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: beverage] :
        ( ~ ( ( X1
              = ( mix @ coffee @ eigen__0 ) )
           => ( X1 != coffee ) )
       => ~ ( hot @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(def_coffee_mixture,definition,
    ( coffee_mixture
    = ( mix @ coffee ) ) ).

thf(there_is_hot_coffee,conjecture,
    ~ sP1 ).

thf(h1,negated_conjecture,
    sP1,
    inference(assume_negation,[status(cth)],[there_is_hot_coffee]) ).

thf(1,plain,
    ( ~ sP3
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(4,plain,
    ( ~ sP1
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(coffee_and_syrup_is_hot_coffee,axiom,
    sP3 ).

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

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

thf(0,theorem,
    ~ sP1,
    inference(contra,[status(thm),contra(discharge,[h1])],[5,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PUZ140^2 : TPTP v8.1.2. Released v6.4.0.
% 0.07/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 22:19:54 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.39  % SZS status Theorem
% 0.12/0.39  % Mode: cade22grackle2xfee4
% 0.12/0.39  % Steps: 28
% 0.12/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------