%------------------------------------------------------------------------------
% File     : PUZ140^2 : TPTP v8.2.0. Released v6.4.0.
% Domain   : Puzzles
% Problem  : A mixture of coffee and syrup that is hot
% Version  : Especial.
% English  : 

% Refs     : 
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.4.0
% Syntax   : Number of formulae    :    9 (   1 unt;   6 typ;   1 def)
%            Number of atoms       :    6 (   4 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :    9 (   0   ~;   0   |;   3   &;   6   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    4 (   0   ^;   2   !;   2   ?;   4   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This version highlights partial application
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thf(syrup_type,type,
    syrup: $tType ).

thf(beverage_type,type,
    beverage: $tType ).

thf(coffee_type,type,
    coffee: beverage ).

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

thf(coffee_mixture_type,type,
    coffee_mixture: syrup > beverage ).

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

%----The mixture of coffee and something
thf(coffee_mixture_definition,definition,
    ( coffee_mixture
    = ( mix @ coffee ) ) ).

%----Any coffee mixture is hot coffee
thf(coffee_and_syrup_is_hot_coffee,axiom,
    ! [S: syrup] :
      ( ( ( coffee_mixture @ S )
        = coffee )
      & ( hot @ ( coffee_mixture @ S ) ) ) ).

%----There is some mixture of coffee and any syrup which is hot coffee
thf(there_is_hot_coffee,conjecture,
    ? [SyrupMixer: syrup > beverage] :
    ! [S: syrup] :
    ? [B: beverage] :
      ( ( B
        = ( SyrupMixer @ S ) )
      & ( B = coffee )
      & ( hot @ B ) ) ).

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