TPTP Problem File: PUZ140^2.p
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% File : PUZ140^2 : TPTP v9.0.0. 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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