%------------------------------------------------------------------------------
% File     : QUA001^1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Quantales
% Axioms   : Tests for Quantales (Boolean sub-algebra below 1)
% Version  : [Hoe09] axioms.
% English  :

% Refs     : [Con71] Conway (1971), Regular Algebra and Finite Machines
%          : [Koz97] Kozen (1997), Kleene Algebra with Tests
%          : [Hoe09] Hoefner (2009), Email to Geoff Sutcliffe
% Source   : [Hoe09]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :   10 (   3 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :   10 (   0   ~;   0   |;   2   &;   7   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg;   7 nst)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    2 (   0   ^   1   !;   1   ?;   2   :)
% SPC      : 

% Comments : Requires QUA001^0.ax
%------------------------------------------------------------------------------
thf(tests,type,
    test: $i > $o ).

thf(test_definition,axiom,
    ! [X: $i] :
      ( ( test @ X )
     => ? [Y: $i] :
          ( ( ( addition @ X @ Y )
            = one )
          & ( ( multiplication @ X @ Y )
            = zero )
          & ( ( multiplication @ Y @ X )
            = zero ) ) ) ).

%------------------------------------------------------------------------------