%------------------------------------------------------------------------------
% File     : KLE001+2 : TPTP v9.0.0. Released v3.6.0.
% Domain   : Kleene Algebra
% Axioms   : de Morgan's laws for tests
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    2 (   0 unt;   0 def)
%            Number of atoms       :    6 (   2 equ)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :    4 (   0   ~;   0   |;   2   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   5 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :    3 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :    4 (   4   !;   0   ?)
% SPC      : 

% Comments : Requires KLE001+1.ax
%------------------------------------------------------------------------------
fof(test_deMorgan1,axiom,
    ! [X0,X1] :
      ( ( test(X0)
        & test(X1) )
     => c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ) ).

fof(test_deMorgan2,axiom,
    ! [X0,X1] :
      ( ( test(X0)
        & test(X1) )
     => c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ) ).

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