%------------------------------------------------------------------------------
% File     : KLE001+5 : TPTP v9.0.0. Released v3.6.0.
% Domain   : Kleene Algebra
% Axioms   : Domain (not Boolean domain!)
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [DS08]  Desharnais & Struth (2008), Modal Semirings Revisited
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

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

% Comments : The domain algebra is not necessarily Boolean
%          : Requires KLE001+0.ax, KLE002+0.ax or KLE003+0.ax
%          : Combined with KLE001+0 generates Idempotent semirings with tests
%            Combined with KLE002+0 generates Kleene Algebra with tests
%            Combined with KLE003+0 generates Omega Algebra with tests
%------------------------------------------------------------------------------
%----Domain axioms (a la Desharnais & Struth)
fof(domain1,axiom,
    ! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ).

fof(domain2,axiom,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).

fof(domain3,axiom,
    ! [X0] : addition(domain(X0),one) = one ).

fof(domain4,axiom,
    domain(zero) = zero ).

fof(domain5,axiom,
    ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).

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