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% File     : KLE001+7 : TPTP v9.0.0. Released v3.6.0.
% Domain   : Kleene Algebra
% Axioms   : Divergence Kleene algebras
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [DMS04] Desharnais et al. (2004), Termination in Modal Kleene
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

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

% Comments : Requires KLE001+6.ax KLE002+0.ax
%          : Based on modal Kleene Algebra
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fof(divergence1,axiom,
    ! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0) ).

fof(divergence2,axiom,
    ! [X0,X1,X2] :
      ( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2))
     => addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ) ).

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