%------------------------------------------------------------------------------
% File     : KLE070+1 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Kleene Algebra (Domain Semirings)
% Problem  : Domain elements satisfy the second lattice absorption law
% Version  : [Hoe08] axioms.
% English  :

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

% Status   : Theorem
% Rating   : 0.18 v9.0.0, 0.19 v8.2.0, 0.22 v8.1.0, 0.25 v7.5.0, 0.28 v7.4.0, 0.10 v7.3.0, 0.24 v7.2.0, 0.28 v7.1.0, 0.22 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.32 v6.1.0, 0.37 v6.0.0, 0.43 v5.5.0, 0.41 v5.4.0, 0.43 v5.3.0, 0.44 v5.2.0, 0.35 v5.1.0, 0.33 v4.1.0, 0.30 v4.0.0
% Syntax   : Number of formulae    :   18 (  17 unt;   0 def)
%            Number of atoms       :   19 (  18 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    1 (   0   ~;   0   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   30 (  30   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Needed for showing that domain elements form a bounded
%            distributive lattice.
%          : Equational encoding
%------------------------------------------------------------------------------
%---Include axioms for domain semiring
include('Axioms/KLE001+0.ax').
%---Include axioms for domain
include('Axioms/KLE001+5.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,
    ! [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(X0) ).

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