%------------------------------------------------------------------------------
% File     : KLE151+1 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Kleene Algebra (Demonic Refinement Algebra)
% Problem  : Sliding of strong iteration
% Version  : [Hoe08] axioms.
% English  : Two ways of grouping an alternation of x's and y's that starts
%            and ends with x.

% Refs     : [vW02]  von Wright (2002), From Kleene Algebra to Refinement A
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.47 v8.2.0, 0.53 v7.5.0, 0.59 v7.4.0, 0.50 v7.3.0, 0.52 v7.1.0, 0.48 v7.0.0, 0.57 v6.4.0, 0.62 v6.2.0, 0.64 v6.1.0, 0.73 v6.0.0, 0.78 v5.5.0, 0.85 v5.4.0, 0.89 v5.3.0, 0.96 v5.2.0, 0.90 v5.0.0, 0.88 v4.1.0, 0.87 v4.0.0
% Syntax   : Number of formulae    :   19 (  15 unt;   0 def)
%            Number of atoms       :   23 (  15 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    4 (   0   ~;   0   |;   0   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   36 (  36   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : The converse inequation holds also (KLE152).
%------------------------------------------------------------------------------
%---Include axioms for demonic refinement algebra
include('Axioms/KLE004+0.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,
    ! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)) ).

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