## TPTP Problem File: KLE147+2.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE147+2 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Demonic Refinement Algebra)
% Problem  : Sliding of strong iteration
% Version  : [Hoe08] axioms.
% English  :

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

% Status   : Theorem
% Rating   : 0.72 v7.4.0, 0.73 v7.3.0, 0.69 v7.2.0, 0.72 v7.1.0, 0.70 v7.0.0, 0.80 v6.4.0, 0.77 v6.3.0, 0.71 v6.2.0, 0.76 v6.1.0, 0.87 v5.5.0, 0.89 v5.4.0, 0.86 v5.3.0, 0.93 v5.2.0, 0.85 v5.1.0, 0.86 v5.0.0, 0.83 v4.1.0, 0.87 v4.0.0
% Syntax   : Number of formulae    :   19 (  14 unit)
%            Number of atoms       :   24 (  15 equality)
%            Maximal formula depth :    5 (   3 average)
%            Number of connectives :    5 (   0   ~;   0   |;   1   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :    6 (   2 constant; 0-2 arity)
%            Number of variables   :   36 (   0 sgn;  36   !;   0   ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
%---Include axioms for demonic refinement algebra
include('Axioms/KLE004+0.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1] :
( leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))))
& leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1))) ) )).

%------------------------------------------------------------------------------
```