%------------------------------------------------------------------------------
% File     : KLE044+2 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Kleene Algebra
% Problem  : Star simplification
% Version  : [Hoe08] axioms.
% English  : Identity can be eliminated from the star of a sum.

% Refs     : [Koz94] Kozen (1994), A Completeness Theorem for Kleene Algebr
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.58 v8.2.0, 0.53 v8.1.0, 0.50 v7.5.0, 0.59 v7.4.0, 0.40 v7.3.0, 0.45 v7.2.0, 0.48 v7.1.0, 0.43 v7.0.0, 0.53 v6.4.0, 0.58 v6.3.0, 0.50 v6.2.0, 0.56 v6.1.0, 0.70 v6.0.0, 0.57 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0, 0.70 v5.1.0, 0.71 v4.1.0, 0.70 v4.0.0
% Syntax   : Number of formulae    :   17 (  13 unt;   0 def)
%            Number of atoms       :   21 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    4 (   0   ~;   0   |;   1   &)
%                                         (   1 <=>;   2  =>;   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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   31 (  31   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Inequational encoding : proof goal is split into 2 inequations
%------------------------------------------------------------------------------
%---Include axioms for Kleene algebra
include('Axioms/KLE002+0.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,
    ! [X0] :
      ( leq(star(addition(one,X0)),star(X0))
      & leq(star(X0),star(addition(one,X0))) ) ).

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