TPTP Problem File: KLE077+1.p

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%------------------------------------------------------------------------------
% File     : KLE077+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (with Domain)
% Problem  : Domain elements satisfy the sixth Kleene module axiom
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [DMS06] Desharnais et al. (2006), Kleene Algebra with Domain
%          : [Lei06] Leiss (2006), Kleene Modules and Linear Languages
%          : [DS08]  Desharnais & Struth (2008), Modal Semirings Revisited
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.97 v7.5.0, 1.00 v7.4.0, 0.93 v7.3.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :   22 (  18 unit)
%            Number of atoms       :   26 (  19 equality)
%            Maximal formula depth :    5 (   3 average)
%            Number of connectives :    4 (   0   ~;   0   |;   0   &)
%                                         (   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   :   39 (   0 sgn;  39   !;   0   ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Equational encoding
%------------------------------------------------------------------------------
%---Include axioms for Kleene algebra with domain
include('Axioms/KLE002+0.ax').
%---Include axioms for domain
include('Axioms/KLE001+5.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
    ! [X0,X1,X2] :
      ( addition(addition(domain(X0),domain(multiplication(X1,domain(X2)))),domain(X2)) = domain(X2)
     => addition(domain(multiplication(star(X1),domain(X0))),domain(X2)) = domain(X2) ) )).

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