TPTP Problem File: KLE094+1.p

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%------------------------------------------------------------------------------
% File     : KLE094+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Modal)
% Problem  : Segerberg
% Version  : [Hoe08] axioms.
% English  : Segerberg's formula holds in every Kleene algebra with Boolean
%            domain.

% Refs     : [DMS06] Desharnais et al. (2006), Kleene Algebra with Domain
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :   31 (  28 unit)
%            Number of atoms       :   34 (  27 equality)
%            Maximal formula depth :    5 (   3 average)
%            Number of connectives :    3 (   0   ~;   0   |;   0   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :   15 (   2 constant; 0-2 arity)
%            Number of variables   :   53 (   0 sgn;  53   !;   0   ?)
%            Maximal term depth    :    6 (   3 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Segerberg's formula expresses induction in propositional dynamic
%            logic.
%          : Equational encoding
%------------------------------------------------------------------------------
%---Include axioms for modal Kleene algebra
include('Axioms/KLE002+0.ax').
%---Include axioms for Boolean domain/codomain
include('Axioms/KLE001+4.ax').
%---Include axioms for diamond and boxes
include('Axioms/KLE001+6.ax').
%--------------------------------------------------------------------------
fof(goals,conjecture,(
    ! [X0,X1] : addition(domain_difference(forward_diamond(star(X0),domain(X1)),domain(X1)),forward_diamond(star(X0),domain_difference(forward_diamond(X0,domain(X1)),domain(X1)))) = forward_diamond(star(X0),domain_difference(forward_diamond(X0,domain(X1)),domain(X1))) )).