## TPTP Problem File: KLE130+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE130+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Modal with Divergence)
% Problem  : Two notions of termination
% Version  : [Hoe08] axioms.
% English  : The lemma compares absence of divergence with a third notion of
%            termination.

% Refs     : [Str08] Struth (2008), Modal Tools for Separation and Refineme
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :   29 (  26 unit)
%            Number of atoms       :   32 (  31 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    :   16 (   2 constant; 0-2 arity)
%            Number of variables   :   49 (   0 sgn;  49   !;   0   ?)
%            Maximal term depth    :    6 (   3 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
%---Include axioms for modal Kleene algebra with divergence
include('Axioms/KLE001+0.ax').
%---Include axioms for Boolean domain/codomain
include('Axioms/KLE001+4.ax').
%---Include axioms for diamond and boxes
include('Axioms/KLE001+6.ax').
%---Include axioms for divergence
include('Axioms/KLE001+7.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0] :
( divergence(X0) = zero
=> ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) ) )).

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