TPTP Problem File: KLE136+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : KLE136+1 : TPTP v9.0.0. Released v4.0.0.
% Domain : Kleene Algebra (Modal with Divergence)
% Problem : Newman's lemma holds in divergence Kleene algebras
% Version : [Hoe08] axioms.
% English :
% Refs : [Ter03] Terese (2003), Term Rewriting Systems
% : [DMS04] Desharnais et al. (2004), Termination in Modal Kleene
% : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source : [Hoe08]
% Names :
% Status : CounterSatisfiable
% Rating : 0.00 v8.1.0, 0.25 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0, 0.33 v7.0.0, 0.00 v6.4.0, 0.33 v6.2.0, 0.45 v6.1.0, 0.55 v6.0.0, 0.69 v5.5.0, 0.62 v5.4.0, 0.71 v5.3.0, 0.86 v5.2.0, 1.00 v4.0.0
% Syntax : Number of formulae : 29 ( 26 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 4 ( 0 ~; 0 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments : The usual relational statement is expressed more abstractly at
% the level of modal Kleene algebras.
% : Equational encoding
%------------------------------------------------------------------------------
%---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,X1] :
( ( divergence(addition(X0,X1)) = zero
& addition(multiplication(X1,X0),multiplication(star(X0),star(X1))) = multiplication(star(X0),star(X1)) )
=> addition(star(addition(X0,X1)),multiplication(star(X0),star(X1))) = multiplication(star(X0),star(X1)) ) ).
%------------------------------------------------------------------------------