TPTP Problem File: KLE132+1.p
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%------------------------------------------------------------------------------
% File : KLE132+1 : TPTP v8.2.0. Released v4.0.0.
% Domain : Kleene Algebra (Modal with Divergence)
% Problem : Every element that satisfies Loeb's formula is wellfounded
% Version : [Hoe08] axioms.
% English :
% Refs : [DS08] Desharnais & Struth (2008), Modal Semirings Revisited
% : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source : [Hoe08]
% Names :
% Status : Theorem
% Rating : 0.47 v7.5.0, 0.53 v7.4.0, 0.40 v7.3.0, 0.52 v7.2.0, 0.55 v7.1.0, 0.52 v7.0.0, 0.50 v6.4.0, 0.54 v6.3.0, 0.50 v6.2.0, 0.52 v6.1.0, 0.60 v6.0.0, 0.65 v5.5.0, 0.70 v5.4.0, 0.75 v5.3.0, 0.78 v5.2.0, 0.65 v5.1.0, 0.67 v4.1.0, 0.65 v4.0.1, 0.70 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 |; 0 &)
% ( 1 <=>; 3 =>; 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 : 50 ( 50 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This is part of a modal correspondence result.
% : 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] : addition(forward_diamond(X0,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))))
=> ! [X2] :
( addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
=> domain(X2) = zero ) ) ).
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