TPTP Problem File: KLE142+2.p
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%------------------------------------------------------------------------------
% File : KLE142+2 : TPTP v9.0.0. Released v4.0.0.
% Domain : Kleene Algebra (Demonic Refinement Algebra)
% Problem : If strong iteration is applied twice, a miracle occurs.
% Version : [Hoe08] axioms.
% English :
% Refs : [vW02] von Wright (2002), From Kleene Algebra to Refinement A
% : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source : [Hoe08]
% Names :
% Status : Theorem
% Rating : 0.45 v9.0.0, 0.42 v7.5.0, 0.50 v7.4.0, 0.33 v7.3.0, 0.45 v7.2.0, 0.48 v7.1.0, 0.39 v7.0.0, 0.40 v6.4.0, 0.46 v6.3.0, 0.38 v6.2.0, 0.48 v6.1.0, 0.57 v5.5.0, 0.63 v5.4.0, 0.64 v5.3.0, 0.63 v5.2.0, 0.50 v5.1.0, 0.52 v5.0.0, 0.46 v4.1.0, 0.48 v4.0.0
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 24 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 0 ~; 0 |; 1 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
%---Include axioms for demonic refinement algebra
include('Axioms/KLE004+0.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X0] :
( leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(strong_iteration(X0))) ) ).
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