TPTP Problem File: KLE042+2.p
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% File : KLE042+2 : TPTP v8.2.0. Released v4.0.0.
% Domain : Kleene Algebra
% Problem : Star sliding
% Version : [Hoe08] axioms.
% English : Two ways of grouping an alternation of x's and y's that starts
% and ends with x.
% Refs : [Koz94] Kozen (1994), A Completeness Theorem for Kleene Algebr
% : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source : [Hoe08]
% Names :
% Status : Theorem
% Rating : 0.69 v8.2.0, 0.67 v7.5.0, 0.75 v7.4.0, 0.60 v7.3.0, 0.66 v7.1.0, 0.65 v7.0.0, 0.70 v6.4.0, 0.73 v6.3.0, 0.75 v6.2.0, 0.72 v6.1.0, 0.73 v6.0.0, 0.83 v5.5.0, 0.93 v5.4.0, 0.89 v5.3.0, 0.96 v5.2.0, 0.95 v5.0.0, 0.96 v4.0.0
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 21 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 0 ~; 0 |; 1 &)
% ( 1 <=>; 2 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Inequational encoding : proof goal is split into 2 inequations
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%---Include axioms for Kleene algebra
include('Axioms/KLE002+0.ax').
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fof(goals,conjecture,
! [X0,X1] :
( leq(multiplication(star(multiplication(X0,X1)),X0),multiplication(X0,star(multiplication(X1,X0))))
& leq(multiplication(X0,star(multiplication(X1,X0))),multiplication(star(multiplication(X0,X1)),X0)) ) ).
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