TPTP Problem File: KLE017+1.p
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%------------------------------------------------------------------------------
% File : KLE017+1 : TPTP v8.2.0. Released v4.0.0.
% Domain : Kleene Algebra (Idempotent Test Semirings)
% Problem : Product of tests is their meet
% Version : [Hoe08] axioms.
% English :
% Refs : [MB85] Manes & Benson (1985), The Inverse Semigroup of a Sum-
% : [Koz97] Kozen (1997), Kleene Algebra with Tests
% : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source : [Hoe08]
% Names :
% Status : Theorem
% Rating : 0.56 v8.2.0, 0.58 v8.1.0, 0.53 v7.5.0, 0.66 v7.4.0, 0.50 v7.3.0, 0.52 v7.1.0, 0.48 v7.0.0, 0.53 v6.4.0, 0.50 v6.3.0, 0.54 v6.2.0, 0.64 v6.1.0, 0.70 v6.0.0, 0.65 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.74 v5.2.0, 0.60 v5.1.0, 0.67 v4.1.0, 0.61 v4.0.1, 0.65 v4.0.0
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 30 ( 17 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 14 ( 1 ~; 0 |; 5 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 31 !; 1 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Inequational encoding
%------------------------------------------------------------------------------
%---Include axioms for idempotent test semiring
include('Axioms/KLE001+0.ax').
%---Include test axioms
include('Axioms/KLE001+1.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2) )
=> ( leq(X2,multiplication(X0,X1))
<=> ( leq(X2,X0)
& leq(X2,X1) ) ) ) ).
%------------------------------------------------------------------------------