TPTP Problem File: KLE022+3.p
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%------------------------------------------------------------------------------
% File : KLE022+3 : TPTP v8.2.0. Released v4.0.0.
% Domain : Kleene Algebra (Idempotent Test Semirings)
% Problem : Decompose x into parts ending in p and p's complement
% Version : [Hoe08] axioms : Augmented.
% English :
% Refs : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source : [Hoe08]
% Names :
% Status : Theorem
% Rating : 0.17 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.13 v6.4.0, 0.15 v6.3.0, 0.17 v6.2.0, 0.20 v6.1.0, 0.27 v6.0.0, 0.26 v5.5.0, 0.30 v5.4.0, 0.32 v5.3.0, 0.37 v5.2.0, 0.30 v5.1.0, 0.33 v4.1.0, 0.30 v4.0.1, 0.39 v4.0.0
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 32 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 1 ~; 0 |; 4 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 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 : 35 ( 34 !; 1 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Inequational encoding : additionally the de Morgan laws
%------------------------------------------------------------------------------
%---Include axioms for idempotent test semiring
include('Axioms/KLE001+0.ax').
%---Include test axioms
include('Axioms/KLE001+1.ax').
%---Include additionally axioms
include('Axioms/KLE001+2.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X0,X1] :
( test(X1)
=> X0 = addition(multiplication(X0,X1),multiplication(X0,c(X1))) ) ).
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