## TPTP Problem File: KLE164+1.p

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```%------------------------------------------------------------------------------
% File     : KLE164+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Demonic Refinement Algebra)
% Problem  : Back's atomicity refinement theorem
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [Bac89] Back (1989), A Method for Refining Atomicity in Parall
%          : [vW02]  von Wright (2002), From Kleene Algebra to Refinement A
%          : [HS07]  Hoefner & Struth (2007), Automated Reasoning in Kleene
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :   19 (  14 unit)
%            Number of atoms       :   32 (  17 equality)
%            Maximal formula depth :   16 (   4 average)
%            Number of connectives :   13 (   0   ~;   0   |;   8   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :    6 (   2 constant; 0-2 arity)
%            Number of variables   :   40 (   0 sgn;  40   !;   0   ?)
%            Maximal term depth    :    8 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
%---Include axioms for demonic refinement algebra
include('Axioms/KLE004+0.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1,X2,X3,X4,X5] :
( ( leq(X0,multiplication(X3,X0))
& leq(multiplication(X4,X1),multiplication(X1,X4))