## TPTP Problem File: KLE072+1.p

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```%------------------------------------------------------------------------------
% File     : KLE072+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Domain Semirings)
% Problem  : Domain elements satisfy the first axiom of Kleene modules
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [DMS06] Desharnais et al. (2006), Kleene Algebra with Domain
%          : [Lei06] Leiss (2006), Kleene Modules and Linear Languages
%          : [DS08]  Desharnais & Struth (2008), Modal Semirings Revisited
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.3.0, 0.14 v7.1.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.30 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.17 v4.0.0
% Syntax   : Number of formulae    :   18 (  17 unit)
%            Number of atoms       :   19 (  18 equality)
%            Maximal formula depth :    4 (   3 average)
%            Number of connectives :    1 (   0   ~;   0   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :    5 (   2 constant; 0-2 arity)
%            Number of variables   :   31 (   0 sgn;  31   !;   0   ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : FOF_THM_RFO_SEQ