## TPTP Problem File: KLE084+1.p

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```%------------------------------------------------------------------------------
% File     : KLE084+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Domain Semirings)
% Problem  : Domain is local with respect to multiplication
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [DS08]  Desharnais & Struth (2008), Modal Semirings Revisited
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.72 v7.5.0, 0.78 v7.4.0, 0.73 v7.3.0, 0.72 v7.2.0, 0.76 v7.1.0, 0.74 v7.0.0, 0.80 v6.4.0, 0.77 v6.3.0, 0.71 v6.2.0, 0.76 v6.1.0, 0.83 v6.0.0, 0.78 v5.5.0, 0.85 v5.4.0, 0.82 v5.3.0, 0.81 v5.2.0, 0.75 v5.1.0, 0.76 v5.0.0, 0.75 v4.1.0, 0.74 v4.0.1, 0.70 v4.0.0
% Syntax   : Number of formulae    :   21 (  20 unit)
%            Number of atoms       :   22 (  21 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    :    8 (   2 constant; 0-2 arity)
%            Number of variables   :   34 (   0 sgn;  34   !;   0   ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Needed to show that two axiomatisations of Boolean domain
%            semirings are equivalent.
%          : Equational encoding
%------------------------------------------------------------------------------
%---Include axioms for domain semiring (Boolean test algebra)
include('Axioms/KLE001+0.ax').
%---Include axioms for Boolean domain/codomain
include('Axioms/KLE001+4.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) )).

%------------------------------------------------------------------------------
```