TPTP Problem File: KLE029+1.p

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%------------------------------------------------------------------------------
% File     : KLE029+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Idempotent Semirings)
% Problem  : Characterisations of meet
% Version  : [Hoe08] axioms.
% English  : Equivalence of characterisation as greatest lower bound and
%            universal characterisation.

% Refs     : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.53 v7.5.0, 0.56 v7.4.0, 0.47 v7.3.0, 0.55 v7.1.0, 0.52 v7.0.0, 0.57 v6.4.0, 0.62 v6.3.0, 0.54 v6.2.0, 0.60 v6.1.0, 0.70 v5.5.0, 0.81 v5.4.0, 0.82 v5.3.0, 0.89 v5.2.0, 0.80 v5.1.0, 0.86 v5.0.0, 0.79 v4.1.0, 0.78 v4.0.1, 0.70 v4.0.0
% Syntax   : Number of formulae    :   15 (  11 unit)
%            Number of atoms       :   25 (  12 equality)
%            Maximal formula depth :   10 (   4 average)
%            Number of connectives :   10 (   0   ~;   0   |;   4   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    4 (   0 propositional; 2-3 arity)
%            Number of functors    :    4 (   2 constant; 0-2 arity)
%            Number of variables   :   33 (   0 sgn;  33   !;   0   ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Inequational encoding
%------------------------------------------------------------------------------
%---Include axioms for idempotent semiring
include('Axioms/KLE001+0.ax').
%---define meet
include('Axioms/KLE001+3.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
    ! [X0,X1,X2] :
      ( ismeet(X0,X1,X2)
    <=> ismeetu(X0,X1,X2) ) )).

%------------------------------------------------------------------------------