%------------------------------------------------------------------------------
% File     : KLE002+1 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Kleene Algebra (Idempotent Semirings)
% Problem  : Multiplication is isotone
% Version  : [Hoe08] axioms.
% English  :

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

% Status   : Theorem
% Rating   : 0.08 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0
% Syntax   : Number of formulae    :   13 (  11 unt;   0 def)
%            Number of atoms       :   15 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    2 (   0   ~;   0   |;   0   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   25 (  25   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Inequational axioms
%------------------------------------------------------------------------------
%---Include axioms for idempotent semiring
include('Axioms/KLE001+0.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,
    ! [X0,X1,X2] :
      ( leq(X0,X1)
     => leq(multiplication(X0,X2),multiplication(X1,X2)) ) ).

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