%=======================================================================
%
%       Partially ordered sets ("posets") with n labeled elements.
%       Is enumerated by EIS A001035 (1,1,3,19,219,4231,130023,...)
%       In this version we use irreflexive relation (<) instead
%       of reflexive (<=).
%
% See also:
%
% http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001035
% http://mathworld.wolfram.com/PartialOrder.html
%
% http://arp.anu.edu.au/~jks/finder.html
%
%=======================================================================

sort {
        ELEM
        cardinality = 3
}


function {
        e:        ELEM,ELEM -> bool.
}


clause {
        e(x,x) -> FALSE.                        % Irreflexive.
        e(x,y) -> FALSE = e(y,x).               % Asymmetric.
        FALSE = e(x,y); FALSE = e(y,z); e(x,z). % Transitive.
}

setting {
        verbosity stats: full
        stack: maximal
}


end