%=======================================================================
%
%       Partially ordered sets ("posets") with n labeled elements.
%       Is enumerated by EIS A001035 (1,1,3,19,219,4231,130023,...)
%
% 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 = 2
}


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


clause {
        e(x,x).                                 % Reflexive.
        FALSE = e(x,y); FALSE = e(y,x); x=y.    % Antisymmetric.
        FALSE = e(x,y); FALSE = e(y,z); e(x,z). % Transitive.
}

setting {
        verbosity stats: full
        stack: maximal
}


end