%=======================================================================
%
%	Connected labeled topologies with n points.
%       I.e. partially ordered sets ("posets") with n labeled elements,
%       with all elements except one having at least one "less than element".
%
%       Is enumerated by EIS A006059 (1,2,9,76,1095,25386,910161,...)
%
% See also:
%
% http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A006059
% http://mathworld.wolfram.com/PartialOrder.html
% http://www.iki.fi/~kartturi/matikka/ModFin/A00169.fnd
% http://www.iki.fi/~kartturi/matikka/ModFin/A001035R.fnd
%
% http://arp.anu.edu.au/~jks/finder.html
%
%=======================================================================

sort {
        ELEM
        cardinality = 7
}


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


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.
        x=y; e(f(x),x); e(f(y),y).              % If x and y are distinct, then at least other has a predecessor,
}

setting {
        verbosity stats: full
        stack: maximal
}


end