%=======================================================================
%
%       
%       Handshaking across a table (everybody shaking), with
%       an extra condition.
%       SEEMS (Check it!) to be enumerated by EIS A000110 (Bell numbers),
%       but aerated (0,1,0,2,0,5,0,15,0,52,0,203,0,877,0,4140,0,21147,...)
%       because we get no solutions when there are odd number of shakers.
%
%       (Funny, because I was hunting for Catalans, resulting from
%       non-crossing handshakes, but these axiomatizations are not
%       enough, as the largest elem can still be connected to
%       anywhere it wishes to.)
%
% See also:
%
% http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000110
% http://www.research.att.com/~njas/sequences/a002694.gif
% http://mathforum.org/advanced/robertd/bell.html
% http://www.iki.fi/~kartturi/matikka/ModFin/A001147A.fnd
%
% http://arp.anu.edu.au/~jks/finder.html
%
%
%==========================================================================

sort {
        ELEM
        cardinality = 18
}


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


clause {
        e(x,x) -> FALSE.                        % No self-handshakings.
        e(x,y) -> e(y,x).                       % Symmetric, if x shakes with y, then vice versa also.
        y=z; FALSE = e(x,y); FALSE = e(x,z).    % Each shakes with exactly one other person.
        e(x,f(x)).                              % Everybody shakes hands with somebody else.
        FALSE = e(x,y); FALSE = (y > x); f(y-1) > x.
        FALSE = e(x,y); FALSE = (y > x); FALSE = (f(y-1) > y).
}

setting {
        verbosity stats: full
        stack: maximal
}


end