%=======================================================================
%
%       Handshaking across a table (everybody shaking):
%       Is enumerated by EIS A001147, but aerated (0,1,0,3,0,15,0,105,0,945,0,10395,...)
%       because we get no solutions when there are odd number of shakers.
%
% See also:
%
% http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001147
% http://www.research.att.com/~njas/sequences/a002694.gif
% http://www.iki.fi/~kartturi/matikka/ModFin/A001147.fnd
%
% http://arp.anu.edu.au/~jks/finder.html
%
% Actually, in this case we could manage with just one bijective
% function f, with no need for relation e. (Both encode same
% thing.)
% See http://www.iki.fi/~kartturi/matikka/ModFin/A000108A.fnd
%
%
%==========================================================================

sort {
        ELEM
        cardinality = 12
}


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

setting {
        verbosity stats: full
        stack: maximal
}


end