%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% (Simplified) Shur numbers problem.
%  Find all subsets S of {1,...,N} such that, for each pair of
% (not necessarily distinct) numbers in S, their sum is not in S
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

shur(N,S):-
    subset(S,int(1,N)) &
    forall(X in S,
      forall(Y in S,
        forall(Z in S,Z =\= X+Y)
      )
    ).


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/*
Example
 
{log}=> Sh = {S : shur(5,S)}.              

Sh = {{},{1},{2},{3},{4},{5},{1,3},{2,3},{1,4},
{3,4},{1,5},{2,5},{3,5},{4,5},{1,3,5},{3,4,5}}

Another solution?  (y/n)y
no
*/