% Schur numbers.
% 
% The range of integers to be partitioned is n and the number of 
% parts is k. The main predicate is assigned. Atom assigned(X,P)
% represents the fact that number X is included in part P.
% The idea is to find a partition of integers {1,2,...,n} into k 
% parts such that each part is sum free, i.e. for any X and Y, 
% X and X+X are in different parts and  if X and Y are in the 
% same part, then X+Y is in a different part.


% Guess
assigned(X,P) v insomeotherpart(X,P) :- number(X), part(P).

% Assign each integer to exactly one part. 
:- number(X), assigned(X,P1), assigned(X,P2), P1!=P2.

% X, Y, and X+Y cannot be in the same part
:-  X <= Y, assigned(X,P), assigned(Y,P), assigned(Z,P), Z = X + Y.