1 % Schur numbers.
   2 % 
   3 % The range of integers to be partitioned is n and the number of 
   4 % parts is k. The main predicate is assigned. Atom assigned(X,P)
   5 % represents the fact that number X is included in part P.
   6 % The idea is to find a partition of integers {1,2,...,n} into k 
   7 % parts such that each part is sum free, i.e. for any X and Y, 
   8 % X and X+X are in different parts and  if X and Y are in the 
   9 % same part, then X+Y is in a different part.
  10 
  11 
  12 % Guess
  13 assigned(X,P) v insomeotherpart(X,P) :- number(X), part(P).
  14 
  15 % Assign each integer to exactly one part. 
  16 :- number(X), assigned(X,P1), assigned(X,P2), P1!=P2.
  17 
  18 % X, Y, and X+Y cannot be in the same part
  19 :-  X <= Y, assigned(X,P), assigned(Y,P), assigned(Z,P), Z = X + Y.