015: Schur's Lemma

language Essence 1.3
$ prob015.essence: Schur's Lemma
$ Problem details available at http://www.csplib.org/Problems/prob015/

$ number of balls
given n : int(1..)
letting ball be domain int(1..n)

$ number of boxes, 3 in CSPLib
given k : int(1..)

find boxes : partition (numParts k) from ball

such that
    forAll nums : set (size 3) of ball .
        (exists x,y,z in nums . x != y /\ x + y = z)
        -> apart(nums, boxes)