% place queens on the chess board
{ q(1..n,1..n) }.
% exactly 1 queen per row/column
:- X = 1..n, not #count{ Y : q(X,Y) } = 1.
:- Y = 1..n, not #count{ X : q(X,Y) } = 1.
% pre-calculate the diagonals
d1(X,Y,X-Y+n) :- X = 1..n, Y = 1..n.
d2(X,Y,X+Y-1) :- X = 1..n, Y = 1..n.
% at most one queen per diagonal
:- D = 1..n*2-1, 2 { q(X,Y) : d1(X,Y,D) }.
:- D = 1..n*2-1, 2 { q(X,Y) : d2(X,Y,D) }.