% get the numbers from predicate board
num(X) :- board(X).
num(X-1) :- num(X), X>1.

{ queen(X,Y) } :- num(X), num(Y), not block(X,Y).

% enforce N queens on the board
:- #count{ queens(X,Y) : queen(X,Y) } != N, board(N).

% forbid other queen in horizontal and vertical direction
:- queen(X,Y), queen(X1,Y), X1 != X.
:- queen(X,Y), queen(X,Y1), Y1 != Y.

% forbid other queen in diagonal direction
:- queen(X,Y), num(Delta), queen(X-Delta,Y-Delta).
:- queen(X,Y), num(Delta), queen(X+Delta,Y+Delta).
:- queen(X,Y), num(Delta), queen(X+Delta,Y-Delta).
:- queen(X,Y), num(Delta), queen(X-Delta,Y+Delta).

#show queen/2.