diagX(X,Y,XmY) :- num(X), num(Y), XmY = X - Y.
diagY(X,Y,XpY) :- num(X), num(Y), XpY = X + Y.

diagXp(D) :- diagX(X,Y,D).
diagYp(D) :- diagY(X,Y,D).

queen(X,Y) v noQueen(X,Y) :- num(X), num(Y), not block(X,Y).
queen(X,Y) v noQueen(X,Y) :- num(Y), num(X), not block(X,Y).

% exactly 1 queen in each row/col
:- num(X), not assignedRow(X).
:- num(X), not assignedCol(X).
assignedRow(X):- queen(X,_).
assignedCol(X):- queen(_,X).
:- queen(X,Y), queen(X,Z), Z != Y.
:- queen(X,Y), queen(Z,Y), Z != X.

% at most 1 queen on each diagonal
:- queen(X,Y), queen(XX,YY), sameDiag(X,Y,XX,YY).
sameDiag(X,Y,XX,YY) :- num(X), num(Y), num(XX), num(YY), num(K), XX = X + K, YY = Y + K.
sameDiag(X,Y,XX,YY) :- num(X), num(Y), num(XX), num(YY), num(K), XX = X + K, YY = Y - K.