Lambda the Ultimate

I was reading "Principles of Database & Knowledge-Base Systems, Vol. 1" by Jeffrey D. Ullman. There is a chapter about Datalog negation and as I was seeing the problems of negation I kept thinking that using the predicate ≠ would solve those problems.

E.g.

bachelor(X) :- male(X) & ¬married(X,Y).

would become:

bachelor(X) :- male(X) & married(Y,Z) & X ≠ Y.

but then I see the following:

p(X) :- r(X) & ¬q(X).
q(X) :- r(X) & ¬p(X).

The problem is this has 2 minimal models and if I'm not mistaken so does this:

p(X) :- r(X) & q(Y) & X ≠ Y.
q(X) :- r(X) & p(Y) & X ≠ Y.

Is there an equivalence between these 2 operators? If so, did I miss it or is it not mentioned that it's unsafe to use ≠ with recursion?