Clearly X is more boring than Y, which contradicts our assumption. Everything is interesting. Then there are uninteresting things. Assuming the axiom of choice, the set of uninteresting things can be well ordered. But this would be interesting.
Nothing is boring.
Everything is equally boring. This follows immediately from the corollary to theorem 2. By modus ponens from theorems 1 and 3. This result is well known generalization of the famous proof by van Fraassen that every integer is interesting. We are not claiming, of course, that the ordering relation is that of being more interesting, simply that there is a least element in the set of uninteresting things.