The formal invalidation of the idea that certainty is impossible is that such a statement is a self-contradiction.
I recommend that you read Introduction to Objectivist Epistemology more than once. Struggle to understand each major idea in there, and then try to invalidate them, especially the axioms. Be honest in your arguments, and fight each idea to the bitter end. Eventually, you will start to realize, just as I did, that Rand was a lot smarter than I gave her credit for and knew what she was talking about, and that I wasn't as good and sophisticated as I thought I was. But I did not take my philosophical shortcomings personally; I learned from them. I am a lot smarter and sharper now because of that mental investment. I would recommend ITOE to everyone.