In that case, you have proven X by contradiction. If you're rigorous enough, you can rule out the 3rd option. As wondering if you're in a situation where your axioms are inconsistent, well that's actually the world mathematics lives in. Godel's Incompleteness Theorems show that, besides some weak axiom systems, the only systems of axioms that can prove they are consistent are the ones that are inconsistent. So we can only tell when systems are inconsistent, never when they are consistent. You just kinda hope it's not all inconsistent.