In general, problems whose solutions are easily checkable are not necessarily easily solvable, and the difficulty of finding the proof also depends on how the software is written, which is why humans, at least, don't try to prove arbitrary programs correct, but write the program and the proof together. But regardless, the tools involved are really not very complicated. While it's possible, I find it hard to justify betting on AI being able to prove a 100KLOC-10MLOC program correct while not being able to write a 10KLOC tool well enough.