Why wouldn't you be able to do that without a proof? I don't see the value of the proof here, just ask the AI to solve the problem you want and the proof isn't needed.
Why would it not be able to find reductions now, but be able to find them just by being told that P=NP is definitely true?
From my understanding, the two are equivalent; if you can reduce an NP problem to a P problem, you've proven P=NP. The rest is application.