[necovek]

The only problem is that "logical correctness" depends on the limits of human brain too: formal logic is based on the usual pre-accepted assumptions and definitions ("axioms").

This is what I consider the limit of the human mind: we have to start with a few assumptions we can't "prove" to build even a formal logic system which we then use to build all the other provably correct systems, but we still add other axioms to make them work.

It's hard for me to even think how AI can help with that.