From the first example, it seems like this paper is so contrived. They pose a statement (y = x^3 - x^2 - 1 + 1 when x > -1) which is true, then provide incorrect reasoning but swapping the multiplicity of -1 and 1, then ask it to provide a proof. Essentially, they are running an injection attack; they give it 90% correct information, then it expects in good faith that -1 and 1 are not swapped, so it takes it verbatim. I don't see how the fact that ChatGPT can sometimes get this wrong, especially when the user is the bad actor trying to trick the computer and isn't actually trying to find a proof, is at all relevant to the Navier-Stokes solution.

I don't think that's an accurate summary of what this paper or its abstract actually claim.