> If P=NP is independent, then we already know that a complete search for a polynomial algorithm for 3SAT will fail A search for a provably polynomial algorith

> If P=NP is independent, then we already know that a complete search for a polynomial algorithm for 3SAT will fail A search for a provably polynomial algorithm will fail, but that doesn't mean that an unprovably polynomial time algorithm couldn't exist. We might come up with strong arguments for why a particular algorithm would be polynomial in practice. Still, I'd say "independent but false" is more likely than "independent but true."