I'm very curious about this and have a proof sketch that it does not in the answers below. The reasons I'm currently thinking about this is because of the new paper on the class $PTFNP$ which can be downloaded here.
closed as off-topic by Joshua Grochow, Emil Jeřábek, Sasho Nikolov, D.W., Kaveh May 2 '17 at 1:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "Your question does not appear to be a research-level question in theoretical computer science. For more information about the scope, please see help center. Your question might be suitable for Computer Science which has a broader scope." – Joshua Grochow, Emil Jeřábek, Sasho Nikolov