The result linked at the beginning shows that there exists, in principle, a coherent probability distribution with certain properties. Edit: in particular, it assigns probability 0 to F or any other contradiction. And while it doesn't always (ever?) know the exact probability it assigns, it does know that P(F)<1-a for any a<1. That statement itself has probability 1. Therefore the part about violating the probabilistic Lob's Theorem clearly holds.

I can't tell at a glance if the distribution satisfies derivation principle #3, but it certainly satisfies #1.