The sentence "p or not p" is a tautology ("true", ⊤) in classical logic, so you can't derive anything useful from it. It can carry some power in non-classical logics, like the intuitionistic logic, where it's not true that "p or not p" for any sentence p.

You can derive anything from false, this is known as the principle of explosion: "ex falso quodlibet", "from false anything":

https://en.wikipedia.org/wiki/Principle_of_explosion

This is just a corollary of the fact that "p or not p" is false (for any value of p).