The most obvious implementation for the easy version will return 0 (or, if the length limit is lifted, fail to return at all).

It's important, however, to be clear on just what constitutes a valid proof. Consider the following implementation:

main() {return 1;}

Not valid because it didn't find a proof, you say? On the contrary, assuming we are dealing with idealized mathematical computers that are perfectly deterministic and have no outside inputs, the fact that a program returns a given value on this run does indeed constitute a proof that it will do so on every run.

The point being that, while you can use concepts like proof to draw rigorous conclusions, in the face of counterintuitive things like self reference, you need some experience actually nailing things down before you can be sure you've closed all the loopholes.