Can president of a corporation fire the CEO?

It depends on the hierarchy structure of the corporation. It also depends on the country.

There is actually nothing that says which is higher-up than the other - many corporations decide that the President has ultimate authority, other corporations decide that the CEO has ultimate authority.

It's so confusing, that to avoid confusion in most companies, the CEO and President are actually the same person.

Look at the official documented hierarchy structure for the corporation you are asking about.