If someone else's patent is invalid, can I continue to apply?

It doesn't make sense. A patent is a big technology that has been disclosed. The disclosed technology has no novelty and creativity required by the patent law, so it doesn't meet the conditions for granting a patent right. Therefore, if you apply for a patent for invention, it will not be authorized after substantive examination. If you apply for a utility model, it can be authorized, but it cannot be effectively protected, and it is also an invalid patent. Don't bother to do meaningless work.