Let's say I am in a court proceeding, and then make swear to tell the truth, the whole truth, and nothing but the truth. I tell the judge I would like to make an opening remark, he says yes, and I say "My opening remark is a false statement." What happens to me?
If they claim that my statement is false and try to prosecute me, then it is in fact not false, and they cannot prosecute. If they claim my statement is true, then it is in fact false, and they cannot not prosecute me.