What do you call for repeatedly making a statement even when the statement has been proved wrong

Question

Let's consider a situation were two persons, person A and person B are arguing about something.
Person A makes a statement as a point in his argument. Then person B proves person A's statement as false and tells person A that he was wrong. Person A in an attempt to win the argument, repeates the statement again and again though he understands the statement has been proved wrong and invalid.
Remember, person A doesn't try to disprove person B's claim that the statement is false. He simply keeps repeating his statement.

Now what what do you call for an activity that involves (preferably while in an argument) repeatedly making a statement by a person even when the statement has been proved wrong or invalid.

Answer 1

Stubborn, or obstinate means "fixed or set in purpose or opinion."

The act or instance of being stubborn is obstinacy.

Answer 2

I would recommend To persist.

According to Cambridge Dictionary :

"to try to do or continue doing something in a determined but often unreasonable way."