Irrefutably means “in a way that cannot be proved wrong.” You use it to say that something has been shown so clearly that arguing against it does not work: the numbers irrefutably show that… It is a word for serious writing. Though actually, speakers sometimes use it as a loud “obviously,” which is weaker than the word promises. If you want to be fair, save it for when the other side really has nowhere left to stand.

無可反駁地、無可否認地