When you say “he has to say he is acting infallibly,” what exactly do you mean? There’s no special formula or particular words that have to be used, but he has to be clear that he’s teaching definitively to meet qualification #3.
Para 46, 45 and others use infallible language
If an encyclical is ex cathedra then it is infallible.
The exact formula has varied over the centuries, but it is clear when you see it. If you are told that you will go to hell if you reject it (enathema was the word they used to commonly use in the encyclical), then you have an infallible statement.
All global conferences of bishops have their documents ratified by the pope. These documents then are said to contain infallible pronouncements. Now it does get a little over my pay grade though as not all Vatican II documents are considered infallible. They say this is because not all of the documents were intended to be infallible.