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Let it be my main phase: I got Omniscience on the field and one Clear the Mind in my graveyard and another one in my hand.
Could I then play forever? Because I would never run out of cards, so these rules would never apply, right?
MTG Arena: If I continue to do this combo over and over again, would at some point my timer start to run out?
I assume your library is empty and your graveyard contains no other cards; otherwise you risk drawing something else (an Island?) and you'll have no Clear the Mind to cast anymore.
Even then, you cannot play forever; it's a "loop", but one with non-mandatory actions, and you'll have to use a shortcut to state how many times you want to perform the action.
720.1b Occasionally the game gets into a state in which a set of actions could be repeated indefinitely (thus creating a “loop”). In that case, the shortcut rules can be used to determine how many times those actions are repeated without having to actually perform them, and how the loop is broken.
This loop is only useful if you have some other effect, e.g. Niv-Mizzet, the Firemind which turns your card draws into damage, or as you mention, Psychic Corrosion to mill your opponent.
(I don't know what happens in this situation in MTG Arena, I don't play it.)
See closely-related question What happens in the event of a standoff in Magic?
If you're playing in paper, you have an infinite but you'll eventually have to pass the turn back, because it's a loop that involves optional actions. So you must create a shortcut that says how many times you're using the loop, and then pass the turn.
In MTGA however, as far as I know, there's no way to stop you from repeating this until the opponent ragequits. Warning: this is against the terms of service and can get you banned. See the result of someone doing something similar with Nexus of Fate.
