“Having stolen magical artifacts from an evil king, a Mage learns the truth behind their powers when he is trapped?and his consciousness split?in an alternate realm. Now he must engage a young pupil in the common realm and teach him the ways of advanced magic so, together, they can stop the king from amassing an army and ruling the five realms. (too many words)”
Yes, you’re right. I realized without the king there’s no stakes in one of my versions. Maybe use the split consciousness more ambiguously in the logline. You don’t?really give its purpose, but hint at it.
Just a suggestion for the actual film, because your story is complicated, focus less on the teaching part and use that time to flesh out the villain.?Why does the king want to rule the five realms?
I suggest making it more personal, honestly, rather than rule the realms. Something like, the artifact from the common realm is a prized possession to the king’s family, and then the arrogant, powerful Mage takes it for himself and hides it, something that is the king’s reminder to his lost family.
I mean honestly, how many fantasy films have “want to rule the world” villains? What if all he wants is to take back what his family has always guarded, something special to him. And he’s willing to do anything to get it back. Or something like that. Just a thought.
Because do we?really?need another rule the world villain?
Anyway, here’s another stab at it:

When a Mage is imprisoned in another realm for stealing an artifact and split from his consciousness, he must return to the common realm to stop the king from amassing an inter-dimensional army.?(~33 words)

“You made me realize something. I need to be more willing to write down more variations on the loglines, even when I know they?re not quite right.”
Yep, until you have everything the way you like it, you should think of alternatives. Even when you do have something you like, try to find something better.

Personally, the first story I ever thought of in sixth grade, I still haven’t finished it. It’s changed a dozen times and only now, 6 years later do I even have an idea I truly like, that I’m really excited to write. (I merged it with another one of my ideas, making it much more franchise-able. ?It’s actually set in the same universe as my first logline, the bio-terrorist one.)