system
A chat on subreddit /r/me_irl
human
Planes don't move like cars by pulling themselves along the ground with wheels. They pull themselves through the air. The speed of the treadmill doesn't matter because it's the jet that pushes the plane. Not it's wheels. 

Think of it like this. If you were on a treadmill wearing skates and matched the treadmills speed you would go nowhere. However if you had a rope tied around your waist that was attached to a wall on the other side of the treadmill, and then you pulled on the rope, no matter how fast that treadmill was spinning, you would move forward. 

That is why a plane can takeoff on a treadmill. The wheels aren't what moves the plane. It's the propeller or jet. They are the rope in this scenario. 

Anyway the Mythbusters did this already in real life and the plane took off. So you can always watch that episode if you want to see it actually work.
gpt
Myth busters screwed up. This guy has a writeup. TLDR it’s a non-trivial question.

Www.gmjacksonphysics.blogspot.com/2018/01/can-jet-take-off-from-conveyor-belt-yes.html?m=1