[Achilles]

The treadmill doesn't mean the plane is stationary relative to the ground at all dude. The treadmill acts on the wheels of the plane which, while now turning really fast, in no way impede it's movement forward. Thus the plane will move forward, air will pass over the wings and it will take off.

Where it the hypothesis does it state that the plane wouldn't be moving over the ground? It states that the treadmill will rotate at the same speed as the plane in the opposite direction. There is no way to conduct an experiment where the plane wouldn't move forward in these conditions since it defies the laws of physics.