I know the aircraft doesn't depend on wheel speed to be able to takeoff,and I said that earlier, it depends upon the relative wind moving, mainly under the wing surface. I was referencing Hoosie's statement of one holding the end of the wheelbarrow with the treadmill rotating the wheel.

Now in his new example, he is putting a propeller and engine on the wheelbarrow. On one wheel, 3 wheels, doesn't matter how many wheels, the propeller now pulling wheelbarrow/airplane forward, yes the engine, if strong enough, can counteract the treadmill as it attempts to move the wheelbarrow/airplane backwards. If WB/AP is in a static position, (treadmill moving it back at same speed engine pulling it forward) it will NOT take off. IF the engine is pulling it forward, at a speed it would normally lift off at (in this case: Takeoff speed = normal rotation speed (at a given weight) + speed to overcome the treadmill's belt speed, then yes it is possible.

So if you have a treadmill that is EXTREMELY long, and the aircraft is actually making forward progress and is able to overcome the treadmill speed AND reach normal takeoff speed, then yes it is possible. If it cannot read that speed, then no, it isn't going to takeoff.