[EricH]

As many people have said, there is no connection between engines and wheels in an airplane. The treadmill could be going backward at lightspeed, but if that plane's engine(s) is (are) going full blast forwards, or close to it, then the plane will move forward, thus getting the lift it needs. Wheel drag will not be enough to stop the plane from taking off unless the pilot is standing on the brakes, in which case he wouldn't take off anyway.

Now, people have used an F-18 as an example, but I'll try a Harrier for an example. Harrier won't go forward at all, but it will take off in its VTOL manner (that's Vertical TakeOff and Landing) and take off. No question about that, right? (Yeah, I'm cheating a bit, but if it's any airplane, I'll just go with a VTOL and take off without the debate. )