The "Plane on a Treadmill" Question

[LabRat]

The thrust of the engines pushes the plane and axles the wheels are spinning on forward (as stated in the problem). Once the plane begins to move, then the treadmill turns on. The treadmill accounts for and this forward motion, speeds up, and causes the wheels to spin around the axle. The friction holding the still plane in one place is gravity, a downward force. Once the treadmill is going, the thrusters create a vector of force in the forward direction enough to overcome the downward force of gravity. The plane continues to move forward faster and faster and the treadmill/wheels continue to spin also, but again, only around the axle. Eventually the plane will gain enough forward speed to create lift under it's wings as it would on a stationary runway.

My initial response was no take off, until I tried to explain why, then I had to change it to damn, I think it will take off.