The airplane will not fly. While on the ground, the propeller has to overcome the rolling resistance of the wheels on the ground, and the acceleration of the treadmill insures that the airplane never moves forward.
Approach the problem this way: The aircraft is stopped as is the treadmill. Start the treadmill running, and the airplane moves backward. Turn the propeller just fast enough to stop the backward motion and the aircraft is now stationary. Repeat and the aircraft will not move from it's original location, and never attain any airspeed.
Approach the problem this way: The aircraft is stopped as is the treadmill. Start the treadmill running, and the airplane moves backward. Turn the propeller just fast enough to stop the backward motion and the aircraft is now stationary. Repeat and the aircraft will not move from it's original location, and never attain any airspeed.