A plane is on an infinitely long conveyor belt. The conveyor belt runs backward at a speed equal to what the plane would be going if the conveyor belt was not there. The plane is on wheels which are working properly.
Can the plane take off?
Yes, the plane can take off.
Proof
The power for the engines come from the turbines, which is acting against the air. Thus the plane will develop a velocity relative to the air around it. With enough thrust it will gain enough speed relative to the air to take off.
The conveyor belt only acts on the wheels, making them rotate faster, but does not impede the motion of the plane.