The plane takes off.

100% positive. There is no doubt.

A plane's speed is NOT measured at the wheel. There is no speedometer hooked up the wheels. This is NOT an assumption; it's a fact. A plane's speed is measured by a tube that air passes through. In it's most basic form, wind comes into the tube, spins a little turbine, and the speed of that turbine is shown on the indicator on the dash. Now, there are other calculations that enter in, to compensate for the speed of the natural wind occuring at the time, but there's no reason to go into that for this problem.

In order for any movement to be recorded, air must come into the tube, which means the aircraft is in motion (again, not including the natural wind from the equation as it was not presented in the hypothetical problem).

The conveyor belt motion is directly proportional to the amount of speed the aircraft has at any given time. That's a given part of the problem.

The only way the conveyor belt moves is if the plane is moving. The only way the plane is "moving" is if its indicator says it's moving. The only way the indicator says it's moving is if wind is coming into the tube & turning the turbine. The only way wind enters the tube is if the aircraft is moving.

Therefore, the plane takes off, regardless of how fast the conveyor belt moves, because once the plane reaches 150+/- MPH, the wings literally get sucked up into the air, which lifts the body of the plane.

There are no "assumptions" necessary for the answer to this hypothetical problem.