Dear lord, there's two of them.
So we're all on the same page... The conveyor moves backward at a speed equal to the airplane's groundspeed.
If the airplane's groundspeed is zero, the conveyor IS NOT MOVING and will thus behave EXACTLY LIKE A NORMAL RUNWAY.
So, you add takeoff power. Let's say the airplane accelerates to 5 knots. The conveyor will be moving backwards at 5 knots, equal to moving forward at -5 knots. The wheels will be turning at 10 knots (5-(-5)=10). If your engine and prop cannot develop enough thrust to overcome 10 knots of rolling resistance, HOW THE HELL DO YOU TAKE OFF FROM A NORMAL RUNWAY???
So then, we've now established that the airplane can move forward. Air is flowing over the wings, albeit slowly. What force is stopping the continued acceleration of the airplane?
There is no such force. The airplane will continue to accelerate. At Vliftoff, the conveyor will be moving at -Vliftoff and the wheels will be turning at 2Vliftoff.
Now, for the "won't take off" the premise of the problem must be changed to "the conveyor will move backward with sufficient speed that the rolling resistance of the wheels matches the forward thrust of the engine and prop at full takeoff power." I have never, ever seen the problem worded that way and that's the only way the plane won't take off.