Your not arguing the point of the conveyer. 
Yes an aircraft WILL fly if you power up the engine and take off, that's what it's supposed to do. An aircraft will not take off if you just spin it's wheels and do not power up the engine. If the moving belt is long enough, the aircraft is not restrained and you use the engine, what normally powers an aircraft to flight then yes an aircraft will take off a moving belt.
To fly an aircraft requires moving air over the entire wing surface above the stall speed then it will fly. That moving air is usually provided by powering up and using thrust to accelerate the aircraft to flight.
An obvious point would be a glider. If you stick a glider on a conveyer it will not take off, it can't. 
Gordy's point about float aircraft. They can land in a moving body of water, either with the flow or against it, the aircraft still fly's one way or the other, the only difference being the actual waterspeed touchdown/take off being different. 
Taking off or landing into wind or downwind being the same, aircraft still takes off at 60ish knots airspeed no matter what, the groundspeed into wind is less, tailwind more.
So if you lot are right we will be seeing airliners shortly with powered wheels? I'm sure Boeing will be keen to take on some of your vast aeronautical knowledge to help produce the next generation airliners. Perhaps you will go into civil airport construction and help producing the first moving runways?
So who's going to stick a glider on a moving belt and film it flying? Why do gliders waste money on tugs and winches when they could just get a conveyer belt to launch?
No good tomorrow being Sunday you lot will have to wait till Monday to patent all these cracker idea's 

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