Can a Plane on a Treadmill Take Off?

Let' say it this way. The airplane is moving forward at 60 kts. Does
that make it more clear?

The airplane is moving forward at 60, the belt, using the model in the
OP, is moving backwards at 60. The wheels are turning at 120 kts. If
it's a 172 it'll lift off into, on a calm day, 60 kts of airspeed over
the wings.

It's a nicely phrased question that caught me at first as well.
Substitute real speeds into what had been posted and the answer becomes
clear to me, although a lawyer in the group might find a (ground) loop
hole.