I get open. Meshed gears reverse direction. Crossed belt reverses direction. Assuming clockwise is forward (F), CCW is reverse (R), I get in order from the crank, belted pinions in brackets:
F (R R) F R F (R F) R F R (F R) F R
The final pulley going CCW will draw the string in, hence lifting the lid. The idlers only change the linear direction, not the rotational direction.
