The Twisted Tantalus (Puzzle Cup)

Greedy or not, here it comes!
This is not your standard greedy cup... oh, no! This cup is much more devious! Here is my own personal twist on a 2000+ year old prank from ancient Greece. I designed it specifically to meet the criteria for the Make 2017 April Fools Day design challenge. I made all of the devious features on this cup very obvious and noticeable, but that doesn't mean you'll figure out the solution to the puzzle easily. You can see the full write up on my contest submission (an