Yuck. That's the drive side? If so, then remove the other cup and take out the axle and try Sheldon's bolt method. But maybe somebody put a non-drive side cup into the drive side, so it may unscrew to the right rather than the left-hand threads that you would expect in the drive side. That could explain the catty-wumpus cup mounting. If you can't get it to budge using a 2-foot cheater bar then take it to a tire shop and see if they'll use their impact wrench on it.

It would probably be a good idea to chase and grease the threads after all that. Good luck!