Are you aware that the right cup has a left hand thread, and unscrews clockwise? From the small dings I see in the photo I suspect that you're not and are turning it tighter not looser..
If you still can't loosen it with a large wrench, try using a bolt and large washers to hold the wrench flat to the cup so it cannot jump off. If that fails, there are various methods for removing very tight cup, but let's cross that bridg if/when we come to it.
I suspect (hope) that simply turning it in the right direction will have you on your way fast enough.
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