Running a bolt into the nut is probably the best first try. However, I'd try the extraction as per sberry's suggestion before I started beating on anything. I'd run a nut and a couple of heavy washers on the bolt first. First washer should be about the diameter of the bolt, second one a washer with a wide enough hole that can catch the rim of the socket opening without protruding into the opening itself. Then snug it all up to the rim and begin tightening the nut with a wrench against the washer in a manner like a gear puller. Put the head of the bolt in the vise, let the socket hang free. If the initial movement doesn't pop it free, add more wide washers until the nut can pass through their collective centers. This allows you to put most of the pressure on the nut instead of beating the socket or trying to twist it once you threaded a bolt down to the bottom of the socket then applying pressure to the socket while crushing down on the inside bottom of the socket with the end of the bolt. It also allows you to apply maximum force with the leverage of a wrench. The pressure applied to the rim of the socket is where it can take it the most, since sockets are made from extruded steel 'cable' that can take more pressure along their length than they can from the inside outward. Use a really high quality bolt. We have to make the same kinds of pullers when servicing old screw-in-bulb Christmas light sockets made mid-60s or before that have a brass threaded 'cup' pressed into a bakelite shell so we can extract the core without breaking the brittle bakelite shell. If it's really stubborn, heating the outside of the socket along with some PB could help. If this doesn't free it, you're in for a trip to your favorite tool supplier.
