Removing post set in concrete
I like Kap's idea...he's a man of not many words!
I really don't like leaving junk like that in the ground...knowing my luck, I'm the one that would have to deal with that in the future. Rather than trying to brute force them out, can you get them out by rigging up a lever over a fulcrum. For instance with out seeing what your working with imagine a good saw horse near the hole, a short piece of chain, or nylon tie down to make a sling around the exposed concrete. Take another old 4x4 over the top of the sawhorse into a loop on the chain/sling, and pry up? If you get it up a bit, kick some dirt in and repeat. Once it's out on top of the ground, cut the post off...and roll the concrete where you need, or put it on a two wheel cart and move it off.
when it comes to breakfast, the chicken is dedicated, the pig is committed.