Though many of the ideas discussed have already been mentioned in this thread, here is an older thread on the subject of fence post removal.
Levers are all well and good, but the best ways all involve diesel engines powering hydraulic rams. Although if the post is strong enough and tamped in tight enough (railway ties or power poles drilled 4’ into the ground to anchor the end of a stock chute, say) you can lift the back end of your tractor up without budging the post. That’s when you push it back and forth with the bucket a few times first.
That is what I did at my neighbor’s house. He had 6x6’s he couldn’t get out of the ground, so we wrapped a chair around it and used the bucket on my tractor. Lifted the rear end of the tractor off the ground; at that point, I just drove forward on two wheels and nudged the 6x6 with the bucket. Viola.
However, not everyone has a tractor at their disposal. Hence using the fulcrum method (not the rhythm method, that’s for not pulling out).
You can do what we did…ignore them for many, many years. Then just go up and poke 'em with your finger and they’ll fall over.
:eek: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: :smack: 
:mad: :mad: :mad: :mad: :mad: :mad: :mad: 
:o :o :o :o :o :o :o :o :dubious: :dubious: :dubious: :dubious: :dubious: :dubious: :dubious: :dubious: :smack: :smack: :smack: :smack: :smack:
Oops, sorry. I stepped away to make my four year old some breakfast, and apparently he found the reply button. :embarassed:
For this method, it helps if one can arrange to have a dog use the post line for a scent marking trail.
I’m not sure what the half-life of a creosote-treated railroad tie is but I think that it may actually be longer than what I’d be willing to wait.
Not that I’m ever adverse to using time as a substitute for work…
Bwahahaha! Well, at least it isn’t sex with sheep. 
Poor you. My fence was put up in olden times when whitewash was king and wood was…well…*wood. * My new-fangled deck will not be so lucky.