First get a sacrificial seat heavy enough to have solid steel rails, mount it off center to maximize
torque. Ammonia attacks the layer of aluminum oxide and reduces friction thereby, it also
to a lesser degree attacks the frame itself, but that is a minor consideration. Liquid Wrench
penetrates the crany between the post and tube and lubricates. To some degree the use of
one interferes with the use of the other, though ammonia, sufficiently strong, eg household
Parsons type, is likely to eventually cut through the Liquid Wrench if you use that first.
Remove the BB turn bike upside down and liberally douse the seat tube with your selected penetrant (Parson's ammonia or Liquid Wrench, your choice) and let sit over nite. If you immediately have a bunch of liquid spill out into the seat, then you will just have to dribble some more down the seat tube and rotate the bike in an arc to distribute the penetrant, If the seat post is sealed at the top pour in 4-5 ounces and let sit. Next day flip bike over and pour out remnant and apply maximal torque to the seat, with luck it will break loose. If not find someone stronger for another effort. If you destroy the clamps on the seat post or the seat rails bend/break then plan B is to cut the post a bit above the top of the tube and get a saw blade long enough to reach the bottom of the residual post and cut at least two vertical slots in the post on the inside til you reach metal. You can then start prying the cut up seat post off the seat tube. A bit of cutting into the metal won't do much damage to the integrity of the seat tube as long as you
don't get carried away. A friend spent a week doing this on an AL post in a steel tube, but
he got it out. Carbon should be easier to cut.