I would soak with penetrating oil from both ends top and inside BB for a few days then try twisting it out or as others have mentioned ways to tackle this.
If that does not work it looks like a lot of the seat post is exposed so the section inside the seat tube is not really that long.

I would cut off most of that seat post leave enough for grab with a pipe wrench or other tool of choice, then from the inside carefully take a hacksaw blade and slice groves thru the post all the way to the seat tube add some penetrating oil if done correctly that section will crack off if hit, at that point oils will work in much better if needed cut more out, it will come out at some point.
I have done this a few times but it will take time and skill.