The seat post on my beautiful BMC SLR01 had long been stuck. The BMC version from 2011 has a square profile seatpost and is fixated with an internal expanding rubber seal. The method described below will however work for all stuck seat posts.
1) Remove seat and open seat post clamp (for BMC users: turn locking screw to «open»)
2) Attach a solid bar to the stuck seat post by clamping it down where the seat should have been. Tighten bolts alternating as always and make sure the bolt cannot move.
3) Hang the bike upside down (breaking rule #49..) and attach the bottom bracket area solid to the roof. I used a normal cargo strap attached to a hook in the roof (make sure the hooks are properly fixed to a roof stiffener). Try to have the seat stay more or less vertical in order to avoid lateral loads when you start working.
4) Get a rubber hammer and get to work! Hit the bar on alternating sides and take breaks to inspect the bike making sure nothing gets damaged and that progress is maintained.
5) Victory! I do not know what that black stuff is but it should not be there. After a good clean-up and applying carbon paste, the seat post was good as new!