This has a ‘stuck seat post’.
The seatpost is alloy, which oxidized inside the seat tube.
I’ve had the problem a few times before, where penetrating oil,
coca cola and a vice have sufficed to resolve the problem.
The seatpost crushed in the vice, and broke when twisted.
I managed to cut the back of the seatpost,
now I will cut it from the inside, or mill it.
I cut a clear line at the back by the seatpost pin,
and managed to wedge a screwdriver in with a hammer.
I then used another screw drive like a chisel and made another split
I cannot take all the credit though,
there is a very influential bike forum
called London Fixed Gear and Single Speed (LFGSS.com), which is great resource for help or info,
where I got a lot of tips from different perspectives .
I recommend it!(Thanks everyone !!)
That is one of the most painful things I have seen.
kinda like a route canal but with Gilco steel !