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Why should I be doing paperwork when someone else has fucked up?
That's how it works.
You go through your insurer. They chase the insurance company of the people upstairs or chase them directly if they are uninsured. Either way your insurance means you should be guaranteed to get a payout for it.
Of course your insurance premium will go up because you're more of a risk, even though it was someone else's fault. Plus you have to notify any other insurance company of the claim, and possible buyers if you sell your property in the next 5 (I think) years.
It's all better than having to pay for it yourself though.
I imagine you go through your own insurer?