@Corinne509 thank you so much for your kind reply. Much appreciated.
We followed the process, to the point. And, our claim is "partially" accepted - so arguably no problem with the way we file the claim.
The problem is that, that part accepted is far from a fair compensation. Our photos clearly show the mess, smoking, vomit, etc. artifacts. Also, guest didn't deny all of their **bleep**. Yet, the paid €125 reimbursement amount doesn't compensate damage, cleaning, etc.- is nothing but ridiculous!
On top of that, we have a massive communication problem with Airbnb. They took comms outside of platform, however they don't accept our email replies. All of our e-mails to them return back to us with a "failure" (not delivered) message. So, none of our e-mails reach to them, or looks so.
Looks like we are going to end up in either arbitrage or in small claims court. What a shame!