Wow. That's disgusting.
The sign is a good first step.
I think you make a huge mistake when you clean up after anyone else. You are teaching them to leave their mess. If it were me, I would bring my own mug/bowl/cutlery and keep it at my own desk. Wash when done, and put it in my own desk drawer. Clean up any mess you make in the kitchen. Let the pigs figure out what to do with their own mess.
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