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Trash service isn't free; it's usually included in a rental though. If you make it too expensive (in dollars, time or transit), people will find ways to dispose of items without paying. Mattresses have a way of showing up in public right-of-ways almost everywhere, but I live in a semi-rural area, and there's so much crap dumped in my woods and mine aren't that bad; one of my neighbors did some development work in preparation of selling some small parcels out of his land and had to have like 13 derelict cars removed that had been dumped in the woods; on my property, the larger things I've seen a really long radiator, a bath tub, a pressure tank from an abandoned (unmapped too) 10 foot deep hand dug well that I also had the pleasure of filling at my expense.

Are there any thrift store 'charities' nearby? maybe they can arrange to pick up some of the furniture and sell it.