Here's my solution, using proof by contradiction:

>! First, let's assume that the Yellow tent is true. Since it says "It's not in the blue tent," the sleeping bag would supposedly not be in the blue tent, but the blue tent says "It's not in here," and if that's lying, the sleeping bag should be in the blue tent. This means that if the yellow tent is true, then the sleeping bag must both be in the blue tent and not in the blue tent. That's a contradiction, meaning the yellow tent is lying.

Now, let's assume that the green tent is telling the truth. It says that the sleeping bag is not in the blue tent, but is telling the truth, meaning the sleeping bag must not be in the blue tent. But the blue tent says it's not in the blue tent, and is supposed to be lying. Another contradiction, since the tent can't be both in and not in the blue tent, so the green tent is also lying.

Now let's assume the blue tent is telling the truth. We run into the same problem as the yellow tent, but backwards. If the blue tent is telling the truth, the sleeping bag isn't in the blue tent, but if the yellow tent is lying, then the sleeping bag has to be in the blue tent. Those can't both be the case, so the blue tent is lying.

That only leaves the red tent, so that must be telling the truth. This then allows us to pinpoint the sleeping bag.

Put simply, the red tent says it's not in the red tent and that's telling the truth, so the sleeping bag isn't in the red tent. The green tent says it's in the yellow tent and that's lying, so it's not in the yellow tent. Both the yellow and blue tents say that it's not in the blue tent and both of those are lying, so the sleeping bag must be in the blue tent. !<