Cooperative solutions
If both aircraft involved in a conflict have TCAS, then between the two TCAS systems they will agree a solution. For example, if you are at Max Altitude, and someone is climbing to your level, although you may not be able to go up, they will still be told to reduce or stop their climb.
If TCAS cannot give you a resolution because of inhibit logic, it will give you a Traffic alert instead and let you figure something out. Actual inhibit inputs are airframe dependent, but can include air data inputs (altitude), gear position, flap position, and so on.
Slight change of thread - is it just my imagination, or have there been quite a lot of fairly basic TCAS questions on PPRUNE? I don't want to be rude, but isn't "everything you ever needed to know about TCAS" taught in pilot school any more?
Although there are lots of clever algorithms inside the box, the end result is actually pretty simple, and (at least I always thought) completely understandable in about 5 minutes.