A resolution technique. When coupled with a complete search algorithm, the resolution rule yields a sound and complete algorithm for deciding the satisfiability of a propositional formula, and, by extension, the validity of a sentence under a set of axioms.
Handling Move Outs-when a tenant moves out, the manager is responsible for inspecting the unit, checking for damages and determining what portion of the security deposit will be returned to the tenant. After move out, they are responsible for cleaning the unit, repairing any damages and finding a new tenant.
If it is in fact a security deposit rather than a holding deposit, damages can be deducted only for unpaid rent in your case. Of course you have an argument that the landlord breached the contract by repeatedly failing to deliver the promised apartment, thus obviating the unpaid rent argument.