Consider the following premises. For all x, x will drink water if and only if x will play a game. For all x, x is not a server. For all x, if x plays a game, then x is drinking water. For all x, x is a server or x will not play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will not drink water.
 From the fact that for all x, x will drink water if and only if x will play a game we can infer that for all x, if x drinks water, then x is playing a game via universal biconditional elimination. From the fact that for all x, if x drinks water, then x is playing a game, and that for all x, if x plays a game, then x is drinking water we can infer that for all x, x will drink water if and only if x will play a game via universal biconditional introduction. From the fact that for all x, x is a server or x will not play a game we can infer that for all x, if x plays a game, then x is a server via universal rewriting. From the fact that for all x, if x plays a game, then x is a server, and that for all x, x is not a server we can infer that for all x, x will not play a game via universal modus tollens. Finally, from the fact that for all x, x will drink water if and only if x will play a game, and that for all x, x will not play a game we can infer that for all x, x will not drink water via universal biconditional elimination. Therefore, the answer is yes.