Consider the following premises. For all x_12, x_12 will sleep if and only if x_12 will drink water. For all x_12, x_12 will cook if and only if x_12 is a server. For all x_12, x_12 will sleep if and only if x_12 is a server. For all x_12, if x_12 sleeps, then x_12 is drinking water. For all x_12, x_12 will not cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 will not drink water.
 From the fact that for all x_12, x_12 will cook if and only if x_12 is a server, and that for all x_12, x_12 will not cook we can infer that for all x_12, x_12 is not a server via universal biconditional elimination. From the fact that for all x_12, x_12 will sleep if and only if x_12 will drink water we can infer that for all x_12, if x_12 drinks water, then x_12 is sleeping via universal biconditional elimination. From the fact that for all x_12, if x_12 drinks water, then x_12 is sleeping, and that for all x_12, if x_12 sleeps, then x_12 is drinking water we can infer that for all x_12, x_12 will drink water if and only if x_12 will sleep via universal biconditional introduction. From the fact that for all x_12, x_12 will sleep if and only if x_12 is a server, and that for all x_12, x_12 is not a server we can infer that for all x_12, x_12 will not sleep via universal biconditional elimination. Finally, from the fact that for all x_12, x_12 will drink water if and only if x_12 will sleep, and that for all x_12, x_12 will not sleep we can infer that for all x_12, x_12 will not drink water via universal biconditional elimination. Therefore, the answer is yes.