Consider the following premises. For all z, z will not drink water. For all z, if z drinks water, then z is driving a car. For all z, z will drive a car if and only if z will drink water. For all z, z is a cashier if and only if z will drive a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is a cashier.
 From the fact that for all z, z will drive a car if and only if z will drink water we can infer that for all z, if z drives a car, then z is drinking water via universal biconditional elimination. From the fact that for all z, if z drinks water, then z is driving a car, and that for all z, if z drives a car, then z is drinking water we can infer that for all z, z will drink water if and only if z will drive a car via universal biconditional introduction. From the fact that for all z, z will drink water if and only if z will drive a car, and that for all z, z will not drink water we can infer that for all z, z will not drive a car via universal biconditional elimination. Finally, from the fact that for all z, z is a cashier if and only if z will drive a car, and that for all z, z will not drive a car we can infer that for all z, z is not a cashier via universal biconditional elimination, which contradicts that There is at least one z for which z is a cashier. Therefore, the answer is no.