Consider the following premises. For all x_12, x_12 is excited. For all x_12, if x_12 were excited, then x_12 is a police officer. For all x_12, x_12 will make tea if and only if x_12 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which neither x_12 will make tea nor x_12 is a lawyer.
 From the fact that for all x_12, x_12 will make tea if and only if x_12 is a police officer we can infer that for all x_12, if x_12 were a police officer, then x_12 is making tea via universal biconditional elimination. From the fact that for all x_12, if x_12 were excited, then x_12 is a police officer, and that for all x_12, x_12 is excited we can infer that for all x_12, x_12 is a police officer via universal modus ponens. From the fact that for all x_12, if x_12 were a police officer, then x_12 is making tea, and that for all x_12, x_12 is a police officer we can infer that for all x_12, x_12 will make tea via universal modus ponens. Finally, from the fact that for all x_12, x_12 will make tea we can infer that for all x_12, x_12 will make tea or x_12 is a lawyer via universal addition, which contradicts that There is at least one x_12 for which neither x_12 will make tea nor x_12 is a lawyer. Therefore, the answer is no.