Consider the following premises. There is at least one x_5 for which x_5 is not a police officer. For all x_5, if x_5 were a police officer, then x_5 is a carpenter. For all x_5, if x_5 were a carpenter, then x_5 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is a carpenter.
 From the fact that for all x_5, if x_5 were a police officer, then x_5 is a carpenter, and that for all x_5, if x_5 were a carpenter, then x_5 is a police officer we can infer that for all x_5, x_5 is a police officer if and only if x_5 is a carpenter via universal biconditional introduction. From the fact that for all x_5, x_5 is a police officer if and only if x_5 is a carpenter we can infer that for all x_5, if x_5 were a carpenter, then x_5 is a police officer via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 were a carpenter, then x_5 is a police officer, and that there is at least one x_5 for which x_5 is not a police officer we can infer that there is at least one x_5 for which x_5 is not a carpenter via existential modus tollens, which contradicts that For all x_5, x_5 is a carpenter. Therefore, the answer is no.