Consider the following premises. There is at least one x_3 for which if x_3 were a carpenter, then x_3 is not a writer. For all x_3, x_3 is a writer and x_3 will make tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 is a carpenter.
 From the fact that for all x_3, x_3 is a writer and x_3 will make tea we can infer that for all x_3, x_3 is a writer via universal simplification. Finally, from the fact that there is at least one x_3 for which if x_3 were a carpenter, then x_3 is not a writer, and that for all x_3, x_3 is a writer we can infer that there is at least one x_3 for which x_3 is not a carpenter via existential modus tollens, which contradicts that For all x_3, x_3 is a carpenter. Therefore, the answer is no.