Consider the following premises. There is at least one x_12 for which if x_12 were a nurse, then x_12 is a server. For all x_12, x_12 is not rich. For all x_12, if x_12 writes a letter, then x_12 is a server. For all x_12, x_12 will write a letter or x_12 is a nurse. For all x_12, x_12 is rich or x_12 will sleep. 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 x_12 will sleep and x_12 is a server.
 From the fact that for all x_12, if x_12 writes a letter, then x_12 is a server, that there is at least one x_12 for which if x_12 were a nurse, then x_12 is a server, and that for all x_12, x_12 will write a letter or x_12 is a nurse we can infer that there is at least one x_12 for which x_12 is a server via existential disjunction elimination. From the fact that for all x_12, x_12 is rich or x_12 will sleep, and that for all x_12, x_12 is not rich we can infer that for all x_12, x_12 will sleep via universal disjunctive syllogism. Finally, from the fact that for all x_12, x_12 will sleep, and that there is at least one x_12 for which x_12 is a server we can infer that there is at least one x_12 for which x_12 will sleep and x_12 is a server via existential conjunction. Therefore, the answer is yes.