Consider the following premises. For all x_11, x_11 is a nurse or x_11 is a carpenter. For all x_11, x_11 is a lawyer or x_11 will sleep. For all x_11, x_11 is not a nurse or x_11 is a server. For all x_11, if x_11 were a carpenter, then x_11 is fast. For all x_11, if x_11 were a server, then x_11 is fast. For all x_11, x_11 is not a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is fast.
 From the fact that for all x_11, x_11 is a nurse or x_11 is a carpenter, and that for all x_11, x_11 is not a nurse or x_11 is a server we can infer that for all x_11, x_11 is a carpenter or x_11 is a server via universal resolution. From the fact that for all x_11, x_11 is a lawyer or x_11 will sleep, and that for all x_11, x_11 is not a lawyer we can infer that for all x_11, x_11 will sleep via universal disjunctive syllogism. Finally, from the fact that for all x_11, if x_11 were a carpenter, then x_11 is fast, that for all x_11, if x_11 were a server, then x_11 is fast, and that for all x_11, x_11 is a carpenter or x_11 is a server we can infer that for all x_11, x_11 is fast via universal disjunction elimination. Therefore, the answer is yes.