Consider the following premises. For all x_14, if x_14 drinks water, then x_14 is a server. For all x_14, if x_14 were a writer, then x_14 is a server. For all x_14, x_14 is a writer or x_14 will cook. For all x_14, if x_14 cooks, then x_14 is poor. For all x_14, x_14 will drink water or x_14 is not poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 is a server or x_14 is a scientist.
 From the fact that for all x_14, x_14 will drink water or x_14 is not poor we can infer that for all x_14, if x_14 were poor, then x_14 is drinking water via universal rewriting. From the fact that for all x_14, if x_14 cooks, then x_14 is poor, and that for all x_14, if x_14 were poor, then x_14 is drinking water we can infer that for all x_14, if x_14 cooks, then x_14 is drinking water via universal transitivity. From the fact that for all x_14, if x_14 cooks, then x_14 is drinking water, and that for all x_14, if x_14 drinks water, then x_14 is a server we can infer that for all x_14, if x_14 cooks, then x_14 is a server via universal transitivity. From the fact that for all x_14, if x_14 were a writer, then x_14 is a server, that for all x_14, if x_14 cooks, then x_14 is a server, and that for all x_14, x_14 is a writer or x_14 will cook we can infer that for all x_14, x_14 is a server via universal disjunction elimination. Finally, from the fact that for all x_14, x_14 is a server we can infer that for all x_14, x_14 is a server or x_14 is a scientist via universal addition. Therefore, the answer is yes.