Consider the following premises. For all x_5, x_5 is not curious. For all x_5, if x_5 were rich, then x_5 is a nurse. For all x_5, if x_5 were a nurse, then x_5 is sleeping. For all x_5, if x_5 sleeps, then x_5 is curious. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is not rich.
 From the fact that for all x_5, if x_5 were a nurse, then x_5 is sleeping, and that for all x_5, if x_5 sleeps, then x_5 is curious we can infer that for all x_5, if x_5 were a nurse, then x_5 is curious via universal transitivity. From the fact that for all x_5, if x_5 were rich, then x_5 is a nurse, and that for all x_5, if x_5 were a nurse, then x_5 is curious we can infer that for all x_5, if x_5 were rich, then x_5 is curious via universal transitivity. Finally, from the fact that for all x_5, if x_5 were rich, then x_5 is curious, and that for all x_5, x_5 is not curious we can infer that for all x_5, x_5 is not rich via universal modus tollens. Therefore, the answer is yes.