Consider the following premises. If David climbs a mountain, then James is sleeping. For all x_15, x_15 will cook. For all x_14, if x_14 cooks, then x_14 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: James is sleeping.
 From the fact that for all x_15, x_15 will cook we can infer that David is cooking via universal instantiation. From the fact that for all x_14, if x_14 cooks, then x_14 is climbing a mountain we can infer that if David cooks, then David is climbing a mountain via universal instantiation. From the fact that if David cooks, then David is climbing a mountain, and that David is cooking we can infer that David is climbing a mountain via modus ponens. Finally, from the fact that if David climbs a mountain, then James is sleeping, and that David is climbing a mountain we can infer that James is sleeping via modus ponens. Therefore, the answer is yes.