Consider the following premises. For all x, x is a doctor. There is at least one x for which if x were a doctor, then x is running. For all x, if x plays tennis, then x is a soldier. For all x, if x goes running, then x is playing tennis. Can we infer the following from them? There is at least one x for which x is a soldier.
 From the fact that there is at least one x for which if x were a doctor, then x is running, and that for all x, if x goes running, then x is playing tennis we can infer that there is at least one x for which if x were a doctor, then x is playing tennis. From the fact that there is at least one x for which if x were a doctor, then x is playing tennis, and that for all x, if x plays tennis, then x is a soldier we can infer that there is at least one x for which if x were a doctor, then x is a soldier. Finally, from the fact that there is at least one x for which if x were a doctor, then x is a soldier, and that for all x, x is a doctor we can infer that there is at least one x for which x is a soldier. Therefore, the answer is yes.