Consider the following premises. For all x_4, x_4 is a server or x_4 is a doctor. There is at least one x_4 for which x_4 is a doctor if and only if x_4 will go running. For all x_4, if x_4 were a server, then x_4 is running. Can we infer the following from them? There is at least one x_4 for which x_4 will go running.
 From the fact that there is at least one x_4 for which x_4 is a doctor if and only if x_4 will go running we can infer that there is at least one x_4 for which if x_4 were a doctor, then x_4 is running. Finally, from the fact that for all x_4, if x_4 were a server, then x_4 is running, that there is at least one x_4 for which if x_4 were a doctor, then x_4 is running, and that for all x_4, x_4 is a server or x_4 is a doctor we can infer that there is at least one x_4 for which x_4 will go running. Therefore, the answer is yes.