Consider the following premises. For all x_7, if x_7 goes running, then x_7 is a doctor. There is at least one x_7 for which x_7 will go running if and only if x_7 is a doctor. For all x_7, x_7 is not a doctor. Can we infer the following from them? There is at least one x_7 for which x_7 will not go running.
 From the fact that there is at least one x_7 for which x_7 will go running if and only if x_7 is a doctor we can infer that there is at least one x_7 for which if x_7 were a doctor, then x_7 is running. From the fact that there is at least one x_7 for which if x_7 were a doctor, then x_7 is running, and that for all x_7, if x_7 goes running, then x_7 is a doctor we can infer that there is at least one x_7 for which x_7 is a doctor if and only if x_7 will go running. Finally, from the fact that there is at least one x_7 for which x_7 is a doctor if and only if x_7 will go running, and that for all x_7, x_7 is not a doctor we can infer that there is at least one x_7 for which x_7 will not go running. Therefore, the answer is yes.