Consider the following premises. For all y_4, if y_4 were rich, then y_4 is running. For all y_4, if y_4 were rich, then y_4 is running. For all y_4, if y_4 goes running, then y_4 is rich. Can we infer the following from them? There is at least one y_4 for which if is not true that y_4 is rich if and only if y_4 will go running.
 From the fact that for all y_4, if y_4 goes running, then y_4 is rich, and that for all y_4, if y_4 were rich, then y_4 is running we can infer that for all y_4, y_4 will go running if and only if y_4 is rich. From the fact that for all y_4, y_4 will go running if and only if y_4 is rich we can infer that for all y_4, if y_4 goes running, then y_4 is rich. Finally, from the fact that for all y_4, if y_4 were rich, then y_4 is running, and that for all y_4, if y_4 goes running, then y_4 is rich we can infer that for all y_4, y_4 is rich if and only if y_4 will go running, which contradicts that There is at least one y_4 for which if is not true that y_4 is rich if and only if y_4 will go running. Therefore, the answer is no.