Consider the following premises. For all x_8, if x_8 goes running, then x_8 is a soldier. For all x_8, x_8 is rich if and only if x_8 is a soldier. For all x_8, x_8 is a soldier if and only if x_8 will go running. For all x_8, x_8 will not go running. Can we infer the following from them? For all x_8, x_8 is not rich.
 From the fact that for all x_8, x_8 is a soldier if and only if x_8 will go running we can infer that for all x_8, if x_8 were a soldier, then x_8 is running. From the fact that for all x_8, if x_8 goes running, then x_8 is a soldier, and that for all x_8, if x_8 were a soldier, then x_8 is running we can infer that for all x_8, x_8 will go running if and only if x_8 is a soldier. From the fact that for all x_8, x_8 will go running if and only if x_8 is a soldier, and that for all x_8, x_8 will not go running we can infer that for all x_8, x_8 is not a soldier. Finally, from the fact that for all x_8, x_8 is rich if and only if x_8 is a soldier, and that for all x_8, x_8 is not a soldier we can infer that for all x_8, x_8 is not rich. Therefore, the answer is yes.