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