Consider the following premises. For all x_6, x_6 will sleep if and only if x_6 will play squash. For all x_6, x_6 is a soldier or x_6 will not sleep. For all x_6, x_6 is not a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not play squash.
 From the fact that for all x_6, x_6 is a soldier or x_6 will not sleep we can infer that for all x_6, if x_6 sleeps, then x_6 is a soldier via universal rewriting. From the fact that for all x_6, if x_6 sleeps, then x_6 is a soldier, and that for all x_6, x_6 is not a soldier we can infer that for all x_6, x_6 will not sleep via universal modus tollens. Finally, from the fact that for all x_6, x_6 will sleep if and only if x_6 will play squash, and that for all x_6, x_6 will not sleep we can infer that for all x_6, x_6 will not play squash via universal biconditional elimination. Therefore, the answer is yes.