Consider the following premises. For all x_5, if x_5 were a police officer, then x_5 is sleeping. For all x_5, if x_5 sleeps, then x_5 is a police officer. There is at least one x_5 for which x_5 is a bartender. For all x_5, if x_5 were a police officer, then x_5 is not a bartender. Can we infer the following from them? There is at least one x_5 for which x_5 will not sleep.
 From the fact that for all x_5, if x_5 were a police officer, then x_5 is not a bartender, and that there is at least one x_5 for which x_5 is a bartender we can infer that there is at least one x_5 for which x_5 is not a police officer. From the fact that for all x_5, if x_5 sleeps, then x_5 is a police officer, and that for all x_5, if x_5 were a police officer, then x_5 is sleeping we can infer that for all x_5, x_5 will sleep if and only if x_5 is a police officer. Finally, from the fact that for all x_5, x_5 will sleep if and only if x_5 is a police officer, and that there is at least one x_5 for which x_5 is not a police officer we can infer that there is at least one x_5 for which x_5 will not sleep. Therefore, the answer is yes.