Consider the following premises. There is at least one x_15 for which x_15 will sleep if and only if x_15 will play a game. For all x_15, x_15 is an office clerk. For all x_15, x_15 will play a game or x_15 is not a nurse. For all x_15, if x_15 were an office clerk, then x_15 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 will not sleep.
 From the fact that for all x_15, x_15 will play a game or x_15 is not a nurse we can infer that for all x_15, if x_15 were a nurse, then x_15 is playing a game via universal rewriting. From the fact that for all x_15, if x_15 were an office clerk, then x_15 is a nurse, and that for all x_15, if x_15 were a nurse, then x_15 is playing a game we can infer that for all x_15, if x_15 were an office clerk, then x_15 is playing a game via universal transitivity. From the fact that for all x_15, if x_15 were an office clerk, then x_15 is playing a game, and that for all x_15, x_15 is an office clerk we can infer that for all x_15, x_15 will play a game via universal modus ponens. From the fact that there is at least one x_15 for which x_15 will sleep if and only if x_15 will play a game we can infer that there is at least one x_15 for which if x_15 plays a game, then x_15 is sleeping via existential biconditional elimination. Finally, from the fact that there is at least one x_15 for which if x_15 plays a game, then x_15 is sleeping, and that for all x_15, x_15 will play a game we can infer that there is at least one x_15 for which x_15 will sleep via existential modus ponens, which contradicts that For all x_15, x_15 will not sleep. Therefore, the answer is no.