Consider the following premises. For all x_15, x_15 is not a lawyer. For all x_15, if x_15 were a police officer, then x_15 is a lawyer. There is at least one x_15 for which x_15 will play a game if and only if x_15 is a police officer. For all x_15, x_15 is a police officer if and only if x_15 will play a game. Can we infer the following from them? There is at least one x_15 for which x_15 will not play a game.
 From the fact that there is at least one x_15 for which x_15 will play a game if and only if x_15 is a police officer we can infer that there is at least one x_15 for which if x_15 were a police officer, then x_15 is playing a game. From the fact that for all x_15, x_15 is a police officer if and only if x_15 will play a game we can infer that for all x_15, if x_15 plays a game, then x_15 is a police officer. From the fact that for all x_15, if x_15 plays a game, then x_15 is a police officer, and that there is at least one x_15 for which if x_15 were a police officer, then x_15 is playing a game we can infer that there is at least one x_15 for which x_15 will play a game if and only if x_15 is a police officer. From the fact that for all x_15, if x_15 were a police officer, then x_15 is a lawyer, and that for all x_15, x_15 is not a lawyer we can infer that for all x_15, x_15 is not a police officer. Finally, from the fact that there is at least one x_15 for which x_15 will play a game if and only if x_15 is a police officer, and that for all x_15, x_15 is not a police officer we can infer that there is at least one x_15 for which x_15 will not play a game. Therefore, the answer is yes.