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