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