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