Consider the following premises. For all z, z will play a game if and only if z is a sailor. There is at least one z for which z is a sailor if and only if z will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all z, if is not true that z will play a game if and only if z is a sailor.
That contradicts the premises. Therefore the answer is no.