Consider the following premises. For all z_1, z_1 is a doctor if and only if z_1 will sleep. For all z_1, z_1 will play a game if and only if z_1 will sleep. For all z_1, if z_1 plays a game, then z_1 is a doctor. Can we infer the following from them? There is at least one z_1 for which the fact that z_1 were a doctor does not imply that z_1 is playing a game.
 From the fact that for all z_1, z_1 is a doctor if and only if z_1 will sleep we can infer that for all z_1, if z_1 were a doctor, then z_1 is sleeping. From the fact that for all z_1, z_1 will play a game if and only if z_1 will sleep we can infer that for all z_1, if z_1 sleeps, then z_1 is playing a game. From the fact that for all z_1, if z_1 were a doctor, then z_1 is sleeping, and that for all z_1, if z_1 sleeps, then z_1 is playing a game we can infer that for all z_1, if z_1 were a doctor, then z_1 is playing a game. From the fact that for all z_1, if z_1 were a doctor, then z_1 is playing a game, and that for all z_1, if z_1 plays a game, then z_1 is a doctor we can infer that for all z_1, z_1 is a doctor if and only if z_1 will play a game. Finally, from the fact that for all z_1, z_1 is a doctor if and only if z_1 will play a game we can infer that for all z_1, if z_1 were a doctor, then z_1 is playing a game, which contradicts that There is at least one z_1 for which the fact that z_1 were a doctor does not imply that z_1 is playing a game. Therefore, the answer is no.