Consider the following premises. For all z_1, if z_1 makes tea, then z_1 is writing a letter. For all z_1, z_1 will play a game. For all z_1, if z_1 plays a game, then z_1 is making tea. Can we infer the following from them? There is at least one z_1 for which z_1 will not write a letter.
 From the fact that for all z_1, if z_1 plays a game, then z_1 is making tea, and that for all z_1, if z_1 makes tea, then z_1 is writing a letter we can infer that for all z_1, if z_1 plays a game, then z_1 is writing a letter. Finally, from the fact that for all z_1, if z_1 plays a game, then z_1 is writing a letter, and that for all z_1, z_1 will play a game we can infer that for all z_1, z_1 will write a letter, which contradicts that There is at least one z_1 for which z_1 will not write a letter. Therefore, the answer is no.