Consider the following premises. For all y_4, y_4 will play a game if and only if y_4 will sleep. For all y_4, y_4 will make tea or y_4 will not play a game. Can we infer the following from them? There is at least one y_4 for which the fact that y_4 sleeps does not imply that y_4 is making tea.
 From the fact that for all y_4, y_4 will play a game if and only if y_4 will sleep we can infer that for all y_4, if y_4 sleeps, then y_4 is playing a game. From the fact that for all y_4, y_4 will make tea or y_4 will not play a game we can infer that for all y_4, if y_4 plays a game, then y_4 is making tea. Finally, from the fact that for all y_4, if y_4 sleeps, then y_4 is playing a game, and that for all y_4, if y_4 plays a game, then y_4 is making tea we can infer that for all y_4, if y_4 sleeps, then y_4 is making tea, which contradicts that There is at least one y_4 for which the fact that y_4 sleeps does not imply that y_4 is making tea. Therefore, the answer is no.