Consider the following premises. For all x_4, if x_4 sleeps, then x_4 is playing a game. For all x_4, x_4 is not a taxi driver or x_4 is a nurse. For all x_4, x_4 is a taxi driver or x_4 will sleep. For all x_4, if x_4 were a nurse, then x_4 is making tea. There is at least one x_4 for which if x_4 makes tea, then x_4 is playing a game. Can we infer the following from them? There is at least one x_4 for which x_4 will play a game.
 From the fact that for all x_4, if x_4 were a nurse, then x_4 is making tea, and that there is at least one x_4 for which if x_4 makes tea, then x_4 is playing a game we can infer that there is at least one x_4 for which if x_4 were a nurse, then x_4 is playing a game. From the fact that for all x_4, x_4 is a taxi driver or x_4 will sleep, and that for all x_4, x_4 is not a taxi driver or x_4 is a nurse we can infer that for all x_4, x_4 will sleep or x_4 is a nurse. Finally, from the fact that for all x_4, if x_4 sleeps, then x_4 is playing a game, that there is at least one x_4 for which if x_4 were a nurse, then x_4 is playing a game, and that for all x_4, x_4 will sleep or x_4 is a nurse we can infer that there is at least one x_4 for which x_4 will play a game. Therefore, the answer is yes.