Consider the following premises. For all x_4, x_4 will not listen to a song. For all x_4, x_4 will listen to a song or x_4 will play a game. For all x_4, if x_4 plays a game, then x_4 is drinking water. There is at least one x_4 for which if x_4 writes a letter, then x_4 is drinking water. Can we infer the following from them? For all x_4, x_4 will not drink water.
 From the fact that for all x_4, x_4 will listen to a song or x_4 will play a game, and that for all x_4, x_4 will not listen to a song we can infer that for all x_4, x_4 will play a game. From the fact that for all x_4, x_4 will play a game we can infer that for all x_4, x_4 will play a game or x_4 will write a letter. Finally, from the fact that for all x_4, if x_4 plays a game, then x_4 is drinking water, that there is at least one x_4 for which if x_4 writes a letter, then x_4 is drinking water, and that for all x_4, x_4 will play a game or x_4 will write a letter we can infer that there is at least one x_4 for which x_4 will drink water, which contradicts that For all x_4, x_4 will not drink water. Therefore, the answer is no.