Consider the following premises. For all x_3, x_3 will listen to a song and x_3 will play a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which neither x_3 will listen to a song nor x_3 will sleep.
 From the fact that for all x_3, x_3 will listen to a song and x_3 will play a game we can infer that for all x_3, x_3 will listen to a song via universal simplification. Finally, from the fact that for all x_3, x_3 will listen to a song we can infer that for all x_3, x_3 will listen to a song or x_3 will sleep via universal addition, which contradicts that There is at least one x_3 for which neither x_3 will listen to a song nor x_3 will sleep. Therefore, the answer is no.