Consider the following premises. There is at least one x_8 for which x_8 is not a scientist or x_8 is excited. For all x_8, x_8 is a scientist and x_8 will play a game. For all x_8, x_8 will not drink water or x_8 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is excited or x_8 will listen to a song.
 From the fact that for all x_8, x_8 is a scientist and x_8 will play a game we can infer that for all x_8, x_8 is a scientist via universal simplification. From the fact that for all x_8, x_8 is a scientist we can infer that for all x_8, x_8 is a scientist or x_8 will drink water via universal addition. From the fact that for all x_8, x_8 is a scientist or x_8 will drink water, and that there is at least one x_8 for which x_8 is not a scientist or x_8 is excited we can infer that there is at least one x_8 for which x_8 will drink water or x_8 is excited via existential resolution. Finally, from the fact that there is at least one x_8 for which x_8 will drink water or x_8 is excited, and that for all x_8, x_8 will not drink water or x_8 will listen to a song we can infer that there is at least one x_8 for which x_8 is excited or x_8 will listen to a song via existential resolution. Therefore, the answer is yes.