Consider the following premises. For all y_4, y_4 will not listen to a song or y_4 is a doctor. For all y_4, y_4 will not sleep or y_4 will play a game. Susan is sleeping. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_4 for which y_4 will play a game or y_4 is a doctor.
 From the fact that Susan is sleeping we can infer that there is at least one y_4 for which y_4 will sleep via existential generalization. From the fact that there is at least one y_4 for which y_4 will sleep we can infer that there is at least one y_4 for which y_4 will sleep or y_4 will listen to a song via existential addition. From the fact that there is at least one y_4 for which y_4 will sleep or y_4 will listen to a song, and that for all y_4, y_4 will not sleep or y_4 will play a game we can infer that there is at least one y_4 for which y_4 will listen to a song or y_4 will play a game via existential resolution. Finally, from the fact that there is at least one y_4 for which y_4 will listen to a song or y_4 will play a game, and that for all y_4, y_4 will not listen to a song or y_4 is a doctor we can infer that there is at least one y_4 for which y_4 will play a game or y_4 is a doctor via existential resolution. Therefore, the answer is yes.