Consider the following premises. For all x_5, if x_5 listens to a song, then x_5 is curious. There is at least one x_5 for which x_5 will play tennis. For all x_5, x_5 is curious or x_5 will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is curious.
 From the fact that for all x_5, x_5 is curious or x_5 will not play tennis we can infer that for all x_5, if x_5 plays tennis, then x_5 is curious via universal rewriting. From the fact that there is at least one x_5 for which x_5 will play tennis we can infer that there is at least one x_5 for which x_5 will play tennis or x_5 will listen to a song via existential addition. Finally, from the fact that for all x_5, if x_5 plays tennis, then x_5 is curious, that for all x_5, if x_5 listens to a song, then x_5 is curious, and that there is at least one x_5 for which x_5 will play tennis or x_5 will listen to a song we can infer that there is at least one x_5 for which x_5 is curious via existential disjunction elimination. Therefore, the answer is yes.