Consider the following premises. For all x_14, if x_14 were a bartender, then x_14 is listening to a song. For all x_14, x_14 is a bartender or x_14 is bored. For all x_14, if x_14 were bored, then x_14 is curious. There is at least one x_14 for which if x_14 listens to a song, then x_14 is curious. For all x_14, x_14 is not curious or x_14 will go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will sleep or x_14 will go running.
 From the fact that for all x_14, if x_14 were a bartender, then x_14 is listening to a song, and that there is at least one x_14 for which if x_14 listens to a song, then x_14 is curious we can infer that there is at least one x_14 for which if x_14 were a bartender, then x_14 is curious via existential transitivity. From the fact that there is at least one x_14 for which if x_14 were a bartender, then x_14 is curious, that for all x_14, if x_14 were bored, then x_14 is curious, and that for all x_14, x_14 is a bartender or x_14 is bored we can infer that there is at least one x_14 for which x_14 is curious via existential disjunction elimination. From the fact that there is at least one x_14 for which x_14 is curious we can infer that there is at least one x_14 for which x_14 is curious or x_14 will sleep via existential addition. Finally, from the fact that there is at least one x_14 for which x_14 is curious or x_14 will sleep, and that for all x_14, x_14 is not curious or x_14 will go running we can infer that there is at least one x_14 for which x_14 will sleep or x_14 will go running via existential resolution. Therefore, the answer is yes.