Consider the following premises. For all x_12, if x_12 goes running, then x_12 is playing tennis. For all x_12, if x_12 listens to a song, then x_12 is playing tennis. For all x_12, if x_12 were a bartender, then x_12 is not playing tennis. There is at least one x_12 for which x_12 is not curious or x_12 will go running. For all x_12, x_12 is curious or x_12 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 is a bartender.
 From the fact that for all x_12, x_12 is curious or x_12 will listen to a song, and that there is at least one x_12 for which x_12 is not curious or x_12 will go running we can infer that there is at least one x_12 for which x_12 will listen to a song or x_12 will go running via existential resolution. From the fact that for all x_12, if x_12 listens to a song, then x_12 is playing tennis, that for all x_12, if x_12 goes running, then x_12 is playing tennis, and that there is at least one x_12 for which x_12 will listen to a song or x_12 will go running we can infer that there is at least one x_12 for which x_12 will play tennis via existential disjunction elimination. Finally, from the fact that for all x_12, if x_12 were a bartender, then x_12 is not playing tennis, and that there is at least one x_12 for which x_12 will play tennis we can infer that there is at least one x_12 for which x_12 is not a bartender via existential modus tollens, which contradicts that For all x_12, x_12 is a bartender. Therefore, the answer is no.