Consider the following premises. For all x_4, x_4 will not take a plane or x_4 will play tennis. There is at least one x_4 for which x_4 will not play tennis or x_4 is a bartender. For all x_4, x_4 is not a sailor or x_4 is a scientist. For all x_4, x_4 will take a plane or x_4 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 is a scientist or x_4 is a bartender.
 From the fact that for all x_4, x_4 will take a plane or x_4 is a sailor, and that for all x_4, x_4 will not take a plane or x_4 will play tennis we can infer that for all x_4, x_4 is a sailor or x_4 will play tennis via universal resolution. From the fact that for all x_4, x_4 is a sailor or x_4 will play tennis, and that for all x_4, x_4 is not a sailor or x_4 is a scientist we can infer that for all x_4, x_4 will play tennis or x_4 is a scientist via universal resolution. Finally, from the fact that for all x_4, x_4 will play tennis or x_4 is a scientist, and that there is at least one x_4 for which x_4 will not play tennis or x_4 is a bartender we can infer that there is at least one x_4 for which x_4 is a scientist or x_4 is a bartender via existential resolution. Therefore, the answer is yes.