Consider the following premises. For all x_4, x_4 will not play tennis or x_4 is happy. For all x_4, x_4 is a politician or x_4 will play tennis. There is at least one x_4 for which x_4 will not make tea. For all x_4, x_4 is not a politician or x_4 will make tea. 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 happy.
 From the fact that for all x_4, x_4 is a politician or x_4 will play tennis, and that for all x_4, x_4 is not a politician or x_4 will make tea we can infer that for all x_4, x_4 will play tennis or x_4 will make tea via universal resolution. From the fact that for all x_4, x_4 will play tennis or x_4 will make tea, and that for all x_4, x_4 will not play tennis or x_4 is happy we can infer that for all x_4, x_4 will make tea or x_4 is happy via universal resolution. Finally, from the fact that for all x_4, x_4 will make tea or x_4 is happy, and that there is at least one x_4 for which x_4 will not make tea we can infer that there is at least one x_4 for which x_4 is happy via existential disjunctive syllogism. Therefore, the answer is yes.