Consider the following premises. For all x_4, x_4 is a taxi driver or x_4 will play tennis. For all x_4, x_4 is not a taxi driver or x_4 is sad. For all x_4, x_4 will not play tennis or x_4 is a poet. There is at least one x_4 for which x_4 is not sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is not a poet.
 From the fact that for all x_4, x_4 is a taxi driver or x_4 will play tennis, and that for all x_4, x_4 is not a taxi driver or x_4 is sad we can infer that for all x_4, x_4 will play tennis or x_4 is sad via universal resolution. From the fact that for all x_4, x_4 will play tennis or x_4 is sad, and that for all x_4, x_4 will not play tennis or x_4 is a poet we can infer that for all x_4, x_4 is sad or x_4 is a poet via universal resolution. Finally, from the fact that for all x_4, x_4 is sad or x_4 is a poet, and that there is at least one x_4 for which x_4 is not sad we can infer that there is at least one x_4 for which x_4 is a poet via existential disjunctive syllogism, which contradicts that For all x_4, x_4 is not a poet. Therefore, the answer is no.