Consider the following premises. There is at least one x_10 for which x_10 is rich and x_10 is a bartender. For all x_10, x_10 will play tennis. For all x_10, if x_10 plays tennis, then x_10 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, either x_10 is rich or x_10 is a writer are not true.
 From the fact that there is at least one x_10 for which x_10 is rich and x_10 is a bartender we can infer that there is at least one x_10 for which x_10 is rich via existential simplification. From the fact that for all x_10, if x_10 plays tennis, then x_10 is a writer, and that for all x_10, x_10 will play tennis we can infer that for all x_10, x_10 is a writer via universal modus ponens. Finally, from the fact that there is at least one x_10 for which x_10 is rich, and that for all x_10, x_10 is a writer we can infer that there is at least one x_10 for which x_10 is rich and x_10 is a writer via existential conjunction, which contradicts that For all x_10, either x_10 is rich or x_10 is a writer are not true. Therefore, the answer is no.