Consider the following premises. For all x_5, x_5 is a bartender. For all x_5, if x_5 were a taxi driver, then x_5 is taking a plane. For all x_5, x_5 is a writer or x_5 is a taxi driver. For all x_5, if x_5 were a writer, then x_5 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will not take a plane.
 From the fact that for all x_5, if x_5 were a writer, then x_5 is taking a plane, that for all x_5, if x_5 were a taxi driver, then x_5 is taking a plane, and that for all x_5, x_5 is a writer or x_5 is a taxi driver we can infer that for all x_5, x_5 will take a plane via universal disjunction elimination. From the fact that for all x_5, x_5 will take a plane, and that for all x_5, x_5 is a bartender we can infer that for all x_5, x_5 will take a plane and x_5 is a bartender via universal conjunction. Finally, from the fact that for all x_5, x_5 will take a plane and x_5 is a bartender we can infer that for all x_5, x_5 will take a plane via universal simplification, which contradicts that There is at least one x_5 for which x_5 will not take a plane. Therefore, the answer is no.