Consider the following premises. There is at least one x_14 for which x_14 will drive a car. For all x_14, x_14 is a janitor. For all x_14, x_14 is a taxi driver and x_14 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 is a janitor and x_14 is a taxi driver.
 From the fact that for all x_14, x_14 is a taxi driver and x_14 is a cashier we can infer that for all x_14, x_14 is a taxi driver via universal simplification. From the fact that for all x_14, x_14 is a taxi driver, and that there is at least one x_14 for which x_14 will drive a car we can infer that there is at least one x_14 for which x_14 is a taxi driver and x_14 will drive a car via existential conjunction. From the fact that there is at least one x_14 for which x_14 is a taxi driver and x_14 will drive a car we can infer that there is at least one x_14 for which x_14 is a taxi driver via existential simplification. Finally, from the fact that for all x_14, x_14 is a janitor, and that there is at least one x_14 for which x_14 is a taxi driver we can infer that there is at least one x_14 for which x_14 is a janitor and x_14 is a taxi driver via existential conjunction. Therefore, the answer is yes.