Consider the following premises. For all x_6, x_6 is a taxi driver or x_6 will not make tea. There is at least one x_6 for which x_6 is a doctor or x_6 will play a game. For all x_6, if x_6 plays a game, then x_6 is making tea. For all x_6, if x_6 were a doctor, then x_6 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not a taxi driver.
 From the fact that for all x_6, x_6 is a taxi driver or x_6 will not make tea we can infer that for all x_6, if x_6 makes tea, then x_6 is a taxi driver via universal rewriting. From the fact that for all x_6, if x_6 plays a game, then x_6 is making tea, and that for all x_6, if x_6 makes tea, then x_6 is a taxi driver we can infer that for all x_6, if x_6 plays a game, then x_6 is a taxi driver via universal transitivity. Finally, from the fact that for all x_6, if x_6 were a doctor, then x_6 is a taxi driver, that for all x_6, if x_6 plays a game, then x_6 is a taxi driver, and that there is at least one x_6 for which x_6 is a doctor or x_6 will play a game we can infer that there is at least one x_6 for which x_6 is a taxi driver via existential disjunction elimination, which contradicts that For all x_6, x_6 is not a taxi driver. Therefore, the answer is no.