Consider the following premises. For all x_6, x_6 will not play tennis or x_6 will work. For all x_6, x_6 will play tennis or x_6 is a taxi driver. For all x_6, x_6 is not a taxi driver. There is at least one x_6 for which if x_6 works, then x_6 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not excited.
 From the fact that for all x_6, x_6 will play tennis or x_6 is a taxi driver, and that for all x_6, x_6 will not play tennis or x_6 will work we can infer that for all x_6, x_6 is a taxi driver or x_6 will work via universal resolution. From the fact that for all x_6, x_6 is a taxi driver or x_6 will work, and that for all x_6, x_6 is not a taxi driver we can infer that for all x_6, x_6 will work via universal disjunctive syllogism. Finally, from the fact that there is at least one x_6 for which if x_6 works, then x_6 is excited, and that for all x_6, x_6 will work we can infer that there is at least one x_6 for which x_6 is excited via existential modus ponens, which contradicts that For all x_6, x_6 is not excited. Therefore, the answer is no.