Consider the following premises. For all x_6, x_6 will not take a plane. For all x_6, if x_6 makes tea, then x_6 is taking a plane. For all x_6, if x_6 works, then x_6 is listening to a song. There is at least one x_6 for which if x_6 listens to a song, then x_6 is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will work.
 From the fact that there is at least one x_6 for which if x_6 listens to a song, then x_6 is making tea, and that for all x_6, if x_6 makes tea, then x_6 is taking a plane we can infer that there is at least one x_6 for which if x_6 listens to a song, then x_6 is taking a plane via existential transitivity. From the fact that for all x_6, if x_6 works, then x_6 is listening to a song, and that there is at least one x_6 for which if x_6 listens to a song, then x_6 is taking a plane we can infer that there is at least one x_6 for which if x_6 works, then x_6 is taking a plane via existential transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 works, then x_6 is taking a plane, and that for all x_6, x_6 will not take a plane we can infer that there is at least one x_6 for which x_6 will not work via existential modus tollens, which contradicts that For all x_6, x_6 will work. Therefore, the answer is no.