Consider the following premises. For all x_6, x_6 is a writer or x_6 will make tea. For all x_6, x_6 is not a writer or x_6 will listen to a song. There is at least one x_6 for which if x_6 makes tea, then x_6 is fast. For all x_6, x_6 is fast or x_6 will not listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not fast.
 From the fact that for all x_6, x_6 is a writer or x_6 will make tea, and that for all x_6, x_6 is not a writer or x_6 will listen to a song we can infer that for all x_6, x_6 will make tea or x_6 will listen to a song via universal resolution. From the fact that for all x_6, x_6 is fast or x_6 will not listen to a song we can infer that for all x_6, if x_6 listens to a song, then x_6 is fast via universal rewriting. Finally, from the fact that there is at least one x_6 for which if x_6 makes tea, then x_6 is fast, that for all x_6, if x_6 listens to a song, then x_6 is fast, and that for all x_6, x_6 will make tea or x_6 will listen to a song we can infer that there is at least one x_6 for which x_6 is fast via existential disjunction elimination, which contradicts that For all x_6, x_6 is not fast. Therefore, the answer is no.