Consider the following premises. For all x_2, if x_2 reads a book, then x_2 is making tea. There is at least one x_2 for which x_2 will read a book or x_2 will drink water. For all x_2, x_2 will make tea or x_2 will not drink water. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will not make tea.
 From the fact that for all x_2, x_2 will make tea or x_2 will not drink water we can infer that for all x_2, if x_2 drinks water, then x_2 is making tea via universal rewriting. Finally, from the fact that for all x_2, if x_2 reads a book, then x_2 is making tea, that for all x_2, if x_2 drinks water, then x_2 is making tea, and that there is at least one x_2 for which x_2 will read a book or x_2 will drink water we can infer that there is at least one x_2 for which x_2 will make tea via existential disjunction elimination, which contradicts that For all x_2, x_2 will not make tea. Therefore, the answer is no.