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