Consider the following premises. For all x_5, if x_5 were a lawyer, then x_5 is a nurse. There is at least one x_5 for which x_5 will sleep. For all x_5, if x_5 were a nurse, then x_5 is reading a book. For all x_5, x_5 is a janitor or x_5 is a lawyer. For all x_5, if x_5 were a janitor, then x_5 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, either x_5 will read a book or x_5 will sleep are not true.
 From the fact that for all x_5, if x_5 were a lawyer, then x_5 is a nurse, and that for all x_5, if x_5 were a nurse, then x_5 is reading a book we can infer that for all x_5, if x_5 were a lawyer, then x_5 is reading a book via universal transitivity. From the fact that for all x_5, if x_5 were a janitor, then x_5 is reading a book, that for all x_5, if x_5 were a lawyer, then x_5 is reading a book, and that for all x_5, x_5 is a janitor or x_5 is a lawyer we can infer that for all x_5, x_5 will read a book via universal disjunction elimination. Finally, from the fact that for all x_5, x_5 will read a book, and that there is at least one x_5 for which x_5 will sleep we can infer that there is at least one x_5 for which x_5 will read a book and x_5 will sleep via existential conjunction, which contradicts that For all x_5, either x_5 will read a book or x_5 will sleep are not true. Therefore, the answer is no.