Consider the following premises. For all x_7, if x_7 were a cashier, then x_7 is reading a book. There is at least one x_7 for which x_7 will not go running or x_7 is a carpenter. For all x_7, x_7 will go running or x_7 is a cashier. For all x_7, x_7 will read a book or x_7 is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not read a book.
 From the fact that for all x_7, x_7 will go running or x_7 is a cashier, and that there is at least one x_7 for which x_7 will not go running or x_7 is a carpenter we can infer that there is at least one x_7 for which x_7 is a cashier or x_7 is a carpenter via existential resolution. From the fact that for all x_7, x_7 will read a book or x_7 is not a carpenter we can infer that for all x_7, if x_7 were a carpenter, then x_7 is reading a book via universal rewriting. Finally, from the fact that for all x_7, if x_7 were a cashier, then x_7 is reading a book, that for all x_7, if x_7 were a carpenter, then x_7 is reading a book, and that there is at least one x_7 for which x_7 is a cashier or x_7 is a carpenter we can infer that there is at least one x_7 for which x_7 will read a book via existential disjunction elimination, which contradicts that For all x_7, x_7 will not read a book. Therefore, the answer is no.