Consider the following premises. For all y, if y were a nurse, then y is climbing a mountain. For all y, y will not read a book. For all y, y will read a book or y is not a doctor. For all y, if y climbs a mountain, then y is a doctor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y is a nurse.
 From the fact that for all y, y will read a book or y is not a doctor we can infer that for all y, if y were a doctor, then y is reading a book via universal rewriting. From the fact that for all y, if y were a doctor, then y is reading a book, and that for all y, y will not read a book we can infer that for all y, y is not a doctor via universal modus tollens. From the fact that for all y, if y climbs a mountain, then y is a doctor, and that for all y, y is not a doctor we can infer that for all y, y will not climb a mountain via universal modus tollens. Finally, from the fact that for all y, if y were a nurse, then y is climbing a mountain, and that for all y, y will not climb a mountain we can infer that for all y, y is not a nurse via universal modus tollens, which contradicts that There is at least one y for which y is a nurse. Therefore, the answer is no.