What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all x_2, if x_2 were a scientist, then x_2 is reading a book. For all x_2, if x_2 reads a book, then x_2 is cooking. For all x_2, if x_2 cooks, then x_2 is a scientist. There is at least one x_2 for which x_2 will not read a book.
There is at least one x_2 for which x_2 is not a scientist can be inferred via the existential modus tollens rule. For all x_2, if x_2 were a scientist, then x_2 is cooking can be inferred via the universal transitivity rule. For all x_2, if x_2 reads a book, then x_2 is a scientist can be inferred via the universal transitivity rule. For all x_2, if x_2 cooks, then x_2 is reading a book can be inferred via the universal transitivity rule.