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 y, y is not an astronaut. For all y, if y were a politician, then y is an astronaut. There is at least one y for which y is a carpenter if and only if y will read a book. For all y, if y reads a book, then y is a politician. For all y, if y were an astronaut, then y is reading a book.
For all y, y is not a politician can be inferred via the universal modus tollens rule. For all y, if y were a politician, then y is reading a book can be inferred via the universal transitivity rule. For all y, if y reads a book, then y is an astronaut can be inferred via the universal transitivity rule. For all y, if y were an astronaut, then y is a politician can be inferred via the universal transitivity rule. There is at least one y for which if y were a carpenter, then y is reading a book can be inferred via the existential biconditional elimination rule. There is at least one y for which if y reads a book, then y is a carpenter can be inferred via the existential biconditional elimination rule.