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_5, x_5 will not read a book. For all x_5, if x_5 reads a book, then x_5 is a carpenter. There is at least one x_5 for which x_5 is a carpenter if and only if x_5 will listen to a song. For all x_5, if x_5 were a carpenter, then x_5 is reading a book.
For all x_5, x_5 is not a carpenter can be inferred via the universal modus tollens rule. For all x_5, x_5 will read a book if and only if x_5 is a carpenter can be inferred via the universal biconditional introduction rule. For all x_5, x_5 is a carpenter if and only if x_5 will read a book can be inferred via the universal biconditional introduction rule. There is at least one x_5 for which if x_5 were a carpenter, then x_5 is listening to a song can be inferred via the existential biconditional elimination rule. There is at least one x_5 for which if x_5 listens to a song, then x_5 is a carpenter can be inferred via the existential biconditional elimination rule.