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: There is at least one x for which if x were an astronaut, then x is a janitor. For all x, if x were an astronaut, then x is a carpenter. For all x, if x were a carpenter, then x is an astronaut. For all x, if x were a janitor, then x is an astronaut. For all x, x is not a carpenter.
For all x, x is not an astronaut can be inferred via the universal modus tollens rule. For all x, if x were a janitor, then x is a carpenter can be inferred via the universal transitivity rule. There is at least one x for which if x were a carpenter, then x is a janitor can be inferred via the existential transitivity rule. For all x, x is an astronaut if and only if x is a carpenter can be inferred via the universal biconditional introduction rule. For all x, x is a carpenter if and only if x is an astronaut can be inferred via the universal biconditional introduction rule. There is at least one x for which x is an astronaut if and only if x is a janitor can be inferred via the existential biconditional introduction rule. There is at least one x for which x is a janitor if and only if x is an astronaut can be inferred via the existential biconditional introduction rule.