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 is not a carpenter. There is at least one x_5 for which if x_5 were a janitor, then x_5 is cooking. For all x_5, if x_5 cooks, then x_5 is a janitor. For all x_5, x_5 is a carpenter if and only if x_5 will cook.
There is at least one x_5 for which x_5 is a janitor if and only if x_5 will cook can be inferred via the existential biconditional introduction rule. There is at least one x_5 for which x_5 will cook if and only if x_5 is a janitor can be inferred via the existential biconditional introduction rule. For all x_5, if x_5 were a carpenter, then x_5 is cooking can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 cooks, then x_5 is a carpenter can be inferred via the universal biconditional elimination rule. For all x_5, x_5 will not cook can be inferred via the universal biconditional elimination rule.