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_14, if x_14 were excited, then x_14 is a cashier. For all x_14, if x_14 were a cashier, then x_14 is excited. For all x_14, if x_14 were excited, then x_14 is a cashier. There is at least one x_14 for which x_14 will sleep if and only if x_14 is a cashier. For all x_14, x_14 will not sleep.
For all x_14, x_14 is excited if and only if x_14 is a cashier can be inferred via the universal biconditional introduction rule. For all x_14, x_14 is a cashier if and only if x_14 is excited can be inferred via the universal biconditional introduction rule. For all x_14, x_14 is a cashier if and only if x_14 is excited can be inferred via the universal biconditional introduction rule. For all x_14, x_14 is excited if and only if x_14 is a cashier can be inferred via the universal biconditional introduction rule. There is at least one x_14 for which if x_14 sleeps, then x_14 is a cashier can be inferred via the existential biconditional elimination rule. There is at least one x_14 for which if x_14 were a cashier, then x_14 is sleeping can be inferred via the existential biconditional elimination rule. There is at least one x_14 for which x_14 is not a cashier can be inferred via the existential biconditional elimination rule.