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_9, if x_9 were a bartender, then x_9 is playing squash. For all x_9, x_9 will not play squash. For all x_9, if x_9 were a bartender, then x_9 is working. For all x_9, if x_9 works, then x_9 is a bartender.
For all x_9, x_9 is not a bartender can be inferred via the universal modus tollens rule. For all x_9, if x_9 works, then x_9 is playing squash can be inferred via the universal transitivity rule. For all x_9, x_9 is a bartender if and only if x_9 will work can be inferred via the universal biconditional introduction rule. For all x_9, x_9 will work if and only if x_9 is a bartender can be inferred via the universal biconditional introduction rule.