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_4, x_4 will not climb a mountain. There is at least one x_4 for which if x_4 were a bartender, then x_4 is sleeping. For all x_4, if x_4 sleeps, then x_4 is a bartender. For all x_4, if x_4 were a bartender, then x_4 is climbing a mountain. For all x_4, if x_4 were a bartender, then x_4 is sleeping.
For all x_4, x_4 is not a bartender can be inferred via the universal modus tollens rule. For all x_4, if x_4 sleeps, then x_4 is climbing a mountain can be inferred via the universal transitivity rule. For all x_4, x_4 will sleep if and only if x_4 is a bartender can be inferred via the universal biconditional introduction rule. For all x_4, x_4 is a bartender if and only if x_4 will sleep can be inferred via the universal biconditional introduction rule. There is at least one x_4 for which x_4 is a bartender if and only if x_4 will sleep can be inferred via the existential biconditional introduction rule. There is at least one x_4 for which x_4 will sleep if and only if x_4 is a bartender can be inferred via the existential biconditional introduction rule.