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, x_9 is a doctor or x_9 is a bartender. There is at least one x_9 for which x_9 will listen to a song if and only if x_9 is a bartender. For all x_9, x_9 is not a doctor.
For all x_9, x_9 is a bartender can be inferred via the universal disjunctive syllogism rule. There is at least one x_9 for which if x_9 listens to a song, then x_9 is a bartender can be inferred via the existential biconditional elimination rule. There is at least one x_9 for which if x_9 were a bartender, then x_9 is listening to a song can be inferred via the existential biconditional elimination rule.