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_7, x_7 is rich. For all x_7, if x_7 were a soldier, then x_7 is a musician. For all x_7, if x_7 were a bartender, then x_7 is not rich. There is at least one x_7 for which if x_7 were a musician, then x_7 is a bartender.
For all x_7, x_7 is not a bartender can be inferred via the universal modus tollens rule. There is at least one x_7 for which if x_7 were a soldier, then x_7 is a bartender can be inferred via the existential transitivity rule.