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: There is at least one x for which if x were a bartender, then x is cooking. For all x, if x were a soldier, then x is a bartender. For all x, if x cooks, then x is a soldier.
For all x, if x cooks, then x is a bartender can be inferred via the universal transitivity rule. There is at least one x for which if x were a bartender, then x is a soldier can be inferred via the existential transitivity rule. There is at least one x for which if x were a soldier, then x is cooking can be inferred via the existential transitivity rule.