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, if x were a bartender, then x is listening to a song. For all x, if x cooks, then x is a carpenter. For all x, x will cook or x will work. There is at least one x for which if x were a carpenter, then x is a bartender. For all x, if x works, then x is a carpenter.
There is at least one x for which if x were a carpenter, then x is listening to a song can be inferred via the existential transitivity rule. There is at least one x for which if x cooks, then x is a bartender can be inferred via the existential transitivity rule. There is at least one x for which if x works, then x is a bartender can be inferred via the existential transitivity rule. For all x, x is a carpenter can be inferred via the universal disjunction elimination rule.