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 y, if y were a carpenter, then y is a musician. For all y, if y were a musician, then y is driving a car. For all y, y is not a musician. There is at least one y for which if y drives a car, then y is a carpenter.
For all y, y is not a carpenter can be inferred via the universal modus tollens rule. For all y, if y were a carpenter, then y is driving a car can be inferred via the universal transitivity rule. There is at least one y for which if y drives a car, then y is a musician can be inferred via the existential transitivity rule. There is at least one y for which if y were a musician, then y is a carpenter can be inferred via the existential transitivity rule.