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 z, z is a writer. There is at least one z for which z is an office clerk. For all z, if z were a cashier, then z is a lawyer. For all z, if z were a writer, then z is a cashier.
For all z, z is a cashier can be inferred via the universal modus ponens rule. For all z, if z were a writer, then z is a lawyer can be inferred via the universal transitivity rule. There is at least one z for which z is an office clerk and z is a writer can be inferred via the existential conjunction rule. There is at least one z for which z is a writer and z is an office clerk can be inferred via the existential conjunction rule.