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_1, if z_1 were a cashier, then z_1 is excited. For all z_1, if z_1 were a taxi driver, then z_1 is playing squash. For all z_1, if z_1 plays squash, then z_1 is an office clerk. There is at least one z_1 for which if z_1 were excited, then z_1 is a taxi driver.
For all z_1, if z_1 were a taxi driver, then z_1 is an office clerk can be inferred via the universal transitivity rule. There is at least one z_1 for which if z_1 were excited, then z_1 is playing squash can be inferred via the existential transitivity rule. There is at least one z_1 for which if z_1 were a cashier, then z_1 is a taxi driver can be inferred via the existential transitivity rule.