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_2, if z_2 were a janitor, then z_2 is happy. For all z_2, z_2 will not work. For all z_2, if z_2 works, then z_2 is happy. There is at least one z_2 for which if z_2 were happy, then z_2 is working.
There is at least one z_2 for which z_2 is not happy can be inferred via the existential modus tollens rule. There is at least one z_2 for which if z_2 were a janitor, then z_2 is working can be inferred via the existential transitivity rule. There is at least one z_2 for which z_2 is happy if and only if z_2 will work can be inferred via the existential biconditional introduction rule. There is at least one z_2 for which z_2 will work if and only if z_2 is happy can be inferred via the existential biconditional introduction rule.