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: There is at least one z_3 for which if z_3 were a server, then z_3 is playing squash. For all z_3, z_3 is a server or z_3 is not a nurse. For all z_3, z_3 is not curious. For all z_3, if z_3 plays squash, then z_3 is a nurse. For all z_3, z_3 is a server if and only if z_3 is curious.
There is at least one z_3 for which if z_3 were a server, then z_3 is a nurse can be inferred via the existential transitivity rule. For all z_3, if z_3 were a nurse, then z_3 is a server can be inferred via the universal rewriting rule. For all z_3, if z_3 were a server, then z_3 is curious can be inferred via the universal biconditional elimination rule. For all z_3, if z_3 were curious, then z_3 is a server can be inferred via the universal biconditional elimination rule. For all z_3, z_3 is not a server can be inferred via the universal biconditional elimination rule.