Consider the following premises. forall z: R_2(z) <-> S(z). forall z: ~S_3(z). exists z: R_2(z) -> S_3(z). Can we infer exists z: ~S(z) from them? If possible, name the inference rules being used at each step.
 From exists z: R_2(z) -> S_3(z), forall z: ~S_3(z) we can infer exists z: ~R_2(z) via existential modus tollens. Finally, from forall z: R_2(z) <-> S(z), exists z: ~R_2(z) we can infer exists z: ~S(z) via existential biconditional elimination. Therefore, the answer is yes.