Consider the following premises. forall z_1: S(z_1) -> Q(z_1). forall z_1: ~R(z_1). forall z_1: Q(z_1) -> S(z_1). exists z_1: R(z_1) <-> Q(z_1). Can we infer exists z_1: ~S(z_1) from them? If possible, name the inference rules being used at each step.
 From exists z_1: R(z_1) <-> Q(z_1), forall z_1: ~R(z_1) we can infer exists z_1: ~Q(z_1) via existential biconditional elimination. From forall z_1: S(z_1) -> Q(z_1), forall z_1: Q(z_1) -> S(z_1) we can infer forall z_1: S(z_1) <-> Q(z_1) via universal biconditional introduction. Finally, from forall z_1: S(z_1) <-> Q(z_1), exists z_1: ~Q(z_1) we can infer exists z_1: ~S(z_1) via existential biconditional elimination. Therefore, the answer is yes.