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