Consider the following premises. forall z: P_3(z) or S_2(z). forall z: ~W_3(z). forall z: S(z) -> W_3(z). exists z: P_3(z) <-> S(z). Can we infer exists z: S_2(z) from them? If possible, name the inference rules being used at each step.
 From forall z: S(z) -> W_3(z), forall z: ~W_3(z) we can infer forall z: ~S(z) via universal modus tollens. From exists z: P_3(z) <-> S(z), forall z: ~S(z) we can infer exists z: ~P_3(z) via existential biconditional elimination. Finally, from forall z: P_3(z) or S_2(z), exists z: ~P_3(z) we can infer exists z: S_2(z) via existential disjunctive syllogism. Therefore, the answer is yes.