Consider the following premises. forall y: P_2(y) -> R(y). forall y: W_3(y) or S_3(y). forall y: P_2(y). exists y: ~W_3(y). Can we infer exists y: S_3(y) and R(y) from them?
 From forall y: P_2(y) -> R(y), forall y: P_2(y) we can infer forall y: R(y). From forall y: W_3(y) or S_3(y), exists y: ~W_3(y) we can infer exists y: S_3(y). Finally, from exists y: S_3(y), forall y: R(y) we can infer exists y: S_3(y) and R(y). Therefore, the answer is yes.