Consider the following premises. forall y: P_2(y) -> U(y). forall y: S_3(y) -> W_2(y). forall y: U(y) -> S_3(y). forall y: ~W_2(y). Can we infer forall y: ~P_2(y) from them?
 From forall y: U(y) -> S_3(y), forall y: S_3(y) -> W_2(y) we can infer forall y: U(y) -> W_2(y). From forall y: P_2(y) -> U(y), forall y: U(y) -> W_2(y) we can infer forall y: P_2(y) -> W_2(y). Finally, from forall y: P_2(y) -> W_2(y), forall y: ~W_2(y) we can infer forall y: ~P_2(y). Therefore, the answer is yes.