Consider the following premises. exists x: U(x) -> S_2(x). forall x: W(x) -> S_2(x). forall x: P_4(x) -> U(x). forall x: W(x) or P_4(x). Can we infer forall x: ~S_2(x) from them?
 From forall x: P_4(x) -> U(x), exists x: U(x) -> S_2(x) we can infer exists x: P_4(x) -> S_2(x). Finally, from forall x: W(x) -> S_2(x), exists x: P_4(x) -> S_2(x), forall x: W(x) or P_4(x) we can infer exists x: S_2(x), which contradicts forall x: ~S_2(x). Therefore, the answer is no.