Consider the following premises. forall y: S_3(y) -> U_4(y). forall y: U_4(y) -> W(y). exists y: W(y). forall y: W(y) -> U_4(y). Can we infer forall y: ~U_4(y) from them?
 From forall y: W(y) -> U_4(y), forall y: U_4(y) -> W(y) we can infer forall y: W(y) <-> U_4(y). From exists y: W(y) we can infer exists y: W(y) or S_3(y). From forall y: W(y) <-> U_4(y) we can infer forall y: W(y) -> U_4(y). Finally, from forall y: W(y) -> U_4(y), forall y: S_3(y) -> U_4(y), exists y: W(y) or S_3(y) we can infer exists y: U_4(y), which contradicts forall y: ~U_4(y). Therefore, the answer is no.