Consider the following premises. forall y: S(y) -> U_4(y). forall y: U_4(y) -> R_1(y). exists y: R_1(y) -> S(y). forall y: ~S(y). Can we infer exists y: ~U_4(y) from them?
 From forall y: U_4(y) -> R_1(y), exists y: R_1(y) -> S(y) we can infer exists y: U_4(y) -> S(y). From forall y: S(y) -> U_4(y), exists y: U_4(y) -> S(y) we can infer exists y: S(y) <-> U_4(y). Finally, from exists y: S(y) <-> U_4(y), forall y: ~S(y) we can infer exists y: ~U_4(y). Therefore, the answer is yes.