Consider the following premises. forall x: S_3(x) <-> R(x). exists x: R(x) or U_1(x). forall x: U_1(x) -> S_3(x). Can we infer forall x: ~S_3(x) from them?
 From forall x: S_3(x) <-> R(x) we can infer forall x: R(x) -> S_3(x). Finally, from forall x: R(x) -> S_3(x), forall x: U_1(x) -> S_3(x), exists x: R(x) or U_1(x) we can infer exists x: S_3(x), which contradicts forall x: ~S_3(x). Therefore, the answer is no.