Consider the following premises. forall x: U(x) or W_4(x). forall x: W_4(x) -> S_3(x). exists x: R(x). forall x: ~U(x). Can we infer forall x: ~(R(x) and S_3(x)) from them?
 From forall x: U(x) or W_4(x), forall x: ~U(x) we can infer forall x: W_4(x). From forall x: W_4(x) -> S_3(x), forall x: W_4(x) we can infer forall x: S_3(x). Finally, from exists x: R(x), forall x: S_3(x) we can infer exists x: R(x) and S_3(x), which contradicts forall x: ~(R(x) and S_3(x)). Therefore, the answer is no.