Consider the following premises. forall y: U_3(y). forall y: R_4(y). exists y: R_4(y) <-> U(y). Can we infer forall y: ~(U_3(y) and U(y)) from them?
 From exists y: R_4(y) <-> U(y) we can infer exists y: R_4(y) -> U(y). From exists y: R_4(y) -> U(y), forall y: R_4(y) we can infer exists y: U(y). Finally, from forall y: U_3(y), exists y: U(y) we can infer exists y: U_3(y) and U(y), which contradicts forall y: ~(U_3(y) and U(y)). Therefore, the answer is no.