Consider the following premises. forall z_2: R_4(z_2) or ~S_4(z_2). forall z_2: S_4(z_2). Can we infer exists z_2: ~(R_4(z_2) or U(z_2)) from them?
 From forall z_2: R_4(z_2) or ~S_4(z_2) we can infer forall z_2: S_4(z_2) -> R_4(z_2). From forall z_2: S_4(z_2) -> R_4(z_2), forall z_2: S_4(z_2) we can infer forall z_2: R_4(z_2). Finally, from forall z_2: R_4(z_2) we can infer forall z_2: R_4(z_2) or U(z_2), which contradicts exists z_2: ~(R_4(z_2) or U(z_2)). Therefore, the answer is no.