Consider the following premises. exists x_4: U_4(x_4) -> ~R_4(x_4). forall x_4: P_4(x_4) -> R_4(x_4). forall x_4: P_4(x_4) or Q_4(x_4). forall x_4: Q_4(x_4) -> R_4(x_4). Can we infer exists x_4: ~U_4(x_4) from them?
 From forall x_4: P_4(x_4) -> R_4(x_4), forall x_4: Q_4(x_4) -> R_4(x_4), forall x_4: P_4(x_4) or Q_4(x_4) we can infer forall x_4: R_4(x_4). Finally, from exists x_4: U_4(x_4) -> ~R_4(x_4), forall x_4: R_4(x_4) we can infer exists x_4: ~U_4(x_4). Therefore, the answer is yes.