Consider the following premises. forall x_6: Q_2(x_6). exists x_6: U(x_6) -> R_4(x_6). forall x_6: R_4(x_6) -> U(x_6). forall x_6: U(x_6) -> ~Q_2(x_6). Can we infer exists x_6: ~R_4(x_6) from them?
 From forall x_6: R_4(x_6) -> U(x_6), exists x_6: U(x_6) -> R_4(x_6) we can infer exists x_6: R_4(x_6) <-> U(x_6). From forall x_6: U(x_6) -> ~Q_2(x_6), forall x_6: Q_2(x_6) we can infer forall x_6: ~U(x_6). Finally, from exists x_6: R_4(x_6) <-> U(x_6), forall x_6: ~U(x_6) we can infer exists x_6: ~R_4(x_6). Therefore, the answer is yes.