Consider the following premises. exists x_13: R(x_13) or ~U(x_13). forall x_13: Q_2(x_13). forall x_13: U(x_13) -> ~Q_2(x_13). forall x_13: U(x_13) <-> R(x_13). Can we infer exists x_13: ~R(x_13) from them?
 From exists x_13: R(x_13) or ~U(x_13) we can infer exists x_13: U(x_13) -> R(x_13). From forall x_13: U(x_13) <-> R(x_13) we can infer forall x_13: R(x_13) -> U(x_13). From exists x_13: U(x_13) -> R(x_13), forall x_13: R(x_13) -> U(x_13) we can infer exists x_13: U(x_13) <-> R(x_13). From forall x_13: U(x_13) -> ~Q_2(x_13), forall x_13: Q_2(x_13) we can infer forall x_13: ~U(x_13). Finally, from exists x_13: U(x_13) <-> R(x_13), forall x_13: ~U(x_13) we can infer exists x_13: ~R(x_13). Therefore, the answer is yes.