Consider the following premises. forall x_4: R(x_4) -> Q(x_4). forall x_4: ~U_2(x_4). forall x_4: R(x_4) <-> Q(x_4). forall x_4: U_2(x_4) <-> Q(x_4). Can we infer exists x_4: R(x_4) from them?
 From forall x_4: U_2(x_4) <-> Q(x_4), forall x_4: ~U_2(x_4) we can infer forall x_4: ~Q(x_4). From forall x_4: R(x_4) <-> Q(x_4) we can infer forall x_4: Q(x_4) -> R(x_4). From forall x_4: Q(x_4) -> R(x_4), forall x_4: R(x_4) -> Q(x_4) we can infer forall x_4: Q(x_4) <-> R(x_4). Finally, from forall x_4: Q(x_4) <-> R(x_4), forall x_4: ~Q(x_4) we can infer forall x_4: ~R(x_4), which contradicts exists x_4: R(x_4). Therefore, the answer is no.