Consider the following premises. forall x_8: U(x_8) or P(x_8). exists x_8: U(x_8) <-> R_4(x_8). forall x_8: Q_1(x_8) -> R_4(x_8). forall x_8: P(x_8) -> Q_1(x_8). Can we infer exists x_8: R_4(x_8) from them?
 From exists x_8: U(x_8) <-> R_4(x_8) we can infer exists x_8: U(x_8) -> R_4(x_8). From forall x_8: P(x_8) -> Q_1(x_8), forall x_8: Q_1(x_8) -> R_4(x_8) we can infer forall x_8: P(x_8) -> R_4(x_8). Finally, from exists x_8: U(x_8) -> R_4(x_8), forall x_8: P(x_8) -> R_4(x_8), forall x_8: U(x_8) or P(x_8) we can infer exists x_8: R_4(x_8). Therefore, the answer is yes.