Consider the following premises. forall x_3: Q_3(x_3) -> R_3(x_3). exists x_3: U(x_3) -> R_3(x_3). forall x_3: ~P_2(x_3) or R_4(x_3). forall x_3: P_2(x_3) or U(x_3). forall x_3: R_4(x_3) -> Q_3(x_3). Can we infer exists x_3: R_3(x_3) from them?
 From forall x_3: R_4(x_3) -> Q_3(x_3), forall x_3: Q_3(x_3) -> R_3(x_3) we can infer forall x_3: R_4(x_3) -> R_3(x_3). From forall x_3: P_2(x_3) or U(x_3), forall x_3: ~P_2(x_3) or R_4(x_3) we can infer forall x_3: U(x_3) or R_4(x_3). Finally, from exists x_3: U(x_3) -> R_3(x_3), forall x_3: R_4(x_3) -> R_3(x_3), forall x_3: U(x_3) or R_4(x_3) we can infer exists x_3: R_3(x_3). Therefore, the answer is yes.