Consider the following premises. exists x_12: P_7(x_12) -> U(x_12). forall x_12: P_7(x_12) or P_12(x_12). forall x_12: P_12(x_12) <-> U(x_12). forall x_12: R_1(x_12) -> ~U(x_12). Can we infer exists x_12: ~R_1(x_12) from them?
 From forall x_12: P_12(x_12) <-> U(x_12) we can infer forall x_12: P_12(x_12) -> U(x_12). From exists x_12: P_7(x_12) -> U(x_12), forall x_12: P_12(x_12) -> U(x_12), forall x_12: P_7(x_12) or P_12(x_12) we can infer exists x_12: U(x_12). Finally, from forall x_12: R_1(x_12) -> ~U(x_12), exists x_12: U(x_12) we can infer exists x_12: ~R_1(x_12). Therefore, the answer is yes.