Consider the following premises. exists x_14: ~P_14(x_14). forall x_14: U(x_14) -> R_1(x_14). forall x_14: P_14(x_14) or U(x_14). Can we infer exists x_14: R_1(x_14) or P(x_14) from them?
 From forall x_14: P_14(x_14) or U(x_14), exists x_14: ~P_14(x_14) we can infer exists x_14: U(x_14). From forall x_14: U(x_14) -> R_1(x_14), exists x_14: U(x_14) we can infer exists x_14: R_1(x_14). Finally, from exists x_14: R_1(x_14) we can infer exists x_14: R_1(x_14) or P(x_14). Therefore, the answer is yes.