Consider the following premises. exists x_6: P_6(x_6) or R(x_6). forall x_6: R(x_6) -> P_4(x_6). forall x_6: ~P_6(x_6) or W_1(x_6). forall x_6: P_4(x_6) <-> W_1(x_6). Can we infer exists x_6: P_4(x_6) from them?
 From exists x_6: P_6(x_6) or R(x_6), forall x_6: ~P_6(x_6) or W_1(x_6) we can infer exists x_6: R(x_6) or W_1(x_6). From forall x_6: P_4(x_6) <-> W_1(x_6) we can infer forall x_6: W_1(x_6) -> P_4(x_6). Finally, from forall x_6: R(x_6) -> P_4(x_6), forall x_6: W_1(x_6) -> P_4(x_6), exists x_6: R(x_6) or W_1(x_6) we can infer exists x_6: P_4(x_6). Therefore, the answer is yes.