Consider the following premises. forall x_2: U(x_2) -> W(x_2). exists x_2: P_2(x_2) or U(x_2). forall x_2: ~P_2(x_2) or W_1(x_2). forall x_2: W_1(x_2) -> W(x_2). Can we infer exists x_2: W(x_2) from them?
 From exists x_2: P_2(x_2) or U(x_2), forall x_2: ~P_2(x_2) or W_1(x_2) we can infer exists x_2: U(x_2) or W_1(x_2). Finally, from forall x_2: U(x_2) -> W(x_2), forall x_2: W_1(x_2) -> W(x_2), exists x_2: U(x_2) or W_1(x_2) we can infer exists x_2: W(x_2). Therefore, the answer is yes.