Consider the following premises. exists x_1: W(x_1) -> U(x_1). forall x_1: U_2(x_1) or Q(x_1). forall x_1: ~U_2(x_1) or W(x_1). forall x_1: U(x_1) <-> Q(x_1). Can we infer exists x_1: U(x_1) from them?
 From forall x_1: U(x_1) <-> Q(x_1) we can infer forall x_1: Q(x_1) -> U(x_1). From forall x_1: U_2(x_1) or Q(x_1), forall x_1: ~U_2(x_1) or W(x_1) we can infer forall x_1: Q(x_1) or W(x_1). Finally, from forall x_1: Q(x_1) -> U(x_1), exists x_1: W(x_1) -> U(x_1), forall x_1: Q(x_1) or W(x_1) we can infer exists x_1: U(x_1). Therefore, the answer is yes.