Consider the following premises. exists x_7: R(x_7) -> W(x_7). forall x_7: ~U_1(x_7) or U_4(x_7). forall x_7: U_1(x_7). forall x_7: U_4(x_7) <-> W(x_7). Can we infer exists x_7: W(x_7) from them?
 From forall x_7: U_4(x_7) <-> W(x_7) we can infer forall x_7: U_4(x_7) -> W(x_7). From forall x_7: U_1(x_7) we can infer forall x_7: U_1(x_7) or R(x_7). From forall x_7: U_1(x_7) or R(x_7), forall x_7: ~U_1(x_7) or U_4(x_7) we can infer forall x_7: R(x_7) or U_4(x_7). Finally, from exists x_7: R(x_7) -> W(x_7), forall x_7: U_4(x_7) -> W(x_7), forall x_7: R(x_7) or U_4(x_7) we can infer exists x_7: W(x_7). Therefore, the answer is yes.