Consider the following premises. forall x_22: ~P(x_22). forall x_22: S(x_22) -> U_4(x_22). exists x_22: P(x_22) or S(x_22). forall x_22: Q(x_22) <-> U_4(x_22). Can we infer exists x_22: Q(x_22) from them?
 From forall x_22: Q(x_22) <-> U_4(x_22) we can infer forall x_22: U_4(x_22) -> Q(x_22). From exists x_22: P(x_22) or S(x_22), forall x_22: ~P(x_22) we can infer exists x_22: S(x_22). From forall x_22: S(x_22) -> U_4(x_22), exists x_22: S(x_22) we can infer exists x_22: U_4(x_22). Finally, from forall x_22: U_4(x_22) -> Q(x_22), exists x_22: U_4(x_22) we can infer exists x_22: Q(x_22). Therefore, the answer is yes.