Consider the following premises. forall x_11: P_6(x_11) or U(x_11). forall x_11: R_4(x_11) -> Q(x_11). forall x_11: ~P_6(x_11) or R_4(x_11). forall x_11: Q(x_11) -> R_4(x_11). forall x_11: Q(x_11) <-> U(x_11). Can we infer exists x_11: ~Q(x_11) from them?
 From forall x_11: Q(x_11) <-> U(x_11) we can infer forall x_11: U(x_11) -> Q(x_11). From forall x_11: Q(x_11) -> R_4(x_11), forall x_11: R_4(x_11) -> Q(x_11) we can infer forall x_11: Q(x_11) <-> R_4(x_11). From forall x_11: P_6(x_11) or U(x_11), forall x_11: ~P_6(x_11) or R_4(x_11) we can infer forall x_11: U(x_11) or R_4(x_11). From forall x_11: Q(x_11) <-> R_4(x_11) we can infer forall x_11: R_4(x_11) -> Q(x_11). Finally, from forall x_11: U(x_11) -> Q(x_11), forall x_11: R_4(x_11) -> Q(x_11), forall x_11: U(x_11) or R_4(x_11) we can infer forall x_11: Q(x_11), which contradicts exists x_11: ~Q(x_11). Therefore, the answer is no.