Consider the following premises. forall x_12: P_8(x_12) or Q_8(x_12). forall x_12: Q_8(x_12) -> R_8(x_12). forall x_12: P_8(x_12) -> R_8(x_12). forall x_12: T(x_12) <-> U_3(x_12). forall x_12: R_8(x_12) -> U_3(x_12). Can we infer exists x_12: ~T(x_12) from them?
 From forall x_12: T(x_12) <-> U_3(x_12) we can infer forall x_12: U_3(x_12) -> T(x_12). From forall x_12: P_8(x_12) -> R_8(x_12), forall x_12: Q_8(x_12) -> R_8(x_12), forall x_12: P_8(x_12) or Q_8(x_12) we can infer forall x_12: R_8(x_12). From forall x_12: R_8(x_12) -> U_3(x_12), forall x_12: R_8(x_12) we can infer forall x_12: U_3(x_12). Finally, from forall x_12: U_3(x_12) -> T(x_12), forall x_12: U_3(x_12) we can infer forall x_12: T(x_12), which contradicts exists x_12: ~T(x_12). Therefore, the answer is no.