Consider the following premises. forall x_10: U_1(x_10) -> T(x_10). exists x_10: T(x_10) -> U_1(x_10). forall x_10: U_1(x_10) and Q_10(x_10). Can we infer forall x_10: ~T(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: U_1(x_10) and Q_10(x_10) we can infer forall x_10: U_1(x_10) via universal simplification. From exists x_10: T(x_10) -> U_1(x_10), forall x_10: U_1(x_10) -> T(x_10) we can infer exists x_10: T(x_10) <-> U_1(x_10) via existential biconditional introduction. From exists x_10: T(x_10) <-> U_1(x_10) we can infer exists x_10: U_1(x_10) -> T(x_10) via existential biconditional elimination. Finally, from exists x_10: U_1(x_10) -> T(x_10), forall x_10: U_1(x_10) we can infer exists x_10: T(x_10) via existential modus ponens, which contradicts forall x_10: ~T(x_10). Therefore, the answer is no.