Consider the following premises. forall x_11: P(x_11) or P_2(x_11). forall x_11: R_11(x_11) -> T(x_11). forall x_11: T(x_11) -> P(x_11). exists x_11: P_2(x_11) -> Q_11(x_11). forall x_11: P(x_11) -> T(x_11). forall x_11: Q_11(x_11) -> R_11(x_11). Can we infer forall x_11: ~T(x_11) from them? If possible, name the inference rules being used at each step.
 From exists x_11: P_2(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> R_11(x_11) we can infer exists x_11: P_2(x_11) -> R_11(x_11) via existential transitivity. From exists x_11: P_2(x_11) -> R_11(x_11), forall x_11: R_11(x_11) -> T(x_11) we can infer exists x_11: P_2(x_11) -> T(x_11) via existential transitivity. From forall x_11: P(x_11) -> T(x_11), forall x_11: T(x_11) -> P(x_11) we can infer forall x_11: P(x_11) <-> T(x_11) via universal biconditional introduction. From forall x_11: P(x_11) <-> T(x_11) we can infer forall x_11: P(x_11) -> T(x_11) via universal biconditional elimination. Finally, from forall x_11: P(x_11) -> T(x_11), exists x_11: P_2(x_11) -> T(x_11), forall x_11: P(x_11) or P_2(x_11) we can infer exists x_11: T(x_11) via existential disjunction elimination, which contradicts forall x_11: ~T(x_11). Therefore, the answer is no.