Consider the following premises. forall x_13: R(x_13) <-> Q(x_13). forall x_13: P_13(x_13) <-> T_2(x_13). forall x_13: Q(x_13) -> P_13(x_13). forall x_13: ~R(x_13). exists x_13: T_2(x_13) -> Q(x_13). Can we infer forall x_13: T_2(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) <-> T_2(x_13) we can infer forall x_13: P_13(x_13) -> T_2(x_13) via universal biconditional elimination. From forall x_13: Q(x_13) -> P_13(x_13), forall x_13: P_13(x_13) -> T_2(x_13) we can infer forall x_13: Q(x_13) -> T_2(x_13) via universal transitivity. From forall x_13: R(x_13) <-> Q(x_13), forall x_13: ~R(x_13) we can infer forall x_13: ~Q(x_13) via universal biconditional elimination. From forall x_13: Q(x_13) -> T_2(x_13), exists x_13: T_2(x_13) -> Q(x_13) we can infer exists x_13: Q(x_13) <-> T_2(x_13) via existential biconditional introduction. Finally, from exists x_13: Q(x_13) <-> T_2(x_13), forall x_13: ~Q(x_13) we can infer exists x_13: ~T_2(x_13) via existential biconditional elimination, which contradicts forall x_13: T_2(x_13). Therefore, the answer is no.