Consider the following premises. forall x_14: T_1(x_14) <-> R(x_14). forall x_14: T_1(x_14) -> P_14(x_14). exists x_14: P_14(x_14) -> R_2(x_14). forall x_14: P_14(x_14) -> T_1(x_14). Can we infer exists x_14: R(x_14) -> R_2(x_14) from them? If possible, name the inference rules being used at each step.
 From forall x_14: P_14(x_14) -> T_1(x_14), forall x_14: T_1(x_14) -> P_14(x_14) we can infer forall x_14: P_14(x_14) <-> T_1(x_14) via universal biconditional introduction. From forall x_14: T_1(x_14) <-> R(x_14) we can infer forall x_14: R(x_14) -> T_1(x_14) via universal biconditional elimination. From forall x_14: P_14(x_14) <-> T_1(x_14) we can infer forall x_14: T_1(x_14) -> P_14(x_14) via universal biconditional elimination. From forall x_14: T_1(x_14) -> P_14(x_14), exists x_14: P_14(x_14) -> R_2(x_14) we can infer exists x_14: T_1(x_14) -> R_2(x_14) via existential transitivity. Finally, from forall x_14: R(x_14) -> T_1(x_14), exists x_14: T_1(x_14) -> R_2(x_14) we can infer exists x_14: R(x_14) -> R_2(x_14) via existential transitivity. Therefore, the answer is yes.