Consider the following premises. s_2 -> R_17(a_17). forall x_17: R_17(x_17) -> S_17(x_17). ~S_17(a_17). r_4 -> s_2. S_17(a_17) -> R_17(a_17). Can we infer r_4 from them? If possible, name the inference rules being used at each step.
 From forall x_17: R_17(x_17) -> S_17(x_17) we can infer R_17(a_17) -> S_17(a_17) via universal instantiation. From S_17(a_17) -> R_17(a_17), R_17(a_17) -> S_17(a_17) we can infer S_17(a_17) <-> R_17(a_17) via biconditional introduction. From r_4 -> s_2, s_2 -> R_17(a_17) we can infer r_4 -> R_17(a_17) via transitivity. From S_17(a_17) <-> R_17(a_17), ~S_17(a_17) we can infer ~R_17(a_17) via biconditional elimination. Finally, from r_4 -> R_17(a_17), ~R_17(a_17) we can infer ~r_4 via modus tollens, which contradicts r_4. Therefore, the answer is no.