Consider the following premises. r_1 -> T(a). r_1 or ~S_15(a). forall x_15: T(x_15) -> S_15(x_15). Can we infer ~(r_1 <-> S_15(a)) from them? If possible, name the inference rules being used at each step.
 From forall x_15: T(x_15) -> S_15(x_15) we can infer T(a) -> S_15(a) via universal instantiation. From r_1 or ~S_15(a) we can infer S_15(a) -> r_1 via rewriting. From r_1 -> T(a), T(a) -> S_15(a) we can infer r_1 -> S_15(a) via transitivity. Finally, from r_1 -> S_15(a), S_15(a) -> r_1 we can infer r_1 <-> S_15(a) via biconditional introduction, which contradicts ~(r_1 <-> S_15(a)). Therefore, the answer is no.