Consider the following premises. Q(a_15) -> t_2. R(a_15) or ~t_2. forall z_3: R(z_3) -> Q(z_3). Can we infer ~(t_2 <-> R(a_15)) from them? If possible, name the inference rules being used at each step.
 From forall z_3: R(z_3) -> Q(z_3) we can infer R(a_15) -> Q(a_15) via universal instantiation. From R(a_15) -> Q(a_15), Q(a_15) -> t_2 we can infer R(a_15) -> t_2 via transitivity. From R(a_15) or ~t_2 we can infer t_2 -> R(a_15) via rewriting. Finally, from t_2 -> R(a_15), R(a_15) -> t_2 we can infer t_2 <-> R(a_15) via biconditional introduction, which contradicts ~(t_2 <-> R(a_15)). Therefore, the answer is no.