Consider the following premises. forall x_7: R_7(x_7) <-> S_7(x_7). S_7(a) -> t. Can we infer ~(R_7(a) -> t) from them? If possible, name the inference rules being used at each step.
 From forall x_7: R_7(x_7) <-> S_7(x_7) we can infer R_7(a) <-> S_7(a) via universal instantiation. From R_7(a) <-> S_7(a) we can infer R_7(a) -> S_7(a) via biconditional elimination. Finally, from R_7(a) -> S_7(a), S_7(a) -> t we can infer R_7(a) -> t via transitivity, which contradicts ~(R_7(a) -> t). Therefore, the answer is no.