Consider the following premises. ~q_4. forall x_7: R_7(x_7) <-> S_7(x_7). S_7(a_7) <-> q_4. Can we infer R_7(a_7) 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_7) <-> S_7(a_7) via universal instantiation. From S_7(a_7) <-> q_4, ~q_4 we can infer ~S_7(a_7) via biconditional elimination. Finally, from R_7(a_7) <-> S_7(a_7), ~S_7(a_7) we can infer ~R_7(a_7) via biconditional elimination, which contradicts R_7(a_7). Therefore, the answer is no.