Consider the following premises. forall x_7: R_4(x_7) <-> S_7(x_7). w <-> R_4(a_7). ~S_7(a_7). Can we infer w from them? If possible, name the inference rules being used at each step.
 From forall x_7: R_4(x_7) <-> S_7(x_7) we can infer R_4(a_7) <-> S_7(a_7) via universal instantiation. From R_4(a_7) <-> S_7(a_7), ~S_7(a_7) we can infer ~R_4(a_7) via biconditional elimination. Finally, from w <-> R_4(a_7), ~R_4(a_7) we can infer ~w via biconditional elimination, which contradicts w. Therefore, the answer is no.