Consider the following premises. forall x_7: Q(x_7) <-> S_7(x_7). ~Q(c). Can we infer ~S_7(c) from them? If possible, name the inference rules being used at each step.
 From forall x_7: Q(x_7) <-> S_7(x_7) we can infer Q(c) <-> S_7(c) via universal instantiation. From Q(c) <-> S_7(c) we can infer S_7(c) -> Q(c) via biconditional elimination. Finally, from S_7(c) -> Q(c), ~Q(c) we can infer ~S_7(c) via modus tollens. Therefore, the answer is yes.