Consider the following premises. Q(a_10) or w_4. w_4 <-> S_10(a_10). forall x_10: Q(x_10) -> S_10(x_10). Can we infer ~S_10(a_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: Q(x_10) -> S_10(x_10) we can infer Q(a_10) -> S_10(a_10) via universal instantiation. From w_4 <-> S_10(a_10) we can infer w_4 -> S_10(a_10) via biconditional elimination. Finally, from Q(a_10) -> S_10(a_10), w_4 -> S_10(a_10), Q(a_10) or w_4 we can infer S_10(a_10) via disjunction elimination, which contradicts ~S_10(a_10). Therefore, the answer is no.