Consider the following premises. P_20(a_20) -> q. p. forall x_20: P_20(x_20). Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall x_20: P_20(x_20) we can infer P_20(a_20) via universal instantiation. From P_20(a_20), p we can infer P_20(a_20) and p via conjunction. From P_20(a_20) and p we can infer P_20(a_20) via simplification. Finally, from P_20(a_20) -> q, P_20(a_20) we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.