All poorly trained allergists and dermatologists are untrustworthy specialists. It is not the case, however, that some specialists are untrustworthy. Therefore, it is not the case that some dermatologists are poorly trained. (P, A, D, U, S)

Translate the following arguments into symbolic form. Then use the quantifier negation rule and the eighteen rules of inference to derive the conclusion of each. Do not use either conditional proof or indirect proof.