What is the ruling regarding the prescribed punishment if the husband performs the Lia'an and mentions the third-party man?

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If the husband performs the Lia'an and mentions the non-mahram man in his oath, the consequence of the accusation against that man is dropped without dispute. The basis for this is that the Lia'an serves as proof regarding one party, thus it serves as proof regarding the other party, similar to testimony. Furthermore, there is a need to accuse the adulterer because he has corrupted the husband's lineage, and mentioning him may be necessary to establish the truthfulness of the accuser through the child's resemblance to the accused, as the Prophet (peace be upon him) established Hilal's truthfulness via the resemblance of the child to Shurayk ibn Sahma. Therefore, the ruling against the husband for accusing the man must be dropped by analogy with the ruling concerning the wife.