Is fasting the two months considered valid if one of its days coincides with the day of Eid al-Adha?

Jurists have differed concerning the interruption of continuous obligatory fasting by breaking the fast on Eid days. The majority hold that it does interrupt the continuity, while the Hanbalis are of the view that it does not, because breaking the fast on Eid is a religious obligation. Sheikh Ibn Uthaymin supported this view, clarifying that breaking the fast due to a valid religious or sensory excuse does not interrupt continuity, such as fasting Ramadan or the days of Eid and Tashreeq as part of an obligatory fast. Accordingly, the questioner's breaking of the fast on Eid day does not interrupt the continuity of their fasting. Furthermore, the recognized months are the lunar (Hijri) months.