Sunnah.com reference : Book 8, Hadith 155English translation : Book 8, Hadith 1109Arabic reference : Book 8, Hadith 1098
Narrated Sahl bin Sa'd (RA) concerning the story of the two (husband and wife) who invoked curses regarding one another:
When they finished invoking curses regarding one another the man said, "I shall have lied against her, O Allah's Messenger, if I keep her (as a wife)." He, then, pronounced her divorce three times, even before Allah's Messenger (ﷺ) commanded him to do so.

[Agreed upon].
وَعَنْ سَهْلِ بْنِ سَعْدٍ ‏-فِي قِصَّةِ اَلْمُتَلَاعِنَيْنِ‏- قَالَ: { فَلَمَّا فَرَغَا مِنْ تَلَاعُنِهِمَا قَالَ: كَذَبْتُ عَلَيْهَا يَا رَسُولَ اَللَّهِ! إِنْ أَمْسَكْتُهَا, فَطَلَّقَهَا ثَلَاثًا قَبْلَ أَنْ يَأْمُرَهُ رَسُولُ اَللَّهِ ‏- صلى الله عليه وسلم ‏-}  مُتَّفَقٌ عَلَيْهِ .‏  1‏ .‏‏1 ‏- صحيح.‏ رواه البخاري (5308)‏ ومسلم (1492)‏ (1)‏.‏