CNN has been fact-checking Republican presidential nominee Donald Trump in real time in its television chyrons, and when Trump made news on Thursday by saying that President Barack Obama founded ISIS, the network corrected him.

But the correction itself wasn't exactly accurate.

In its fact-check, CNN said that Abu Bakr al-Baghdadi founded the terrorist group. But while he's the "caliph," or leader, of ISIS, Abu Musab al-Zarqawi is the bloodthirsty zealot who's generally regarded as the group's founder.

ISIS was born out of Al Qaeda in Iraq, a group that rose up after the US invasion of that country. AQI quickly gained a reputation for being even more indiscriminately violent than its parent organization, and Zarqawi is the man responsible for that vision.

Al Qaeda's central leadership eventually disowned its Iraqi affiliate after Zarqawi defied orders and continued sanctioning the killing of Muslims in Iraq. He declared the creation of an Islamic State in 2006 before he was killed in a US airstrike.