What is the ruling if someone swears, 'If I do X, then it is upon me for Allah that I free my slave,' upon violating the oath?

Primary text

If one swears, 'If I do X, then it is upon me for Allah that I free my slave,' and then violates the oath, the slave is not freed. Instead, the person incurs the expiation (kaffara) for a broken oath, similar to what is prescribed for conditional vows (Nathr al-lajaj). This is because the oath did not suspend the freeing of the slave directly; rather, the oath was made concerning the conditionality of the freeing.