No. In the first generation of Muslims, when Islam was only in Hijaz, there would be a certain amount of domestic slaves. By the time of the second generation, Islam would have spread past Syria, Persia, and Africa, so all those slaves in those countries would have come under Muslim rule. No new slaves were created, but existing slaves in other countries came under the Islamic state. Your claim was that if there were X number of slaves in the first generation, then by the 4th generation, if no slaves were taken from the war captives, then those X slaves should have all died out and slavery would be gone. But I pointed out that that wasn't correct because while there initially may have been only X slaves, the Y number of existing slaves in Syria would be added to that, plus the Z number in persia, plus the W number in africa, and so on. So you thought that by the time the 4th generation had come, all slaves in the state had been living under 4 generations of Islamic rule, which is not true for anyone except the slaves of Hijaz in the arabian peninsula.
The Islamic ruling and laws pertaining to slavery never changed. But once they were enforced in the society, the practice of slavery was gradually being removed, as its sources were restricted and slaves were continually freed.