Does one have to repeat a prayer in which the worshiper delayed in the prostration of forgetfulness for ten minutes, knowing that he does not remember which prayer it was?

If you prostrate for forgetfulness a short time before leaving the prayer place, that is sufficient for you and you are not required to repeat the prayer. However, if you prostrate after a long separation, your prayer is invalid, and you must repeat the four-rak'ah prayers (Dhuhr, Asr, Isha) if you predominantly believe they were four rak'ahs, or all five prayers if you are in doubt.