What is the ruling on doubting the designation of one's prayer intention while performing it?

If a person doubts during their prayer whether they intended it to be Dhuhr or Asr or another prayer, then if they recall the intention before performing any pillar, such as bowing (rukūʿ) or prostrating (sujūd), their prayer is valid and they should complete it. However, if they do not recall the intention until after performing a pillar, then their prayer is invalidated according to many scholars, and they must repeat it, because specifying the intention is a condition, and it has been removed by the doubt. Imam Ahmad was asked about an Imam who prayed Asr, thinking it was Dhuhr, and prolonged it, then remembered. He replied: "He must repeat it."