Should the prayer be repeated if one doubts the validity of their ablution after having committed one of its nullifiers?

If a person is certain that he has nullified his ablution and then doubts whether he performed ablution afterwards or not, he remains in a state of impurity until he performs ablution, because certainty is not dispelled by doubt. Therefore, whoever prays while in a state of impurity, despite the possibility of performing ablution, his prayer is invalid and must be repeated after performing ablution, whether he did so intentionally, forgot, or was ignorant; because the Prophet, peace and blessings be upon him, said: "Allah does not accept a prayer without purification."