Are the three divorces mentioned in the question valid, and is it permissible for the wife to return to her husband after the third divorce?

If a man divorces his wife three times after consummation of the marriage or lawful privacy, she is considered irrevocably divorced (Bainunah Kubra) and is not lawful for him until she marries another man. However, if he divorces her after the marriage contract but before consummation or lawful privacy, the divorce in this case is considered a minor irrevocable divorce (Bainunah Sughra), and it is not permissible for the husband to take her back except with a new contract, and she does not have to observe an 'iddah (waiting period). Consequently, this man's taking back his wife is not valid, and his divorce after taking her back is not considered because it did not occur to a valid subject. Therefore, this man has, in reality, only divorced once, after which he may marry this woman with a new contract. If he took her back believing it was lawful, he is not blameworthy for taking her back, and if a pregnancy occurs, it is attributed to him.