Divorce of invalid Nikah

19 yr Female marries 20 yr old guy, both marry without the permission or knowledge of there family and friends, Nikah was carried out in the mosque with all other necessary rquirenments such as witnessess etc.

However recently the girl has found out that the nikah is not valid as she had not sought the fathers permission and did not even attempt to tell him about it. She is going on the follwoing evidence that her Nikah is not valid.


The marriage contract done in this manner is not valid, because it is not valid for a woman to give herself in marriage, rather it is essential that her guardian (wali) be present and give his consent. The Prophet (peace and blessings of Allaah be upon him) said: There is no marriage except with a guardian. Narrated by al-Tirmidhi (1101); classed as saheeh by al-Albaani in Irwa al-Ghaleel (1893).
And the Prophet (peace and blessings of Allaah be upon him) said: Any woman who gets married without the permission of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid. Narrated by al-Tirmidhi (1102), classed as saheeh by al-Albaani in Irwa al-Ghaleel (1840).
Even if the marriage was done in accordance with the madhhab of Abu Haneefah does not alter the ruling in the slightest, because the opinion of anyone does not outweigh the words of the Messenger (peace and blessings of Allaah be upon him), and the Messenger (peace and blessings of Allaah be upon him) ruled as you know, that a woman cannot give herself in marriage and that the marriage of one who gave herself in marriage is invalid.
Shaykh Ahmad Shaakir (may Allaah have mercy on him) said some very important words about this matter:
What no one among the scholars doubts is that the hadeeth There is no marriage except with a guardian is a saheeh hadeeth, which is proven by means of an isnaad which almost reaches the level of mutawaatir. This is the view of all the scholars, which is supported by the Quraan, and no one disagreed with that as far as we know except the Hanafis and those who followed them. The early ones among them may be excused, as it may be that the hadeeth did not reach them at that time with a saheeh isnaad. As for the later ones among them, they fell pray to sectarianism and tried hard to prove the reports weak or misinterpret them without any proof

In regards to the above the girl accepts that the nikah is most definitely invalid, however now she and the guy want to separate, but in order to this is it compulsary for them to take divorce, or should they just go there separate ways without a divorce as it was a invalid marriage in the first place.
The reason they are confused on this matter is because of the following

Based on this, this girls marriage that was done in this manner is not valid, because it was done without the presence or consent of her guardian. The basic principle is that they should be separated, and there is no need for a divorce because the marriage was not valid in the first place. But as some scholars regard marriage without a wali as valid (even though this is a weak view), then divorce should be done. It is sufficient for the husband to speak the words of divorce, and it is not necessary to bring the witnesses who witnessed the marriage.
Ibn Qudaamah (may Allaah have mercy on him) said: If a woman gets married in an invalid manner, it is not permissible for someone else to marry her until she is divorced or the marriage is annulled. End quote from al-Mughni (7/9). (how strong is this view?)
If he divorces her and her iddah has ended, then it is permissible for her to marry someone else

Therefore can you please help me find out wheather the couple should obtain divorce or shall they go separate ways and repent for the years of zina they have committed.