Is it required for a woman to divorce before marrying another if the marriage took place without a guardian (wali) or witnesses and without the (explicit) formula, taking into account the different jurisprudential opinions regarding its invalidity (butlan) or فساد (fasad)?

Marriage without a guardian (wali) or witnesses is a matter of scholarly disagreement regarding its invalidity (butlan) and irregularity (fasad). In case of its irregularity, separation occurs either by annulment (faskh (definition)) or divorce (talaq (definition)). As for "al-mutarakah" (abandonment) according to the Hanafis, it means the husband leaves the wife. For a wife with whom cohabitation has occurred, it is effected by a verbal statement such as "I have abandoned you." For a wife with whom cohabitation has not occurred, it is effected either by a verbal statement or by leaving her with the intention of not returning to her.