Is secret customary marriage (zawaj urfi) between a man and a woman, which then ends in separation, considered zina (fornication/adultery)?

Marriage has pillars without which it cannot be contracted: a guardian or his representative, two just witnesses, and a formula indicating the contract. If these pillars are absent, as in merely writing a document, the marriage is not contracted, and cohabiting with her is considered zina (fornication/adultery). Sincere repentance is obligatory by ceasing the sin, regretting it, and resolving not to return to it, along with frequently seeking forgiveness.