Does the divorce mentioned in the urfi marriage contract, which the husband admitted to having included falsely to appease his other wife, count as a valid divorce according to Islamic law or not?

Scholars differ on whether writing a divorce effects a divorce or if it depends on the intention. The more preponderant opinion is that it does not take effect unless there is a firm intention to effect it. However, if he pronounces it verbally, it takes effect even if he is joking, for the Prophet, peace and blessings be upon him, said: "There are three matters, serious in which are serious, and playful in which are serious: marriage, divorce, and return (to marriage)." Assuming the divorce has occurred, the husband can reconcile with his wife if this was the first or second divorce and she is still within her waiting period ('iddah). As for " عرفي" (customary marriage), if it is intended to mean a valid, but unregistered marriage, then it is valid. But if it is intended to mean marriage without a guardian (wali), then it is void.