What is the ruling regarding a husband's statement "we are divorced" if he claims the intention was to inform and not to originate (a divorce), and he does not recall making the statement, while the wife doubts his intention, and must the wife believe him if he had explicitly divorced her twice before?

The Shariah has placed divorce in the husband's hand. If the husband says, "We are divorced," and claims that he intended to inform [about a past event] and not to initiate [a divorce], he is to be believed in that, and the wife must believe him. If the divorce does not take effect when one is certain of uttering the aforementioned phrase, then it is even more unlikely to take effect when one is in doubt about it. One should be wary of being lax in matters of divorce due to its negative consequences.