What is the Shar'i ruling regarding a man who swore an oath of divorce upon his wife that she not do something, then she did it out of forgetfulness?

A husband's statement to his wife, "If you do this, you are divorced," is called a conditional divorce.

If the condition is met, the majority of jurists hold that the divorce takes effect. However, some scholars, such as Sheikh Al-Islam Ibn Taymiyyah, are of the view that the matter depends on the husband's intention: if he intended divorce, it occurs; but if he intended a threat or encouragement, the divorce does not occur. Instead, it is considered an oath for which expiation is due (feeding ten needy persons, or clothing them, or freeing a slave, or fasting three days if he cannot find these). This latter opinion is the preferred one.

The fact that the wife did what he forbade her from due to forgetfulness does not change the ruling.