Is the explicit mention of 'adultery' required in the concluding part of the testimony during Li'an?

Primary text

Some jurists stipulate that after the statement 'I am among the truthful,' the phrase 'regarding what I have accused my wife with concerning adultery' must be explicitly added, and likewise for the wife's rebuttal. However, this stipulation is not necessary because Allah the Exalted revealed and clarified the matter without including this specific requirement.