Act on the mafhūm of the reports that have come down, that is, on what they imply, so long as it does not clash with something plainly established.
Two words to hold apart. Manṭūq is what the words actually say: the ruling is right there in the speech. Mafhūm is what the words do NOT say: a ruling for a case the speech never mentioned at all, which you still reach from the wording.
Here the case nobody mentioned takes the same ruling as the case that was mentioned. There are two names for it, depending on strength. If the unmentioned case has an even stronger claim to the ruling, that is faḥwā al-khiṭāb. If its claim is only equal, that is laḥn al-khiṭāb.
The example everyone knows. "Do not say uff to them", about your parents. If even that small word of disrespect is forbidden, then hitting them or cursing them is forbidden far more strongly. Nobody had to say so. That is faḥwā al-khiṭāb.
Here the wording points to the unmentioned case taking the opposite ruling to the one that was stated. This is the kind the schools argue about.
How many kinds are there? The answer comes in layers, so take it in order or it will not add up. Those who accept mafhūm al-mukhālafa count ten kinds in all, of differing strength. Ibn ʿĀbidīn (d. 1252H) names five that are well known: the plain sense of a word (lughah), exclusivity (ḥaṣr), state (ḥāl), time (zamān) and place (makān). He then notes that the last three of those five are really sub-cases of mafhūm al-ṣifah, a qualifying attribute, in the usūlīs' own reckoning. He lists them separately only to round out the benefit. Four more are named further down.
Example of lughah, the plain sense of a word: "khamr is forbidden because it intoxicates." The implication is that a drink which does not intoxicate is not ruled khamr. Examples of ḥaṣr, exclusivity: "ribā is only in deferred exchange", and "shufʿa applies only to what has not been divided."
Example of ṣifah, a qualifying attribute: "zakāt is due on free-grazing sheep." The words "free-grazing" are doing the work. The implication is that sheep you feed in a pen carry no zakāt, because the ruling was tied to the attribute of grazing. Now compare this with the laqab example below. The two look almost the same on the page, and telling them apart is the whole point.
Four more named kinds, with real examples. Mafhūm al-sharṭ, tied to a stated condition: "if they are pregnant, spend on them" implies no such duty if she is not pregnant. Mafhūm al-ghāya, tied to an end point, an "until" or ḥattā: the ʿidda verse and the fasting verse. Mafhūm al-ʿadad, tied to a set number: "eighty lashes" means exactly that, no more and no less. And mafhūm al-laqab, tied to a bare noun with no attribute attached: "on sheep there is zakāt." Laqab is the weakest kind, and the most disputed even among those who accept mafhūm al-mukhālafa in general. Set it beside the ṣifah example above and the difference shows: "on FREE-GRAZING sheep there is zakāt" hangs the ruling on an attribute, while "on SHEEP there is zakāt" hangs it on a bare noun with nothing attached.
Now the real split between the schools. The Shāfiʿīs and most of the theologians hold that mafhūm al-mukhālafa counts as a valid proof, ḥujja, in every kind except laqab. The Ḥanafīs, like the Ẓāhirīs, do not take it into account at all in the speech of the Lawgiver. Their reasoning is that the purposes of the Sharīʿa cannot be fully encompassed, unlike the purposes of a human speaker. But here is the part to hold onto: the Ḥanafīs DO take it into account inside the jurists' own technical statements, in every kind, laqab included. An example: "Jumuʿa prayer is upon free men" implies it is not obligatory on women or on slaves. So the same reasoning is refused in one place and used in another, and that is on purpose.
Two Ḥanafī proofs for rejecting it in revelation. First, Allah names four sacred months. That does not imply oppression is allowed in the other eight. Oppression is forbidden always. Second, if mafhūm al-mukhālafa really were reliable, Allah would not have needed to state the opposite ruling outright. Yet He does, both in the verse on menstruation and in the verse on step-daughters.
Sitting in the right class of book is not the last word. Taṣḥīḥ means a scholar declaring a view to be the sound one. Where scholars have declared sound a report from outside the six ẓāhir al-riwāya books, that report is followed instead. For the tier itself and the six books, see Masāʾil al-Uṣūl in the next branch.