It is established by reason. Its formulation is as follows: The assumed partner of the Creator is either or two gods, or one god, or something other than God. This is not hidden from the intelligent. If it is something other, then otherness is of two types: Independent otherness, which is represented by the self-sufficient. The one who is not in need of others. Whose existence is valid with the absence of others. And dependent otherness. Which is represented by the one who is in need of others. Dependent on the existence of others. Like the attribute with the substance. And like our existence with the Creator. And with this concept of otherness. Multiplicity is necessitated. And if multiplicity is necessitated, the matter cannot be devoid of three cases: either The multiples are all independent, or all dependent. Or one of them is independent and the other is dependent. If they are both dependent, they are created and in need of others. So they cannot be gods. And if one of them is independent and the other is dependent. The creation of the dependent is known. And the divinity of the independent is established. If they are both independent in the sense of independence previously mentioned, then they cannot be devoid of either being homogeneous or heterogeneous. If they are homogeneous, they must be created. For homogeneity and similarity are attributes of creation. And they are impossible for the eternal. If they are heterogeneous, they cannot be devoid of either being contiguous or distinct. Contiguity and distinction are from the signs of creation. As their contiguity is not more preferential than their distinction, nor their distinction, more preferential than their contiguity, except by a determiner. Then this determiner cannot be devoid of either being with it, or not. If it is with it, then the same argument that was made in the first case applies, and it leads to an infinite regress. And what regresses is not established.

The formulation of this proof can be considered an innovation by Al-Mahdi, even if some of the premises mentioned in it were used by others. In this formulation, the precision of the construction and the sequence are evident. Except for the last link, which is represented by the case where the determiner is not with anything else. Its owners have fallen. But the discussion of the determiner is fundamentally not part of the original proof, but rather an additional verification. Therefore, the fall of this link does not detract from the proof.

See: Ibn Tumart, Risala fi Anna al-Shari'a la tuthbat bil-'aql (Treatise on the fact that Sharia is not established by reason), pp. 171-172. 210