The body, as an object that takes up space, can always be divided (at least conceptually)
We need to consider what this means in practise and not just as words:
Extension is a specific property of matter: I can pick up a piece of bamboo that has a certain length (or extension); and then I can break it into two pieces, one piece which I let drop to the ground and the other i take with me.
And what I can do with bamboo, I can do with rocks, with houses, planets and galaxies.
Or I can do it to the body of a dead man - a cadaver or corpse; or to a Barbary duck hunted in the long grass on some autumnal day creased with clouds.
Or to a molecule, and then the atom, and then a proton and then till we reach a true simple atom, and in itself nothing composite being pure and simple extension.
But then time - is time extension? In one way, yes: each day is divided from from another by the night, and every hour into minutes; and in another way, no: for I cannot break a day in half, except by metaphor - I cannot even hold it; what I see by outer sense is motion, is change - energia - and time is measured by motion, and by motion that moves in regular cycles - the pendulum.
And also space; for space surely has extension but unlike a piece of bamboo cannot be broken; though one can and does mark off one part of space from another - and thus the invention of territory and territorialisation - except of course this is not space itself; but what is in space: ground, earth and air; like time it seems too, we cannot grasp it; but that it is but a stage, in the sense of ground.
And in this sense, too - time; but notably Descarte took time to be an inner sense (and then Kant took space too to be an inner sense).
Now we note, that marking is prior to breaking; for to break a piece of bamboo I must break it at a specific place, though I may care not at which place I break it.
And this is true for atoms - in their true sense; for an atom as a pure extensionless point is arguably nothing; and merely marks a position and a point in space; whereas as a string - it has parts; so that it can curve, twist or close up into a loop; but merely to have extension in one direction and not another is to replay this first error; and therefore and thus branes.
Decartes argues that the mind is indivisible because it lacks extension ... the mind is simple and non-spatial
But all these simplest attributes of extension, can I do this with a mind? Is it even conceptually possible to concieve this?
Two different computers - not just in location but also in terms of hardware can run the same program; but then again the same thought can be expressed in writing and written in two different scripts in two different languages, as in:
cogito, ergo sum
I think, therefore I am
and written in many books, or as graffiti on some walls.
But we do not think of this as thought itself being split.
Perhaps, genetically identical twins are splittings of the same person? But no, they are from conception two different persons sharing exactly the same genetic material; their consciousness of being here, is seperate in each - and was never unitary as in a single consciousness or mind.
Thus your A does not hold: a thought expressed is not the thought itself; and merely places or translates the thought from the world of thought into the world of matter - and matter is essentially described by extension, and one of the properties of extension is that it can be split - so being able to split such a translated thought doesn't demonstrate the splitting of thought, but the splitting of extension.
Thus also your B does not hold; for no mind has been demonstrated in a computer; but simply that the expression of thinking can be automated; and this automation - this motion of matter - or extension in motion - is in essence no different from a thought expressed in writing in a book; and we do not think a book thinks, or that it has mind; even though we might ourselves think new things or recollect old feelings when our mind passes
Since the mind and body have different attributes, they must not be the same thing ...
Liebniz principle of indiscernability says if two things have exactly the same properties, then the two things are indiscernible (but not neccesarily the same); here we have two things which differ in some essential properties (and not accidental ones).
Therefore they cannot be indiscernible, but discernable; and generally we do exactly that - almost all thought has distinguished the animate from the inanimate .
... their "unity" notwithstanding.
Spinoza, have a conception of Unity, still did not take the world of thought and extension to be the same, but differing modes of something other.
And adopting too a principle of plenitude, argued where there is two which cannot be reduced to one; there must be more and in fact, an infinite number not discernible to us - ever and in principle.