As I discuss in this question, by far the most popular school of Hindu philosophy is the Vedanta school, which bases its tenets on the doctrines laid out in the Brahma Sutras, a work by the sage Vyasa that summarizes and systematizes the philosophical teachings of the Upanishads. You can read the Brahma Sutras here. In any case, in Adhyaya 3 Pada 3 of the Brahma Sutras, Vyasa says this:
- eka ātmanaḥ śarīre bhāvāt
Some deny the existence of the soul, its existence being dependent on the existence of the body.
- vyatirekastadbhāvabhāvitvānna tūpalabdhivat
But this is not so; there is a distinction (between the soul and the body) because consciousness may not exist even when the body exists, as it is in the case of perception.
This translation is written from the viewpoint of the Advaita philosopher Adi Shankaracharya, who believed that Sutra 53 is presenting the view of the Charvaka school that the soul is the same as the body, and that Sutra 54 is presenting a logical argument that there exists a soul which is different from the body.
But most commentators on the Brahma Sutras do not think that these Sutras have anything to do with the soul being different from the body. For instance Ramanujacharya thinks that these Sutras are about the fact that during meditation, one must conceive of one's own soul in its released state, not its state while inhabiting a body; see this section of Ramanujacharya's Sri Bhashya. And Nimbarka and Srikantha Sivacharya agree with him, as you can see here and here.
So my question is, how do Vedantic philosophies other than Advaita, like Dvaita, Visistadvaita, Achintya Bhedabheda, etc. prove that there exists a soul different from the body? I'm particularly interested in whether they think Anumana or inference is sufficient to prove it, or whether Sabda Pramana or scriptural testimony is required. Most of the Astika schools other than the Vedanta school believe it can be proven through Anumana as I discuss here. Now as I discuss in this answer, the Vedanta school believes that the existence of Brahman cannot be proven through Anumana, but only through Sabda Pramana. But it may be that the existence of the Jivatma requires different means of proof than the existence of Brahman.