I fail to see how this pertains to Hindu Dharma or any of the Dharmic traditions for that matter.
First and foremost, "religion", as understood today, is not what Dharma is. This has been repeated ad nauseum on this forum and elsewhere. Hinduism, as a 'religion' is concerned more with experience rather than things like testimony, belief, and history (of its principal figures).
Thus, applying Abrahamic paradigms to Dharma not only convolutes the essence of the latter, but also confuses those who are either new to it or are not familiar with the underpinnings of its philosophy.
Hindus are not and should not be concerned with "explaining" themselves and their 'beliefs' to others. It not only detracts from one's sadhana (spiritual practice), it actually positively hinders it (as a distraction). That is why Hindu Dharma is a journey for the individual. It is not a 'one-size fits all' path and never was. Those who come from (or still remain) in ideologies that cater to egotistic fantasies (aka Abrahamic nonsense), will neither understand nor appreciate the profundity of the Dharmic approach.
Ergo, if someone is trying to "disprove" your beliefs, the best manner to counter them is to ignore them in totality.
I would also comment that a syllogistic approach to these issues is futile as that is a very weak form of 'logic'. Nyaya and other Hindu theories of logic take many more pointers into consideration before arriving at any given conclusion.
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