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Is FindInstance guaranteed to find an instance if one exists? Conversely, if it does not find an instance, does that mean an instance does not exist at all? Finally, is there a way to change the Method Automatic option and if so what are the alternatives?

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    $\begingroup$ I do not know the exact internals but: Quite certainly, more than one single algorithm is used and there are no guarantees that an instance can be found even if there exists one. $\endgroup$ Jan 22, 2018 at 21:57

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