I'm surprised no one has mentioned disambiguate in this context. It sounds horrible and outlandish on first hearing, has a reasonably transparent meaning (which may shed some light on the semantics of dis-), and seems to be used almost exclusively by linguists.

If you disprove something, you haven't necessarily proved the opposite. If you disprove something, you have indeed proved its negation. If you disapprove of an action, you do indeed approve of not doing that action (so, disapproving X is approving not-X).

(That is, when you disprefer that George be elected, you prefer the negation, that George not be elected, rather than just you do not prefer that George be elected, which is compatible with indifference.)

"Disprove" is fairly negative. "Prove" -> establish as true; "disprove" -> establish as false. I'd say "disprove" is like "disagree".

To me, dis- negates in words like disagree, and displease. If you disagree with a position, that (generally) implies that you agree with the opposite position. If you displease someone, you make them angry or unhappy, you don't leave them feeling neutral.

On the other hand, I feel that dis- neutralises in words like disprove, disapprove, disenchant, disentangle, disembark, discharge, and so on. If you disprove something, you haven't necessarily proved the opposite. If you disapprove of an action, that doesn't mean you would approve of the opposite action. If you're disenchanted, it doesn't necessarily mean you now hate what you were formerly enchanted with. And clearly once you disentangle something it's back to zero; you haven't "anti-tangled" it.

And the exact meaning of "dis-" varies from word to word, but it always includes reversing the polarity of some semantic component (rather than just neutralizing it). Connect X to Y = position X such that it is joined to Y Disconnect X from Y = position X such that it is separated from Y Approve X = assert that X is good Disapprove X = assert that X is bad Prefer X = when selecting from a set choices, choice X first Disprefer X = when selecting from a set of choices, chose X last

The ones which are close to the meaning of 'not X' are so only because the phenomena of often (though not always) viewed as binary. But, as the remain forms clearly indicate, this doesn't come automatically from the meaning of the prefix.

Bakan Muş, bakanlık konferans salonunda Türkiye İhracatçılar Meclisi (TİM) ile düzenlediği basın toplantısında ağustos ayı dış ticaret rakamlarını açıkladı. İhracatta 2021 yılı boyunca ortaya konulan güçlü performansın ağustos ayında da devam ettiğine işaret eden Muş, "İhracatımız geçtiğimiz yılın ağustos ayına göre yaklaşık yüzde 52'lik artışla 18,9 milyar dolar seviyesinde gerçekleşmiştir. Memnuniyetle ifade etmek isterim ki bu rakam ile en yüksek ağustos ayı ihracat rakamına ulaşmış bulunuyoruz. Ayrıca, son 12 aylık ihracat değerimiz de 207,5 milyar dolar ile yeni bir cumhuriyet rekoru kırmayı başarmıştır" diye konuştu. Muş, yıl sonunda ihracatın 210 milyar dolara ulaşacağına olan inancının tam olduğuna dikkati çekerek, şunları kaydetti:

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MacGregor’s team took a second look at these data. And it found that all the excess light came from a two-minute period on March 24. A massive flare explains all the extra light, MacGregor now says.