Multiple times I've read dialogs like this example:
— This conjecture hasn't been proved.
— Yes it has been proved in 2003.
This seems odd to me: the answerer first says "yes", but proceeds to contradict his own beginning. I'd suppose the answer should rather have been something like "No, it has been proved in 2003.", meaning "You're wrong, it has been proved in 2003."
Is it actually normal usage of "yes" in English?
Answer
According to On the syntax of yes and no in English (alt link: download PDF), English uses the polarity-based system, in contrast to languages like Japanese that use the truth-based system. (This is exactly what Janus Bahs Jacquet alludes to in their comment.)
The reply, in your case, does not get its polarity from the original statement. Instead, its polarity comes from the word "yes", (so it's not wrong to say it that way).
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