When it comes to getting stuck lids off of jars, I have gotten tons of mileage out of the idea that the vacuum seal is actually what's keeping the lid of e.g. a pickle jar stuck, rather than just tightness. If you take the tip of a butter knife, or the sharp end of a bottle opener and slip it under the lip of the lid and pry carefully until you hear the "pop" of breaking the air seal, the jar should be way easier to open.
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