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Time streams. You go back in time and kill your grandfather and all you've done is create a reality where your grandfather was killed. You still exist because you're in the stream where your grandfather wasn't killed. The thing is, unless your magic time machine can move to different streams, you're stuck in your new stream where you don't exist and you exist as a paradox. Your living grandfather exists in another stream altogether, so in the reality you're stuck in, you have no grandfather and thus lineage.
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