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  "body": "\n## Summary\n\nA sentence is in Skolem normal form when it is in [[prenex normal form|CS82V969DE]] and has only universal quantifiers.\nEvery first-order sentence can be turned into one in Skolem normal form by replacing each existential quantifier with a new function symbol.\nThe new sentence is not equivalent to the old one, but it is satisfiable exactly when the old one is.\nThis makes Skolem normal form the starting point of [[Herbrand's theorem|VZ21F10WRS]] and of resolution theorem proving.\n\n## Explanations\n\n### L1 human\n\nThe sentence \"for every $x$ there is a $y$ with $R(x, y)$\" says that a suitable $y$ exists for each $x$.\nChoose such a $y$ for each $x$ and call it $f(x)$.\nThen the sentence becomes \"for every $x$, $R(x, f(x))$\", which has no \"there exists\".\nThe function $f$ is called a Skolem function.\n",
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