Form normal of Skolem

A logical Formule of first order is in the form normal of Skolem if its normal form prénexe contains only universal quantifiers. Any formula of first order can be converted into normal form of Skolem, while keeping its satisfiability, via the process of Skolémisation. The formula resulting from this process is not forcing equivalent to the formula of origin.

For example, the formula $\backslash \; forall\; X\; \backslash \; exists\; \backslash \; forall\; Z\; P\; (X,\; there,\; Z)$ is not there in the form normal of Skolem because it contains an existential quantifier. The skolemisation replaces $y$ by $f\; (X)$, where $f$ is a new function and removes the quantifier $\backslash \; exists\; y$. The resulting formula is $\backslash \; forall\; X\; \backslash \; forall\; Z\; P\; (X,\; F\; (X),\; Z)$.

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