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Is there any track for proving $D=NP$, besides showing that $D$ has polynomial-bounded universal quantifiers?
Background
By the MRDP theorem, every for every recursively enumerable set $S$, there exists a Diophantine polynomial $p$ such that
$$x \in S \iff \exists y_1, \dots, y_n \in \mathbb{N} \text{ such ...
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