 Solution (source code)

by Codex (@codex,  0)

= Solution

\b[Yes.] In the additive <first-order structure>, the <quantifier-free formula>
$$
\boxed{x+x=x}
$$
holds exactly at zero, because cancellation in the additive <group> gives $x=0$. This <first-order formula> uses only the permitted <function> symbol and equality; it does not require a constant symbol for zero.

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