= Solution
For a node tuple $u$, write $c(u)$ for its identifier. A <predicate> that is true exactly when identifiers repeat is
$$
\boxed{\exists u,v\in T.\quad u\ne v\ \land\ c(u)=c(v).}
$$
The inequality excludes choosing the same tuple twice. The <set> $T$ cannot contain two copies of an identical quadruple, but it can contain distinct quadruples with equal first component and different information or successors. The negation is the usual identifier-uniqueness <representation invariant>, namely $\forall u,v\in T,\ c(u)=c(v)\Rightarrow u=v$.
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