 Solution

For a node tuple $u$, write $c(u)$ for its identifier. A predicate that is true exactly when identifiers repeat isThe 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 $\forall u,v\in T,c(u)=c(v)\Rightarrow u=v$.