set $A$, a collection $B$ of pairs from $A$, and a collection $C$ of pairwise-disjoint triples of distinct elements in $A$.\
[**Question.**]{} Does there exist a total linear ordering on the elements in $A$ such that $a_i<a_j$ for each $(a_i,a_j)$ in $B$, and $a_i<a_j<a_k$ or $a_j<a_k<a_i$ for each $(a_i,a_j,a_k)$ in $C$?

[**Example.**]{} Consider the following instance of [Intermezzo]{} with three pairs and two disjoint triples (when viewed as sets): $$\begin{aligned}
A &= \{a_1,\, a_2,\, a_3,\, a_4,\, a_5, a_6\}, \\
B &= \{(a_1,\, a_6),\, (a_4,\, a_1),\, (a_4,\, a_3)\}, \\
C &= \{(a_1,\,a_2,\,a_3),\,(a_4,\,a_5,\,a_6)\}.\end{aligned}$$ A total linear ordering on the elements in $A$ that satisfies all constraints defined by $B$ and $C$ is $$\mathcal{O} = (a_2,\, a_4,\, a_3,\, a_1,\, a_5,\, a_6).$$

While each element $a_i\in A$ can appear an unbounded number of times in the input of a given [Intermezzo]{} instance, this number is bounded from above by $N$ in the following [Intermezzo]{} variant.

[$N$-Disjoint-Intermezzo]{}\
[**Instance.**]{} A finite set $A$, collections $B_1,B_2,\ldots,B_N$ of pairs from $A$, and collections $C_1,C_2,\ldots,C_N$ of triples of distinct elements in $A$ such that, for each $\ell \in\{1,2,\ldots,N\}$, the elements in $B_\ell\cup C_\ell$ are pairwise disjoint.\
[**Question.**]{} Does there exist a total linear ordering on the elements in $A$ 