3-DIMENSIONAL MATCHING: given three finite sets $S_1,S_2,S_3$ and a
ternary relation $R$ on those sets, is there a subrelation $S$ of $R$ such that
each element of $S_1,S_2,S_3$ occurs exactly once in $S$?
More formally, this problem can be defined as the following set:
$\{ \langle S_1,S_2,S_3,R\rangle \mid S_1,S_2,S_3\text{ finite sets}\;\wedge\;|S_1|=|S_2|=|S_3|\;\wedge\;R\subseteq (S_1\times S_2\times S_3)\;\wedge\;\exists S\subseteq R: (\forall i\in\{1,2,3\}: \forall e\in S_i: \exists!\langle e_1,e_2,e_3\rangle\in S: e_i=e) \}$