6. Let $S_{1}, S_{2}, S_{3}$ be infinite subsets of the set of integers $\mathbf{Z}$, and satisfy:
(1) For any permutation $i, j, k$ of $1, 2, 3$, if $x \in S_{i}, y \in S_{j}$, then $x-y \in S_{k}$;
(2) There exist $1 \leqslant i<j \leqslant 3$ such that $S_{i} \cap S_{j}=\varnothing$.
Then, the number of such triplets of sets $\left(S_{1}, S_{2}, S_{3}\right)$ is ( ).
(A) 1
(B) 3
(C) 6
(D) Greater than 6
6.D.

For any positive integer $k$, take
$$
\begin{array}{l}
S_{1}=S_{2}=\{x \mid x \equiv k(\bmod 2 k)\}, \\
S_{3}=\{x \mid x \equiv 0(\bmod 2 k)\} .
\end{array}
$$