Let C_{n} denote the n-dimensional unit cube, consisting of the 2^{n} points
\left\{\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mid x_{i} \in\{0,1\} \text { for all } 1 \leq i \leq n\right\}
A tetrahedron is equilateral if all six side lengths are equal. Find the smallest positive integer n for which there are four distinct points in C_{n} that form a non-equilateral tetrahedron with integer side lengths.