Formulating a constraint to exclude a single point from the feasible region of an IP?
You need to add an integer cut of the form:
$$
 \sum_i |x_i - y_i| \ge 1
$$
where $y_i$ is your point your want to exclude.

We can rewrite this as:
$$
  \begin{align}
     &amp;\sum_i z_i \ge 1 \\
      &amp;z_i \le |x_i - y_i|
  \end{align}
$$
The last inequality is identical to $z_i \le \max\{x_i-y_i, -(x_i-y_i)\}$. This again can be implemented using additional binary variables:
$$
 \begin{align}
    &amp;z_i\le x_i-y_i+M_i\delta_i \\
    &amp;z_i\le -(x_i-y_i)+M_i(1-\delta_i) \\
    &amp;\delta_i \in \{0,1\} \\
    &amp;M_i = U_i - L_i = 200
 \end{align}
$$
There are two special cases we can handle more efficiently. If $y_i=L_i=-100$ then we can write $z_i = x_i - y_i$. If $y_i=U_i=100$ then we can write $z_i=-(x_i-y_i)$.