Integer linear programming formulation of formula in DNF

Question

I have multiple sets, e.g.,

$$\{1, 2\}, \{2, 3, 4\}, \{1, 4\}$$

Each variable $1, 2, 3, 4$ is binary. I need to represent the following condition without additional variables

$$(1 \land 2) \lor (2 \land 3 \land 4) \lor (1 \land 4)$$

Basically, I need to enforce that either $1$ and $2$ are 1s, or $2$ and $3$ and $4$ are ones, or $1$ and $4$ are 1s, but not all of them. Constants can be added as needed, as well as equalities, inequalities, etc. How can I do that?