Arrow's impossibility theorem
Let the set of alternatives be $A = \left\{a_1,a_2,...,a_k\right\}$. Let the number of players be $n$. Let the set of preference orderings over $A$ be $\mathcal{P}$. Then the set of preference profiles is the Cartesian product 
$$
\mathcal{P}^n = \times_{i=1}^{n} \mathcal{P}.
$$
Let us denote the preference ordering
$$
a_1 \succ a_2 \succ ... \succ a_k 
$$
by $p^*$. Define the Social Choice Function $F$ by
$$
\forall p \in \mathcal{P}^n: F(p) = p^*.
$$
This SCF $F$ clearly has universal domain, is not a dictatorship, and is also independent of irrelevant alternatives. (Or any alternatives for that matter.)