  The goal of this paper is to provide a short proof of the discontinuity of
phase transition for the random-cluster model on the square lattice with
parameter $q>4$. This result was recently shown via the so-called Bethe ansatz
for the six-vertex model. Our proof also exploits the connection to the
six-vertex model, but does not rely on the Bethe ansatz. Our argument is soft
and only uses very basic properties of the random-cluster model (for example,
we do not need the Russo--Seymour--Welsh theory).
