A function $f:\mathbb R\to\mathbb R$ is called *Świątkowski* if for any connected subset $C\subset \mathbb R$ and points $a,b\in C$ with $f(a)<f(b)$ there exists a continuity point $x\in C\setminus\{a,b\}$ of the function $f$ such that $f(a)<f(x)<f(b)$.

Problem.Is each Świątkowski function $f:\mathbb R\to\mathbb R$ with closed graph continuous?

(The problem was written 01.05.2018 by Julia Wódka from Lódz on page 108 of Volume 1 of the Lviv Scottish Book).