The Freiling theorem states:
Let $S = \{f: [0,1]\rightarrow A$ : $A$ is a countable subset of $[0,1]\}$ . Consider the following statement:
For each $f$ in $S$, there exist $x$ and $y$ in $[0,1]$ such that $x$ is not in $f(y)$ and $y$ is not in $f(x)$.
I would like to know if it is possible to give a proof of the falsity of the CH (Continuum Hypothesis) using the Freiling theorem of Symmetry?