Is the following proposition correct?

$X_1, X_2, X_3$ are uniformly at random sampled from a finite set $\mathcal X$ without replacement. $f : \mathcal X^2 \rightarrow \mathbb R_{\ge0}$ is symmetric: $ f(x, y) = f(y, x) $, then:

$$ \mathbb E_{X_1, X_2, X_3} f^\frac{1}{2}(X_1, X_2) f^\frac{1}{2}(X_1, X_3) f^\frac{1}{2}(X_2, X_3) \le ( \mathbb E_{X_1, X_2} f(X_1, X_2) )^\frac{3}{2} $$

I tried to use Hoeffding's result $$ \mathbb E f\left( \sum_{i = 1}^n X_i \right) \le \mathbb E f\left( \sum_{i = 1}^n Y_i \right) $$ ($X_i$ are uniformly at random sampled without replacement, $Y_i$ are uniformly at random sampled with replacement, $f$ is convex and continuous) by combining two elements from set $\mathcal X$ to form a new set: $\{ ( X_i, X_j ) : i \ne j, X_i, X_j \in \mathcal X \}$. However, the sampling process for new set is no longer uniformly at random so I cannot use Hoeffding's result.