# How to formally prove that random guess is the best attack

How to formally argue that there exists no efficient $$A$$ who can come up with a $$e$$ such that \begin{align}x&=PRF(e,0) \land \\ y &= PRF(e,1) \land \\ x &= H(y)\end{align} where $$H$$ is a secure hash function and $$|x|=|y|=\ell$$?

Note that it's easy to argue that if $$A$$ just guesses randomly, the success probability for each guess is negligible (something like $$\frac{1}{2^{\ell}}$$). But how to argue there is no better algorithm than guessing?