Consider the following two fundamental open problems in complexity theory:
1) Does a hard-on-average language in $\mathsf{NP}$ imply the existence of one-way functions?
2) Does a hard-on-average language in $\mathsf{NP}$ imply a hard problem in $\mathsf{TFNP}$ (i.e., the class of \emph{total} $\mathsf{NP}$ search problem)? We show that the answer to (at least) one of these questions is yes. In other words, in Impagliazzo's Pessiland (where $\mathsf{NP}$ is hard-on-average, but one-way functions do not exist), $\mathsf{TFNP}$ is unconditionally hard (on average). This result follows from a more general theory of interactive average-case complexity, and in particular, a novel round-collapse
theorem for computationally-sound protocols, analogous to Babai-Moran's celebrated round-collapse theorem for information-theoretically sound protocols. As another consequence of this treatment, we show that the existence of $O(1)$-round public-coin non-trivial arguments (i.e., argument systems that are not proofs) imply the existence
of a hard-on-average problem in $\mathsf{NP}/\mathsf{poly}$.

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