  We show that there is a constant $k$ such that Buss's intuitionistic theory
$\mathsf{IS}^1_2$ does not prove that SAT requires co-nondeterministic circuits
of size at least $n^k$. To our knowledge, this is the first unconditional
unprovability result in bounded arithmetic in the context of worst-case
fixed-polynomial size circuit lower bounds. We complement this result by
showing that the upper bound $\mathsf{NP} \subseteq \mathsf{coNSIZE}[n^k]$ is
unprovable in $\mathsf{IS}^1_2$.
