  We prove, under a computational complexity hypothesis, that it is consistent
with the true universal theory of p-time algorithms that a specific p-time
function extending $n$ bits to $m \geq n^2$ bits violates the dual weak
pigeonhole principle: every string $y$ of length $m$ equals the value of the
function for some $x$ of length $n$. The function is the truth-table function
assigning to a circuit the table of the function it computes and the hypothesis
is that every language in P has circuits of a fixed polynomial size $n^d$.
