  We investigate quantifier-free induction for Lisp-like lists constructed
inductively from the empty list $\mathit{nil}$ and the operation
$\mathit{cons}$, that adds an element to the front of a list. First we show
that, for $m \geq 1$, quantifier-free $m$-step induction does not simulate
quantifier-free $(m + 1)$-step induction. Secondly, we show that for all $m
\geq 1$, quantifier-free $m$-step induction does not prove the right
cancellation property of the concatenation operation on lists defined by
left-recursion.
