egreg is correct regarding the solution, but the diagnosis is wrong. The problem is not that the tree has no root. It has a perfectly good root. Moreover, it does not superimpose nodes if compiled with an appropriate engine (e.g. pdfTeX).
\documentclass[border=10pt]{standalone}
\usepackage{prooftrees}
\begin{document}
\begin{prooftree}
{
to prove={ A \lor B \lor C \lor D \lor E }
}
[ A ]
[ B ]
[ C ]
\end{prooftree}
\end{document}
produces

Now, admittedly, this probably is not what you meant or want, but it is reasonably sensible output, given the input.
Suppose we instead try
\begin{forest}
[ A ]
[ B ]
[ C ]
\end{forest}
which produces

This is because Forest takes [ A ]
to be the root and, hence, the entire tree. Everything after the tree specification is passed to TikZ, but there are no relevant commands here, so [ B ]
and [ C ]
are parsed as text. Since we are inside a tikzpicture
environment, we are using the null
font and the text is ignored. Hence, we effectively have
\begin{forest}
[ A ]
\end{forest}
The reason that the prooftree
environment behaves differently is because the tree specified by the user is actually a sub-tree of the tree the environment typesets. prooftree
embeds the user's tree specification in a larger tree which includes the line numbers, justifications and 'to prove' line, as appropriate. Hence, the inner forest
environment reads
[ A ]
[ B ]
[ C ]
as part of the tree specification, so these end up being nodes in the tikzpicture
and get typeset in the normal font, which is switched back by TikZ for node text.
The user provided root in a prooftree
is 'never' the root of the typeset tree. I'm not sure it is possible to make a prooftree
attempt to set a rootless tree and, although I would not wish to rule this possibility out, I can say that it is most unlikely that anybody would do so by accident.
[ A [ B [ C ] ] ]
seems more reasonable input