  We discuss the argument proposed in Ref.~\cite{Frauchiger-Renner}, and show
that it does not particularly illustrate any inconsistency in quantum
mechanics, but rather the well known difficulty often described as the
\textquotedblleft shifty split\textquotedblright: the exact point at which the
von Neumann reduction postulate should be applied is ill defined. This is the
origin of the famous Schr\"{o}dinger's cat or Wigner's friend paradoxes.
  We investigate the argument of Ref.~\cite{Frauchiger-Renner} and show that it
combines statements obtained by different agents assuming very different
positions of the shifty split, and therefore applying the reduction postulate
in different ways. This results in the introduction of several different state
vectors, while such descriptions are considered as incompatible in standard
quantum mechanics. To our knowledge, no interpretation of quantum mechanics
includes this possibility; the argument thus refers to a new form of quantum
mechanics that should be specified more precisely.
