If you're planning on using the list environment to create a list-like structure, you need to be familiar with its syntax. From source2e (section 54 List, and related environments, p 269):
The generic commands for creating an indented environment – enumerate,
itemize, quote, etc – are:
\list{<LABEL>}{<COMMANDS>} ... \endlist
which can be invoked by the user as the list environment. The LABEL argument specifies item labeling. COMMANDS contains commands for changing the
horizontal and vertical spacing parameters.
Each item of the environment is begun by the command \item[ITEMLABEL]
which produces an item labeled by ITEMLABEL. If the argument is missing, then
the LABEL argument of the \list command is used as the item label.
The label is formed by putting \makelabel{<ITEMLABEL>} in an hbox whose
width is either its natural width or else \labelwidth, whichever is larger. The \list command defines \makelabel to have the default definition:
\makelabel{<ARG>} == BEGIN \hfil ARG END
which, for a label of width less than \labelwidth, puts the label flushright, \labelsep to the left of the item’s text. However, \makelabel can be \let to another command by the \list's COMMANDS argument.
A \usecounter{<foo>} command in the second argument causes the counter
foo to be initialized to zero, and stepped by every \item command without an
argument. (\label commands within the list refer to this counter.)
It's important to note the last paragraph, where a \usecounter{<counter>} identifies the counter to be used with the list. You haven't defined a counter, although you do say it should be list.
Instead, let's define the counter to be mylistcntr and add \usecounter{mylistcntr} to the second argument for list:
\documentclass{report}
\newcounter{mylistcntr}
\begin{document}
We number the properties by a double numbering technique,
such that it is easy to refer to them.
\begin{enumerate}
\item
The observed properties hold for all $S$--boxes.
We analyze if the output of an $S$--box can or cannot change
if one modifies the inputs of an $S$--box in the following way:
\begin{list}{(\alph{mylistcntr})}{\usecounter{mylistcntr}\itemsep 0mm}
\item fix the inputs $e$ and $f$E
\item one is allowed to change $c$ and $d$ to an arbitrary value $c'$ and $d'$
\item one changes the inputs $a$ and $b$ as described in the properties
\end{list}
\begin{description}
\item[1.1.]
$\neg (\forall c,d,c',d',e,f : S_i(0,0,c,d,e,f) \neq S_i(1,0,c',d',e,f) )$
\item[1.2.]
$\neg (\forall c,d,c',d',e,f : S_i(0,1,c,d,e,f) \neq S_i(1,1,c',d',e,f) )$
\item[1.3.]
$\forall c,d,c',d',e,f : S_i(0,1,c,d,e,f) \neq S_i(1,0,c',d',e,f)$
\item[1.4.]
$\forall c,d,c',d',e,f : S_i(0,0,c,d,e,f) \neq S_i(1,1,c',d',e,f)$
\end{description}
\end{enumerate}
\end{document}
For a left-aligned enumeration (a), (b), ... you can use
\begin{list}
{(\alph{mylistcntr})}
{\usecounter{mylistcntr}%
\def\makelabel#1{\rlap{#1}\hss}% Left-aligned label
\itemsep 0mm}
You'll also note the following changes (some cosmetic, others not):
\not= is similar to \neq (fewer keystrokes).S_{i} is similar to S_i (fewer keystrokes)description is already defines as a list environment, and therefore doesn't take any additional arguments.
{1.4}on entering the environment supposed to be there for? – Bernard May 04 '17 at 23:33latex-2.09when it clearly isn't? – cfr May 04 '17 at 23:33listdirectly in a document. What are you trying to do exactly? What is\alph{list}supposed to do? – cfr May 04 '17 at 23:36