\usepackage{stmaryrd}
\usepackage{slashed}
\begin{document}
-\def\iwjtest{{/\mkern-9mu\Sqsupset}}
-\newcommand{\iwjtestx}{\mathrel{\ooalign{$\Sqsubset$ $\sslash$}}}
-\newcommand{\iwjtesty}{{%
+\newcommand{\nothaspatch}{{%
+ \declareslashed{}{\sslash}{-0.04}{0}{\Sqsupset}\slashed{\Sqsupset}}}
+\newcommand{\notinpatch}{{%
\declareslashed{}{\sslash}{-0.04}{0}{\Sqsubset}\slashed{\Sqsubset}}}
+\newcommand{\haspatch}{\Sqsupset}
+\newcommand{\inpatch}{\Sqsubset}
sponge
$ A \sqsubseteq B $
$ A \not \sqsubseteq B $
$ A \nsqsubseteq B $
$ A \Sqsubset B $
$ A \Sqsupset B $
-$ \sslash $
-$ \iwjtest $
-$ \iwjtestx $
-$ \iwjtesty $
-$ A \iwjtesty B $
+$ A \haspatch B $
+$ A \nothaspatch B $
+$ A \inpatch B $
+$ A \notinpatch B $
\end{document}