\usepackage{MnSymbol}
\usepackage{stmaryrd}
\usepackage{slashed}
+\usepackage{txfonts}
\begin{document}
\newcommand{\nothaspatch}{{%
\declareslashed{}{\sslash}{-0.04}{0}{\Sqsupset}\slashed{\Sqsupset}}}
\declareslashed{}{\sslash}{-0.04}{0}{\Sqsubset}\slashed{\Sqsubset}}}
\newcommand{\haspatch}{\Sqsupset}
\newcommand{\inpatch}{\Sqsubset}
+
+\newcommand{\pa}[1]{\varmathbb #1}
+\newcommand{\pay}[1]{\pa{#1}^+}
+\newcommand{\pan}[1]{\pa{#1}^-}
+
+\newcommand{\p}{\pa{P}}
+\newcommand{\py}{\pay{P}}
+\newcommand{\pn}{\pan{P}}
+
sponge
$ A \sqsubseteq B $
$ A \not \sqsubseteq B $
$ A \nothaspatch B $
$ A \inpatch B $
$ A \notinpatch B $
+$ A \nothaspatch \pa{C} $
+$ A \nothaspatch \py $
+$ A \nothaspatch \p_C^+ $
+$ A \nothaspatch \pan{C} $
\end{document}