\documentclass[a4paper]{article}
\usepackage{MnSymbol}
\usepackage{stmaryrd}
\usepackage{slashed}
\usepackage{txfonts}
\usepackage{accents}

\renewcommand{\ge}{\geqslant}
\renewcommand{\le}{\leqslant}

\newcommand{\has}{\sqsupseteq}
\newcommand{\isin}{\sqsubseteq}

\newcommand{\nothaspatch}{{%
  \declareslashed{}{\sslash}{-0.04}{0}{\Sqsupset}\slashed{\Sqsupset}}}
\newcommand{\notpatchisin}{{%
  \declareslashed{}{\sslash}{-0.04}{0}{\Sqsubset}\slashed{\Sqsubset}}}
\newcommand{\haspatch}{\Sqsupset}
\newcommand{\patchisin}{\Sqsubset}

\newcommand{\pa}[1]{\mathbb #1}
\newcommand{\pay}[1]{\pa{#1}^+}
\newcommand{\pan}[1]{\pa{#1}^-}

\newcommand{\p}{\pa{P}}
\newcommand{\py}{\pay{P}}
\newcommand{\pn}{\pan{P}}

%\newcommand{\hasparents}{\underaccent{1}{>}}
%\newcommand{\hasparents}{{%
%  \declareslashed{}{_{_1}}{0}{-0.8}{>}\slashed{>}}}
\newcommand{\hasparents}{>_{\mkern-7.0mu _1}}
\newcommand{\areparents}{<_{\mkern-14.0mu _1\mkern+5.0mu}}

\begin{document}

sponge
$ C \hasparents X $
$ C > X $
$ X \areparents C $
$ X < C $
$ D \isin C $
$ A \sqsubseteq B $
$ A \not \sqsubseteq B $
$ A \nsqsubseteq B $
$ A \le B $
$ A \Sqsubset B $
$ A \Sqsupset B $
$ A \haspatch B $
$ A \nothaspatch B $
$ A \patchisin B $
$ A \notpatchisin B $
$ A \nothaspatch \pa{C} $
$ A \nothaspatch \py $
$ A \nothaspatch \p_C^+ $
$ A \nothaspatch \pan{C} $
\end{document}
