Modifying the symbol for non-forking

Question

I want to modify the following lines of code

\documentclass{article}
\usepackage{amsmath,amssymb}
\def\forkindep{\mathrel{\raise0.2ex\hbox{\ooalign{\hidewidth$\vert^{d}$\hidewidth\cr\raise-0.9ex\hbox{$\smile$}}}}}

 \begin{document}
 $A \underset{C}{\forkindep}B$
 \end{document}

found in What is the LaTeX symbol for "forking independent" (model theory)? to have a line followed by a prime symbol (i.e. |') in the forking independence relation. I attempted to do this by changing the $\vert$ to $\vert^{'}$. However this cause the line segment to not align properly with the smile symbol (I want the line segment bisect the smile, but it is a little to the left the command). I was wondering how I could fix this issue.

Answer 1

I can offer a variant of my solution to the problem of the linked question:

\documentclass[a4paper]{article}
\newcommand{\forkindep}[1][]{%
  \mathrel{
    \mathop{
      \vcenter{
        \hbox{\oalign{\noalign{\kern-.3ex}\hfil$\vert$\hfil\cr
              \noalign{\kern-.7ex}
              $\smile$\cr\noalign{\kern-.3ex}}}
      }
    }\displaylimits_{#1}
  }
}
\newcommand{\nonforkindep}[1][]{%
  \mathrel{
    \mathop{
      \vcenter{
        \hbox{\oalign{\noalign{\kern-.3ex}\hfil$\vert$\rlap{$'$}\hfil\cr
              \noalign{\kern-.7ex}
              $\smile$\cr\noalign{\kern-.3ex}}}
      }
    }\displaylimits_{#1}
  }
}

\begin{document}
$A\forkindep[C]B$ $A\nonforkindep[C]B$
\[
A\forkindep[C]B\quad A\nonforkindep[C]B
\]
\end{document}