\documentclass{article}
    \usepackage{tikz}
    \usepackage{pgfplots}
\usepackage{pgfplots.assert}
        \usetikzlibrary{
            intersections,
            %
            pgfplots.fillbetween,
        }
\begin{document}


\makeatletter
\begin{tikzpicture}
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	%\gdef\B{\pgfsyssoftpath@movetotoken {20.3125pt}{-13.50049pt}\pgfsyssoftpath@linetotoken {20.3125pt}{148.49728pt}\pgfsyssoftpath@linetotoken {142.1875pt}{148.49728pt}\pgfsyssoftpath@linetotoken {142.1875pt}{-13.50049pt}\pgfsyssoftpath@closepathtoken {20.3125pt}{-13.50049pt}}

	\gdef\A{%
		\pgfsyssoftpath@movetotoken {13.5416pt}{109.61292pt}%
		\pgfsyssoftpath@curvetosupportatoken {15.42046pt}{106.41112pt}%
		\pgfsyssoftpath@curvetosupportbtoken {18.43355pt}{101.53322pt}%
		\pgfsyssoftpath@curvetotoken {20.31241pt}{98.6516pt}%
		\pgfsyssoftpath@curvetosupportatoken {22.19127pt}{95.76997pt}%
		\pgfsyssoftpath@curvetosupportbtoken {25.20435pt}{91.40561pt}%
		\pgfsyssoftpath@curvetotoken {27.0832pt}{88.84418pt}%
	}

	% WORKS:
	\gdef\Ax{%
		\pgfsyssoftpath@movetotoken {13.5416pt}{109.61292pt}%
		\pgfsyssoftpath@curvetosupportatoken {15.42046pt}{106.41112pt}%
		\pgfsyssoftpath@curvetosupportbtoken {18.43355pt}{101.53322pt}%
		%\pgfsyssoftpath@curvetotoken {20.31241pt}{98.6516pt}%
		\pgfsyssoftpath@curvetotoken {20.31249pt}{98.6516pt}%
		\pgfsyssoftpath@curvetosupportatoken {22.19127pt}{95.76997pt}%
		\pgfsyssoftpath@curvetosupportbtoken {25.20435pt}{91.40561pt}%
		\pgfsyssoftpath@curvetotoken {27.0832pt}{88.84418pt}%
	}
	\gdef\B{\pgfsyssoftpath@movetotoken {20.3125pt}{-13.50049pt}\pgfsyssoftpath@linetotoken {20.3125pt}{148.49728pt}}

	% WORKS:
	\gdef\Bx{\pgfsyssoftpath@movetotoken {20.3125pt}{-13.50049pt}\pgfsyssoftpath@linetotoken {20.3126pt}{148.49728pt}}

	\draw[blue, name path=A] \pgfextra\pgfsetpathandBB\A\endpgfextra;
	\draw[red, name path=C] \pgfextra\pgfsetpathandBB\B\endpgfextra;

	%\tracingmacros=2 \tracingcommands=2
	\pgfintersectionofpaths%
		{%
			\pgfsetpath\A
		}%
		{%
			\pgfsetpath\B
		}%

	\pgfplotsassertequalstok{1}{\pgfintersectionsolutions}{}

	\foreach \i in {1,...,\pgfintersectionsolutions} {%
		\begingroup
		\pgftransformshift{\pgfpointintersectionsolution{\i}}%
		\node at (0,0) {\i};
		\endgroup
	}%

	\pgfpointintersectionsolution{1}
	\pgfplotsassertequalstok{20.31378pt,98.5964pt}{\the\pgf@x,\the\pgf@y}{solution 1}

\end{tikzpicture}


\end{document}

