\frac{dx_{1}}{dt} = 0\\
\frac{dx_{2}}{dt} = 0\\
\frac{dx_{3}}{dt} = 0\\
\frac{dx_{4}}{dt} = \left(-1 \cdot k_{20} \cdot \left(k_{1} \cdot k_{21} \cdot x_{4} - k_{2} \cdot x_{5}\right) + 1 \cdot k_{20} \cdot \left(k_{5} \cdot x_{6} - k_{6} \cdot x_{9} \cdot x_{4}\right) + -1 \cdot k_{20} \cdot k_{7} \cdot x_{4} + 1 \cdot k_{20} \cdot \left(k_{12} \cdot x_{11} - k_{13} \cdot x_{4} \cdot x_{8}\right) + 1 \cdot k_{20} \cdot \left(k_{17} \cdot x_{7} - k_{18} \cdot x_{4} \cdot x_{8}\right)\right) / k_{20}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{20} \cdot \left(k_{1} \cdot k_{21} \cdot x_{4} - k_{2} \cdot x_{5}\right) + -1 \cdot k_{20} \cdot \left(k_{3} \cdot k_{23} \cdot x_{5} - k_{4} \cdot x_{6}\right) + -1 \cdot k_{20} \cdot \left(k_{15} \cdot k_{22} \cdot x_{5} - k_{16} \cdot x_{7}\right)\right) / k_{20}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{20} \cdot \left(k_{3} \cdot k_{23} \cdot x_{5} - k_{4} \cdot x_{6}\right) + -1 \cdot k_{20} \cdot \left(k_{5} \cdot x_{6} - k_{6} \cdot x_{9} \cdot x_{4}\right)\right) / k_{20}\\
\frac{dx_{7}}{dt} = \left(1 \cdot k_{20} \cdot \left(k_{15} \cdot k_{22} \cdot x_{5} - k_{16} \cdot x_{7}\right) + -1 \cdot k_{20} \cdot \left(k_{17} \cdot x_{7} - k_{18} \cdot x_{4} \cdot x_{8}\right)\right) / k_{20}\\
\frac{dx_{8}}{dt} = \left(-1 \cdot k_{20} \cdot \left(k_{8} \cdot x_{9} \cdot x_{8} - k_{9} \cdot x_{10}\right) + 1 \cdot k_{20} \cdot \left(k_{12} \cdot x_{11} - k_{13} \cdot x_{4} \cdot x_{8}\right) + -1 \cdot k_{20} \cdot k_{7} \cdot x_{8} + 1 \cdot k_{20} \cdot \left(k_{17} \cdot x_{7} - k_{18} \cdot x_{4} \cdot x_{8}\right)\right) / k_{20}\\
\frac{dx_{9}}{dt} = \left(1 \cdot k_{20} \cdot \left(k_{5} \cdot x_{6} - k_{6} \cdot x_{9} \cdot x_{4}\right) + -1 \cdot k_{20} \cdot \left(k_{8} \cdot x_{9} \cdot x_{8} - k_{9} \cdot x_{10}\right) + -1 \cdot k_{20} \cdot k_{7} \cdot x_{9}\right) / k_{20}\\
\frac{dx_{10}}{dt} = \left(1 \cdot k_{20} \cdot \left(k_{8} \cdot x_{9} \cdot x_{8} - k_{9} \cdot x_{10}\right) + -1 \cdot k_{20} \cdot \left(k_{10} \cdot k_{22} \cdot x_{10} - k_{11} \cdot x_{11}\right)\right) / k_{20}\\
\frac{dx_{11}}{dt} = \left(1 \cdot k_{20} \cdot \left(k_{10} \cdot k_{22} \cdot x_{10} - k_{11} \cdot x_{11}\right) + -1 \cdot k_{20} \cdot \left(k_{12} \cdot x_{11} - k_{13} \cdot x_{4} \cdot x_{8}\right)\right) / k_{20}