In [the paper](http://link.springer.com/article/10.1007/BF02941339), page 149, the super Jacobi identity is given by
\begin{align}
J(x, y,z) := (-1)^{|x||z|}[[x, y],z] +(-1)^{|z||y|}[[z,x], y]+(-1)^{|y||x|}[[y,z],x] = 0.
\end{align}
But in [the article](https://en.wikipedia.org/wiki/Lie_superalgebra), the super Jacobi identity is given by
\begin{align}
[x,[y,z]]=[[x,y],z]+(-1)^{|x| |y|}[y,[x,z]].
\end{align}
Are these two definitions equivalent? Thank you very much.