TxGraffiti's claw-free graph zero forcing conjecture

Let $G$ be a graph. The parameters $Z(G)$ and $Z_+(G)$ denote the standard and positive semidefinite zero forcing numbers of $G$, respectively. A graph is claw-free if it has no induced subgraph isomorphic to $K_{1,3}$. TxGraffiti's conjecture. If $G$ is claw-free, then

$$Z_+(G)=Z(G).$$

The conjecture proposes that the greater flexibility of positive semidefinite forcing does not reduce the forcing number for claw-free graphs. It is presented as a conjecture generated by the TxGraffiti conjecturing program; its resolution is not established in the supplied source.