Randall Holmes says he has a proof of the consistency of NF relative to ZFC (and in fact something weaker, I think). He’s said this for a while, he’s published a few versions of his proof (mostly different in presentation in the interests of clarity, rather than patching bugs), and I think the general feeling is that he probably does have a proof but it hasn’t yet been thoroughly checked by others. (Who may be holding off because he’s still changing his mind about the best way of writing it down.)
Randall Holmes says he has a proof of the consistency of NF relative to ZFC (and in fact something weaker, I think). He’s said this for a while, he’s published a few versions of his proof (mostly different in presentation in the interests of clarity, rather than patching bugs), and I think the general feeling is that he probably does have a proof but it hasn’t yet been thoroughly checked by others. (Who may be holding off because he’s still changing his mind about the best way of writing it down.)