There is a long list of large cardinal axioms. Most of them deemed to be consistent with ZFC but there are also some axioms like existence of Reinhardt or $\omega$-huge cardinals which are natural generalization of these axioms but are provably inconsistent with ZFC.
It seems to me that almost all proofs for inconsistency of these large cardinal axioms are similar to the well-known Kunen's method in his inconsistency theorem based on iterating some elementary embedding or directly follow from this theorem as a straightforward result, but I'm not sure if this feeling is true for all large cardinal axioms which are known to be inconsistent with ZFC.
Question: Is there any large cardinal axiom which is known to be inconsistent with ZFC but its inconsistency proof is essentially different from proof of Kunen inconsistency theorem?