May 23 (Reuters) - The California State Teachers'

Retirement System has voted against the re-election of Exxon

Chairman Darren Woods and of its Lead Director Joseph Hooley, an

online record shows.

Representatives for the big pension system did not

immediately comment on the reasons for the votes. Exxon faces a

campaign for votes against the two directors after it sued

climate activists who had filed a shareholder resolution meant

for its May 29 annual meeting.