Catalysis of the reaction: 5-enolpyruvoyl-6-hydroxy-2-succinyl-cyclohex-3-ene-1-carboxylate = (1R,6R)-2-succinyl-6-hydroxycyclohexa-2,4-diene-1-carboxylate + pyruvate.
6-hydroxy-2-succinylcyclohexa-2,4-diene-1-carboxylate synthase activity