IIUC, when proving / disproving arbitrary propositions (the terms of a contract) in an interactive proof, you need as many game steps as there are alternating exists/forall quantifiers, but each step can otherwise be kept constant size using a zkSNARK.
Then the sideledger manager can either concede and send T units to your address A with a reference to having paid said claim, or he can show you have already spent from address A on the side-chain since E was current, or closed your account on the main chain.
Read my blog!