Lipmaa, Parisella, and Siim [Eurocrypt, 2024] proved the extractability of the KZG polynomial commitment scheme under the falsifiable assumption ARSDH. They also proved that variants of fully optimized zk-SNARKs like Plonk can be made knowledge-sound in the random oracle model (ROM) under the ARSDH assumption. However, they did not consider various batching optimizations, resulting in their variant of Plonk having approximately 3.5 times longer argument. Our contributions are: (1) We prove that several batch-opening protocols for KZG, used in modern zk-SNARKs, have computational special soundness under the ARSDH assumption. (2) We prove that interactive Plonk has computational special soundness under the ARSDH assumption and a new falsifiable assumption SplitRSDH. We also prove that two minor modifications of the interactive Plonk have computational special soundness under only the ARSDH and a simpler variant of SplitRSDH. The Fiat-Shamir transform can be applied to obtain non-interactive versions, which are secure in the ROM under the same assumptions. We define a new type-safe oracle framework of the AGMOS (AGM with oblivious sampling) and prove SplitRSDH is secure in it.