We prove a limitation on a variant of the KPT theorem proposed for propositional proof systems by Pich and Santhanam (2020), for all proof systems that prove the disjointness of two NP sets that are hard to distinguish.

@article{abs-2004-02448,
  title = {A limitation on the KPT interpolation},
  author = {Jan Krajíček},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 16, Issue 3},
  year = {2020},
  doi = {10.23638/lmcs-16(3:9)2020}
}