Strengthening the coNP lower bound for RmbC

Determine whether the coNP lower bound for the validity problem of RmbC can be strengthened.

Background

The paper obtains coNP-hardness for the validity problem of RmbC by conservativity over the positive classical fragment. It does not establish a stronger lower bound, leaving unresolved whether the computational hardness can be raised to a higher complexity class and thereby narrow the gap with the coNEXPTIME upper bound.

References

Can hardness beyond NP be achieved with a constant number of solutions?

— Squaring Up by Selection: NP-Completeness at Three Simple Roots  (2609.28909 - Bassik, 24 Sep 2026) in Problem 2.2, Section 6 (Open problems)

We leave this, and the question of whether the \textsf{coNP} lower bound can be strengthened, as open problems.

— Self-extensional logics of formal inconsistency: Decidability and limits for paraconsistency  (2608.28443 - Coniglio et al., 28 Aug 2026) in Speculative Remark in Section 6.2, “An upper bound”