3 problems

Separation conjecture. For every derivation $T\vdash_{\mathsf{SKS}}R$, there is a derivation of the form

Interpolation conjecture. For every derivation $T\vdash_{\mathsf{SKS}}R$, there is a structure $P$ and derivations

Negative-translation equivalence conjecture. If the notion of a negative translation into $\mathsf{IL}$ is rigorously defined, then all negative translations are equivalent in…