QRAT Polynomially Simulates ∀ \text -Exp+Res

The proof system \(\forall \text {-Exp+Res}\) formally captures expansion-based solving of quantified Boolean formulas (QBFs) whereas the \(\mathsf {QRAT}\) proof system captures QBF preprocessing. From previous work it is known that certain families of formulas have short proofs in \(\mathsf {QRAT}\) but not in \(\forall \text {-Exp+Res}\). However, it was not known if the two proof systems were incomparable (i.e., if there also existed QBFs with short \(\forall \text {-Exp+Res}\) proofs but without short \(\mathsf {QRAT}\) proofs), or if \(\mathsf {QRAT}\) polynomially simulates \(\forall \text {-Exp+Res}\). We close this gap of the QBF-proof-complexity landscape by presenting a polynomial simulation of \(\forall \text {-Exp+Res}\) in \(\mathsf {QRAT}\). Our simulation shows how definition introduction combined with extended-universal reduction can mimic the concept of universal expansion.