[show abstract][hide abstract] ABSTRACT: A conjecture of Padmanabhan, on provability in cancellative semigroups, is
addressed. Several of Levi’s group theory commutator theorems are proved for
cancellative semigroups. The proofs, found by automated deduction, support
[show abstract][hide abstract] ABSTRACT: We present short single axioms for ortholattices, orthomodular lattices, and modular ortholattices, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. We also give multiequation bases in terms of the Sheffer stroke and in terms of join, meet, and complementation. Proofs are omitted but are available in an associated technical report and on the Web. We used computers extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms.