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. 1.

Short single axioms for ortholattices, orthomodular lattices, and modular ortholattices are presented, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. Other equational bases in terms of the Sheffer stroke and in terms of join, meet, and complement are presented. Proofs are omitted but are available in an associated technical report. Computers were used extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms. The notion of computer proof is addressed. 1

Abstract. The skew Boolean propositional calculus (SBP C) is a generalization of the classical propositional calculus that arises naturally in the study of certain well-known deductive systems. In this article, we consider a candidate presentation of SBP C and prove it constitutes a Hilbert-style axiomatization. The problem reduces to establishing that the logic presented by the candidate axiomatization is algebraizable in the sense of Blok and Pigozzi. In turn, this is equivalent to verifying four particular formulas are derivable from the candidate presentation. Automated deduction methods played a central role in proving these four theorems. In particular, our approach relied heavily on the method of proof sketches. 1.