Superposition Modulo Linear Arithmetic SUP(LA

Abstract. The hierarchical superposition based theorem proving cal-culus of Bachmair, Ganzinger, and Waldmann enables the hierarchic combination of a theory with full first-order logic. If a clause set of the combination enjoys a sufficient completeness criterion, the calculus is even complete. We instantiate the calculus for the theory of linear arith-metic. In particular, we develop new effective versions for the standard superposition redundancy criteria taking the linear arithmetic theory into account. The resulting calculus is implemented in SPASS(LA) and extends the state of the art in proving properties of first-order formulas over linear arithmetic.