Abstract. Sledgehammer is a component of Isabelle/HOL that employs firstorder automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is successful, produces a snippet that replays the proof in Isabelle. We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture. Isabelle users are now pleasantly surprised by SMT proofs for problems beyond the ATPs ’ reach. Remarkably, the best SMT solver performs better than the best ATP on most of our benchmarks. 1

A common proof format for solvers for Satisfiability Modulo Theories (SMT) is proposed, based on the Edinburgh Logical Framework (LF). Two problems arise: checking very large proofs, and keeping proofs compact in the presence of complex side conditions on rules. Incremental checking combines parsing and proof checking in a single step, to avoid building in-memory representations of proof subterms. LF with Side Conditions (LFSC) extends LF to allow side conditions to be expressed using a simple first-order functional programming language. Experimental data with an implementation show very good proof checking times and memory usage on benchmarks including the important example of resolution inferences.

The main contribution of this thesis is the application of the first-order theorem prover DARWIN, the implementation of the Model Evolution calculus, to software verification problems. It is attempted to embed the theorem prover as a decision procedure in the KEY system for formal specification and verification. As a true first-order calculus, Model Evolution does not have to rely on ground instantiations, giving it an advantage in reasoning with quantifiers and uninterpreted function symbols that is required for the class of proof obligations that are examined. This work is also a first approach towards satisfiability modulo theories in Model Evolution. It gives a heuristic implementation that is shown to be successful for a number of examples and discusses alternative possibilities to lift ground procedures of satisfiability modulo theories to the first-order calculus.

Abstract. Isabelle/HOL is a popular interactive theorem prover based on higherorder logic. It owes its success to its ease of use and powerful automation. Much of the automation is performed by external tools: The metaprover Sledgehammer relies on resolution provers and SMT solvers for its proof search, the counterexample generator Quickcheck uses the ML compiler as a fast evaluator for ground formulas, and its rival Nitpick is based on the model finder Kodkod, which performs a reduction to SAT. Together with the Isar structured proof format and a new asynchronous user interface, these tools have radically transformed the Isabelle user experience. This paper provides an overview of the main automatic proof and disproof tools. 1