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Anecdotal evidence suggests that most “theorems” initially given to an interactive theorem prover do not hold, typically because of a typo or a missing assumption, but sometimes because of a deep flaw. Modern proof assistants for higher-order logic (HOL) provide counterexample generators that can be run on putative theorems or on specific subgoals in a… (More)

- Jasmin Christian Blanchette, Sascha Böhme, Lawrence C. Paulson
- Journal of Automated Reasoning
- 2011

Sledgehammer is a component of Isabelle/HOL that employs resolution-based first-order 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… (More)

- Jasmin Christian Blanchette, Lukas Bulwahn, Tobias Nipkow
- FroCoS
- 2011

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… (More)

The TPTP World is a well-established infrastructure for automatic theorem provers. It defines several concrete syntaxes, notably an untyped firstorder form (FOF) and a typed first-order form (TFF0), that have become de facto standards in the automated reasoning community. This paper introduces the TFF1 format, an extension of TFF0 with rank-1 polymorphism.… (More)

Sledgehammer for Isabelle/HOL integrates automatic theorem provers to discharge interactive proof obligations. This paper considers a tighter integration of the superposition prover SPASS to increase Sledgehammer’s success rate. The main enhancements are native support for hard sorts (simple types) in SPASS, simplification that honors the orientation of… (More)

Previous work formalized the C++ memory model in Isabelle/HOL in an effort to clarify the proposed standard's semantics. Here we employ the model finder Nitpick to check litmus test programs that exercise the memory model, including a simple locking algorithm. Nitpick is built on Kodkod (Alloy's backend) but understands Isabelle's richer logic; hence it can… (More)

This thesis describes work on two components of the interactive theorem prover Isabelle/HOL that generate proofs and counterexamples for higher-order conjectures by harnessing external first-order reasoners. Our primary contribution is the development of Nitpick, a counterexample generator that builds on a first-order relational model finder based on a… (More)

- Jasmin Christian Blanchette, David Greenaway, Cezary Kaliszyk, Daniel Kühlwein, Josef Urban
- Journal of Automated Reasoning
- 2016

Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the fact selector, heuristically ranks the thousands of facts (lemmas, definitions, or axioms) available and selects a subset, based on syntactic similarity to the current proof goal. We introduce MaSh, an alternative that learns from successful proofs.… (More)

- Jasmin Christian Blanchette, Sascha Böhme, Andrei Popescu, Nicholas Smallbone
- Logical Methods in Computer Science
- 2013

Most automatic theorem provers are restricted to untyped or monomorphic logics, and existing translations from polymorphic logics are bulky or unsound. Recent research shows how to exploit monotonicity to encode ground types efficiently: monotonic types can be safely erased, while nonmonotonic types must generally be encoded. We extend this work to rank-1… (More)