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Proofs and Refutations, and Z3
"... Z3 [3] is a stateoftheart Satisfiability Modulo Theories (SMT) solver freely available from Microsoft Research. It solves the decision problem for quantifierfree formulas with respect to combinations of theories, such as arithmetic, bitvectors, arrays, and uninterpreted functions. Z3 is used in ..."
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Z3 [3] is a stateoftheart Satisfiability Modulo Theories (SMT) solver freely available from Microsoft Research. It solves the decision problem for quantifierfree formulas with respect to combinations of theories, such as arithmetic, bitvectors, arrays, and uninterpreted functions. Z3 is used in various software analysis and testcase generation projects at Microsoft Research and elsewhere. The requirements from the userbase range from establishing validity, dually unsatisfiability, of firstorder formulas; to identify invalid, dually satisfiable, formulas. In both cases, there is often a need for more than just a yes/no answer from the prover. A model can exhibit why an invalid formula is not provable, and a proofobject can certify the validity of a formula. This paper describes the proofproducing internals of Z3. We also briefly introduce the modelproducing facilities. We emphasize two features that can be of general interest: (1) we introduce a notion of implicit quotation to avoid introducing auxiliary variables, it simplifies the creation of proof objects considerably; (2) we produce natural deduction style proofs to facilitate modular proof reconstruction.
Comparing Proof Systems for Linear Real Arithmetic with LFSC ∗
"... LFSC is a highlevel declarative language for defining proof systems and proof objects for virtually any logic. One of its distinguishing features is its support for computational side conditions on proof rules. Side conditions facilitate the design of proof systems that reflect closely the sort of ..."
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LFSC is a highlevel declarative language for defining proof systems and proof objects for virtually any logic. One of its distinguishing features is its support for computational side conditions on proof rules. Side conditions facilitate the design of proof systems that reflect closely the sort of highperformance inferences made by SMT solvers. This paper investigates the issue of balancing declarative and computational inference in LFSC focusing on (quantifierfree) Linear Real Arithmetic. We discuss a few alternative proof systems for LRA and report on our comparative experimental results on generating and checking proofs in them. 1
The Combined KEAPPA IWIL Workshops Proceedings Proceedings of the workshops Knowledge Exchange: Automated Provers and Proof Assistants
"... Existing automated provers and proof assistants are complementary, to the point that their cooperative integration would benefit all efforts in automating reasoning. Indeed, a number of specialized tools incorporating such integration have been built. The issue is, however, wider, as we can envisage ..."
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Existing automated provers and proof assistants are complementary, to the point that their cooperative integration would benefit all efforts in automating reasoning. Indeed, a number of specialized tools incorporating such integration have been built. The issue is, however, wider, as we can envisage cooperation among various automated provers as well as among various proof assistants. This workshop brings together practitioners and researchers who have experimented with knowledge exchange among tools supporting automated reasoning. Organizers: Piotr Rudnicki, Geoff Sutcliffe
Proofs in Satisfiability Modulo Theories
"... Satisfiability Modulo Theories (SMT) solvers4 check the satisfiability of firstorder formulas written in a language containing interpreted predicates and functions. These interpreted symbols are defined either by firstorder axioms (e.g. the axioms of equality, or array axioms for operators read a ..."
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Satisfiability Modulo Theories (SMT) solvers4 check the satisfiability of firstorder formulas written in a language containing interpreted predicates and functions. These interpreted symbols are defined either by firstorder axioms (e.g. the axioms of equality, or array axioms for operators read and write,...) or by a