Interactive theorem proving requires a lot of human guidance. Proving a property involves (1) figuring out why it holds, then (2) coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDDor SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and a...

In this memo, we discuss the topic of automated theorem proving. This note is intended to serve as an introduction for someone interested in the topic but who doesn’t have extensive background in formal proof systems. The topics covered in this memo are kept at a somewhat conceptual level and pointers are provided to appropriate references for more in-depth treatment of specific topics. In the ...

Many mathematical proofs are hard to generate for humans and even harder for automated theorem provers. Classical techniques of automated theorem proving involve the application of basic rules, of built-in special procedures, or of tactics. Melis (Melis 1993) introduced a new method for analogical reasoning in automated theorem proving. In this paper we show how the derivational analogy replay ...

We present a novel application of automated theorem proving for the logical simulation of evolvable systems. Modelled using a logical framework, these systems are built hierarchically from components where each component is specified as a first order theory and may have an associated supervisory component. The supervisory component monitors and possibly changes its associated component. The sim...

Many mathematical proofs are hard to generate for humans and even harder for automated theorem provers. Classical techniques of automated theorem proving involve the application of basic rules, of built-in special procedures, or of tactics. Melis (Melis 1993) introduced a new method for analogical reasoning in automated theorem proving. In this paper we show how the derivational analogy replay ...

IPR is an automatic theorem-proving system intended particularly for use in higher-level mathematics. It discovers the proofs of theorems in mathematics applying known theorems and deenitions. Theorems and deenitions are stored in the knowledge base in the form of sequents rather than formulas or rewrite rules. Because there is more easily-accessible information in a sequent than there is in th...

Herbrand's theorem plays an important role both in proof theory and in computer science. Given a Herbrand skeleton, which is basically a number specifying the count of disjunctions of the matrix, we would like to get a computable bound on the size of terms which make the disjunction into a quasitautology. This is an important problem in logic, speciically in the complexity of proofs. In compute...

Practical formal veriication of complex computer systems requires proof robustness and eeciency to protect against inevitable mistakes and system spec-iication and design changes. PVS is a theorem-proving system based on higher-order logic with which we demonstrate the kind of robust code proofs needed for veriication of realistic-sized computing systems.