We give an overview of issues surrounding computerverified theorem proving in the standard pure-mathematical context.

Our goal is to use a theorem prover in order to verify in-variance properties of distributed systems in a \model checking like" manner. A system S is described by a set of sequential components, each one given by a transition relation and a predicate Init deening the set of initial states. In order to verify that P is an invariant of S, we try to compute, in a model checking like manner, the we...

A proof document for origami theorem proving is a record of entire process of reasoning about origami construction and theorem proving. It is produced at the completion of origami theorem proving as a kind of proof certificate. It describes in detail how the whole process of an origami construction and the subsequent theorem proving are carried out in our computational origami system. In partic...

Verification is a hard task, but much progress has been achieved recently. Many verification problems have been shown decidable by reducing them to modelchecking finite state transition systems. Verification of infinite state transition systems has achieved tremendous progress too, by showing that many particular cases were themselves decidable, such as timed automata [1] or some forms of pushd...

When one is seeking an expansion proof for a theorem of higher-order logic, not all necessary substitution terms can be generated by unification of formulas already present, so certain expansion options [5] are applied, and then a search for a p-acceptable mating [2] is made, using Huet's higher-order unification algorithm [8] to generate all remaining substitution terms. The expansion options ...

Automated Theorem Provers are computer programs written to prove, or help in proving, mathematical and non-mathematical theorems. Automated Theorem Proving (ATP) is a rapidly advancing field and contains many potential research areas. This paper is an overview of this important field. It starts by giving the needed mathematical background followed by an overview. The overview includes historica...

Uniform proofs systems have recently been proposed [Mil91] as a proof-theoretic foundation and generalization of logic programming. In [Mom92a] an extension with constructive negation is presented preserving the nature of abstract logic programming language. Here we adapt this approach to provide a complete theorem proving technique for minimal, intuitionistic and classical logic, which is tota...

Mechanized proof assistants are powerful verification tools, but proof developments can still be difficult and timeconsuming. When verifying a family of related programs, the effort can be reduced by proof reuse. In this paper, we show how to engineer proofs for product lines built from feature modules. Each module contains proof fragments which are composed together to build a complete proof o...

In this paper we describe the theorem prover METEOR which is a high-performance Model Elimination prover running in sequential, parallel and distributed computing environments. METEOR has a very high inference rate, but as is the case with better chess-playing programs speed alone is not su cient when exploring large search spaces; intelligent search is necessary. We describe modi cations to tr...