Cayley's Theorem
The article formalizes the Cayley's theorem saying that every group G is isomorphic to a subgroup of the symmetric group on G.
Classification results in quasigroup and loop theory via a combination of automated reasoning tools
We present some novel classification results in quasigroup and loop theory. For quasigroups up to size 5 and loops up to size 7, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques --- including machine learning and computer algebra --- which we present here. Moreover, each result has been automatically verified, again using a variety of techniques...
Cocktail: a tool for deriving correct programs.
Cocktail is a tool for deriving correct programs from their specifications. The present version is powerful enough for educational purposes. The tool yields support for many sorted first order predicate logic, formulated in a pure type system with parametric constants (CPTS), as the specification language, a simple While-language, a Hoare logic represented in the same CPTS for deriving programs from their specifications and a simple tableau based automated theorem prover for verifying proof obligations....
Complexity of theorem-proving procedures : some general properties
Computational complexity of a statistical theoremhood testing procedure for propositional calculus with pseudo-random inputs
Conway's Games and Some of their Basic Properties
We formulate a few basic concepts of J. H. Conway's theory of games based on his book [6]. This is a first step towards formalizing Conway's theory of numbers into Mizar, which is an approach to proving the existence of a FIELD (i.e., a proper class that satisfies the axioms of a real-closed field) that includes the reals and ordinals, thus providing a uniform, independent and simple approach to these two constructions that does not go via the rational numbers and hence does for example not need...
Corrigendum to “Realizations of Loops and Groups defined by short identities”