This note presents purely mechanical proofs of the Levi commutator problem in group theory. The problem was solved first by using the theorem prover EQP, developed by William McCune at the Argonne National Laboratory. The fastest proof was found by using Peers-mcd, the Clause-Diffusion parallelization of EQP, developed by the author at the University of Iowa. 1 The Levi commutator problem The L...

We prove several results showing that the algebraic $K$ -theory of valuation rings behaves as though such were regular Noetherian, in particular an analogue Geisser–Levine theorem. also give some new proofs known concerning cdh descent -theory.

1 0 Introduction. Computer assisted proofs are becoming an important factor of present day mathematics. Since there exist short theorems having arbitrarily long proofs (a consequence of GG odel's incompletness theorems, see 4, 6, 23]) and the power of computers is growing exponentially, this shoudbe expected. The general scheme for constructing computer assisted proofs is actually very simple a...

In the last few years field of logic-based knowledge representation took a lot inspiration from database theory. A vital example is that finite model semantics in description logics (DLs) reconsidered as desirable alternative to classical one and query entailment has replaced knowledge-base satisfiability (KBSat) checking key inference problem. However, despite considerable effort, overall pict...

We present a finite element scheme capable of preserving the nonnegative and bounded solutions of the generalized Burgers-Huxley equation. Proofs of existence and uniqueness of a solution to the continuous problem together with some results concerning the boundedness and the nonnegativity of the solution are given. Under appropriate conditions on the mesh and the initial and boundary data, boun...

We solve three enumerative problems concerning the families of planar maps. More precisely, we establish algebraic equations for the generating function of loopless triangulations in which all vertices have degree at least d, for a certain value d chosen in {3, 4, 5}. The originality of the problem lies in the fact that degree restrictions are placed both on vertices and faces. Our proofs first...

We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them has been posed by George Andrews in 1980, the other two are by Guoce Xin and Christian Krattenthaler. Our proofs employ computer algebra methods, namely the holonomic ansatz proposed by Doron Zeilberger and variations thereof. These variati...

We develop a systematic algorithmic framework that unites global and local classification problems for functional separable spaces apply it to attack concerning the Banach space C[0,1] of real-valued continuous functions on unit interval. prove problem (binary) regular among almost everywhere linear, pointwise linear-time Lipshitz is $\Sigma^0_2$-complete. show function $f\colon [0,1] \rightarr...

In order to compare the quality of proofs, it is necessary to measure artifacts of the proofs, and evaluate the measurements to determine differences between the proofs. This paper discounts the approach of ranking proofs by their measured proof artifacts, and takes the position that different proofs are good proofs. The position is based on proofs in the TSTP solution library, which are genera...