The CADE ATP System Competition (CASC) evaluates the performance of sound, fully automatic, classical logic, ATP systems. The evaluation is in terms of the number of problems solved, the number of acceptable proofs and models produced, and the average runtime for problems solved, in the context of a bounded number of eligible problems chosen from the TPTP problem library and other useful source...

We study the number c n ( N ) $$ {c}_n^{(N)} of -step self-avoiding walks on -dimensional hypercube, and identify an -dependent connective constant μ {\mu}_N amplitude A {A}_N such that is O O\left({\mu}_N^n\right) for all , asymptotically {A}_N{\mu}_N^n as long ≤ 2 p n\le {2}^{pN} any fixed < 1 p<\frac{1}{2} . refer to regime ≪ / n\ll {2}^{N/2} dilute phase. discuss conjectures concerning diff...