A monoid is a set $S$ together with a binary operation $\cdot:S \times S \rightarrow S$ such that: The binary operation $\cdot$ is associative, that is, $(a\cdot b) \cdot c=a\cdot (b \cdot c)$ for ...
By theorems, I mean the ones you can find in an undergraduate course of mathematics, not the ones you can find in a textbook of automated proofs. I mean by "proved by a computer" that an existing ...
The Wikipedia page on automated theorem proving states: Despite these theoretical limits, in practice, theorem provers can solve many hard problems... However it is not clear whether these 'hard ...