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The SHUNYATA program constructs proof methods by analyzing proofs of simple theorems in mathematical theories such as group theory and uses these methods to form prooh of new theorems in the same or in other theories. Such methods are capable of generating proo& of theorems whose complexity represents the state of the art in automated theorem proving. They(More)
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines that process informal concepts such as computable (total) functions beyond the limits of any given Turing machine or(More)