I follow (1) and grant (2). (3) Follows from (1) and (2).
(4) We know that the set of all proofs is recursively enumerable, i.e. there is a program that outputs all proofs.
Are you asserting that the set of proofs is finite? This would surprise me but seems to be required for (8) to contradict what I know.
No, the set of proofs is infinite. There is a program that outputs all proofs; it’s just that it takes forever to do so.
...but a finite amount of time to output any specific proof off the list.
I follow (1) and grant (2). (3) Follows from (1) and (2).
Are you asserting that the set of proofs is finite? This would surprise me but seems to be required for (8) to contradict what I know.
No, the set of proofs is infinite. There is a program that outputs all proofs; it’s just that it takes forever to do so.
...but a finite amount of time to output any specific proof off the list.