As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
By that definition of validation humans never proved anything, because they sometimes say that 1=1 is false.
As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
Gödel sentence for some formal system can’t be proven in that system, but it can be proven in more powerful system. Humans that see the sentence to be true are just (reasoning in a way equivalent to) using a more powerful formal system. And everything in that system is computably verifiable.
By that definition of validation humans never proved anything, because they sometimes say that 1=1 is false.
Gödel sentence for some formal system can’t be proven in that system, but it can be proven in more powerful system. Humans that see the sentence to be true are just (reasoning in a way equivalent to) using a more powerful formal system. And everything in that system is computably verifiable.