<appear gone> and <appear to have gone>

[NewAmerica]

Which sentence is correct? (4) is surely grammatically correct but logically flawed (too certain to declare that). (1) seems correct to me but I am not sure. (2) and (3) appear odd to me.

(1) Those days of profound discoveries in science appear gone.
(2) Those days of profound discoveries in science appear to have gone.
(3) Those days of profound discoveries in science appear having gone.
(4) Those days of profound discoveries in science are gone.

Source: English sentence making practice by me.

 

[much_rice]

(1) Those days of profound discoveries in science appear gone. grammatical but awkward
(2) Those days of profound discoveries in science appear to have gone.
(3) Those days of profound discoveries in science appear having gone.
(4) Those days of profound discoveries in science are gone. grammatical if a bit dramatic

If you add "to be" to (1), it becomes a much more natural sentence:
- Those days of profound discoveries in science appear (or seem) to be gone.

 

[NewAmerica]

Thank you.

Why doesn't "having gone" work there?