OK. I've seen it. Kubrick may have.
See also:
Universe (1960) Canadian short film documentary on space. Wally Gentleman, who did the effects worked on 2001 as a SFX supervisor. Referring to the opening shot of 2001 - "Called “Earth occultation zonk” by the effects crew, it was based on one of Wally Gentleman’s sequences from Universe, in which the Sun was seen emerging from the side of both Earth and Moon." (from Michael Benson - Space Odyssey Stanley Kubrick, Arthur C. Clarke, and the Making of a Masterpiece)
Doroga k Zvezdam (1957) A Russian film that does much of what Man in Space did and took it a step farther. The wheel space station is particularly good. The Russians also made some nifty looking SF films including the film Battle Beyond he Sun was cut from - Nebo Zovyot (195?) and Mechte Navstrechu - A Dream Come True - 1962 which was cut up to make Queen of Blood. Aside from being plodding and dull, (particularly Nebo Zovyot) both of these films look pretty good.
Mostly, according to Kubrick, he was not inspired by previous films... And according to Clarke, he was shown a lot of them and hated Destination Moon and... very much hated Things to Come. I would say it is more likely that Clarke and members of the FX team were inspired by some previous films.