We ultimately lose.
Reason's why.
1. The vex can just wait us out as according to some lore they ate a constant in the flower game.
2. We can be killed.
3. If the witness can kill guardians at range while tanking a direct blast from the traveller what can the winnower do as it's a capital G God.
4. Video game logic and plot armour got us some wins.
5. The hive could just swarm sol with war moons and crash them into earth or force a battle of attrition until we fall or are last guardian standing.
6. Guardian offensive capabilities are limited by earth's naval power and technology level just look at how many pyramid ships earth took out during lightfall.
Spoiler we took out zero it was a sweep the traveller barely took out one.
Personally I think it would be the vex or hive that take us out eventually.
The vex through strategy and hive through overwhelming force.
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I don't think we lose, just gain understanding in the end...the end of the design, the end of a thought. I'm not being cryptic, more literal than anything, a thing that thought of everything, and its design is a storied explanation...that's what's hard for me to explain, doesn't make much sense. The vex are one part of understanding.