Translation:We are looking for a large donkey and a big machine.
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Yes, but in British and American English, even the animal is not "arse." This is Scottish English and perhaps Irish English, and even then I do not believe "arse" is a standard spelling. Further, most Americans would not refer to a donkey as an "ass," unless it was a specific subspecies, such as the Somali wild ass.
The word 'arse' is a British English word for 'bum' or 'bottom', what in Czech would be 'prdel'.
'Arse' is not a variant spelling of 'ass', but rather a different though related word.
In American English, the word 'ass' can mean either 'donkey' or the same as the British 'arse'.
Nowadays in American English, 'donkey' and '❤❤❤❤❤❤❤' are used more often then 'ass', but you still see the latter.
For example: "He made a complete ass of himself." That means he made a fool of himself. The reference is to the animal, not to the bum/bottom.
As far as I know, British English does not use 'arse' to mean the animal. So the DL program is wrong if it translates Czech 'osel' to mean 'arse'. It means 'ass'.
Czech basically has only one present tense, which could be translated -- using this exercise and your question as an example -- as either "we look for" or "we are looking for."
From what I've seen, DL USUALLY uses the "XXXing" form of the verb in its English translations. Since we rarely have context, I generally go with that version, too, and it's been working out well. :-)
This seems like an old problem with longer sentences on the phone app. Sometimes the solution is pre-filled. We can't really help you but you can try asking in the main Duolingo forum. If yes, then please attach screenshots and mention the type of your device and whether you use a web browser or the app.