We haven't labored in vain is the English equivalent of 'Laboravimus non frustra'. In the word by word translation, the verb 'laboravimus' means '[we] have labored, labored'. The adverb 'non 'means 'not'. The adverb 'frustra' means 'vainlessly'.
(Tu) me frustras (informal) Usted me frustra (formal)
The motto of Rose Hill School is 'Nisi Dominus Frustra'.
Poundswick Grammar School's motto is 'Nisi Dominus Frustra'.
The motto of Durban Girls' College is 'Nisi Dominus Frustra'.
The motto of Metropolitan Borough of Chelsea is 'Nisi Dominus Frustra'.
The motto of Glenlola Collegiate School is 'Nisi dominus frustra'.
The Park School Yeovil's motto is 'Nisi dominus frustra'.
Non, non, non!
Non = no, not
King's Own Scottish Borderers's motto is 'Nisi Dominus Frustra'.
City of Bath Technical School's motto is 'Nisi Dominus Frustra'.
The motto of Mount Temple Comprehensive School is 'Nisi Dominus Frustra'.