私 watashi is I, me; 殺さない korosanai is the negative of 殺す korosu, to kill; もの mono is the thing, so 私を殺さないもの is the thing that does not kill me; は marks it as the topic; 強くする tsuyoku suru is to make strong. The sentence is Nietzsche's, the eighth of the Maxims and Arrows that open Twilight of the Idols (1889): Was mich nicht umbringt, macht mich stärker, under a heading the English drops as the design does, from the war-school of life.
The Japanese is the house's plain Japanese for the German, with the relative clause the sentence turns on kept whole.
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