תָּנוּ רַבָּנַן: יוֹם שֶׁנִּבְרָא בּוֹ אָדָם הָרִאשׁוֹן, כֵּיוָן שֶׁשָּׁקְעָה עָלָיו חַמָּה, אָמַר: אוֹי לִי, שֶׁבִּשְׁבִיל שֶׁסָּרַחְתִּי עוֹלָם חָשׁוּךְ בַּעֲדִי, וְיַחְזוֹר עוֹלָם לְתוֹהוּ וָבוֹהוּ, וְזוֹ הִיא מִיתָה שֶׁנִּקְנְסָה עָלַי מִן הַשָּׁמַיִם. הָיָה יוֹשֵׁב בְּתַעֲנִית וּבוֹכֶה כׇּל הַלַּיְלָה, וְחַוָּה בּוֹכָה כְּנֶגְדּוֹ. כֵּיוָן שֶׁעָלָה עַמּוּד הַשַּׁחַר, אָמַר: מִנְהָגוֹ שֶׁל עוֹלָם הוּא. עָמַד וְהִקְרִיב שׁוֹר שֶׁקַּרְנָיו קוֹדְמִין לְפַרְסוֹתָיו, שֶׁנֶּאֱמַר: ״וְתִיטַב לַיהוה מִשּׁוֹר פָּר מַקְרִן מַפְרִיס״.
The Sages taught: On the day that Adam the first man was created, when the sun set upon him he said: Woe is me, as because I sinned, the world is becoming dark around me, and the world will return to the primordial state of chaos and disorder. And this is the death that was sentenced upon me from Heaven. He spent all night fasting and crying, and Eve was crying opposite him. Once dawn broke, he said: Evidently, the sun sets and night arrives, and this is the order of the world. He arose and sacrificed a bull whose horns preceded its hoofs in the order that they were created, as it is stated: “And it shall please the Lord better than a bullock that has horns and hoofs” (Psalms 69:32). This verse is referring to the one particular bull whose horns preceded its hoofs.
(90) The first time Adam witnessed the sinking of the sun he was also seized with anxious fears. It happened at the conclusion of the Sabbath, and Adam said, "Woe is me! For my sake, because I sinned, the world is darkened, and it will again become void and without form. Thus will be executed the punishment of death which God has pronounced against me!" All the night he spent in tears, and Eve, too, wept as she sat opposite to him. When day began to dawn, he understood that what he had deplored was but the course of nature, and he brought an offering unto God, a unicorn whose horn was created before his hoofs, and he sacrificed it on the spot on which later the altar was to stand in Jerusalem.
Here is the origin of the Jewish version of the unicorn. There was once a unicorn in the world. But alas, Adam sacrificed it. This would seem to explain a difficult point with the earlier midrash. If Adam sacrificed an animal then there would be no other descendants of that animal. So what animal must that have been? The unicorn! Another great story.