And the explanation of the evidence that the Prophet Muhammad (peace be upon him) negated the acceptance of the prayer of the person who, after committing an act that nullifies ablution (such as urination or defecation, etc.), prays without ablution—not the negation of the acceptance of the prayer of every person who stands for prayer without having committed any act that necessitates ablution.
Hadith Referenceصحيح ابن خزيمه / كتاب: الوضوء / Q11
It is narrated from Sayyiduna Abu Hurairah (may Allah be pleased with him) that he said: The Messenger of Allah (peace and blessings be upon him) said: "When any one of you breaks his ablution, his prayer is not accepted until he performs ablution again."
Hadith Referenceصحيح ابن خزيمه / كتاب: الوضوء / 11
Hadith Takhrij«صحيح بخارى ، كتاب الوضوء ، باب لا تقبل صلاة بغير طهور ، رقم الحديث: 135 ، صحيح مسلم ، الطهارة ، باب وجوب الطهارة للصلاة 225 ، سنن ترمذي: 7 ، سنن ابي داود: 60 ، مسند احمد 308/2 ، 318 ، 7732»