How did Krishna resolve the conflict?
This is mentioned in Mahabharata: Karna Parva
[Krishna sais] The son of Dharma (Yudhishthira) does not deserve death. Thy vow also, O Arjuna, should be kept. Listen now to my counsels that will be agreeable to thee, to counsels in consequence of which Yudhishthira without being actually deprived of life may yet be dead. As long as one that is deserving of respect continues to receive respect, one is said to live in the world of men. When, however, such a person meets with disrespect, he is spoken of as one that is dead though alive. This king hath always been respected by thee and by Bhima and the twins, as also by all heroes and all persons in the world that are venerable for years. In some trifle then show him disrespect. Therefore, O Partha, address this Yudhishthira as 'thou' when his usual form of address is 'your honour.' A superior, O Bharata, by being addressed as 'thou,' is killed though not deprived of life. Bear thyself thus, O son of Kunti, towards king Yudhishthira, the just. Adopt this censurable behaviour, O perpetuator of Kuru's race! This best audition of all auditions, hath been declared by both Atharvan and Angiras. Men desiring good should always act in this way without scruples of any kind. Without being deprived of life a superior is yet said to be killed if that venerable one is addressed as 'thou.' Conversant with duty as thou art, address king Yudhishthira the just, in the manner I have indicated.
And then Arjuna showed some disrespect towards Yudhishthira as mentioned in next chapter.
This complete chapter contains many useful teachings such as
- Truth may be unutterable, and even falsehood may be utterable where falsehood would become truth and truth would become falsehood. In a situation of peril to life and in marriage, falsehood becomes utterable. In a situation involving the loss of one's entire property, falsehood becomes utterable. On an occasion of marriage, or of enjoying a woman, or when life is in danger, or when one's entire property is about to be taken away, or for the sake of a Brahmana, falsehood may be uttered. These five kinds of falsehood have been declared to be sinless. On these occasions falsehood would become truth and truth would become falsehood.
He is a fool that practises truth without knowing the difference between truth and falsehood. One is said to be conversant with morality when one is able to distinguish between truth and falsehood.
- Story of Kausika who always used to speak the truth. Due to his one truth, robbers found out the persons they sought and slew them all. In consequence of that great sin, Kausika fell into a grievous hell.
Meaning of Krishna's advice to Yudhisthira before Drona Vadh
What does Krishna mean when he says falsehood may be uttered on the occasion of enjoying a woman?