What is the ruling of Islamic law regarding a couple who have been living in the same house for six years without speaking to each other, due to the husband's refusal to sell the house or to transfer half of its ownership to the wife, who participated in its construction? And is the husband permitted to refuse divorce for this reason?

A husband and wife abandoning each other is not permissible, due to the prohibition by the Prophet (peace be upon him) against a Muslim abandoning his brother for more than three days, and whoever does that is as if he has shed his blood. Both spouses must repent to Allah and reconcile their relationship, for reconciling relationships is better than fasting, prayer, and charity.