Any person, company or corporation who shall, by themselves or by or through their grantors, have been in the actual continuous and undisputed possession of any portion of any of said lands within the limits of said grant for a period of ten years next immediately preceding the date of the entering of the said decree of said land court confirming said grant to said trustees, or who shall be the owner of any portion of the said lands under any deed or conveyance from the original town of Socorro, or from or by or through any conveyance from any of the original settlers or lotholders within the limits of said grant, or from any deed or conveyance from any other lawful authority, shall be entitled to a deed as against said trustees to that portion of said land of which he, it or they shall have been so in possession, or to which he, it or they shall have title thereto as aforesaid: provided, however, that the action of said city council or trustees in refusing said deed to any person, company or corporation shall not be final, but all question as to the right of said person, company or corporation to said deed or deeds shall be left to the determination of the district court in the county where said grant is situated, in a proper proceeding instituted therefor by said individual, company or corporation within thirty days after the refusal of said city council or trustees to execute said deed, and the court in determining the right of said person, company or corporation to said deed or deeds for said lands as against said city and trustees shall be governed by the same rules of law and equity as now govern the courts of this state in determining the rights and titles to lands as between individuals, subject to the provisions of this article.