The owner or owners in fee of any lands constituting a portion of the district, which lands are not within the corporate limits of any city or village, may file with the board a petition praying that such lands be excluded and taken from the district. It shall describe the lands which the petitioners desire to have excluded and set out that the lands have not and cannot acquire any benefit from the water resources or other operations of the district. Such petition must be acknowledged in the same manner and form as required in case of a conveyance of land and be accompanied by a deposit of money sufficient to pay all costs of the exclusion proceedings. The secretary of the board shall cause a notice of filing of such petition to be published in the county in which the lands, or the major portion thereof, are located. The notice shall state the filing of such petition, the names of petitioners, descriptions of lands mentioned in the petition, and the prayer of the petitioners and notify all persons interested to appear at the office of the board at the time named in the notice, showing cause in writing, if any, why the petition should not be granted. The board at the time and place mentioned in the notice, or at the time or times to which the hearing of the petition may be adjourned, shall proceed to hear the petition and all objections thereto presented in writing by any person showing cause why the prayer of the petition should not be granted. The filing of such petition shall be deemed and taken as an assent by each and all such petitioners to the exclusion from the district of the lands mentioned in the petition or any part thereof. The board, if the allegations of the petition are found to be true, shall order that the lands mentioned in the petition or some portion thereof be excluded from a district and, if the board finds that the allegations are not true, shall order that the petition be denied. In case a contract has been made between the district and the United States or any agency thereof, no change shall be made in the boundaries of the district unless the Secretary of the Interior assents to the change in writing and such assent is filed with the board. Upon such assent, any lands excluded from the district shall upon order of the board be discharged from all liens in favor of the United States under the contract with the United States or under bonds deposited with its agents. Appeal may be taken to the district court of the district in which the lands, or the major portion thereof, are located by filing a transcript of the proceedings thereon in the manner and form as provided by sections 25-1901 to 25-1937.