Exhibit 5.1

May 1, 2023

Core Laboratories Inc.

6316 Windfern Road,

Houston, Texas 77040

Ladies and Gentlemen:

We have acted as counsel for Core Laboratories Inc., a Delaware corporation (the “Company”), as successor to Core Laboratories N.V. (“Core Lab N.V.”) in connection with the Post-Effective Amendment No. 1 to the following registration statements on Form S-8 previously files with the Securities and Exchange Commission by Core Lab N.V. (collectively, the “Registration Statements”): (i) Registration No. 33-98588, (ii) Registration No. 33-98590, (iii) Registration No. 33-80473, (iv) Registration No. 333-40639, (v) Registration No. 333-40641, (vi) Registration No. 333-43859, (vii) Registration No. 333-73772, (viii) Registration No. 333-73774, (ix) Registration No. 333-231277, and (x) Registration No. 333-248137 under the Securities Act of 1933, as amended (the “Act”). The Registration Statements relate to the registration under the Act of shares of the Company’s common stock, par value $0.01 per share (the “Shares”), issuable in respect of awards under the Company Plans (as defined below).

On May 1, 2023, the Company completed reorganization transactions pursuant to which, among other things, the Company acquired all of the issued and outstanding common shares of Core Lab N.V. and the Company assumed, among all other compensation or benefit plans, each of the following equity-based incentive plans: (i) the Core Laboratories N.V. 2020 Long Term Incentive Plan, (ii) the 2014 Non-Employee Director Stock Incentive Plan, (iii) the Core Laboratories, Inc. Profit Sharing and Retirement Plan (collectively, including any schedules or appendices thereto, as amended from time to time, the “Core Lab N.V. Incentive Plans” and following such assumption and amendment by the Company, the “Company Incentive Plans”). The Company also assumed each outstanding stock option (together with any associated tandem stock appreciation right), stock appreciation right, performance share unit, restricted share unit, deferred share unit, restricted stock and other share-based award granted by Core Lab N.V. pursuant to the Core Lab N.V. Incentive Plans (collectively, the “Core Lab N.V. Incentive Awards”), and such outstanding awards were exchanged for a substantially equivalent incentive award based on the Shares of the Company (collectively, the “Company Incentive Awards”) pursuant to the Company Incentive Plans. The Company Incentive Awards are subject to substantially the same terms and conditions as the Core Lab N.V. Incentive Awards, except, in the case of equity-based Core Lab N.V. Incentive Awards, the securities issuable upon exercise or settlement of the Company Incentive Awards, as applicable, are Shares (or their cash equivalent) rather than common shares of Core Lab N.V. (or their cash equivalent).

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In reaching the opinions set forth herein, we have examined and are familiar with originals or copies, certified or otherwise identified to our satisfaction, of such documents and records of the Company and such statutes, regulations and other instruments as we deemed necessary or advisable for purposes of this opinion, including (i) the Registration Statements, (ii) certain resolutions adopted by the board of directors of the Company, (iii) the Core Lab N.V. Incentive Plans, and (iv) such other certificates, instruments, and documents as we have considered necessary for purposes of this opinion letter. As to any facts material to our opinions, we have made no independent investigation or verification of such facts and have relied, to the extent that we deem such reliance proper, upon certificates of public officials and officers or other representatives of the Company.

We have assumed (i) the legal capacity of all natural persons, (ii) the genuineness of all signatures, (iii) the authority of all persons signing all documents submitted to us on behalf of the parties to such documents, (iv) the authenticity of all documents submitted to us as originals, (v) the conformity to authentic original documents of all documents submitted to us as copies, and (vi) that all information contained in all documents reviewed by us is true, correct and complete, and (vii) that the Shares will be issued in accordance with the terms of the Company Incentive Plans.

Based on the foregoing and subject to the limitations set forth herein, and having due regard for the legal considerations we deem relevant, we are of the opinion that the Shares have been duly authorized and, when the Shares are issued by the Company in accordance with the terms of the Company Incentive Plans and the instruments executed pursuant to the Company Incentive Plans, as applicable, that govern the awards to which any Share relates, the Shares will be validly issued, fully paid and non-assessable.

This opinion is limited in all respects to the General Corporation Law of the State of Delaware. We express no opinion as to any other law or any matter other than as expressly set forth above, and no opinion as to any other law or matter may be inferred or implied herefrom. The opinions expressed herein are rendered as of the date hereof and we expressly disclaim any obligation to update this letter or advise you of any change in any matter after the date hereof.

This opinion letter may be filed as an exhibit to the Registration Statements. In giving this consent, we do not thereby admit that we come within the category of persons whose consent is required under Section 7 of the Act.

Very truly yours,

/s/ Vinson & Elkins L.L.P.

Vinson & Elkins L.L.P.