EX-5.1

Exhibit 5.1

Paul, Weiss, Rifkind, Wharton & Garrison LLP

1285 Avenue of the Americas

New York, New York 10019-6064

December 22, 2023

Andretti Acquisition Corp.

7615 Zionsville Road

Indianapolis, Indiana 46268

Andretti Acquisition Corp. Registration Statement on Form S-4

Ladies and Gentlemen:

We have acted as special counsel to Andretti Acquisition Corp., a Cayman Islands exempted company (the “Company”), in connection with the Registration Statement on Form S-4, as amended (the “Registration Statement”), of the Company, filed with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (the “Act”), and the rules and regulations thereunder (the “Rules”). You have asked us to furnish our opinion as to the legality of the securities being registered under the Registration Statement. The Registration Statement relates to the registration under the Act of (i) 31,535,365 shares (the “Shares”) of Common Stock of the New Company (as defined below), par value $0.0001 per share (the “New Company Common Stock”), (ii) 25,050,000 warrants to purchase shares of New Company Common Stock (the “Warrants”) and (iii) 25,050,000 shares of New Company Common Stock issuable upon exercise of the Warrants (“Warrant Shares” and, together with the Shares and Warrants, the “Securities”), in connection with the Business Combination Agreement, dated as of September 6, 2023 (the “Business Combination Agreement”), by and among the Company, Tigre Merger Sub, Inc. and Zapata Computing, Inc. (“Zapata”), and the transactions contemplated thereunder.

In connection with and immediately prior to the consummation of the business combination contemplated by the Business Combination Agreement (the “Business Combination”), the Company will change its jurisdiction of incorporation (the “Domestication”) by effecting a deregistration under the Cayman Islands Companies Act (As Revised) and a domestication under Section 388 of the General Corporation Law of the State of Delaware (the “DGCL”) by filing a notice of deregistration with the Cayman Islands Registrar of Companies, together with the necessary accompanying documents, and a certificate of corporate domestication (the “Certificate of Domestication”) simultaneously with a certificate of incorporation (the “Proposed Certificate of Incorporation”) with the Secretary of State of the State of Delaware (the “DE Secretary of State”). The Domestication is expected to be effectuated immediately prior to the consummation of the Business Combination (the “Closing”) and is subject to the approval of the shareholders of the Company. At the time of the Domestication, the Company will be renamed “Zapata Computing Holdings Inc.” (we herein refer to the Company on and after the time of the Domestication as the “New Company”).

The Shares consist of (i) 7,894,801 Shares resulting from the automatic conversion of 7,894,801 of the Company’s issued and outstanding Class A ordinary shares, par value $0.0001 per share (the “Class A Ordinary Shares”), by operation of law, on a one-for-one basis, into 7,894,801 shares of New Company Common Stock upon effectiveness of the Domestication, (ii) 5,750,000 Shares resulting from the automatic conversion of 5,750,000 of the Company’s issued and outstanding Class B ordinary shares, par value $0.0001 per share (the “Class B Ordinary Shares”), by operation of law, on a one-for-one basis, into 5,750,000 shares of New Company Common Stock upon effectiveness of the Domestication and (iii) 17,584,918 Shares resulting from the issuance of New Company Common Stock to Zapata’s securityholders in connection with the consummation of the Business Combination.

The Warrants consist of 25,050,000 warrants to acquire 25,050,000 Class A Ordinary Shares that will become warrants to acquire the corresponding number of shares of New Company Common Stock upon the Domestication. No other changes will be made to the terms of the outstanding Warrants as a result of the Domestication.

The Business Combination is subject to satisfaction or waiver of a number of conditions, including, among others, approval and adoption of the Business Combination Agreement by the Company’s shareholders as well as completion of the Domestication.

In connection with the furnishing of this opinion, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the following documents (collectively, the “Documents”):

the Registration Statement;

the Business Combination Agreement;

the form of Proposed Certificate of Incorporation to be effective upon the Domestication;

the form of bylaws of the New Company to be effective upon the Domestication; and

the Public Warrant Agreement, dated as of January 12, 2022, between the Company and Continental Stock Transfer & Trust Company (the “Public Warrant Agreement”).

In addition, we have examined such corporate records of the Company that we have considered appropriate; resolutions of the board of directors of the Company relating to, among other things, the Registration Statement, the Business Combination, the Domestication and the Public Warrant Agreement, certified by the Company; and such other certificates, agreements and documents that we deemed relevant and necessary as a basis for the opinions expressed below. We have also relied upon the factual matters contained in the representations and warranties of the Company made in the Documents and upon certificates of public officials and the officers of the Company.

In our examination of the documents referred to above, we have assumed, without independent investigation, the genuineness of all signatures, the legal capacity of all individuals who have executed any of the documents reviewed by us, the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as certified, photostatic, reproduced or conformed copies of valid existing agreements or other documents, the authenticity of all the latter documents and that the statements regarding matters of fact in the certificates, records, agreements, instruments and documents that we have examined are accurate and complete. We have further assumed that, before the issuance of the Securities, the conditions to consummating the transactions contemplated by the Business Combination Agreement, including with respect to the filing procedure for effecting a domestication under Section 388 of the DGCL, will have been satisfied or duly waived.

In addition to the foregoing, for the purpose of rendering our opinions as expressed herein, we have assumed that:

Prior to effecting the Domestication: (i) the Registration Statement, as finally amended, will have become effective under the Act; (ii) the shareholders of the Company will have approved, among other things, the Business Combination Agreement and the Domestication; and (iii) all other necessary action will have been taken under the applicable laws of the Cayman Islands to authorize and permit the Domestication, and any and all consents, approvals and authorizations from applicable Cayman Islands governmental and regulatory authorities required to authorize and permit the Domestication will have been obtained.

The current draft of the Proposed Certificate of Incorporation, in the form thereof submitted for our review, without alteration or amendment (other than identifying the appropriate date), will be duly authorized and executed and thereafter be duly filed with the DE Secretary of State in accordance with Section 103 of the DGCL, that no other certificate or document, other than the Certificate of Domestication as required under Section 388 of the DGCL, has been, or prior to the filing of the Proposed Certificate of Incorporation will be, filed by or in respect of the Company or the New Company with the DE Secretary of State and that the Company or the New Company will pay all fees and other charges required to be paid in connection with the filing of the Proposed Certificate of Incorporation.

Each Class A Ordinary Share and Class B Ordinary Share outstanding immediately prior to the effectiveness of the Domestication was duly authorized, validly issued, fully paid and non-assessable under the laws of the Cayman Islands and has been entered in the register of members (shareholders).

Based upon the above, and subject to the stated assumptions, exceptions and qualifications, we are of the opinion that:

Upon the effectiveness of the Domestication and the Business Combination as contemplated by the Business Combination Agreement, the Shares will be duly authorized, validly issued, fully paid and non-assessable.

Upon effectiveness of the Domestication, each Warrant will be a valid and binding obligation of the New Company, enforceable against the New Company in accordance with its terms, except that (i) the enforceability of the Warrants may be subject to bankruptcy, insolvency, reorganization, fraudulent conveyance or transfer, moratorium or similar laws affecting creditors’ rights generally and possible judicial action giving effect to governmental actions relating to persons or transactions or foreign laws affecting creditors’ rights and subject to general principles of equity (regardless of whether enforceability is considered in a proceeding in equity or at law) and (ii) we express no opinion as to the validity, legally binding effect or enforceability of provisions of the Public Warrant Agreement related to adjustments to the conversion rate in an amount that a court would determine in the circumstances under applicable law to be commercially unreasonable or a penalty or forfeiture.

The Warrant Shares have been duly authorized by all necessary corporate action on the part of the Company and, when issued, delivered and paid for in accordance with the terms of the Public Warrant Agreement, the Warrant Shares will be validly issued, fully paid and non-assessable.

The opinions expressed above are limited to the laws of the State of New York and the General Corporation Law of the State of Delaware. Our opinion is rendered only with respect to the laws, and the rules, regulations and orders under those laws, that are currently in effect.

We hereby consent to use of this opinion as an exhibit to the Registration Statement and to the use of our name under the heading “Legal Matters” contained in the prospectus included in the Registration Statement. In giving this consent, we do not thereby admit that we come within the category of persons whose consent is required by the Act or the Rules.

Very truly yours,

/s/ Paul, Weiss, Rifkind, Wharton & Garrison LLP

PAUL, WEISS, RIFKIND, WHARTON & GARRISON LLP