Exhibit 5.1

Seaport West 155 Seaport Boulevard Boston, MA 02210-2600   617 832 1000 main 617 832 7000 fax

June 14, 2024

Zapata Computing Holdings Inc.

100 Federal Street, 20th Floor

Boston, MA 02110

Re: Registration Statement on Form S-8

Ladies and Gentlemen:

We are familiar with the Registration Statement on Form S-8 (the “Registration Statement”) being filed by Zapata Computing Holdings Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), on the date hereof. The Registration Statement relates to the offer and sale by the Company of up to 8,468,701 shares (the “Shares”) of its common stock, par value $0.0001 per share (“Common Stock”), consisting of:

1. 3,491,146 shares of Common Stock (the “2024 EIP Shares”) issuable under the Company’s 2024 Equity and Incentive Plan (the “2024 EIP”);

2. 581,858 shares of Common Stock (the “2024 ESPP Shares”) issuable under the Company’s 2024 Employee Stock Purchase Plan (the “2024 ESPP”);

3. 2,895,697 shares of Common Stock (the “2018 Plan Shares”) issuable upon the exercise of stock options granted under the Zapata Computing, Inc. 2018 Stock Incentive Plan (the “2018 Plan” and such options, the “2018 Plan Options”), which 2018 Plan Options were assumed by the Registrant pursuant to the Business Combination Agreement, dated September 6, 2023, by and among the Company (formerly known as Andretti Acquisition Corp.), Tigre Merger Sub, Inc. and Zapata Computing, Inc.;

4. 900,000 shares of Common Stock (the “Inducement Shares”) issuable upon exercise of nonstatutory stock options granted pursuant to award agreements dated May 13, 2024 and June 3, 2024, each as an inducement to an employee’s acceptance of employment with the Company (the “Inducement Awards”); and

5. 600,000 shares of Common Stock (the “2024 Inducement Plan Shares” and, together with the 2024 EIP Shares, the 2024 ESPP Shares, the 2018 Plan Shares and the Inducement Shares, the “Shares”) issuable under the Company’s 2024 Inducement Stock Incentive Plan (the “2024 Inducement Plan”).

In arriving at the opinion expressed below, we have examined the Certificate of Incorporation and Bylaws of the Company, the records of meetings and consents of the Company’s Board of Directors, or committees thereof, records of the proceedings of its stockholders deemed to be relevant to this opinion letter, the 2024 EIP, the 2024 ESPP, the 2018 Plan, the 2018 Plan Options, the Inducement Awards and the 2024 Inducement Plan, each as provided to us by the Company, and the Registration Statement.

In addition, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to authentic original documents of all documents submitted to us as copies and the due authorization, execution and delivery of all documents by all persons other than the Company, where authorization, execution and delivery are prerequisites to the effectiveness of such documents. We have also made such investigations of law as we have deemed appropriate as a basis for the opinions expressed below.

Zapata Computing Holdings Inc.

June 14, 2024

Page 2

We have assumed that the purchase price or other consideration to be received by the Company for the Shares, other than the 2018 Plan Shares and the Inducement Shares, will be valid consideration equal to or in excess of the par value thereof.

In rendering the opinion expressed below, we express no opinion other than as to the Delaware General Corporation Law.

On the basis of the foregoing, it is our opinion that (i) the 2024 EIP Shares, when issued and delivered in accordance with the terms of the 2024 EIP and the awards thereunder, (ii) the 2024 ESPP Shares, when issued and delivered in accordance with the terms of the 2024 ESPP, (iii) the 2018 Plan Shares, when issued and delivered in accordance with the terms of the 2018 Plan and the 2018 Plan Options, (iv) the Inducement Shares, when issued and delivered in accordance with the respective Inducement Award, and (v) the 2024 Inducement Plan Shares, when issued and delivered in accordance with the terms of the 2024 Inducement Plan and the awards thereunder, in each case against the Company’s receipt of the purchase price or other consideration therefor, will be validly issued, fully paid and non-assessable.

This opinion is to be used only in connection with the offer and sale of the Shares while the Registration Statement is in effect.

This opinion is being delivered solely for the benefit of the Company and such other persons as are entitled to rely upon it pursuant to the applicable provisions of the Securities Act. This opinion may not be used, quoted, relied upon or referred to for any other purpose, nor may it be used, quoted, relied upon or referred to by any other person, for any purpose, without our prior written consent.

This opinion is based upon currently existing statutes, rules and regulations and judicial decisions and is rendered as of the date hereof, and we disclaim and obligation to advise you of any change in any of the foregoing sources of law or subsequent developments in law or changes in facts or circumstances which might affect any matters or opinions set forth herein.

We consent to the filing of this opinion as an exhibit to the Registration Statement. In giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

This opinion letter shall be interpreted in accordance with the Core Opinion Principles jointly issued by the Committee on Legal Opinions of the American Bar Association’s Business Law Section and the Working Group on Legal Opinions Foundation as published in 74 Business Lawyer 815 (2019).

Very truly yours,
FOLEY HOAG LLP
By:	/s/ Stacie S. Aarestad
	a Partner