EXHIBIT 3.1
 
                                    RESTATED
                          CERTIFICATE OF INCORPORATION
                                 OF VERITY, INC.
 
     VERITY, INC., a corporation organized and existing under and by virtue of
the General Corporation Law of the State of Delaware, DOES HEREBY CERTIFY:
 
1.   (a)  The present name of the corporation is Verity, Inc.
 
     (b)  The name under which the corporation was originally incorporated is
          Verity Delaware Corporation and the date of filing of its original
          Certificate of Incorporation with the Secretary of State was June 28,
          1995.
 
2.   The Restated Certificate of Incorporation only restates and integrates and
does not further amend the provisions of the corporation's Certificate of
Incorporation as theretofore amended or supplemented. There is no discrepancy
between those provisions and the provisions of the restated certificate. The
corporation's Certificate of Incorporation is restated to read in its entirety
as follows:
 
     FIRST:    The name of the Corporation is Verity, Inc. (hereinafter
               sometimes referred to as the "Corporation").
 
     SECOND:   The address of the registered office of the Corporation in the
               State of Delaware is the Prentice-Hall Corporation System, Inc.,
               32 Loockerman Square, Suite L-100, in the City of Dover, County
               of Kent. The name of the registered agent at that address is The
               Prentice-Hall Corporation System, Inc.
 
     THIRD:    The purpose of the Corporation is to engage in any lawful act or
               activity for which a corporation may be organized under the
               General Corporation Law of Delaware.
 
     FOURTH:
 
                                      STOCK
 
     The Corporation is authorized to issue two classes of shares to be
designated respectively Preferred Stock, having a par value of $0.001 per share
("Preferred"), and Common Stock, having a par value of $0.001 per share
("Common"). The total number of shares of Preferred this Corporation shall have
authority to issue to 1,999,995, and the total number of shares of Common this
Corporation shall have authority to issue is 200,000,000.
 
     The shares of Preferred authorized by this Certificate of Incorporation may
be issued from time to time in one or more series. The Board of Directors of
this Corporation is authorized to determine, alter or eliminate any or all of
the rights, preferences, privileges and restrictions granted to or imposed upon
any wholly unissued series of Preferred, and to fix, alter, or reduce the number
of shares comprising any such series (but not below the number of such shares
then
 
 
<PAGE>   2
 
outstanding) and the designation thereof, or any of them, and to provide for
rights and terms of redemption or conversion of the shares of any such series.
 
     The relative rights, preferences, privileges and restrictions granted to or
imposed upon the Common and the Preferred are as follows:
 
     SECTION 1. DESIGNATION AND AMOUNT.
 
     A series of Preferred Shares is designated Series A Preferred Stock (the
"Series A Preferred Stock"), $.001 par value per share, and the number of shares
constituting such series is 500,000.
 
     SECTION 2. DIVIDENDS AND DISTRIBUTIONS.
 
          (A)  The dividend rate on the shares of Series A Preferred Stock shall
be for each quarterly dividend (hereinafter referred to as a "quarterly dividend
period"), which quarterly dividend periods shall commence on January 1, April 1,
June 1 and October 1 each year (each such date being referred to herein as a
"Quarterly Dividend Payment Date") (or in the case of original issuance, from
the date of original issuance) and shall end on and include the day next
preceding the first date of the next quarterly dividend period, at a rate per
quarterly dividend period (rounded to the nearest cent) equal to the greater of
(a) $1,500 or (b) subject to the provisions for adjustment hereinafter set
forth, 100 times the aggregate per share amount of all cash dividends, and 100
times the aggregate per share amount (payable in cash, based upon the fair
market value at the time the non-cash dividend or other distribution is declared
as determined in good faith by the Board of Directors) of all non-cash dividends
or other distributions other than a dividend payable in shares of Common Stock
or a subdivision of the outstanding shares of Common Stock (by reclassification
or otherwise), declared (but not withdrawn) on the Common Stock, par value $.001
per share, of the Corporation (the "Common Stock") during the immediately
preceding quarterly dividend period, or, with respect to the first quarterly
dividend period, since the first issuance of any share or fraction of a share of
Series A Preferred Stock. In the event this Company shall at any time after
October 2, 1996 (the "Rights Declaration Date") (i) declare any dividend on
Common Stock payable in shares of Common Stock, (ii) subdivide the outstanding
Common Stock, or (iii) combine the outstanding Common Stock into a smaller
number of shares, then in each such case the amount to which holders of shares
of Series A Preferred Stock were entitled immediately prior to such event under
clause (b) of the preceding sentence shall be adjusted by multiplying such
amount by a fraction the numerator of which is the number of shares of Common
Stock outstanding immediately after such event and the denominator of which is
the number of shares of Common Stock that were outstanding immediately prior to
such event.
 
          (B)  Dividends shall begin to accrue and be cumulative on outstanding
shares of Series A Preferred Stock from the Quarterly Dividend Payment Date next
preceding the date of issue of such shares of Series A Preferred Stock, unless
the date of issue of such shares is prior to the record date for the first
Quarterly Dividend Payment Date, in which case dividends on such shares shall
begin to accrue from the date of issue of such shares, or unless the date of
issue is a Quarterly Dividend Payment Date or is a date after the record date
for the determination of holders of shares of Series A Preferred Stock entitled
to receive a quarterly dividend and before
 
 
                                       2.
<PAGE>   3
 
such Quarterly Dividend Payment Date, in either of which events such dividends
shall begin to accrue and be cumulative from such Quarterly Dividend Payment
Date. Accrued but unpaid dividends shall not bear interest. Dividends paid on
the shares of Series A Preferred Stock in an amount less than the total amount
of such dividends at the time accrued and payable on such shares shall be
allocated pro rata on a share-by-share basis among all such shares at the time
outstanding. The Board of Directors may fix a record date for the determination
of holders of shares of Series A Preferred Stock entitled to receive payment of
a dividend or distribution declared thereon, which record date shall be no more
than 45 days prior to the date fixed for the payment thereof.
 
     SECTION 3. VOTING RIGHTS.
 
     The holders of shares of Series A Preferred Stock shall have the following
voting rights:
 
          (A)  Subject to the provision for adjustment hereinafter set forth,
each share of Series A Preferred Stock shall entitle the holder thereof to 100
votes on all matters submitted to a vote of the stockholders of the Corporation.
In the event the Corporation shall at any time after the Rights Declaration Date
(i) declare any dividend on Common Stock payable in shares of Common Stock, (ii)
subdivide the outstanding Common Stock, or (iii) combine the outstanding Common
Stock into a smaller number of shares, then in each such case the number of
votes per share to which holders of shares of Series A Preferred Stock were
entitled immediately prior to such event shall be adjusted by multiplying such
number by a fraction the numerator of which is the number of shares of Common
Stock outstanding immediately after such event and the denominator of which is
the number of shares of Common Stock that were outstanding immediately prior to
such event.
 
          (B)  Except as otherwise provided herein, in the Certificate of
Incorporation or by law, the holders of shares of Series A Preferred Stock and
the holders of shares of Common Stock shall vote together as one class on all
matters submitted to a vote of stockholders of the Corporation.
 
          (C)  Except as set forth herein, in the Certificate of Incorporation
and in the By-laws, holders of Series A Preferred Stock shall have no special
voting rights and their consent shall not be required (except to the extent they
are entitled to vote with holders of Common Stock as set forth herein) for
taking any corporate action.
 
     SECTION 4. REACQUIRED SHARES.
 
     Any shares of Series A Preferred Stock purchased or otherwise acquired by
the Corporation in any manner whatsoever shall be retired and cancelled promptly
after the acquisition thereof. All such shares shall upon their cancellation
become authorized but unissued shares of Preferred Stock and may be reissued as
part of a new series of Preferred Stock to be created by resolution or
resolutions of the Board of Directors, subject to the conditions and
restrictions on issuance set forth herein.
 
                                       3.
<PAGE>   4
 
     SECTION 5. LIQUIDATION, DISSOLUTION OR WINDING UP.
 
          (A)  In the event of any voluntary or involuntary liquidation,
dissolution or winding up of the Corporation, the holders of the Series A
Preferred Stock shall be entitled to receive the greater of (a) $6,000 per
share, plus accrued dividends to the date of distribution, whether or not earned
or declared, or (b) an amount per share, subject to the provision for adjustment
hereinafter set forth, equal to 100 times the aggregate amount to be distributed
per share to holders of Common Stock. In the event the Corporation shall at any
time after the Rights Declaration Date (i) declare any dividend on Common Stock
payable in shares of Common Stock, (ii) subdivide the outstanding Common Stock,
or (iii) combine the outstanding Common Stock into a smaller number of shares,
then in each such case the amount to which holders of shares of Series A
Preferred Stock were entitled immediately prior to such event pursuant to clause
(b) of the preceding sentence shall be adjusted by multiplying such amount by a
fraction the numerator of which is the number of shares of Common Stock
outstanding immediately after such event and the denominator of which is the
number of shares of Common Stock that were outstanding immediately prior to such
event.
 
     SECTION 6. CONSOLIDATION, MERGER, ETC.
 
     In case the Corporation shall enter into any consolidation, merger,
combination or other transaction in which the shares of Common Stock are
exchanged for or changed into other stock or securities, cash and/or any other
property, then in any such case the shares of Series A Preferred Stock shall at
the same time be similarly exchanged or changed in an amount per share (subject
to the provision for adjustment hereinafter set forth) equal to 100 times the
aggregate amount of stock, securities, cash and/or any other property (payable
in kind), as the case may be, into which or for which each share of Common Stock
is changed or exchanged. In the event the Corporation shall at any time after
the Rights Declaration Date (i) declare any dividend on Common Stock payable in
shares of Common Stock, (ii) subdivide the outstanding Common Stock, or (iii)
combine the outstanding Common Stock into a smaller number of shares, then in
each such case the amount set forth in the preceding sentence with respect to
the exchange or change of shares of Series A Preferred Stock shall be adjusted
by multiplying such amount by a fraction the numerator of which is the number of
shares of Common Stock outstanding immediately after such event and the
denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.
 
     SECTION 7. NO REDEMPTION.
 
     The shares of Series A Preferred Stock shall not be redeemable.
 
     SECTION 8. FRACTIONAL SHARES.
 
     Series A Preferred Stock may be issued in fractions of a share which shall
entitle the holder, in proportion to such holder's fractional shares, to
exercise voting rights, receive dividends, participate in distributions and have
the benefit of all other rights of holders of Series A Preferred Stock. All
payments made with respect to fractional shares hereunder shall be rounded to
the nearest whole cent.
 
                                       4.
<PAGE>   5
 
     SECTION 9. CERTAIN RESTRICTIONS.
 
          (A)  Whenever quarterly dividends or other dividends or distributions
payable on the Series A Preferred Stock as provided in Section 2 are in arrears,
thereafter and until all accrued and unpaid dividends and distributions, whether
or not declared, on shares of Series A Preferred Stock outstanding shall have
been paid in full, the Corporation shall not:
 
               (i)  declare or pay dividends on, make any other distributions
on, or redeem or purchase or otherwise acquire for consideration any shares of
stock ranking junior (either as to dividends or upon liquidation, dissolution or
winding up) to the Series A Preferred Stock;
 
               (ii) declare or pay dividends on or make any other distributions
on any shares of stock ranking on a parity (either as to dividends or upon
liquidation, dissolution or winding up) with the Series A Preferred Stock,
except dividends paid ratably on the Series A Preferred Stock and all such
parity stock on which dividends are payable or in arrears in proportion to the
total amounts to which the holders of all such shares are then entitled;
 
               (iii) redeem or purchase or otherwise acquire for consideration
shares of any stock ranking on a parity (either as to dividends or upon
liquidation, dissolution or winding up) with the Series A Preferred Stock,
provided that the Corporation may at any time redeem, purchase or otherwise
acquire shares of any such parity stock in exchange for shares of any stock of
the Corporation ranking junior (either as to dividends or upon dissolution,
liquidation or winding up) to the Series A Preferred Stock; or
 
               (iv) purchase or otherwise acquire for consideration any shares
of Series A Preferred Stock, or any shares of stock ranking on a parity with the
Series A Preferred Stock, except in accordance with a purchase offer made in
writing or by publication (as determined by the Board of Directors) to all
holders of such shares upon such terms as the Board of Directors, after
consideration of the respective annual dividend rates and other relative rights
and preferences of the respective series and classes shall determine in good
faith will result in fair and equitable treatment among the respective series or
classes.
 
     (B)  The Corporation shall not permit any subsidiary of the Corporation to
purchase or otherwise acquire for consideration any shares of stock of the
Corporation unless the Corporation could, under paragraph (A) of this Section 9,
purchase or otherwise acquire such shares at such time and in such manner.
 
     SECTION 10. RANKING.
 
     The Series A Preferred Stock shall be junior to all other Series of the
Corporation's preferred stock as to the payment of dividends and the
distribution of assets, unless the terms of any series shall provide otherwise.
 
     SECTION 11. AMENDMENT.
 
                                       5.
<PAGE>   6
 
     The Certificate of Incorporation of the Corporation shall not be amended in
any manner which would materially alter or change the powers, preferences or
special rights of the Series A Preferred Stock so as to affect them adversely
without the affirmative vote of the holders of two-thirds or more of the
outstanding shares of Series A Preferred Stock voting together as a single
class.
 
FIFTH:    The following provisions are inserted for the management of the
          business and the conduct of the affairs of the Corporation, and for
          further definition, limitation and regulation of the powers of the
          Corporation and of its directors and stockholders:
 
A.        The business and affairs of the Corporation shall be managed by or
          under the direction of the Board of Directors. In addition to the
          powers and authority expressly conferred upon them by statute or by
          this Certificate of Incorporation or the By-Laws of the Corporation,
          the directors are hereby empowered to exercise all such powers and do
          all such acts and things as may be exercised or done by the
          Corporation.
 
B.        The directors of the Corporation need not be elected by written ballot
          unless the By-Laws so provide.
 
C.        On and after closing date of the first sale of the Corporation's
          Common Stock pursuant to a firmly underwritten registered public
          offering the ("IPO"), any action required or permitted to be taken by
          the stockholders of the Corporation must be effected at a duly called
          annual or special meeting of stockholders of the Corporation and may
          not be effected by any consent in writing by such stockholders. Prior
          to such sale, unless otherwise provided by law, any action which may
          otherwise be taken at any meeting of the stockholders may be taken
          without a meeting and without prior notice, if a written consent
          describing such actions is signed by the holders of outstanding shares
          having not less than the minimum number of votes which would be
          necessary to authorize or take such action at a meeting at which all
          shares entitled to vote thereon were present and voted.
 
D.        Special meetings of stockholders of the Corporation may be called only
          (1) by the Board of Directors pursuant to a resolution adopted by a
          majority of the total number of authorized directors (whether or not
          there exist any vacancies in previously authorized directorships at
          the time any such resolution is presented to the Board for adoption)
          or (2) by the holders of not less than ten percent (10%) of all of the
          shares entitled to cast votes at the meeting.
 
SIXTH:
 
A.        The number of directors shall initially be set at five (5) and,
          thereafter, shall be fixed from time to time exclusively by the Board
          of Directors pursuant to a resolution adopted by a majority of the
          total number of authorized directors (whether or not there exist any
          vacancies in previously authorized directorships at the time any such
          resolution is presented to the Board for adoption). Upon the
 
                                       6.
<PAGE>   7
 
          closing of the IPO, the directors shall be divided into three classes
          with the term of office of the first class (Class I) to expire at the
          first annual meeting of the stockholders following the IPO; the term
          of office of the second class (Class II) to expire at the second
          annual meeting of stockholders held following the IPO; the term of
          office of the third class (Class III) to expire at the third annual
          meeting of stockholders; and thereafter for each such term to expire
          at each third succeeding annual meeting of stockholders after such
          election. Subject to the rights of the holders of any series of
          Preferred Stock then outstanding, a vacancy resulting from the removal
          of a director by the stockholders as provided in Article SIXTH,
          Section C below may be filled at a special meeting of the stockholders
          held for that purpose. All directors shall hold office until the
          expiration of the term for which elected, and until their respective
          successors are elected, except in the case of the death, resignation,
          or removal of any director.
 
B.        Subject to the rights of the holders of any series of Preferred Stock
          then outstanding, newly created directorships resulting from any
          increase in the authorized number of directors or any vacancies in the
          Board of Directors resulting from death, resignation or other cause
          (other than removal from office by a vote of the stockholders) may be
          filled only by a majority vote of the directors then in office, though
          less than a quorum, and directors so chosen shall hold office for a
          term expiring at the next annual meeting of stockholders at which the
          term of office of the class to which they have been elected expires,
          and until their respective successors are elected, except in the case
          of the death, resignation, or removal of any director. No decrease in
          the number of directors constituting the Board of Directors shall
          shorten the term of any incumbent director.
 
C.        Subject to the rights of the holders of any series of Preferred Stock
          then outstanding, any directors, or the entire Board of Directors, may
          be removed from office at any time, with or without cause, but only by
          the affirmative vote of the holders of at least a majority of the
          voting power of all of the then outstanding shares of capital stock of
          the Corporation entitled to vote generally in the election of
          directors, voting together as a single class. Vacancies in the Board
          of Directors resulting from such removal may be filled by a majority
          of the directors then in office, though less than a quorum, o by the
          stockholders as provided in Article SIXTH, Section A above. Directors
          so chosen shall hold office for a term expiring at the next annual
          meeting of stockholders at which the term of office of the class to
          which they have been elected expires, and until their respective
          successors are elected, except in the case of the death, resignation,
          or removal of any director.
 
SEVENTH:  The Board of Directors is expressly empowered to adopt, amend or
          repeal By-Laws of the Corporation. Any adoption, amendment or repeal
          of By-Laws of the Corporation by the Board of Directors shall require
          the approval of a majority of the total number of authorized directors
          (whether or not there exist any vacancies in previously authorized
          directorships at the time any resolution providing for adoption,
          amendment or repeal is presented to the Board). The stockholders shall
          also have power to adopt, amend or repeal the By-Laws of the
          Corporation. Any adoption, amendment or repeal of By-Laws of the
          Corporation by the stockholders
 
                                       7.
<PAGE>   8
 
          shall require, in addition to any vote of the holders of any class or
          series of stock of the Corporation required by law or by this
          Certificate of Incorporation, the affirmative vote of the holders of
          at least sixty-six and two-thirds percent (66-2/3%) of the voting
          power of all of the then outstanding shares of the capital stock of
          the Corporation entitled to vote generally in the election of
          directors, voting together as a single class.
 
EIGHTH:   A director of the Corporation shall not be personally liable to the
          Corporation or its stockholders for monetary damages for breach of
          fiduciary duty as a director, except for liability (i) for any breach
          of the director's duty of loyalty to the Corporation or its
          stockholders, (ii) for acts or omissions not in good faith or which
          involved intentional misconduct or a knowing violation of law, (iii)
          under Section 174 of the Delaware General Corporation Law, or (iv) for
          any transaction from which the director derived an improper personal
          benefit.
 
          If the Delaware General Corporation Law is hereafter amended to
          authorize the further elimination or limitation of the liability of a
          director, then the liability of a director of the Corporation shall be
          eliminated or limited to the fullest extent permitted by the Delaware
          General Corporation Law, as so amended.
 
          Any repeal or modification of the foregoing provisions of this Article
          EIGHT by the stockholders of the Corporation shall not adversely
          affect any right or protection of a director of the Corporation
          existing at the time of such repeal or modification.
 
NINTH:    The Corporation reserves the right to amend or repeal any provision
          contained in this Certificate of Incorporation in the manner
          prescribed by the laws of the State of Delaware and all rights
          conferred upon stockholders are granted subject to this reservation;
          provided, however, that, notwithstanding any other provision of this
          Certificate of Incorporation or any provision of law which might
          otherwise permit a lesser vote or no vote, but in addition to any vote
          of the holders of any class or series of the stock of this Corporation
          required by law or by this Certificate of Incorporation, the
          affirmative vote of the holders of at 66-2/3% of the voting power of
          all of the then outstanding shares of the capital stock of the
          Corporation entitled to vote generally in the election of directors,
          voting together as a single class, shall be required to amend or
          repeal this Article NINTH, Article FIFTH, Article SIXTH, Article
          SEVENTH or Article EIGHT.
 
3.   This Restated Certificate of Incorporation was duly adopted by the Board of
Directors in accordance with the applicable provisions of Section 245 of the
General Corporation Law of the State of Delaware.
 
 
                                       8.
<PAGE>   9
 
     IN WITNESS WHEREOF, Verity, Inc. has caused this Restated Certificate of
Incorporation to be signed by Gary J. Sbona, its Chief Executive Officer, this
28th day of September, 2000.
 
                                              VERITY, INC.
                                              a Delaware corporation
 
                                              By: /s/ Gary J. Sbona
                                                  ------------------------------
                                                  Gary J. Sbona
                                                  Chief Executive Officer