Document:

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                                                                   EXHIBIT 10.73

                            PARTICIPATION CERTIFICATE

         This PARTICIPATION CERTIFICATE is delivered by AppliedTheory
Corporation, a Delaware corporation (the "Company"), to ____________, a
_________ [TYPE AND JURISDICTION OF ENTITY] (the "PARTICIPANT"), pursuant to
that certain Amendment Agreement (the "AMENDMENT AGREEMENT") between the Company
and the Participant, among other Investors, dated the date hereof. Capitalized
terms which are not defined herein shall have the meaning set forth in the
Amendment Agreement. In connection therewith, the Company hereby certifies to
the Participant as follows:

         1. The Company hereby irrevocably participates and transfers to
Participant the right to receive certain percentages of the consideration (such
percentages of the consideration shall hereinafter be referred to as the
"PARTICIPANT'S INTEREST" and, together with the other rights of the Participant
hereunder, as the "PARTICIPATION") otherwise paid and payable, directly or
indirectly, to the Company, its subsidiaries, its shareholders, its affiliates
or any other person on behalf of the Company (each, a "PAYEE") by or on behalf
of any acquirer in connection with each Sale of the Company up to and including
the earlier of the Last Sale Date and the date of a Relevant Sale, as set forth
below:

         a. [___]% of the consideration up to $10,000,000 shall be paid to the
Participant.

         b. [___]% of the consideration between $10,000,000 and $30,000,000
shall be paid to the Participant.

         c. [____]% of the consideration between $30,000,000 and $50,000,000
shall be paid to the Participant.

         d. [___]% of the consideration above $50,000,000 shall be paid to the
Participant.

         For the avoidance of doubt, in a case where a Sale of the Company
resulted in consideration of $10,000,000, then, with respect to the next Sale of
the Company, the schedule would commence with paragraph (b) above.

         2. The Company represents and warrants to the Participant as of the
date hereof that this Certificate has been duly and validly authorized, executed
and delivered by the Company and is legal, valid, binding and enforceable
against the Company in accordance with its terms.

         3. The Company has not, directly or indirectly, assigned, transferred,
participated, sold, conveyed, disposed of or terminated, in whole or in part,
any of its right, title and interest in and to the Participated Interest, except
to the other Investors in accordance with the Amendment Agreement and the
participation certificates issued in connection therewith, and is not a party to
any other agreement or obligation which would result in any of the foregoing.
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         4. Neither the execution, delivery and performance of this Certificate,
nor this transfer of the Participation by the Company, has resulted, or will
result, in any breach of any provision of, or constitute a default (or an event
which with or without notice and/or lapse of time would constitute a default)
under any agreement or instrument to which the Company is a party or by which it
is bound, or any statute, order, rule or regulation applicable to it of any
court or other governmental agency.

         5. The Company agrees not to sell, assign, divide, subparticipate,
pledge, or otherwise transfer or encumber the Participation, the Participated
Interest, or any portion thereof or interest therein, and agrees to take all
steps necessary to ensure that no other Payee takes any such action, without the
prior written consent of the Participant.

         6. Whenever a Payee is to receive or collect any consideration pursuant
to a Sale of the Company, the Company shall take all steps necessary to ensure
that the Participant's Interests in such cash or other payment or property is
paid to Participant on the Payment Date. If any payments or distributions made,
or caused to be made, by the Company to Participant hereunder are made in error
or are otherwise required to be returned or disgorged by the Company for any
reason, Participant shall immediately return such payments and distributions to
the Company.

         7. Payments and deliveries to the Company or Participant in connection
with this Certificate shall be made as may be reasonably directed in writing by
Participant or the Company, as applicable.

         8. Nothing herein shall be deemed to limit the rights of the
Participant as Investor under the Amendment Agreement.

         9. Article 6 of the Purchase Agreement (except for Section 6.5 thereof)
is hereby incorporated herein by reference and shall apply to this Participation
Certificate with such changes as may be necessary mutatis mutandis to conform to
this Participation Certificate.

         10. The Company agrees that the Participant may rely upon the
representations of Company contained herein.

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                  Dated:            July __, 2001

                                       APPLIEDTHEORY CORPORATION

                                       By:______________________________________
                                            Name:  Danny Stroud
                                            Title:    Chief Executive Officer

ACCEPTED AND ACKNOWLEDGED:

By:      ________________________
         Name:
         Title:

                  [SIGNATURE PAGE TO PARTICIPATION CERTIFICATE]<PAGE>   1
                                                                   EXHIBIT 10.74

                          FORM OF REVOLVING CREDIT NOTE

                                                              New York, New York
[AMOUNT OF REVOLVING CREDIT COMMITMENT]                       July 10, 2001

         FOR VALUE RECEIVED, the undersigned, APPLIEDTHEORY CORPORATION, a
Delaware corporation (the "Maker"), hereby promises to pay to the order of
______________________________ (the "Lender"), at [NAME AND ADDRESS OF LENDER]
on the Revolving Credit Termination Date as defined in the Credit Agreement
dated as of July 10, 2001, among the Maker and the Lenders thereunder (as the
same may be amended, modified or supplemented from time to time in accordance
with its terms, the "Credit Agreement") or earlier as provided for in the Credit
Agreement, the lesser of the principal sum of [AMOUNT OF LENDER'S REVOLVING
CREDIT COMMITMENT] ($_________) or the aggregate unpaid principal amount of all
Revolving Credit Loans to the Maker from the Lender pursuant to the terms of the
Credit Agreement, in lawful money of the United States of America in immediately
available funds, and to pay interest from the date thereof on the principal
amount hereof from time to time outstanding, in like funds, at said office, at a
rate or rates per annum and, in each case, and payable on such dates as
determined pursuant to the terms of the Credit Agreement.

         The Maker promises to pay interest, on demand, on any overdue principal
and fees and, to the extent permitted by law, overdue interest from their due
dates at a rate or rates determined as set forth in the Credit Agreement.

         The Maker hereby waives diligence, presentment, demand, protest and
notice of any kind whatsoever. The non-exercise by the holder of any of its
rights hereunder in any particular instance shall not constitute a waiver
thereof in that or any subsequent instance.

         All borrowings evidenced by this Revolving Credit Note and all payments
and prepayments of the principal hereof and interest hereon and the respective
dates thereof shall be endorsed by the holder hereof on the schedule attached
hereto and made a part hereof, or on a continuation thereof which shall be
attached hereto and made a part hereof, or otherwise recorded by such holder in
its internal records; provided, however, that the failure of the holder hereof
to make such a notation or any error in such a notation shall not in any manner
affect the obligation of the Maker to make payments of principal and interest in
accordance with the terms of this Revolving Credit Note and the Credit
Agreement.
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         This Revolving Credit Note is one of the Revolving Credit Notes
referred to in the Credit Agreement (and is secured by the Collateral,
Subsidiary Guarantees and the Parent Guarantee referred to therein), which,
among other things, contains provisions for the acceleration of the maturity
hereof upon the happening of certain events, for optional and mandatory
prepayment of the principal hereof prior to the maturity hereof and for the
amendment or waiver of certain provisions of the Credit Agreement, all upon the
terms and conditions therein specified.

         THIS REVOLVING CREDIT NOTE SHALL BE CONSTRUED IN ACCORDANCE WITH AND
GOVERNED BY THE LAWS OF THE STATE OF NEW YORK, WITHOUT REGARD TO CHOICE OF LAW
DOCTRINE, AND ANY APPLICABLE LAWS OF THE UNITED STATES OF AMERICA.

                             SIGNATURE PAGE FOLLOWS

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         IN WITNESS WHEREOF, the Maker has caused this instrument to be duly
executed by an officer thereunto duly authorized.

                                                 APPLIEDTHEORY CORPORATION

                                                 By:___________________________
                                                       Name:
                                                       Title:

                                       3<PAGE>   1
                                                                   EXHIBIT 10.75

                                PARENT GUARANTEE

                                     MADE BY

                            APPLIEDTHEORY CORPORATION

                                   IN FAVOR OF

                          THE LENDERS IDENTIFIED HEREIN

                            DATED AS OF JULY 10, 2001
<PAGE>   2
                                TABLE OF CONTENTS

SECTION 1. DEFINED TERMS...................................................   2
   1.1     Definitions.....................................................   2
   1.2     Other Definitional Provisions...................................   3
SECTION 2. GUARANTEE.......................................................   3
   2.1     Guarantee.......................................................   3
   2.2     [INTENTIONALLY OMITTED].........................................   3
   2.3     No Subrogation..................................................   3
   2.4     Amendments, Etc. With Respect To The Obligations................   4
   2.5     Guarantee Absolute And Unconditional............................   4
   2.6     Reinstatement...................................................   5
   2.7     Payments........................................................   5
SECTION 3. REPRESENTATIONS AND WARRANTIES..................................   5
SECTION 4. COVENANTS.......................................................   5
SECTION 5. MISCELLANEOUS...................................................   6
   5.1     Amendments In Writing...........................................   6
   5.2     Notices.........................................................   6
   5.3     No Waiver By Course Of Conduct; Cumulative Remedies.............   6
   5.4     Enforcement Expenses; Indemnification...........................   6
   5.5     Successors And Assigns..........................................   7
   5.6     Set-Off.........................................................   7
   5.7     [INTENTIONALLY OMITTED].........................................   7
   5.8     Severability....................................................   7
   5.9     Section Headings................................................   7
   5.10    Integration.....................................................   7
   5.11    GOVERNING LAW...................................................   7
   5.12    Submission To Jurisdiction; Waivers.............................   8
   5.13    Acknowledgements................................................   8
   5.14    [INTENTIONALLY OMITTED].........................................   8
   5.15    Release Of Parent...............................................   8
   5.16    WAIVER OF JURY TRIAL............................................   9

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                  PARENT GUARANTEE, dated as of July 10, 2001, made by
APPLIEDTHEORY CORPORATION (the "PARENT" or "PARENT GUARANTOR"), a Delaware
corporation, in favor of the Lenders as set forth in, and pursuant to, the
Revolving Credit Agreement, dated as of July 10, 2001 (as amended, supplemented
or otherwise modified from time to time, the "LOAN AGREEMENT"), among the
Parent, the Subsidiaries (as defined in the Loan Agreement) and the Lenders (as
defined in the Loan Agreement).

                              W I T N E S S E T H:

                  WHEREAS, the Parent Guarantor is the parent of each of the
Subsidiaries;

                  WHEREAS, pursuant to the Loan Agreement, the Lenders agreed to
make the Loans to the Parent and each of the Subsidiaries upon the terms and
subject to the conditions set forth therein;

                  WHEREAS, the proceeds of certain of the Loans will be used by
one or more of the Subsidiaries in connection with the operation of their
respective businesses;

                  WHEREAS, the Parent and the Subsidiaries are engaged in
related businesses, and each of the Parent and each Subsidiary will derive
substantial direct and indirect benefit from the making of the Loans under the
Loan Agreement; and

                  WHEREAS, it is a condition precedent to the obligation of the
Lenders to make the Loans that the Parent shall have executed and delivered this
Guarantee to the Lenders;

                  NOW, THEREFORE, in consideration of the premises and to induce
the Lenders to enter into the Loan Agreement and to make the Loans, the Parent
hereby agrees with the Lenders as follows:

                            SECTION 1. DEFINED TERMS

                  1.1 Definitions

                  (a) Unless otherwise defined herein, terms defined in the Loan
Agreement and used herein shall have the meanings given to them in the Loan
Agreement.

                  (b) The following terms shall have the following meanings:

                  "GUARANTEE": this Parent Guarantee, as the same may be
amended, supplemented or otherwise modified from time to time.

                  "OBLIGATIONS": the collective reference to the unpaid
principal of and interest on the Loans and all other obligations and liabilities
of the Subsidiaries, severally and jointly, to the Lenders (including, without
limitation, interest accruing at the then applicable rate provided in the Loan
Agreement after the maturity of the Loans and interest accruing at the then
applicable rate provided in the Loan Agreement after the filing of any petition
in bankruptcy, or the commencement of any insolvency, reorganization or like
proceeding, relating to any Subsidiary, if a claim for post-filing or
post-petition interest is allowed in such proceeding) whether direct or
indirect, absolute or contingent, due or to become due, or now existing or

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hereafter incurred, which may arise under, out of, or in connection with, the
Loan Agreement, this Guarantee or the other Loan Documents, or any other
document made, delivered or given in connection therewith, in each case whether
on account of principal, interest, fees, indemnities, costs, expenses or
otherwise (including, without limitation, all reasonable fees and disbursements
of counsel to the Lenders that are required to be paid by any Subsidiary
pursuant to the terms of any of the foregoing agreements).

                  1.2 Other Definitional Provisions

                  (a) The words "hereof," "herein", "hereto" and "hereunder" and
words of similar import when used in this Guarantee shall refer to this
Guarantee as a whole and not to any particular provision of this Guarantee, and
Section and Schedule references are to this Guarantee unless otherwise
specified.

                  (b) The meanings given to terms defined herein shall be
equally applicable to both the singular and plural forms of such terms.

                              SECTION 2. GUARANTEE

                  2.1 Guarantee

                  (a) The Parent hereby, unconditionally and irrevocably,
guarantees to the Lenders and their respective successors, indorsees,
transferees and assigns, the prompt and complete payment and performance by each
of the Subsidiaries when due (whether at the stated maturity, by acceleration or
otherwise) of the Obligations.

                  (b) [INTENTIONALLY OMITTED]

                  (c) [INTENTIONALLY OMITTED]

                  (d) The guarantee contained in this Section 2 shall remain in
full force and effect until all the Obligations and the obligations of the
Parent under the guarantee contained in this Section 2 shall have been satisfied
by payment in full.

                  (e) No payment made by any of the Subsidiaries, the Parent,
any other guarantor or any other Person or received or collected by the Lenders
from the Subsidiaries, the Parent, any other guarantor or any other Person by
virtue of any action or proceeding or any set-off or appropriation or
application at any time or from time to time in reduction of or in payment of
the Obligations shall be deemed to modify, reduce, release or otherwise affect
the liability of the Parent hereunder which shall, notwithstanding any such
payment (other than any payment made by the Parent in respect of the Obligations
or any payment received or collected from the Parent in respect of the
Obligations), remain liable for the Obligations up to the maximum liability of
the Parent hereunder until the Obligations are paid in full.

                  2.2 [INTENTIONALLY OMITTED]

                  2.3 No Subrogation. Notwithstanding any payment made by the
Parent hereunder or any set-off or application of funds of the Parent by the
Lenders, the Parent shall not be entitled to be subrogated to any of the rights
of the Lenders against the Subsidiaries or any collateral security or guarantee
or right of offset held by the Lenders for the payment of the Obligations,

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nor shall the Parent seek or be entitled to seek any contribution or
reimbursement from the Subsidiaries in respect of payments made by the Parent
hereunder, until all amounts owing to the Lenders by the Subsidiaries on account
of the Obligations are paid in full. If any amount shall be paid to the Parent
on account of such subrogation rights at any time when all of the Obligations
shall not have been paid in full, such amount shall be held by the Parent in
trust for the Lenders, segregated from other funds of the Parent, and shall,
forthwith upon receipt by the Parent, be turned over to the Lenders in the exact
form received by the Parent (duly indorsed by the Parent to the Lenders, if
required), to be applied against the Obligations, whether matured or unmatured,
in such order as the Lenders may determine.

                  2.4 Amendments, Etc. With Respect To The Obligations. The
Parent shall remain obligated hereunder notwithstanding that, without any
reservation of rights against the Parent and without notice to or further assent
by the Parent, any demand for payment of any of the Obligations made by the
Lenders may be rescinded by the Lenders and any of the Obligations continued,
and the Obligations, or the liability of any other Person upon or for any part
thereof, or any collateral security or guarantee therefor or right of offset
with respect thereto, may, from time to time, in whole or in part, be renewed,
extended, amended, modified, accelerated, compromised, waived, surrendered or
released by the Lenders, and the Loan Agreement and the other Loan Documents and
any other documents executed and delivered in connection therewith may be
amended, modified, supplemented or terminated, in whole or in part, as the
Lenders may deem advisable from time to time, and any collateral security,
guarantee or right of offset at any time held by the Lenders for the payment of
the Obligations may be sold, exchanged, waived, surrendered or released. The
Lenders shall have no obligation to protect, secure, perfect or insure any Lien
at any time held by them as security for the Obligations or for the guarantee
contained in this Section 2 or any property subject thereto.

                  2.5 Guarantee Absolute And Unconditional. The Parent waives
any and all notice of the creation, renewal, extension or accrual of any of the
Obligations and notice of or proof of reliance by the Lenders upon the guarantee
contained in this Section 2 or acceptance of the guarantee contained in this
Section 2; the Obligations, and any of them, shall conclusively be deemed to
have been created, contracted or incurred, or renewed, extended, amended or
waived, in reliance upon the guarantee contained in this Section 2; and all
dealings between the Subsidiaries and the Parent, on the one hand, and the
Lenders, on the other hand, likewise shall be conclusively presumed to have been
had or consummated in reliance upon the guarantee contained in this Section 2.
The Parent waives, to the extent permitted by law, diligence, presentment,
protest, demand for payment and notice of default or nonpayment to or upon any
of the Subsidiaries or the Parent with respect to the Obligations. The Parent
understands and agrees that the guarantee contained in this Section 2 shall be
construed as a continuing, absolute and unconditional guarantee of payment
without regard to (a) the validity or enforceability of the Loan Agreement or
any other Loan Document, any of the Obligations or any other collateral security
therefor or guarantee or right of offset with respect thereto at any time or
from time to time held by the Lenders, (b) any defense, set-off or counterclaim
(other than a defense of payment or performance) which may at any time be
available to or be asserted by any of the Subsidiaries or any other Person
against the Lenders, or (c) any other circumstance whatsoever (with or without
notice to or knowledge of any Subsidiary or the Parent) which constitutes, or

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might be construed to constitute, an equitable or legal discharge of such
Subsidiary for the Obligations, or of the Parent under the guarantee contained
in this Section 2, in bankruptcy or in any other instance. When making any
demand hereunder or otherwise pursuing its rights and remedies hereunder against
the Parent, the Lenders may, but shall be under no obligation to, make a similar
demand on or otherwise pursue such rights and remedies as they may have against
any Subsidiary or any other Person or against any collateral security or
guarantee for the Obligations or any right of offset with respect thereto, and
any failure by the Lenders to make any such demand, to pursue such other rights
or remedies or to collect any payments from such Subsidiary or any other Person
or to realize upon any such collateral security or guarantee or to exercise any
such right of offset, or any release such Subsidiary or any other Person or any
such collateral security, guarantee or right of offset, shall not relieve the
Parent of any obligation or liability hereunder, and shall not impair or affect
the rights and remedies, whether express, implied or available as a matter of
law, of the Lenders against the Parent. For the purposes hereof, "demand" shall
include the commencement and continuance of any legal proceedings.

                  2.6 Reinstatement. The guarantee contained in this Section 2
shall continue to be effective, or be reinstated, as the case may be, if at
anytime payment, or any part thereof, of any of the Obligations is rescinded or
must otherwise be restored or returned by the Lenders upon the insolvency,
bankruptcy, dissolution, liquidation or reorganization of any Subsidiary or the
Parent, or upon or as a result of the appointment of a receiver, intervenor or
conservator of, or trustee or similar officer for, any Subsidiary or the Parent
or any substantial part of its property, or otherwise, all as though such
payments had not been made.

                  2.7 Payments. The Parent hereby guarantees that payments
hereunder will be paid to the Lenders without set-off or counterclaim in U.S.
dollars at the address set forth or referred to in Section 11.1 of the Loan
Agreement.

                   SECTION 3. REPRESENTATIONS AND WARRANTIES

                  To induce the Lenders to enter into the Loan Agreement and to
make the Loans thereunder, the Parent hereby represents and warrants to the
Lenders that the representations and warranties set forth in Section 4 of the
Loan Agreement as they relate to the Parent or to the Loan Documents to which
the Parent is a party, each of which is hereby incorporated herein by reference,
are true and correct as of each time such representations are deemed to be made
pursuant to such Loan Agreement, and the Lenders shall be entitled to rely on
each of them as if they were fully set forth herein, PROVIDED that each
reference in each such representation and warranty to the knowledge of each
Subsidiary shall, for the purposes of this Section 3, be deemed to be a
reference to the Parent's knowledge.

                              SECTION 4. COVENANTS

                  The Parent covenants and agrees with the Lenders that, from
and after the date of this Guarantee until the Obligations shall have been paid
in full, the Parent (x) shall take, and/or shall refrain from taking, as the
case may be, each action that is necessary to be taken or not taken, as the case
may be, so that no Default or Event of Default is caused by the failure to take

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such action or to refrain from taking such action by the Parent and (y) without
limitation, shall take, and/or refrain from taking, as the case may be, all
actions so that all covenants in Articles 6 and 7 of the Loan Agreements are
performed in accordance with their terms.

                            SECTION 5. MISCELLANEOUS

                  5.1 Amendments In Writing. None of the terms or provisions of
this Guarantee may be waived, amended, supplemented or otherwise modified except
in accordance with Section 11.6 of the Loan Agreement.

                  5.2 Notices. All notices, requests and demands to or upon the
Lenders or the Parent hereunder shall be effected in the manner provided for in
Section 11.1 of the Loan Agreement and delivered to the address set forth
therein.

                  5.3 No Waiver By Course Of Conduct; Cumulative Remedies. The
Lenders shall not by any act (except by a written instrument pursuant to Section
5.1), delay, indulgence, omission or otherwise be deemed to have waived any
right or remedy hereunder or to have acquiesced in any Default or Event of
Default. No failure to exercise, nor any delay in exercising, on the part of the
Lenders, any right, power or privilege hereunder shall operate as a waiver
thereof. No single or partial exercise of any right, power or privilege
hereunder shall preclude any other or further exercise thereof or the exercise
of any other right, power or privilege. A waiver by the Lenders of any right or
remedy hereunder on any one occasion shall not be construed as a bar to any
right or remedy which the Lenders would otherwise have on any future occasion.
The rights and remedies herein provided are cumulative, may be exercised singly
or concurrently and are not exclusive of any other rights or remedies provided
by law.

                  5.4 Enforcement Expenses; Indemnification

                  (a) The Parent agrees to pay, or reimburse the Lenders for,
all its costs and expenses incurred after the occurrence and during the
continuace of an Event of Default in collecting against the Parent under the
guarantee contained in Section 2 or otherwise enforcing or preserving any rights
under this Guarantee and the other Loan Documents to which the Parent is a
party, including, without limitation, the reasonable fees and disbursements of
counsel to the Lenders.

                  (b) The Parent agrees to pay, and to save the Lenders harmless
from, any and all liabilities with respect to, or resulting from any delay in
paying, any and all stamp, excise, sales or other taxes which may be payable or
determined to be payable in connection with any of the transactions contemplated
by this Guarantee.

                  (c) The Parent agrees to pay, and to save the Lenders harmless
from, any and all liabilities, obligations, losses, damages, penalties, actions,
judgments, suits, costs, expenses or disbursements of any kind or nature
whatsoever with respect to the execution, delivery, enforcement, performance and
administration of this Guarantee to the extent any Subsidiary would be required
to do so pursuant to the Loan Agreement.

                  (d) The agreements in this Section shall survive repayment of
the Obligations and all other amounts payable under the Loan Agreement and the
other Loan Documents.

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<PAGE>   8
                  5.5 Successors And Assigns. This Guarantee shall be binding
upon the successors and assigns of the Parent and shall inure to the benefit of
the Lenders and their respective successors and assigns; PROVIDED that the
Parent may not assign, transfer or delegate any of its rights or obligations
under this Guarantee without the prior written consent of the Lenders.

                  5.6 Set-Off. The Parent hereby irrevocably authorizes the
Lenders at any time and from time to time while an Event of Default shall have
occurred and be continuing, without notice to the Parent (any such notice being
expressly waived by the Parent), to set-off and appropriate and apply any and
all deposits (general or special, time or demand, provisional or final), in any
currency, and any other credits, indebtedness or claims, in any currency, in
each case whether direct or indirect, absolute or contingent, matured or
unmatured, at any time held or owing by the Lenders to or for the credit or the
account of the Parent, or any part thereof in such amounts as the Lenders may
elect, against and on account of the obligations and liabilities of the Parent
to the Lenders hereunder and claims of every nature and description of the
Lenders against the Parent, in any currency, whether arising hereunder, under
the Loan Agreement, any other Loan Document or otherwise, as the Lenders may
elect, whether or not the Lenders have made any demand for payment and although
such obligations, liabilities and claims may be contingent or unmatured. The
Lenders shall notify the Parent promptly of any such set-off and the application
made by the Lenders of the proceeds thereof, PROVIDED that the failure to give
such notice shall not affect the validity of such set-off and application. The
rights of the Lenders under this Section are in addition to other rights and
remedies (including, without limitation, other rights of set-off) which the
Lenders may have.

                  5.7 [INTENTIONALLY OMITTED]

                  5.8 Severability. Any provision of this Guarantee which is
prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction,
be ineffective to the extent of such prohibition or unenforceability without
invalidating the remaining provisions hereof, and any such prohibition or
unenforceability in any jurisdiction shall not invalidate or render
unenforceable such provision in any other jurisdiction.

                  5.9 Section Headings. The Section headings used in this
Guarantee are for convenience of reference only and are not to affect the
construction hereof or be taken into consideration in the interpretation hereof.

                  5.10 Integration. This Guarantee and the other Loan Documents
represent the agreement of the Parent and the Lenders with respect to the
subject matter hereof and thereof, and there are no promises, undertakings,
representations or warranties by the Lenders relative to subject matter hereof
and thereof not expressly set forth or referred to herein or in the other Loan
Documents.

                  5.11 GOVERNING LAW. THIS GUARANTEE SHALL BE GOVERNED BY, AND
CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE LAW OF THE STATE OF NEW YORK.

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<PAGE>   9
                  5.12 Submission To Jurisdiction; Waivers. The Parent hereby
irrevocably and unconditionally:

                  (a) submits for itself and its property in any legal action or
proceeding relating to this Guarantee and the other Loan Documents to which it
is a party, or for recognition and enforcement of any judgment in respect
thereof, to the non-exclusive general jurisdiction of the Courts of the State of
New York, located in New York County, New York, the courts of the United States
of America for the Southern District of New York, and appellate courts from any
thereof;

                  (b) consents that any such action or proceeding may be brought
in such courts and waives any objection that it may now or hereafter have to the
venue of any such action or proceeding in any such court or that such action or
proceeding was brought in an inconvenient court and agrees not to plead or claim
the same;

                  (c) agrees that service of process in any such action or
proceeding may be effected by mailing a copy thereof by registered or certified
mail (or any substantially similar form of mail), postage prepaid, to the Parent
at its address referred to in Section 5.2 or at such other address of which the
Lenders shall have been notified pursuant thereto;

                  (d) agrees that nothing herein shall affect the right to
effect service of process in any other manner permitted by law or shall limit
the right to sue in any other jurisdiction; and

                  (e) waives, to the maximum extent not prohibited by law, any
right it may have to claim or recover in any legal action or proceeding referred
to in this Section any special, exemplary, punitive or consequential damages.

                  5.13 Acknowledgements. The Parent hereby acknowledges that:

                  (a) it has been advised by counsel in the negotiation,
execution and delivery of this Guarantee and the other Loan Documents to which
it is a party;

                  (b) the Lenders have no fiduciary relationship with or duty to
the Parent arising out of or in connection with this Guarantee or any of the
other Loan Documents, and the relationship between the Parent, on the one hand,
and the Lenders, on the other hand, in connection herewith or therewith is
solely that of debtor and creditor; and

                  (c) no joint venture is created hereby or by the other Loan
Documents or otherwise exists by virtue of the transactions contemplated hereby
among the Parent and the Lenders.

                  5.14 [INTENTIONALLY OMITTED]

                  5.15 Release Of Parent

                  Subject to Section 2.6, the Parent will be released from all
liability hereunder concurrently with the repayment in full of all amounts owed
under the Loan Agreement and the Loans.

                                       8
<PAGE>   10
                  5.16 WAIVER OF JURY TRIAL. THE PARENT AND, BY ACCEPTANCE OF
THE BENEFITS HEREOF, EACH LENDER, HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES
TRIAL BY JURY IN ANY LEGAL ACTION OR PROCEEDING RELATING TO THIS GUARANTEE AND
FOR ANY COUNTERCLAIM THEREIN.

                                       9
<PAGE>   11
                  IN WITNESS WHEREOF, the undersigned has caused this Guarantee
to be duly executed and delivered as of the date first above written.

                                APPLIEDTHEORY CORPORATION

                                By:         /s/ Danny E. Stroud
                                         ---------------------------------------
                                         Name:  Danny E. Stroud
                                         Title:  President and CEO

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