In normal contract negotiations, a contract is formed upon the acceptance of an offer. A conditional acceptance attempting to impose further terms to the contract comprises a counteroffer, which is actually a rejection.
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If there was a valid acceptance of the original contract for the full asking price, then you may be able to use the terms of the purchase and sale agreement (if you have one) to expedite the closing. If there was only an acceptance of the price terms, then the other terms are still subject to the "gap-filler" contract provisions.
I hope this helps answer your questions.
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