No, because inheritance tax and capital-gains tax are two separate tax categories. Inheritance tax, which is reported on an inheritance-tax return, is based on determining the value of the decedent's assets at the time of death. If the value of the estate at that time falls below the basic deduction, no inheritance tax is due and no inheritance tax return need be filed -- end of story. If you go over the basic deduction, the story continues.
Capital-gains tax on an inherited property that has subsequently been sold is reported on a kakutei shinkoku and is based on a comparison of the sales price with the purchase price. An heir will not have paid anything to acquire the inherited property, so the purchase price is the one paid by the parent (an American-style step-up in basis does not exist in Japan). Further, that price is divided into land value and house value, with the latter adjusted according to depreciation (i.e., the value of the house after depreciation is regarded as the purchase price).
So the formula reformulated -- omitting any buyer's fees associated with the original purchase and adding one further item -- is:
Money you sell it for - (money the parent bought it for - house depreciation + fees for selling) - special deductions applicable when selling real estate
Special deductions can get complicated and I'm not qualified to discuss them, but a couple (selling a personal residence and selling an akiya) are pretty substantial. Also, IF inheritance tax was actually paid on the property, the heir(s) can take a deduction based on that amount as long as the property is sold within three years of the inheritance-tax reporting deadline. Anyway, if the result of the above calculation is a negative figure, you have a capital loss (which, however, can only be used to offset gains connected with other real-estate transactions). If it is a positive figure, you have a capital gain and tax will be calculated according to how long the property has been owned, with five years marking the point at which tax changes from a short-term 39.63% to a long-term 20.315% (combined income and residence tax).
This site gives some useful information and simplified examples. One example posits a property bought in 2015 for 50 million yen, 20 million for the house and 30 million for the land. The property is inherited and sold for 60 million yen either in 2020 (less than five years) or in 2021 (after five years have passed). Depreciation on the house is set at 2.79 million (don't know where they got this figure), and selling expenses are 5 million.
Capital gain:
- 60 million - (20 million - 2.79 million + 30 million + 5 million) = 7.79 million
- 7.79 million x 39.63% = about 3.08 million
- 7.79 million x 20.315% = about 1.58 million