You are wrong and you now have a huge problem. The ones who will be "taken" will be the unrighteous. The answer which the Lord gave in regard to the ones who will be "taken" was in answer to the following question from His disciples:
"Tell us, when shall these things be? and what shall be the sign of thy coming, and of the end of the age?" (Mt. 24:3).
Earlier the Lord Jesus spoke the parable of the "tares of the field" where He described what would occur at the "end of the age":
"He that soweth the good seed is the Son of man; The field is the world; the good seed are the children of the kingdom; but the tares are the children of the wicked one; The enemy that sowed them is the devil; the harvest is the end of the age; and the reapers are the angels. As therefore the tares are gathered and burned in the fire; so shall it be in the end of this age. The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity; And shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth. Then shall the righteous shine forth as the sun in the kingdom of their Father. Who hath ears to hear, let him hear" (Mt. 13:37-43).
Here we can see that the Lord Jesus speaks of a harvest that will happen at the "end of the age." And at the end of the age the ones who will be "taken" will be those who offend and not the saints, as you imagine!
That leaves you with a huge problem in regard to this post-tribulation coming of the Lord Jesus:
"But as the days of Noe were, so shall also the coming of the Son of man be. For as in the days that were before the flood they were eating and drinking, marrying and giving in marriage, until the day that Noe entered into the ark, And knew not until the flood came, and took them all away; so shall also the coming of the Son of man be. Then shall two be in the field; the one shall be taken, and the other left. Two women shall be grinding at the mill; the one shall be taken, and the other left" (Mt.24:37-41).
If the ones taken are the saints, as you imagine, then by the time all the saints are caught up to meet the Lord in the air and all those who offend are taken out of the world then no one will be left on the face of the earth when He comes.
How do you solve that problem?
No problem.
You used Mat.13 verses which describe the last judgment, not the return of Christ.
For one thing at the return of Christ the bodies of the wicked are laying on the ground, and taken nowhere.
Then you claim a wicked beast worshipper is grinding at the mill with a righteous person.
Perhaps you think they will be in bed together.
At Christs coming only the righteous are gathered by angels (if necessary) and the wicked remain as the example of Lot and Noah shows.
This does not mean that those not gathered are all wicked either, it depends on where they are, and who they are.
Deu 30:1 And it shall come to pass, when all these things are come upon thee, the blessing and the curse, which I have set before thee, and thou shalt call them to mind among all the nations, whither the LORD thy God hath driven thee,
Deu 30:2 And shalt return unto the LORD thy God, and shalt obey his voice according to all that I command thee this day, thou and thy children, with all thine heart, and with all thy soul;
Deu 30:3 That then the LORD thy God will turn thy captivity, and have compassion upon thee, and will return and gather thee from all the nations, whither the LORD thy God hath scattered thee.
Deu 30:4 If any of thine be driven out unto the outmost parts of heaven, from thence will the LORD thy God gather thee, and from thence will he fetch thee:
Deu 30:5 And the LORD thy God will bring thee into the land which thy fathers possessed, and thou shalt possess it; and he will do thee good, and multiply thee above thy fathers.
Rev 18:1 And after these things I saw another angel come down from heaven, having great power; and the earth was lightened with his glory.
Rev 18:2 And he cried mightily with a strong voice, saying, Babylon the great is fallen, is fallen, and is become the habitation of devils, and the hold of every foul spirit, and a cage of every unclean and hateful bird.
Rev 18:3 For all nations have drunk of the wine of the wrath of her fornication, and the kings of the earth have committed fornication with her, and the merchants of the earth are waxed rich through the abundance of her delicacies.
Rev 18:4 And I heard another voice from heaven, saying, Come out of her, my people, that ye be not partakers of her sins, and that ye receive not of her plagues.
First the resurrection at His appearing then follows the gathering by angels out of Babylon, many on foot.
Jer 50:1 The word that the LORD spake against Babylon and against the land of the Chaldeans by Jeremiah the prophet.
Jer 50:2 Declare ye among the nations, and publish, and set up a standard; publish, and conceal not: say, Babylon is taken, Bel is confounded, Merodach is broken in pieces; her idols are confounded, her images are broken in pieces.
Jer 50:3 For out of the north there cometh up a nation against her, which shall make her land desolate, and none shall dwell therein: they shall remove, they shall depart, both man and beast.
Jer 50:4 In those days, and in that time, saith the LORD, the children of Israel shall come, they and the children of Judah together, going and weeping: they shall go, and seek the LORD their God.
Jer 50:5 They shall ask the way to Zion with their faces thitherward, saying, Come, and let us join ourselves to the LORD in a perpetual covenant that shall not be forgotten.
Jer 50:6 My people hath been lost sheep: their shepherds have caused them to go astray, they have turned them away on the mountains: they have gone from mountain to hill, they have forgotten their restingplace.
Jer 50:7 All that found them have devoured them: and their adversaries said, We offend not, because they have sinned against the LORD, the habitation of justice, even the LORD, the hope of their fathers.
Jer 50:8 Remove out of the midst of Babylon, and go forth out of the land of the Chaldeans, and be as the he goats before the flocks.
Jer 50:9 For, lo, I will raise and cause to come up against Babylon an assembly of great nations from the north country: and they shall set themselves in array against her; from thence she shall be taken: their arrows shall be as of a mighty expert man; none shall return in vain.
Jer 50:10 And Chaldea shall be a spoil: all that spoil her shall be satisfied, saith the LORD.
Added comment-
Those gathered to amageddon, get there on their own means of transport.
LA