Allah Taala said in Quran:

يَا أَيُّهَا الَّذِينَ آمَنُواْ إِذَا قُمْتُمْ إِلَى الصَّلاةِ فاغْسِلُواْ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى الْمَرَافِقِ وَامْسَحُواْ بِرُؤُوسِكُمْ وَأَرْجُلَكُمْ إِلَى الْكَعْبَينِ وَإِن كُنتُمْ جُنُبًا فَاطَّهَّرُواْ وَإِن كُنتُم مَّرْضَى أَوْ عَلَى سَفَرٍ أَوْ جَاءَ أَحَدٌ مِّنكُم مِّنَ الْغَائِطِ أَوْ لاَمَسْتُمُ النِّسَاءَ فَلَمْ تَجِدُواْ مَاءً فَتَيَمَّمُواْ صَعِيدًا طَيِّبًا فَامْسَحُواْ بِوُجُوهِكُمْ وَأَيْدِيكُم مِّنْهُ مَا يُرِيدُ اللّهُ لِيَجْعَلَ عَلَيْكُم مِّنْ حَرَجٍ وَلَكِن يُرِيدُ لِيُطَهِّرَكُمْ وَلِيُتِمَّ نِعْمَتَهُ عَلَيْكُمْ لَعَلَّكُمْ تَشْكُرُونَ

We need this part:

فاغْسِلُواْ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى الْمَرَافِقِ وَامْسَحُواْ بِرُؤُوسِكُمْ وَأَرْجُلَكُمْ إِلَى الْكَعْبَينِ

Here transliteration:

faighsiloo wujoohakum waaydiyakum ila almarafiqi waimsahoo biruoosikum waarjulakum ila alkaAAbayni

The main question, how to read? Waarjulakum like in Quran? Or waArjulikum like shia wants?

So due to correct reading is “wa Arjulakum” then in this case we should to wash the feet as it is “ma’toof” on “Wujoohakum”

Brother al-Hajjaj said: addressing to shias:

The Qur’an we use uses the word “wa Arjulakum” yet you guys wipe off your feet based on the fact that the word in the Qur’an is “wa Arjulikum”. Now, having said this we are faced with two options:
1- The current word in the Qur’an (wa Arjulakum) is correct, and therefore feet must be washed as faces must be washed.
2- The current word in the Qur’an is incorrect, and originally it was (wa Arjulikum), and therefore feet must be wiped off just like the heads.
If you go with option 1, then you must agree with AhluSunnah and wash your feet.
If you go with option 2, then you must agree with our charge that the Shi’ites believe in the distortion of the Qur’an.

The Shi’ites’ argument for wiping off the feet is that the word must be (wa Arjulikum) as it is ma’toof on the word (Biru’oosikum). We AhluSunnah say it is (wa Arjulakum) as apparant in the Qur’an, and it is ma’toof on (Wujoohakum).
The Shi’ites for centuries have based their ruling of wiping off their feet on the fact that the word is recited (wa Arjulikum).
As such, how do you look at this issue? Because if the word is “as is”, then the (Nasb) refers to the verb washing (faghsiloo فاغسلوا). Unless we go by the Shi’ites charge, that the Sahabah have changed and altered the Qur’an, there is no logical explanation to wiping off the feet if you base it on the word as it exists in the Qur’an.

The Messenger [sallalahu alaihi wa ala alihi wa sallam] said: “al-Muslimoona inda shurootihim” meaning, Muslims stand firm by their words (conditions).

“Narrated Ghalib b. al-Huzail, I asked Abu Ja’far [as] about His saying: (وامسحوا برؤوسكم وأرجلكم إلى الكعبين) is it with khafdh (kasra) or nasb (fat-ha), he replied: it is with khafdh (kasra).

Sources: Tafseer al-Ayyashi, Al-Ayyashi al-Samarqandi, vol.1, p. 330
Tafseer al-Saafi, al-Faydh al-Kashaani, vol.2, p.16
Al-Hadaa’iq al-Naadhira, al-Muhaqqiq al-Bahraani, vol.2, p.289 & vol.8, p.104.
Jawaahirul-Kalaam, al-Sheikh al-Jawahiri, vol.2, p.207
Kitaab al-Tharah I, Sayyid Galbaygani p. 89
Fiqhul-Saadiq [as], Sayyid Muhammad Sadiq al-Ruhani, vol.1, p.277
Tahtheeb al-Ahkaam, al-Sheikh al-Tusi, vol.1, p.71
Wasaa’el al-Shi’a, al-Hur al-‘Aamili, Chapter 25, Narration # 1097, 1099
Mustadrak al-Wasaa’el, al-Mirza al-Nuri, Chapter 23, Narration # 1/712, 1/714
Al-tafseer al-Asfaa, al-Faydh al-Kashaani, vol.1, p.264

According to Mustadrak al-Wasaa’el, narration 1/712: wa Arjulikum is the recitation of Ahlul-Bayt.

Now, Allamah al-Hilli, in his “al-Risalah al-Sa’diyyah” says:

“وتقرير الاستدلال أن نقول: عطف الله تعالى الأرجل على الرؤوس لوجوه: الأول: أنها مجرورة ولم يتقدم اسم مجرور عليه بحيث يعطف عليه سوى الرؤوس فتعين العطف عليها”

Publisher: Kitab khanah Omomi Hazrat Ayatollah al-Odhma Mir’ishi Najafi, Qum
1st edition, 1410, Behmen Press, Qum, p. 89

I will attempt here to translate it to the best of my ability, but advise you to refer to the book itself:

“In presentation of our argument we say, Allah ta’ala have referred(atafa) the feet back to heads, which has several points to present: One: That (the word Arjul) is majroor (maksoor), though no majroor noun has preceded it in order to refer it to, save the heads, and in this case it is mandatory to refer (atf) it back to (heads).”

So according to Allamah al-Hilli, the word Arjul is to be read “Arjulikum”.

Interesting enough, Allamah al-Hilli, as well as al-Sharif al-Murtadha, rejects what you’ve suggested regarding (atf ala alaqrab). He wrote:

“It cannot be said, Majroor bil-mujawarah (ala alaqrab as you put it), because we say the scholars have negated that. Al-Kasaa’i said: there is no instance in the Qur’an where (jar) was based on mujawarah, and his statement is a Hujjah….. Furthermore, (jar) through majawarah never comes along with the letter (waw).

So please reshuffle your argument, and solve this issue for me in order to put it to rest.

But what seems most interesting, is the narration reported by Al-Ayyashi in his Tafseer, on the same reference mentioned above which literally says:

“58- Ali b. Abi Hamzah said: I asked Abu Ibrahim [as] about His saying: (O ye who believe! when ye prepare for prayer) down to His saying (to the ankles), he said: Allah has told the Truth. I said, may I be your ransom, how should (the person) perform the ablution? He said: twice -twice. I said, (should he) wipe off? He said, once -once. I said, once by the water? He said, yes. I said, may I be your ransom, what about the feet? he said, wash them (good) washing”