Assalamualaikum Warahmatullahi Ta'ala Wabarakatuh.
The distinction between a true Muslim and a Kaffir is the matter of the Solat @ Prayer to Allah Subhanahu Wa Ta'ala.
Keeping one's prayers is the core essence of being a Muslim, who submits to the worship of Almighty Allahu Ta'ala.
Failure to do so makes a human being a Kaffir @ Disbeliever of Allah Subhanahu Wa Ta'ala. Period. No qualms about it.
The Solat is the first thing that will be taken into consideration of each and every human being on Earth when they stand before Him on the Day of Judgment in the Yaum Al Mahsyar.
How did the order to pray for us come into being?
It took place in the Ascension of the Prophet Muhammad Sallalahu Alaihi Wassallam in his Night Journey up to the Seventh Heavens @ 'Israk n Mikraj.
Here is the translated authentic hadith.
Narrated Abu Dhar:
Allah's Apostle said, "While I was at Mecca the roof of my house was opened and Jibreel Alaihis Salam descended, opened my chest, and washed it with Zam-zam water.
Then he brought a golden tray full of wisdom and faith and having poured its contents into my chest, he closed it.
Then he took my hand and ascended with me to the nearest heaven, when I reached the nearest heaven, Jibreel Alaihis Salam said to the gatekeeper of the heaven, 'Open (the gate).'
The gatekeeper asked, 'Who is it?' Jibreel Alaihis Salam answered: 'Jibreel.' He asked, 'Is there anyone with you?' Jibreel Alaihis Salam replied, 'Yes, Muhammad is with me.' He asked, 'Has he been called?' Jibreel Alaihis Salam said, 'Yes.'
So the gate was opened and we went over the nearest heaven and there we saw a man sitting with some people on his right and some on his left.
When he looked towards his right, he laughed and when he looked toward his left he wept.
Then he said, 'Welcome! O pious Prophet and pious son.' I asked Jibreel Alaihis Salam, 'Who is he?' He replied, 'He is Saiyidina Adam Alaihis Salam and the people on his right and left are the souls of his offspring.
Those on his right are the people of Paradise and those on his left are the people of Hell and when he looks towards his right he laughs and when he looks towards his left he weeps.'
Then he ascended with me till he reached the second heaven and he (Jibreel Alaihis Salam) said to its gatekeeper, 'Open (the gate).'
The gatekeeper said to him the same as the gatekeeper of the first heaven had said and he opened the gate.
Anas said: "Abu Dhar added that the Prophet met Prophets Adam, Idris, Moses, Jesus and Abraham, he (Abu Dhar) did not mention on which heaven they were but he mentioned that he (the Prophet ) met Adam on the nearest heaven and Abraham on the sixth heaven.
Anas said, "When Jibreel Alaihis Salam along with the Prophet passed by Nabi Idris Alaihis Salam, the latter said, 'Welcome! O pious Prophet and pious brother.'
The Prophet asked, 'Who is he?' Gabriel replied, 'He is Idris." The Prophet added, "I passed by Moses and he said, 'Welcome! O pious Prophet and pious brother.'
I asked Jibreel Alaihis Salam, 'Who is he?' Jibreel Alaihis Salam replied, 'He is Moses.' Then I passed by Eesa @ Jesus and he said, 'Welcome! O pious brother and pious Prophet.'
I asked, 'Who is he?' Jibreel Alaihis Salam replied, 'He is Eesa @ Jesus.
Then I passed by Abraham and he said, 'Welcome! O pious Prophet and pious son.'
I asked Jibreel Alaihis Salam, 'Who is he?' Jibreel Alaihis Salam replied, 'He is Abraham. The Prophet added, 'Then Jibreel Alaihis Salam ascended with me to a place where I heard the creaking of the pens."
Ibn Hazm and Anas bin Malik said: The Prophet said, "Then Allah enjoined fifty prayers on my followers when I returned with this order of Allah, I passed by Moses who asked me, 'What has Allah enjoined on your followers?'
I replied, 'He has enjoined fifty prayers on them.'
Moses said, 'Go back to your Lord (and appeal for reduction) for your followers will not be able to bear it.'
(So I went back to Allah and requested for reduction) and He reduced it to half.
When I passed by Moses again and informed him about it, he said, 'Go back to your Lord as your followers will not be able to bear it.'
So I returned to Allah and requested for further reduction and half of it was reduced.
I again passed by Moses and he said to me: 'Return to your Lord, for your followers will not be able to bear it.
So I returned to Allah and He said, 'These are five prayers and they are all (equal to) fifty (in reward) for My Word does not change.'
I returned to Moses and he told me to go back once again.
I replied, 'Now I feel shy of asking my Lord again.'
Then Jibreel Alaihis Salam took me till we '' reached Sidrat-il-Muntaha (Lote tree of; the utmost boundry) which was shrouded in colors, indescribable.
Then I was admitted into Paradise where I found small (tents or) walls (made) of pearls and its earth was of musk."
Such is the way, we Muslims came to inherit the Call to Solat @ Prayer to Allah Subhanahu Wa Ta'ala.
Thus, true Muslims, no matter where or in what situation they are will hasten to Prayer when the time comes.
There is no excuse for a male Muslim to miss or neglect his prayers save for those who aren't aware of it, by way of being in a coma and incapacitated from even moving their eyes or able of rational thought.
The Solat is the very first thing that differentiates a Muslim from a Kaffir. He who doesn't prostrate himself before Allah will find his due punishments in this life and in the hereafter.
Muslim women who are having their menses or have just delivered their child are exempted from the period where they are having their menses or post natal discharges. They do not have to repeat any such missed prayers due to their conditions.
Islam is the ultimate faith for us Mankind and to those of us capable of rational thought, it is best to learn about the faith proper and not make any assumptions about it due to ignorance or biased feedback or data.
Prayer is the connecting link between Man and his Creator. Failure to pray negates those who refuse to submit to Him from qualifying for His Mercy.
Watch how true Muslims prostrate before the Almighty throughout the world. Be a Muslim and live as Allah SWT commands us to. Insya Allah.