it is permitted to separate them.
Explanation:
The Gemara in Shabbos 74b: Rav Menashe said, “eh who grinds up wood chips is punishable for Tochen-Grinding.” Rav Ashi said, “If he is particular about their size then he is punishable for Mechatech-Cutting.” (According to Rashi)
Someone who cuts things according a particular size transgresses Mechatech.
The Rambam (Hilchot Shabbat 11:7) writes: One who take a wood chip and whittled down make a toothpick or to open a lock is punishable.”
The Tal Orot explains that one is particular on the size is punishable for Mechatech even if he could have picked his teeth without doing anything to it. The Tal Orot understood the Rambam that cutting the chip is just chopping off the end but not whittling it, meaning that it was sharp enough as it is .
The Shulchan Aruch HaRav (314:16) writes that Mechatech is when he is particular to cut something when he needs it. The Ketzot Hashulchan understands from here that it is only where the objectis only usable if it cut to the exact size and if not it is ruined.
According to this we can understand many Rishonim like the Aruch and the Meiri the he needs to cut it for what he needs.
The modern day Poskim discuss cutting Toilet paper on Shabbat.
Or L’Tziyon (Chelek 2 41:6) writes, “It is forbidden to cut Toilet paper on Shabbat, even doing it in a strange way (Shinui) and even if not on the lines. The footnote adds, “The is a prohibition from the Torah of Mechatech. And even if not on the perforated lines.
R’ Ovadia Yosef (Yabia Omer 9:108:185) He who writes that cutting Toilet paper on Shabbat is a prohibition from the Torah is not true. R’ Shlomo Zalman Auerbach since when you tear the toilet paper you are not particular about where the e perforation is on paper, whether it is longer or shorter and it is just to make it easier to tear it is not Mechatech.
In Shemirat Shabbat (23:19) it is written: We are not allowed cut Toilet paper on Shabbat and Yom Tov on the perforation or not.
If he has no Toilet Paper ready from before Shabbat then there is place to be lenient for Kavod Habriut (so one should not be dirty) to tear the the toilet paper with a difference, that he tears it wit his elbow in a non-perforated place.
IN footnote 62 there he writes: Why only not on the perforation so not do Mechatech the you are tearing the paper according to a specific size. RSZA Zt” l said to me that since you are not particular the size he is definately not transgressing Mechatech.
Using R’ Shlomo Zalman’s idea, R’ Ovadia Yosef ruled it is permitted to cut toilet paper even if it is not Kavod Habriot.
The Shemirat Shabbat wrote it was forbidden so as not to take sides in a Machloket here.
When it comes to containers stuck together everyone is lenient. The Or L’Tziyon (Chelek 2:7 in the footnote) It is permitted separate containers witch are attached by their lids.
So too in Shemirat Shabbat (9:11) it says , “I is even permitted to separate two attached containers of Leben.
The Orchot Shabbat and the Menuchat Ahava do not permit separating the Lebens.
There is a difference between toilet paper that you are cutting of a piece in certain size and using that piece. With Leben you are not cutting something of just breaking so you can eat it easier.
