Some cup was put onto every table by some man.

The predicate "P3" stands for "_ put _ onto _". We rearrange the above sentence into the active form so that it fits the form of the predicate. This gives us "some man put some cup onto every table", which we use to get the matrix form as shown.

All dogs bark
Someone works for Nadia
There's a time at which everyone eats every doughnut
Everyone loves someone
Only philosophers wear only diamonds
Every cat that cleans himself cleans an animal that catches mice
If someone is tall, then he is bigger than Rachel
Every dog that has an owner obeys him
The man Karen adores is friends with Bob