I'm confused by this sentence in the problem statement:
"the murderers have agreed that their testimonies will have no contradictions between them"

Does that mean that tests like this are invalid?
3
A 1 2
B 1 3
C 1 1

In this test there are 3 people and each one conflicts with at least one another. If one person is declared a murderer, there is still a contradiction between the other two.
No 2 people can be declared murderers because there is always a contradiction between any 2 of them.