When Cora was killed, Anna and Beth were questioned by the police about the manner of her death by poison.
Anna: If it was a murder, Beth did it.
Beth: If it was not suicide, it was murder.
The policemen made the following assumptions:
$1$. If neither Anna nor Beth lied, it was an accident.
$2$. If either Anna or Beth lied, it was not an accident.
Subsequent development revealed these assumptions were correct.
What was the manner of Cora's death: accident suicide or murder?