Prolog: is valid distribution Rule - prolog

Question

I am new to Prolog, how should I think to find the right solution without pre-defined/built-in predicates?
Writing a rule is required is_valid_distribution rule
Test the distribution of students and teachers over classes
students([s1,s2,s3,s4]).
teachers([t1,t2, t3]).
Constraints:
A student is not allowed to be in two classes at the same time, nor twice in one class!
Sum of students in two classes = the total number of students (i.e All students are present).
Teachers could be more than two in the same class, but every class must has at least one teacher.
Class not allowed to be empty or has just teachers, i.e. class must have at least one student and one teacher.
Develop a general solution, i.e. your rules must solve the problem with different facts like:
students([s1,s2,s3,s4, ahmad, ali, maya]).
teachers([t1,t2, omar]).
Don't define any other facts.
You are invited to define any necessary rules which maight help you solve the problem!
succeeded tests:
is_valid_distribution([t1,s1,s2], [t2,s3,s4]). % idial case
is_valid_distribution([t1,s1,s2], [t2,t3,s3,s4]). % more than one teacher in one class is allowed.
faild tests:
is_valid_distribution([t1,s1,s2], [t2,s1,s3,s4]). % student appears in two classes at same time.
is_valid_distribution([t1,s1,s1], [t2,s3,s4]). % student appears twice in one class.
is_valid_distribution([t1,s1,s2], [t1,s3,s4]). % teacher appears in two classes at same time.
is_valid_distribution([t1,t1, s1,s2], [t2,s3,s4]). % teacher appears twice in one class
is_valid_distribution([t1,s1,s2], [t2,s3]). % sum of students != all students.
is_valid_distribution([t1,s1,s2], [s3,s4]). % no teachers in class2.
is_valid_distribution([], [t1,t2,s1,s2,s3,s4]). % empty class not allowed
is_valid_distribution([t1], [t1,t2,s1,s2,s3,s4]). % class with one teacher is not allowed.

Answer 1

Your solution can have the following general structure:
is_valid_distribution(Class1, Class2) :-
students(Students),
teachers(Teachers),
no_student_twice(Students, Class1, Class2), % constraint 1
all_students_in_some_class(Students, Class1, Class2), % constraint 2
at_least_one_teacher_per_class(Teachers, Class1, Class2), % constraint 3
at_least_one_student_per_class(Students, Class1, Class2). % constraint 4
Now you "only" need to implement rules capturing the different constraints. I won't show you all of them, but here for example is the implementation of constraint 4:
at_least_one_student_per_class(Students, Class1, Class2) :-
% there is some student in class 1
member(Student1, Students),
member(Student1, Class1),
% there is some student in class 2
member(Student2, Students),
member(Student2, Class2).
I hope this gives you a starting point.