Reducibility of 2 boolean satisfiability problems
Problem A is reducible to Problem B in following manner: 


Pick a variable in problem A and set it to 
0
Now we have a formula of size n-1, if satisfiable with B then return satisfiable 
Else, pick problem A again and set the variable to 1 
Now we have a formula of size n-1 again, if satisfiable with B then return satisfiable else return unsatisfiable 


In other words: Split problem A into two problems B using any variable. If B says unsatisfiable for both 0 and 1 then it is unsatisfiable. If it says satisfiable for at least one of the two, then it is satisfiable.