Help Semantic Tableaux

Does anyone know how Semantic Tableaux works?..
Here is an example:

|| (a=>b) ^ c

c||(a=>b) (a=>b) || c

c,a|| || c, a, b b,c||a

I need it to work in java.. any ideas? I am having problems developing it when the tableaux splits into 2 when 2 options are needed. this is what ive got so far..

Code:

public class Algorithm { 
	
	
	LinkedList left; 
	LinkedList right; 
	
	//Gains Node root from parser and passes to Algorithm and creates and new linkedlist left and right 
	public Algorithm(Node root) { 
		
		parent = new LinkedList(); 
		left = new LinkedList(); 
		right = new LinkedList(); 
		right.addElement(root, 0); //adds root to rightList and sets the count of that tree to 0 (heirarchy/treeid) 
		int count = 0; 
		
		while((left.length() > 0) || (right.length() > 0)){ 
			
			while (right.length() > 0) 
			{ 
				
				Node temp = right.getElement(); 
				
				if(temp.data == "^")	
				{ 
					
					right.deleteElement(); 
					
					left.addElement(temp.left, count); 
					right.addElement(temp.right, count); 
					count++; 
					left.addElement(temp.right, count); 
					right.addElement(temp.left, count); 
					
					Node tmp = temp.left; 
					System.out.println(tmp.data); 
					tmp = temp.right; 
					System.out.println(tmp.data);	
					
				} 
				
				if (temp.data == "=>") 
				{ 
					
					System.out.println(temp.data );	
					Node tmp = temp.left; 
					System.out.println(tmp.data); 
					tmp = temp.right; 
					System.out.println(tmp.data); 
					
					right.deleteElement(); 
					
					left.addElement(temp.left, count); 
					right.addElement(temp.right, count); 
					
				} 
				
				
				if (temp.data == "v") 
				{ 
					
					right.deleteElement(); 
					
					left.addElement(temp.left, count); 
					right.addElement(temp.right, count); 
					count++; 
					left.addElement(temp.right, count); 
					right.addElement(temp.left, count); 
					
					Node tmp = temp.left; 
					System.out.println(tmp.data); 
					tmp = temp.right; 
					System.out.println(tmp.data); 
				} 
				
				if (temp.data == "-") 
				{ 
					left.addElement(temp.right, count); 
					right.deleteElement(); 
					
					
					
				} 
			} 
			
			while(left.length() > 0) 
			{ 
				
				Node temp = (Node) left.getElement(); 
				
				if(temp.data == "^") 
				{ 
					left.addElement(temp.left, count); 
					left.addElement(temp.right, count); 
					left.deleteElement(); 
					Node tmp = (Node) left.data; 
					System.out.println(tmp.data); 
					tmp = (Node) right.data; 
					System.out.println(tmp.data); 
				} 
				
				if(temp.data == "v") 
				{ 
					left.addElement(temp.left, count); 
					right.addElement(temp.right, count); 
					count++; 
					left.addElement(temp.right, count); 
					left.addElement(temp.left, count); 
					left.deleteElement(); 
					Node tmp = (Node) left.data; 
					System.out.println(tmp.data); 
					tmp = (Node) right.data; 
					System.out.println(tmp.data); 
				} 
				
				if(temp.data == "=>") 
				{ 
					left.addElement(temp.right, count); 
					right.addElement(temp.left, count); 
					count ++; 
					right.addElement(temp.right, count); 
					right.addElement(temp.left, count); 
					left.deleteElement(); 
					Node tmp = (Node) left.data; 
					System.out.println(tmp.data); 
					tmp = (Node) right.data; 
					System.out.println(tmp.data); 
				} 
				
				if(temp.data == "-") 
				{ 
					right.addElement(temp.left, count); 
					left.deleteElement(); 
				} 
				
			}	
			
} 

} 


} 

class Node 
{ 
	public String data; 
	public Node left ; 
	public Node right ; 
	
}