We can use the first three lines to conclude ~L

1.      (S & (S>W)) & (W>~L)

2.      W & (W>~L)

3.      Therefore ~L

 

Similarly, we can use the next two lines to conclude ~I

1.      D & (D>~I)

2.      Therefore ~I

 

We can now use the above to conclude C

1.      (~L & ~I) is equivalent to  ~(L v I)

2.      ~(L v I) & ((L v I) v C)

3.      Therefore C

 

Now we can conclude using the following:

1.      C & (C>B)

2.      Therefore B