SOLUTION: Hi there! I have been stuck on this one logic problem for the longest time. I am a junior in college and have seen my prof in her office hours every day for the last two weeks to

1)  ~H -> (~T -> R)
2)  H v (E -> F)
3)  ~T v E
4)  ~ H * D 
/   R v F
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5)  ~H                          4      Simplification 
6)  ~T -> R                     1,5    Modus Ponens
7)  E -> F                      2,5    Disjunctive Syllogism
8)  (~T -> R) * (E -> F)        6,7    Conjunction
9)  R v F                       8,3    Constructive Dilemma