Question 983140
<pre>
What are you using "U" for ? 

I will assume you are using U for "implies", "condition",
->, >, &#8835; are the symbols commonly used for that, not U.
I will use -> instead.

1. (~F v X) -> (P v T)
2. F -> P
3. ~P                       / T

4. ~P -> ~F       2, Transposition  (sometimes called "contrapositive")
5. ~F           4,3, Modus ponens
6. ~F v X         5, Addition
7. P v T        1,6, Modus ponens
8. T            7,3, Disjunctive syllogism

Edwin</pre>