Question 1089639
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1.  ~(Z v Y) &#8594; ~W                            Premise
2.  ~U &#8594; ~(Z v Y)                            Premise
3.  (~U &#8594; ~W) &#8594; (T &#8594; S)                      Premise
4.   S &#8594; (R v P)                             Premise
5.   [T &#8594; (RvP)] &#8594; [(~R v K) • ~K]           Premise
{ To show conclusion: ~K }
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::6.  ~U                                       Assumption, start of Conditional Proof (CP)
::7.   ~(Z v Y)                                6,2  Modus Ponens (MP)
::8.   ~W                                      7,1  MP
9.   ~U&#8594;~W                                   6-8, CP
10. T&#8594;S                                      9,3  MP
11.  T&#8594;(R v P)                               10,4 Hypothetical Syllogism (HS)
12.  (~R v K) • ~K                           11,5 MP
13.  ~K                                      12   Simplification (Simp), conclusion