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Jan 21st, 2019
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  1. Show validity using resolution:
  2. Premises:
  3. (note: v = or, ^ = and)
  4.  
  5. 1. ~q v s
  6. 2. ~(s ^ p)
  7. 3. (p -> q) ^ r
  8. 4. p -> r -> p
  9. therefore: ~(s -> p)
  10.  
  11. Derivation:
  12. 5. ~s v ~p 2 DeMorgans
  13. 6. ~p v ~q 1, 5 res
  14. 7. p -> q from 3
  15. 8. ~p v q from 7
  16. 9. r from 3
  17. 10. ~p v ~p 6, 8 res
  18. 11. ~p from 10
  19. 12. p -> r -> p <=> ~(~p v r) v p <=> (p ^ ~r) v p
  20. 13. p ^ ~r from 11 and 12
  21. 14. p from 13
  22. 15. ~r from 13
  23.  
  24. Contradictions between lines 15 and 9, 14 and 11.
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