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  1. "1. ((~C->((~C->~C)->~C))->((~C->(~C->~C))->(~C->~C))) Axiom (A2)
  2. 2. (~C->((~C->~C)->~C)) Axiom (A1)
  3. 3. ((~C->(~C->~C))->(~C->~C)) Modus Ponens: 2, 1
  4. 4. (~C->(~C->~C)) Axiom (A1)
  5. 5. (~C->~C) Modus Ponens: 4, 3
  6. 6. (~C->(C->~C)) Axiom (A1)
  7. 7. ((~C->(C->~C))->(~C->(~C->(C->~C)))) Axiom (A1)
  8. 8. (~C->(~C->(C->~C))) Modus Ponens: 6, 7
  9. 9. ((~C->(~C->(C->~C)))->((~C->~C)->(~C->(C->~C)))) Axiom (A2)
  10. 10. ((~C->~C)->(~C->(C->~C))) Modus Ponens: 8, 9
  11. 11. ((C->((C->C)->C))->((C->(C->C))->(C->C))) Axiom (A2)
  12. 12. (((C->((C->C)->C))->((C->(C->C))->(C->C)))->(~C->((C->((C->C)->C))->((C->(C->C))->(C->C))))) Axiom (A1)
  13. 13. (~C->((C->((C->C)->C))->((C->(C->C))->(C->C)))) Modus Ponens: 11, 12
  14. 14. (C->((C->C)->C)) Axiom (A1)
  15. 15. ((C->((C->C)->C))->(~C->(C->((C->C)->C)))) Axiom (A1)
  16. 16. (~C->(C->((C->C)->C))) Modus Ponens: 14, 15
  17. 17. ((~C->((C->((C->C)->C))->((C->(C->C))->(C->C))))->((~C->(C->((C->C)->C)))->(~C->((C->(C->C))->(C->C))))) Axiom (A2)
  18. 18. ((~C->(C->((C->C)->C)))->(~C->((C->(C->C))->(C->C)))) Modus Ponens: 13, 17
  19. 19. (~C->((C->(C->C))->(C->C))) Modus Ponens: 16, 18
  20. 20. (C->(C->C)) Axiom (A1)
  21. 21. ((C->(C->C))->(~C->(C->(C->C)))) Axiom (A1)
  22. 22. (~C->(C->(C->C))) Modus Ponens: 20, 21
  23. 23. ((~C->((C->(C->C))->(C->C)))->((~C->(C->(C->C)))->(~C->(C->C)))) Axiom (A2)
  24. 24. ((~C->(C->(C->C)))->(~C->(C->C))) Modus Ponens: 19, 23
  25. 25. (~C->(C->C)) Modus Ponens: 22, 24
  26. 26. (C->(~D->C)) Axiom (A1)
  27. 27. ((C->(~D->C))->(~C->(C->(~D->C)))) Axiom (A1)
  28. 28. (~C->(C->(~D->C))) Modus Ponens: 26, 27
  29. 29. ((C->(~D->C))->(C->(C->(~D->C)))) Axiom (A1)
  30. 30. (((C->(~D->C))->(C->(C->(~D->C))))->(~C->((C->(~D->C))->(C->(C->(~D->C)))))) Axiom (A1)
  31. 31. (~C->((C->(~D->C))->(C->(C->(~D->C))))) Modus Ponens: 29, 30
  32. 32. ((~C->((C->(~D->C))->(C->(C->(~D->C)))))->((~C->(C->(~D->C)))->(~C->(C->(C->(~D->C)))))) Axiom (A2)
  33. 33. ((~C->(C->(~D->C)))->(~C->(C->(C->(~D->C))))) Modus Ponens: 31, 32
  34. 34. (~C->(C->(C->(~D->C)))) Modus Ponens: 28, 33
  35. 35. (~C->(~D->~C)) Axiom (A1)
  36. 36. ((~C->(~D->~C))->(~C->(~C->(~D->~C)))) Axiom (A1)
  37. 37. (~C->(~C->(~D->~C))) Modus Ponens: 35, 36
  38. 38. ((~C->(~D->~C))->(C->(~C->(~D->~C)))) Axiom (A1)
  39. 39. (((~C->(~D->~C))->(C->(~C->(~D->~C))))->(~C->((~C->(~D->~C))->(C->(~C->(~D->~C)))))) Axiom (A1)
  40. 40. (~C->((~C->(~D->~C))->(C->(~C->(~D->~C))))) Modus Ponens: 38, 39
  41. 41. ((~C->((~C->(~D->~C))->(C->(~C->(~D->~C)))))->((~C->(~C->(~D->~C)))->(~C->(C->(~C->(~D->~C)))))) Axiom (A2)
  42. 42. ((~C->(~C->(~D->~C)))->(~C->(C->(~C->(~D->~C))))) Modus Ponens: 40, 41
  43. 43. (~C->(C->(~C->(~D->~C)))) Modus Ponens: 37, 42
  44. 44. ((C->(C->(~D->C)))->((C->C)->(C->(~D->C)))) Axiom (A2)
  45. 45. (((C->(C->(~D->C)))->((C->C)->(C->(~D->C))))->(~C->((C->(C->(~D->C)))->((C->C)->(C->(~D->C)))))) Axiom (A1)
  46. 46. (~C->((C->(C->(~D->C)))->((C->C)->(C->(~D->C))))) Modus Ponens: 44, 45
  47. 47. ((~C->((C->(C->(~D->C)))->((C->C)->(C->(~D->C)))))->((~C->(C->(C->(~D->C))))->(~C->((C->C)->(C->(~D->C)))))) Axiom (A2)
  48. 48. ((~C->(C->(C->(~D->C))))->(~C->((C->C)->(C->(~D->C))))) Modus Ponens: 46, 47
  49. 49. (~C->((C->C)->(C->(~D->C)))) Modus Ponens: 34, 48
  50. 50. ((~C->((C->C)->(C->(~D->C))))->((~C->(C->C))->(~C->(C->(~D->C))))) Axiom (A2)
  51. 51. ((~C->(C->C))->(~C->(C->(~D->C)))) Modus Ponens: 49, 50
  52. 52. ((C->(~C->(~D->~C)))->((C->~C)->(C->(~D->~C)))) Axiom (A2)
  53. 53. (((C->(~C->(~D->~C)))->((C->~C)->(C->(~D->~C))))->(~C->((C->(~C->(~D->~C)))->((C->~C)->(C->(~D->~C)))))) Axiom (A1)
  54. 54. (~C->((C->(~C->(~D->~C)))->((C->~C)->(C->(~D->~C))))) Modus Ponens: 52, 53
  55. 55. ((~C->((C->(~C->(~D->~C)))->((C->~C)->(C->(~D->~C)))))->((~C->(C->(~C->(~D->~C))))->(~C->((C->~C)->(C->(~D->~C)))))) Axiom (A2)
  56. 56. ((~C->(C->(~C->(~D->~C))))->(~C->((C->~C)->(C->(~D->~C))))) Modus Ponens: 54, 55
  57. 57. (~C->((C->~C)->(C->(~D->~C)))) Modus Ponens: 43, 56
  58. 58. ((~C->((C->~C)->(C->(~D->~C))))->((~C->(C->~C))->(~C->(C->(~D->~C))))) Axiom (A2)
  59. 59. ((~C->(C->~C))->(~C->(C->(~D->~C)))) Modus Ponens: 57, 58
  60. 60. (~C->(C->(~D->~C))) Modus Ponens: 6, 59
  61. 61. ((~D->~C)->((~D->C)->D)) Axiom (A3)
  62. 62. (((~D->~C)->((~D->C)->D))->(~C->((~D->~C)->((~D->C)->D)))) Axiom (A1)
  63. 63. (~C->((~D->~C)->((~D->C)->D))) Modus Ponens: 61, 62
  64. 64. (((~D->~C)->((~D->C)->D))->(C->((~D->~C)->((~D->C)->D)))) Axiom (A1)
  65. 65. ((((~D->~C)->((~D->C)->D))->(C->((~D->~C)->((~D->C)->D))))->(~C->(((~D->~C)->((~D->C)->D))->(C->((~D->~C)->((~D->C)->D)))))) Axiom (A1)
  66. 66. (~C->(((~D->~C)->((~D->C)->D))->(C->((~D->~C)->((~D->C)->D))))) Modus Ponens: 64, 65
  67. 67. ((~C->(((~D->~C)->((~D->C)->D))->(C->((~D->~C)->((~D->C)->D)))))->((~C->((~D->~C)->((~D->C)->D)))->(~C->(C->((~D->~C)->((~D->C)->D)))))) Axiom (A2)
  68. 68. ((~C->((~D->~C)->((~D->C)->D)))->(~C->(C->((~D->~C)->((~D->C)->D))))) Modus Ponens: 66, 67
  69. 69. (~C->(C->((~D->~C)->((~D->C)->D)))) Modus Ponens: 63, 68
  70. 70. ((C->((~D->~C)->((~D->C)->D)))->((C->(~D->~C))->(C->((~D->C)->D)))) Axiom (A2)
  71. 71. (((C->((~D->~C)->((~D->C)->D)))->((C->(~D->~C))->(C->((~D->C)->D))))->(~C->((C->((~D->~C)->((~D->C)->D)))->((C->(~D->~C))->(C->((~D->C)->D)))))) Axiom (A1)
  72. 72. (~C->((C->((~D->~C)->((~D->C)->D)))->((C->(~D->~C))->(C->((~D->C)->D))))) Modus Ponens: 70, 71
  73. 73. ((~C->((C->((~D->~C)->((~D->C)->D)))->((C->(~D->~C))->(C->((~D->C)->D)))))->((~C->(C->((~D->~C)->((~D->C)->D))))->(~C->((C->(~D->~C))->(C->((~D->C)->D)))))) Axiom (A2)
  74. 74. ((~C->(C->((~D->~C)->((~D->C)->D))))->(~C->((C->(~D->~C))->(C->((~D->C)->D))))) Modus Ponens: 72, 73
  75. 75. (~C->((C->(~D->~C))->(C->((~D->C)->D)))) Modus Ponens: 69, 74
  76. 76. ((~C->((C->(~D->~C))->(C->((~D->C)->D))))->((~C->(C->(~D->~C)))->(~C->(C->((~D->C)->D))))) Axiom (A2)
  77. 77. ((~C->(C->(~D->~C)))->(~C->(C->((~D->C)->D)))) Modus Ponens: 75, 76
  78. 78. (~C->(C->((~D->C)->D))) Modus Ponens: 60, 77
  79. 79. ((C->((~D->C)->D))->((C->(~D->C))->(C->D))) Axiom (A2)
  80. 80. (((C->((~D->C)->D))->((C->(~D->C))->(C->D)))->(~C->((C->((~D->C)->D))->((C->(~D->C))->(C->D))))) Axiom (A1)
  81. 81. (~C->((C->((~D->C)->D))->((C->(~D->C))->(C->D)))) Modus Ponens: 79, 80
  82. 82. ((~C->((C->((~D->C)->D))->((C->(~D->C))->(C->D))))->((~C->(C->((~D->C)->D)))->(~C->((C->(~D->C))->(C->D))))) Axiom (A2)
  83. 83. ((~C->(C->((~D->C)->D)))->(~C->((C->(~D->C))->(C->D)))) Modus Ponens: 81, 82
  84. 84. (~C->((C->(~D->C))->(C->D))) Modus Ponens: 78, 83
  85. 85. ((~C->((C->(~D->C))->(C->D)))->((~C->(C->(~D->C)))->(~C->(C->D)))) Axiom (A2)
  86. 86. ((~C->(C->(~D->C)))->(~C->(C->D))) Modus Ponens: 84, 85
  87. 87. (~C->(C->D)) Modus Ponens: 28, 86
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