TSTP Solution File: ALG021+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : ALG021+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 18:04:46 EDT 2022
% Result : Theorem 1.69s 1.92s
% Output : Proof 1.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG021+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 8 18:50:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.69/1.92 % SZS status Theorem
% 1.69/1.92 (* PROOF-FOUND *)
% 1.69/1.92 (* BEGIN-PROOF *)
% 1.69/1.92 % SZS output start Proof
% 1.69/1.92 1. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 1.69/1.92 2. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 3. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 4. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 5. (-. (((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0)))))) ((op (e3) (e3)) = (e0)) ((op (e2) (e2)) = (e0)) ((op (e1) (e1)) = (e0)) ((op (e0) (e0)) = (e0)) ### DisjTree 1 2 3 4
% 1.69/1.92 6. (-. ((((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0))))) \/ ((((op (e0) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e1))))) \/ ((((op (e0) (e0)) = (e2)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e2))))) \/ (((op (e0) (e0)) = (e3)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) = (e3))))))))) ((op (e0) (e0)) = (e0)) ((op (e1) (e1)) = (e0)) ((op (e2) (e2)) = (e0)) ((op (e3) (e3)) = (e0)) ### ConjTree 5
% 1.69/1.92 7. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 1.69/1.92 8. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3)))))) ((op (e0) (e0)) = (e0)) ### ConjTree 7
% 1.69/1.92 9. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom
% 1.69/1.92 10. (-. (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3)))))) ((op (e0) (e1)) = (e1)) ### ConjTree 9
% 1.69/1.92 11. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom
% 1.69/1.92 12. (-. (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3)))))) ((op (e0) (e2)) = (e2)) ### ConjTree 11
% 1.69/1.92 13. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom
% 1.69/1.92 14. (-. (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3)))))) ((op (e0) (e3)) = (e3)) ### ConjTree 13
% 1.69/1.92 15. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 16. (-. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ ((op (e1) (e0)) = (e3)))))) ((op (e1) (e0)) = (e1)) ### ConjTree 15
% 1.69/1.92 17. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 18. (-. (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3)))))) ((op (e1) (e1)) = (e0)) ### ConjTree 17
% 1.69/1.92 19. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 20. (-. (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3)))))) ((op (e1) (e2)) = (e3)) ### ConjTree 19
% 1.69/1.92 21. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 22. (-. (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3)))))) ((op (e1) (e3)) = (e2)) ### ConjTree 21
% 1.69/1.92 23. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 24. (-. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3)))))) ((op (e2) (e0)) = (e2)) ### ConjTree 23
% 1.69/1.92 25. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 26. (-. (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e2) (e1)) = (e3)))))) ((op (e2) (e1)) = (e3)) ### ConjTree 25
% 1.69/1.92 27. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 28. (-. (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3)))))) ((op (e2) (e2)) = (e0)) ### ConjTree 27
% 1.69/1.92 29. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 30. (-. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3)))))) ((op (e2) (e3)) = (e1)) ### ConjTree 29
% 1.69/1.92 31. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 32. (-. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3)))))) ((op (e3) (e0)) = (e3)) ### ConjTree 31
% 1.69/1.92 33. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 34. (-. (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3)))))) ((op (e3) (e1)) = (e2)) ### ConjTree 33
% 1.69/1.92 35. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 36. (-. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3)))))) ((op (e3) (e2)) = (e1)) ### ConjTree 35
% 1.69/1.92 37. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 38. (-. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3)))))) ((op (e3) (e3)) = (e0)) ### ConjTree 37
% 1.69/1.92 39. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 1.69/1.92 40. ((op (e0) (e0)) = (e0)) ((e0) != (op (e0) (e0))) ### Sym(=)
% 1.69/1.92 41. ((op (op (e0) (e0)) (e0)) != (op (e0) (op (e0) (e0)))) ((op (e0) (e0)) = (e0)) ### NotEqual 39 40
% 1.69/1.92 42. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 1.69/1.92 43. ((op (e0) (e1)) = (e1)) ((e1) != (op (e0) (e1))) ### Sym(=)
% 1.69/1.92 44. ((op (op (e0) (e0)) (e1)) != (op (e0) (op (e0) (e1)))) ((op (e0) (e1)) = (e1)) ((op (e0) (e0)) = (e0)) ### NotEqual 42 43
% 1.69/1.92 45. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 1.69/1.92 46. ((op (e0) (e2)) = (e2)) ((e2) != (op (e0) (e2))) ### Sym(=)
% 1.69/1.92 47. ((op (op (e0) (e0)) (e2)) != (op (e0) (op (e0) (e2)))) ((op (e0) (e2)) = (e2)) ((op (e0) (e0)) = (e0)) ### NotEqual 45 46
% 1.69/1.92 48. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 1.69/1.92 49. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 1.69/1.92 50. ((op (op (e0) (e0)) (e3)) != (op (e0) (op (e0) (e3)))) ((op (e0) (e3)) = (e3)) ((op (e0) (e0)) = (e0)) ### NotEqual 48 49
% 1.69/1.92 51. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom
% 1.69/1.92 52. ((e0) != (e0)) ### NotEqual
% 1.69/1.92 53. ((op (op (e0) (e1)) (e0)) != (op (e1) (e0))) ((op (e0) (e1)) = (e1)) ### NotEqual 51 52
% 1.69/1.92 54. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 55. ((op (e0) (op (e1) (e0))) != (op (e0) (e1))) ((op (e1) (e0)) = (e1)) ### NotEqual 52 54
% 1.69/1.92 56. ((e1) != (e1)) ### NotEqual
% 1.69/1.92 57. ((e1) != (op (e0) (op (e1) (e0)))) ((op (e0) (e1)) = (e1)) ((op (e1) (e0)) = (e1)) ### Trans-sym 55 56
% 1.69/1.92 58. ((op (op (e0) (e1)) (e0)) != (op (e0) (op (e1) (e0)))) ((op (e1) (e0)) = (e1)) ((op (e0) (e1)) = (e1)) ### Trans 53 57
% 1.69/1.92 59. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom
% 1.69/1.92 60. ((op (op (e0) (e1)) (e1)) != (op (e1) (e1))) ((op (e0) (e1)) = (e1)) ### NotEqual 59 56
% 1.69/1.92 61. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 62. ((op (e0) (op (e1) (e1))) != (op (e0) (e0))) ((op (e1) (e1)) = (e0)) ### NotEqual 52 61
% 1.69/1.92 63. ((e0) != (op (e0) (op (e1) (e1)))) ((op (e0) (e0)) = (e0)) ((op (e1) (e1)) = (e0)) ### Trans-sym 62 52
% 1.69/1.92 64. ((op (op (e0) (e1)) (e1)) != (op (e0) (op (e1) (e1)))) ((op (e1) (e1)) = (e0)) ((op (e0) (e0)) = (e0)) ((op (e0) (e1)) = (e1)) ### Trans 60 63
% 1.69/1.92 65. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom
% 1.69/1.92 66. ((e2) != (e2)) ### NotEqual
% 1.69/1.92 67. ((op (op (e0) (e1)) (e2)) != (op (e1) (e2))) ((op (e0) (e1)) = (e1)) ### NotEqual 65 66
% 1.69/1.92 68. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 69. ((op (e0) (op (e1) (e2))) != (op (e0) (e3))) ((op (e1) (e2)) = (e3)) ### NotEqual 52 68
% 1.69/1.92 70. ((e3) != (e3)) ### NotEqual
% 1.69/1.92 71. ((e3) != (op (e0) (op (e1) (e2)))) ((op (e0) (e3)) = (e3)) ((op (e1) (e2)) = (e3)) ### Trans-sym 69 70
% 1.69/1.92 72. ((op (op (e0) (e1)) (e2)) != (op (e0) (op (e1) (e2)))) ((op (e1) (e2)) = (e3)) ((op (e0) (e3)) = (e3)) ((op (e0) (e1)) = (e1)) ### Trans 67 71
% 1.69/1.92 73. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom
% 1.69/1.92 74. ((op (op (e0) (e1)) (e3)) != (op (e1) (e3))) ((op (e0) (e1)) = (e1)) ### NotEqual 73 70
% 1.69/1.92 75. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 76. ((op (e0) (op (e1) (e3))) != (op (e0) (e2))) ((op (e1) (e3)) = (e2)) ### NotEqual 52 75
% 1.69/1.92 77. ((e2) != (op (e0) (op (e1) (e3)))) ((op (e0) (e2)) = (e2)) ((op (e1) (e3)) = (e2)) ### Trans-sym 76 66
% 1.69/1.92 78. ((op (op (e0) (e1)) (e3)) != (op (e0) (op (e1) (e3)))) ((op (e1) (e3)) = (e2)) ((op (e0) (e2)) = (e2)) ((op (e0) (e1)) = (e1)) ### Trans 74 77
% 1.69/1.92 79. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom
% 1.69/1.92 80. ((op (op (e0) (e2)) (e0)) != (op (e2) (e0))) ((op (e0) (e2)) = (e2)) ### NotEqual 79 52
% 1.69/1.92 81. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 82. ((op (e0) (op (e2) (e0))) != (op (e0) (e2))) ((op (e2) (e0)) = (e2)) ### NotEqual 52 81
% 1.69/1.92 83. ((e2) != (op (e0) (op (e2) (e0)))) ((op (e0) (e2)) = (e2)) ((op (e2) (e0)) = (e2)) ### Trans-sym 82 66
% 1.69/1.92 84. ((op (op (e0) (e2)) (e0)) != (op (e0) (op (e2) (e0)))) ((op (e2) (e0)) = (e2)) ((op (e0) (e2)) = (e2)) ### Trans 80 83
% 1.69/1.92 85. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom
% 1.69/1.92 86. ((op (op (e0) (e2)) (e1)) != (op (e2) (e1))) ((op (e0) (e2)) = (e2)) ### NotEqual 85 56
% 1.69/1.92 87. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 88. ((op (e0) (op (e2) (e1))) != (op (e0) (e3))) ((op (e2) (e1)) = (e3)) ### NotEqual 52 87
% 1.69/1.92 89. ((e3) != (op (e0) (op (e2) (e1)))) ((op (e0) (e3)) = (e3)) ((op (e2) (e1)) = (e3)) ### Trans-sym 88 70
% 1.69/1.92 90. ((op (op (e0) (e2)) (e1)) != (op (e0) (op (e2) (e1)))) ((op (e2) (e1)) = (e3)) ((op (e0) (e3)) = (e3)) ((op (e0) (e2)) = (e2)) ### Trans 86 89
% 1.69/1.92 91. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom
% 1.69/1.92 92. ((op (op (e0) (e2)) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) = (e2)) ### NotEqual 91 66
% 1.69/1.92 93. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 94. ((op (e0) (op (e2) (e2))) != (op (e0) (e0))) ((op (e2) (e2)) = (e0)) ### NotEqual 52 93
% 1.69/1.92 95. ((e0) != (op (e0) (op (e2) (e2)))) ((op (e0) (e0)) = (e0)) ((op (e2) (e2)) = (e0)) ### Trans-sym 94 52
% 1.69/1.92 96. ((op (op (e0) (e2)) (e2)) != (op (e0) (op (e2) (e2)))) ((op (e2) (e2)) = (e0)) ((op (e0) (e0)) = (e0)) ((op (e0) (e2)) = (e2)) ### Trans 92 95
% 1.69/1.92 97. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom
% 1.69/1.92 98. ((op (op (e0) (e2)) (e3)) != (op (e2) (e3))) ((op (e0) (e2)) = (e2)) ### NotEqual 97 70
% 1.69/1.92 99. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 100. ((op (e0) (op (e2) (e3))) != (op (e0) (e1))) ((op (e2) (e3)) = (e1)) ### NotEqual 52 99
% 1.69/1.92 101. ((e1) != (op (e0) (op (e2) (e3)))) ((op (e0) (e1)) = (e1)) ((op (e2) (e3)) = (e1)) ### Trans-sym 100 56
% 1.69/1.92 102. ((op (op (e0) (e2)) (e3)) != (op (e0) (op (e2) (e3)))) ((op (e2) (e3)) = (e1)) ((op (e0) (e1)) = (e1)) ((op (e0) (e2)) = (e2)) ### Trans 98 101
% 1.69/1.92 103. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom
% 1.69/1.92 104. ((op (op (e0) (e3)) (e0)) != (op (e3) (e0))) ((op (e0) (e3)) = (e3)) ### NotEqual 103 52
% 1.69/1.92 105. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 106. ((op (e0) (op (e3) (e0))) != (op (e0) (e3))) ((op (e3) (e0)) = (e3)) ### NotEqual 52 105
% 1.69/1.92 107. ((e3) != (op (e0) (op (e3) (e0)))) ((op (e0) (e3)) = (e3)) ((op (e3) (e0)) = (e3)) ### Trans-sym 106 70
% 1.69/1.92 108. ((op (op (e0) (e3)) (e0)) != (op (e0) (op (e3) (e0)))) ((op (e3) (e0)) = (e3)) ((op (e0) (e3)) = (e3)) ### Trans 104 107
% 1.69/1.92 109. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom
% 1.69/1.92 110. ((op (op (e0) (e3)) (e1)) != (op (e3) (e1))) ((op (e0) (e3)) = (e3)) ### NotEqual 109 56
% 1.69/1.92 111. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 112. ((op (e0) (op (e3) (e1))) != (op (e0) (e2))) ((op (e3) (e1)) = (e2)) ### NotEqual 52 111
% 1.69/1.92 113. ((e2) != (op (e0) (op (e3) (e1)))) ((op (e0) (e2)) = (e2)) ((op (e3) (e1)) = (e2)) ### Trans-sym 112 66
% 1.69/1.92 114. ((op (op (e0) (e3)) (e1)) != (op (e0) (op (e3) (e1)))) ((op (e3) (e1)) = (e2)) ((op (e0) (e2)) = (e2)) ((op (e0) (e3)) = (e3)) ### Trans 110 113
% 1.69/1.92 115. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom
% 1.69/1.92 116. ((op (op (e0) (e3)) (e2)) != (op (e3) (e2))) ((op (e0) (e3)) = (e3)) ### NotEqual 115 66
% 1.69/1.92 117. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 118. ((op (e0) (op (e3) (e2))) != (op (e0) (e1))) ((op (e3) (e2)) = (e1)) ### NotEqual 52 117
% 1.69/1.92 119. ((e1) != (op (e0) (op (e3) (e2)))) ((op (e0) (e1)) = (e1)) ((op (e3) (e2)) = (e1)) ### Trans-sym 118 56
% 1.69/1.92 120. ((op (op (e0) (e3)) (e2)) != (op (e0) (op (e3) (e2)))) ((op (e3) (e2)) = (e1)) ((op (e0) (e1)) = (e1)) ((op (e0) (e3)) = (e3)) ### Trans 116 119
% 1.69/1.92 121. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom
% 1.69/1.92 122. ((op (op (e0) (e3)) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) = (e3)) ### NotEqual 121 70
% 1.69/1.92 123. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 124. ((op (e0) (op (e3) (e3))) != (op (e0) (e0))) ((op (e3) (e3)) = (e0)) ### NotEqual 52 123
% 1.69/1.92 125. ((e0) != (op (e0) (op (e3) (e3)))) ((op (e0) (e0)) = (e0)) ((op (e3) (e3)) = (e0)) ### Trans-sym 124 52
% 1.69/1.92 126. ((op (op (e0) (e3)) (e3)) != (op (e0) (op (e3) (e3)))) ((op (e3) (e3)) = (e0)) ((op (e0) (e0)) = (e0)) ((op (e0) (e3)) = (e3)) ### Trans 122 125
% 1.69/1.92 127. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 128. ((op (e0) (e0)) = (e0)) ((e0) != (op (e0) (e0))) ### Sym(=)
% 1.69/1.92 129. ((op (op (e1) (e0)) (e0)) != (op (e1) (op (e0) (e0)))) ((op (e0) (e0)) = (e0)) ((op (e1) (e0)) = (e1)) ### NotEqual 127 128
% 1.69/1.92 130. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 131. ((op (e0) (e1)) = (e1)) ((e1) != (op (e0) (e1))) ### Sym(=)
% 1.69/1.92 132. ((op (op (e1) (e0)) (e1)) != (op (e1) (op (e0) (e1)))) ((op (e0) (e1)) = (e1)) ((op (e1) (e0)) = (e1)) ### NotEqual 130 131
% 1.69/1.92 133. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 134. ((op (e0) (e2)) = (e2)) ((e2) != (op (e0) (e2))) ### Sym(=)
% 1.69/1.92 135. ((op (op (e1) (e0)) (e2)) != (op (e1) (op (e0) (e2)))) ((op (e0) (e2)) = (e2)) ((op (e1) (e0)) = (e1)) ### NotEqual 133 134
% 1.69/1.92 136. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 137. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 1.69/1.92 138. ((op (op (e1) (e0)) (e3)) != (op (e1) (op (e0) (e3)))) ((op (e0) (e3)) = (e3)) ((op (e1) (e0)) = (e1)) ### NotEqual 136 137
% 1.69/1.92 139. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 140. ((op (op (e1) (e1)) (e0)) != (op (e0) (e0))) ((op (e1) (e1)) = (e0)) ### NotEqual 139 52
% 1.69/1.92 141. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 142. ((op (e1) (op (e1) (e0))) != (op (e1) (e1))) ((op (e1) (e0)) = (e1)) ### NotEqual 56 141
% 1.69/1.92 143. ((e0) != (op (e1) (op (e1) (e0)))) ((op (e1) (e1)) = (e0)) ((op (e1) (e0)) = (e1)) ### Trans-sym 142 52
% 1.69/1.92 144. ((op (op (e1) (e1)) (e0)) != (op (e1) (op (e1) (e0)))) ((op (e0) (e0)) = (e0)) ((op (e1) (e0)) = (e1)) ((op (e1) (e1)) = (e0)) ### Trans 140 143
% 1.69/1.92 145. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 146. ((op (op (e1) (e1)) (e1)) != (op (e0) (e1))) ((op (e1) (e1)) = (e0)) ### NotEqual 145 56
% 1.69/1.92 147. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 148. ((op (e1) (op (e1) (e1))) != (op (e1) (e0))) ((op (e1) (e1)) = (e0)) ### NotEqual 56 147
% 1.69/1.92 149. ((e1) != (op (e1) (op (e1) (e1)))) ((op (e1) (e0)) = (e1)) ((op (e1) (e1)) = (e0)) ### Trans-sym 148 56
% 1.69/1.92 150. ((op (op (e1) (e1)) (e1)) != (op (e1) (op (e1) (e1)))) ((op (e0) (e1)) = (e1)) ((op (e1) (e0)) = (e1)) ((op (e1) (e1)) = (e0)) ### Trans 146 149
% 1.69/1.92 151. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 152. ((op (op (e1) (e1)) (e2)) != (op (e0) (e2))) ((op (e1) (e1)) = (e0)) ### NotEqual 151 66
% 1.69/1.92 153. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 154. ((op (e1) (op (e1) (e2))) != (op (e1) (e3))) ((op (e1) (e2)) = (e3)) ### NotEqual 56 153
% 1.69/1.92 155. ((e2) != (op (e1) (op (e1) (e2)))) ((op (e1) (e3)) = (e2)) ((op (e1) (e2)) = (e3)) ### Trans-sym 154 66
% 1.69/1.92 156. ((op (op (e1) (e1)) (e2)) != (op (e1) (op (e1) (e2)))) ((op (e0) (e2)) = (e2)) ((op (e1) (e2)) = (e3)) ((op (e1) (e3)) = (e2)) ((op (e1) (e1)) = (e0)) ### Trans 152 155
% 1.69/1.92 157. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 158. ((op (op (e1) (e1)) (e3)) != (op (e0) (e3))) ((op (e1) (e1)) = (e0)) ### NotEqual 157 70
% 1.69/1.92 159. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 160. ((op (e1) (op (e1) (e3))) != (op (e1) (e2))) ((op (e1) (e3)) = (e2)) ### NotEqual 56 159
% 1.69/1.92 161. ((e3) != (op (e1) (op (e1) (e3)))) ((op (e1) (e2)) = (e3)) ((op (e1) (e3)) = (e2)) ### Trans-sym 160 70
% 1.69/1.92 162. ((op (op (e1) (e1)) (e3)) != (op (e1) (op (e1) (e3)))) ((op (e0) (e3)) = (e3)) ((op (e1) (e3)) = (e2)) ((op (e1) (e2)) = (e3)) ((op (e1) (e1)) = (e0)) ### Trans 158 161
% 1.69/1.92 163. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 164. ((op (op (e1) (e2)) (e0)) != (op (e3) (e0))) ((op (e1) (e2)) = (e3)) ### NotEqual 163 52
% 1.69/1.92 165. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 166. ((op (e1) (op (e2) (e0))) != (op (e1) (e2))) ((op (e2) (e0)) = (e2)) ### NotEqual 56 165
% 1.69/1.92 167. ((e3) != (op (e1) (op (e2) (e0)))) ((op (e1) (e2)) = (e3)) ((op (e2) (e0)) = (e2)) ### Trans-sym 166 70
% 1.69/1.92 168. ((op (op (e1) (e2)) (e0)) != (op (e1) (op (e2) (e0)))) ((op (e3) (e0)) = (e3)) ((op (e2) (e0)) = (e2)) ((op (e1) (e2)) = (e3)) ### Trans 164 167
% 1.69/1.92 169. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 170. ((op (op (e1) (e2)) (e1)) != (op (e3) (e1))) ((op (e1) (e2)) = (e3)) ### NotEqual 169 56
% 1.69/1.92 171. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 172. ((op (e1) (op (e2) (e1))) != (op (e1) (e3))) ((op (e2) (e1)) = (e3)) ### NotEqual 56 171
% 1.69/1.92 173. ((e2) != (op (e1) (op (e2) (e1)))) ((op (e1) (e3)) = (e2)) ((op (e2) (e1)) = (e3)) ### Trans-sym 172 66
% 1.69/1.92 174. ((op (op (e1) (e2)) (e1)) != (op (e1) (op (e2) (e1)))) ((op (e3) (e1)) = (e2)) ((op (e2) (e1)) = (e3)) ((op (e1) (e3)) = (e2)) ((op (e1) (e2)) = (e3)) ### Trans 170 173
% 1.69/1.92 175. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 176. ((op (op (e1) (e2)) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) = (e3)) ### NotEqual 175 66
% 1.69/1.92 177. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 178. ((op (e1) (op (e2) (e2))) != (op (e1) (e0))) ((op (e2) (e2)) = (e0)) ### NotEqual 56 177
% 1.69/1.92 179. ((e1) != (op (e1) (op (e2) (e2)))) ((op (e1) (e0)) = (e1)) ((op (e2) (e2)) = (e0)) ### Trans-sym 178 56
% 1.69/1.92 180. ((op (op (e1) (e2)) (e2)) != (op (e1) (op (e2) (e2)))) ((op (e3) (e2)) = (e1)) ((op (e2) (e2)) = (e0)) ((op (e1) (e0)) = (e1)) ((op (e1) (e2)) = (e3)) ### Trans 176 179
% 1.69/1.92 181. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 182. ((op (op (e1) (e2)) (e3)) != (op (e3) (e3))) ((op (e1) (e2)) = (e3)) ### NotEqual 181 70
% 1.69/1.92 183. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 184. ((op (e1) (op (e2) (e3))) != (op (e1) (e1))) ((op (e2) (e3)) = (e1)) ### NotEqual 56 183
% 1.69/1.92 185. ((e0) != (op (e1) (op (e2) (e3)))) ((op (e1) (e1)) = (e0)) ((op (e2) (e3)) = (e1)) ### Trans-sym 184 52
% 1.69/1.92 186. ((op (op (e1) (e2)) (e3)) != (op (e1) (op (e2) (e3)))) ((op (e3) (e3)) = (e0)) ((op (e2) (e3)) = (e1)) ((op (e1) (e1)) = (e0)) ((op (e1) (e2)) = (e3)) ### Trans 182 185
% 1.69/1.92 187. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 188. ((op (op (e1) (e3)) (e0)) != (op (e2) (e0))) ((op (e1) (e3)) = (e2)) ### NotEqual 187 52
% 1.69/1.92 189. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 190. ((op (e1) (op (e3) (e0))) != (op (e1) (e3))) ((op (e3) (e0)) = (e3)) ### NotEqual 56 189
% 1.69/1.92 191. ((e2) != (op (e1) (op (e3) (e0)))) ((op (e1) (e3)) = (e2)) ((op (e3) (e0)) = (e3)) ### Trans-sym 190 66
% 1.69/1.92 192. ((op (op (e1) (e3)) (e0)) != (op (e1) (op (e3) (e0)))) ((op (e2) (e0)) = (e2)) ((op (e3) (e0)) = (e3)) ((op (e1) (e3)) = (e2)) ### Trans 188 191
% 1.69/1.92 193. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 194. ((op (op (e1) (e3)) (e1)) != (op (e2) (e1))) ((op (e1) (e3)) = (e2)) ### NotEqual 193 56
% 1.69/1.92 195. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 196. ((op (e1) (op (e3) (e1))) != (op (e1) (e2))) ((op (e3) (e1)) = (e2)) ### NotEqual 56 195
% 1.69/1.92 197. ((e3) != (op (e1) (op (e3) (e1)))) ((op (e1) (e2)) = (e3)) ((op (e3) (e1)) = (e2)) ### Trans-sym 196 70
% 1.69/1.92 198. ((op (op (e1) (e3)) (e1)) != (op (e1) (op (e3) (e1)))) ((op (e2) (e1)) = (e3)) ((op (e3) (e1)) = (e2)) ((op (e1) (e2)) = (e3)) ((op (e1) (e3)) = (e2)) ### Trans 194 197
% 1.69/1.92 199. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 200. ((op (op (e1) (e3)) (e2)) != (op (e2) (e2))) ((op (e1) (e3)) = (e2)) ### NotEqual 199 66
% 1.69/1.92 201. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 202. ((op (e1) (op (e3) (e2))) != (op (e1) (e1))) ((op (e3) (e2)) = (e1)) ### NotEqual 56 201
% 1.69/1.92 203. ((e0) != (op (e1) (op (e3) (e2)))) ((op (e1) (e1)) = (e0)) ((op (e3) (e2)) = (e1)) ### Trans-sym 202 52
% 1.69/1.92 204. ((op (op (e1) (e3)) (e2)) != (op (e1) (op (e3) (e2)))) ((op (e2) (e2)) = (e0)) ((op (e3) (e2)) = (e1)) ((op (e1) (e1)) = (e0)) ((op (e1) (e3)) = (e2)) ### Trans 200 203
% 1.69/1.92 205. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 206. ((op (op (e1) (e3)) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) = (e2)) ### NotEqual 205 70
% 1.69/1.92 207. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 208. ((op (e1) (op (e3) (e3))) != (op (e1) (e0))) ((op (e3) (e3)) = (e0)) ### NotEqual 56 207
% 1.69/1.92 209. ((e1) != (op (e1) (op (e3) (e3)))) ((op (e1) (e0)) = (e1)) ((op (e3) (e3)) = (e0)) ### Trans-sym 208 56
% 1.69/1.92 210. ((op (op (e1) (e3)) (e3)) != (op (e1) (op (e3) (e3)))) ((op (e2) (e3)) = (e1)) ((op (e3) (e3)) = (e0)) ((op (e1) (e0)) = (e1)) ((op (e1) (e3)) = (e2)) ### Trans 206 209
% 1.69/1.92 211. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 212. ((op (e0) (e0)) = (e0)) ((e0) != (op (e0) (e0))) ### Sym(=)
% 1.69/1.92 213. ((op (op (e2) (e0)) (e0)) != (op (e2) (op (e0) (e0)))) ((op (e0) (e0)) = (e0)) ((op (e2) (e0)) = (e2)) ### NotEqual 211 212
% 1.69/1.92 214. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 215. ((op (e0) (e1)) = (e1)) ((e1) != (op (e0) (e1))) ### Sym(=)
% 1.69/1.92 216. ((op (op (e2) (e0)) (e1)) != (op (e2) (op (e0) (e1)))) ((op (e0) (e1)) = (e1)) ((op (e2) (e0)) = (e2)) ### NotEqual 214 215
% 1.69/1.92 217. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 218. ((op (e0) (e2)) = (e2)) ((e2) != (op (e0) (e2))) ### Sym(=)
% 1.69/1.92 219. ((op (op (e2) (e0)) (e2)) != (op (e2) (op (e0) (e2)))) ((op (e0) (e2)) = (e2)) ((op (e2) (e0)) = (e2)) ### NotEqual 217 218
% 1.69/1.92 220. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 221. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 1.69/1.92 222. ((op (op (e2) (e0)) (e3)) != (op (e2) (op (e0) (e3)))) ((op (e0) (e3)) = (e3)) ((op (e2) (e0)) = (e2)) ### NotEqual 220 221
% 1.69/1.92 223. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 224. ((op (op (e2) (e1)) (e0)) != (op (e3) (e0))) ((op (e2) (e1)) = (e3)) ### NotEqual 223 52
% 1.69/1.92 225. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 226. ((op (e2) (op (e1) (e0))) != (op (e2) (e1))) ((op (e1) (e0)) = (e1)) ### NotEqual 66 225
% 1.69/1.92 227. ((e3) != (op (e2) (op (e1) (e0)))) ((op (e2) (e1)) = (e3)) ((op (e1) (e0)) = (e1)) ### Trans-sym 226 70
% 1.69/1.92 228. ((op (op (e2) (e1)) (e0)) != (op (e2) (op (e1) (e0)))) ((op (e3) (e0)) = (e3)) ((op (e1) (e0)) = (e1)) ((op (e2) (e1)) = (e3)) ### Trans 224 227
% 1.69/1.92 229. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 230. ((op (op (e2) (e1)) (e1)) != (op (e3) (e1))) ((op (e2) (e1)) = (e3)) ### NotEqual 229 56
% 1.69/1.92 231. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 232. ((op (e2) (op (e1) (e1))) != (op (e2) (e0))) ((op (e1) (e1)) = (e0)) ### NotEqual 66 231
% 1.69/1.92 233. ((e2) != (op (e2) (op (e1) (e1)))) ((op (e2) (e0)) = (e2)) ((op (e1) (e1)) = (e0)) ### Trans-sym 232 66
% 1.69/1.92 234. ((op (op (e2) (e1)) (e1)) != (op (e2) (op (e1) (e1)))) ((op (e3) (e1)) = (e2)) ((op (e1) (e1)) = (e0)) ((op (e2) (e0)) = (e2)) ((op (e2) (e1)) = (e3)) ### Trans 230 233
% 1.69/1.92 235. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 236. ((op (op (e2) (e1)) (e2)) != (op (e3) (e2))) ((op (e2) (e1)) = (e3)) ### NotEqual 235 66
% 1.69/1.92 237. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 238. ((op (e2) (op (e1) (e2))) != (op (e2) (e3))) ((op (e1) (e2)) = (e3)) ### NotEqual 66 237
% 1.69/1.92 239. ((e1) != (op (e2) (op (e1) (e2)))) ((op (e2) (e3)) = (e1)) ((op (e1) (e2)) = (e3)) ### Trans-sym 238 56
% 1.69/1.92 240. ((op (op (e2) (e1)) (e2)) != (op (e2) (op (e1) (e2)))) ((op (e3) (e2)) = (e1)) ((op (e1) (e2)) = (e3)) ((op (e2) (e3)) = (e1)) ((op (e2) (e1)) = (e3)) ### Trans 236 239
% 1.69/1.92 241. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 242. ((op (op (e2) (e1)) (e3)) != (op (e3) (e3))) ((op (e2) (e1)) = (e3)) ### NotEqual 241 70
% 1.69/1.92 243. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 244. ((op (e2) (op (e1) (e3))) != (op (e2) (e2))) ((op (e1) (e3)) = (e2)) ### NotEqual 66 243
% 1.69/1.92 245. ((e0) != (op (e2) (op (e1) (e3)))) ((op (e2) (e2)) = (e0)) ((op (e1) (e3)) = (e2)) ### Trans-sym 244 52
% 1.69/1.92 246. ((op (op (e2) (e1)) (e3)) != (op (e2) (op (e1) (e3)))) ((op (e3) (e3)) = (e0)) ((op (e1) (e3)) = (e2)) ((op (e2) (e2)) = (e0)) ((op (e2) (e1)) = (e3)) ### Trans 242 245
% 1.69/1.92 247. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 248. ((op (op (e2) (e2)) (e0)) != (op (e0) (e0))) ((op (e2) (e2)) = (e0)) ### NotEqual 247 52
% 1.69/1.92 249. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 250. ((op (e2) (op (e2) (e0))) != (op (e2) (e2))) ((op (e2) (e0)) = (e2)) ### NotEqual 66 249
% 1.69/1.92 251. ((e0) != (op (e2) (op (e2) (e0)))) ((op (e2) (e2)) = (e0)) ((op (e2) (e0)) = (e2)) ### Trans-sym 250 52
% 1.69/1.92 252. ((op (op (e2) (e2)) (e0)) != (op (e2) (op (e2) (e0)))) ((op (e0) (e0)) = (e0)) ((op (e2) (e0)) = (e2)) ((op (e2) (e2)) = (e0)) ### Trans 248 251
% 1.69/1.92 253. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 254. ((op (op (e2) (e2)) (e1)) != (op (e0) (e1))) ((op (e2) (e2)) = (e0)) ### NotEqual 253 56
% 1.69/1.92 255. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 256. ((op (e2) (op (e2) (e1))) != (op (e2) (e3))) ((op (e2) (e1)) = (e3)) ### NotEqual 66 255
% 1.69/1.92 257. ((e1) != (op (e2) (op (e2) (e1)))) ((op (e2) (e3)) = (e1)) ((op (e2) (e1)) = (e3)) ### Trans-sym 256 56
% 1.69/1.92 258. ((op (op (e2) (e2)) (e1)) != (op (e2) (op (e2) (e1)))) ((op (e0) (e1)) = (e1)) ((op (e2) (e1)) = (e3)) ((op (e2) (e3)) = (e1)) ((op (e2) (e2)) = (e0)) ### Trans 254 257
% 1.69/1.92 259. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 260. ((op (op (e2) (e2)) (e2)) != (op (e0) (e2))) ((op (e2) (e2)) = (e0)) ### NotEqual 259 66
% 1.69/1.92 261. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 262. ((op (e2) (op (e2) (e2))) != (op (e2) (e0))) ((op (e2) (e2)) = (e0)) ### NotEqual 66 261
% 1.69/1.92 263. ((e2) != (op (e2) (op (e2) (e2)))) ((op (e2) (e0)) = (e2)) ((op (e2) (e2)) = (e0)) ### Trans-sym 262 66
% 1.69/1.92 264. ((op (op (e2) (e2)) (e2)) != (op (e2) (op (e2) (e2)))) ((op (e0) (e2)) = (e2)) ((op (e2) (e0)) = (e2)) ((op (e2) (e2)) = (e0)) ### Trans 260 263
% 1.69/1.92 265. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 266. ((op (op (e2) (e2)) (e3)) != (op (e0) (e3))) ((op (e2) (e2)) = (e0)) ### NotEqual 265 70
% 1.69/1.92 267. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 268. ((op (e2) (op (e2) (e3))) != (op (e2) (e1))) ((op (e2) (e3)) = (e1)) ### NotEqual 66 267
% 1.69/1.92 269. ((e3) != (op (e2) (op (e2) (e3)))) ((op (e2) (e1)) = (e3)) ((op (e2) (e3)) = (e1)) ### Trans-sym 268 70
% 1.69/1.92 270. ((op (op (e2) (e2)) (e3)) != (op (e2) (op (e2) (e3)))) ((op (e0) (e3)) = (e3)) ((op (e2) (e3)) = (e1)) ((op (e2) (e1)) = (e3)) ((op (e2) (e2)) = (e0)) ### Trans 266 269
% 1.69/1.92 271. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 272. ((op (op (e2) (e3)) (e0)) != (op (e1) (e0))) ((op (e2) (e3)) = (e1)) ### NotEqual 271 52
% 1.69/1.92 273. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 274. ((op (e2) (op (e3) (e0))) != (op (e2) (e3))) ((op (e3) (e0)) = (e3)) ### NotEqual 66 273
% 1.69/1.92 275. ((e1) != (op (e2) (op (e3) (e0)))) ((op (e2) (e3)) = (e1)) ((op (e3) (e0)) = (e3)) ### Trans-sym 274 56
% 1.69/1.92 276. ((op (op (e2) (e3)) (e0)) != (op (e2) (op (e3) (e0)))) ((op (e1) (e0)) = (e1)) ((op (e3) (e0)) = (e3)) ((op (e2) (e3)) = (e1)) ### Trans 272 275
% 1.69/1.92 277. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 278. ((op (op (e2) (e3)) (e1)) != (op (e1) (e1))) ((op (e2) (e3)) = (e1)) ### NotEqual 277 56
% 1.69/1.92 279. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 280. ((op (e2) (op (e3) (e1))) != (op (e2) (e2))) ((op (e3) (e1)) = (e2)) ### NotEqual 66 279
% 1.69/1.92 281. ((e0) != (op (e2) (op (e3) (e1)))) ((op (e2) (e2)) = (e0)) ((op (e3) (e1)) = (e2)) ### Trans-sym 280 52
% 1.69/1.92 282. ((op (op (e2) (e3)) (e1)) != (op (e2) (op (e3) (e1)))) ((op (e1) (e1)) = (e0)) ((op (e3) (e1)) = (e2)) ((op (e2) (e2)) = (e0)) ((op (e2) (e3)) = (e1)) ### Trans 278 281
% 1.69/1.92 283. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 284. ((op (op (e2) (e3)) (e2)) != (op (e1) (e2))) ((op (e2) (e3)) = (e1)) ### NotEqual 283 66
% 1.69/1.92 285. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 286. ((op (e2) (op (e3) (e2))) != (op (e2) (e1))) ((op (e3) (e2)) = (e1)) ### NotEqual 66 285
% 1.69/1.92 287. ((e3) != (op (e2) (op (e3) (e2)))) ((op (e2) (e1)) = (e3)) ((op (e3) (e2)) = (e1)) ### Trans-sym 286 70
% 1.69/1.92 288. ((op (op (e2) (e3)) (e2)) != (op (e2) (op (e3) (e2)))) ((op (e1) (e2)) = (e3)) ((op (e3) (e2)) = (e1)) ((op (e2) (e1)) = (e3)) ((op (e2) (e3)) = (e1)) ### Trans 284 287
% 1.69/1.92 289. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 290. ((op (op (e2) (e3)) (e3)) != (op (e1) (e3))) ((op (e2) (e3)) = (e1)) ### NotEqual 289 70
% 1.69/1.92 291. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 292. ((op (e2) (op (e3) (e3))) != (op (e2) (e0))) ((op (e3) (e3)) = (e0)) ### NotEqual 66 291
% 1.69/1.92 293. ((e2) != (op (e2) (op (e3) (e3)))) ((op (e2) (e0)) = (e2)) ((op (e3) (e3)) = (e0)) ### Trans-sym 292 66
% 1.69/1.92 294. ((op (op (e2) (e3)) (e3)) != (op (e2) (op (e3) (e3)))) ((op (e1) (e3)) = (e2)) ((op (e3) (e3)) = (e0)) ((op (e2) (e0)) = (e2)) ((op (e2) (e3)) = (e1)) ### Trans 290 293
% 1.69/1.92 295. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 296. ((op (e0) (e0)) = (e0)) ((e0) != (op (e0) (e0))) ### Sym(=)
% 1.69/1.92 297. ((op (op (e3) (e0)) (e0)) != (op (e3) (op (e0) (e0)))) ((op (e0) (e0)) = (e0)) ((op (e3) (e0)) = (e3)) ### NotEqual 295 296
% 1.69/1.92 298. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 299. ((op (e0) (e1)) = (e1)) ((e1) != (op (e0) (e1))) ### Sym(=)
% 1.69/1.92 300. ((op (op (e3) (e0)) (e1)) != (op (e3) (op (e0) (e1)))) ((op (e0) (e1)) = (e1)) ((op (e3) (e0)) = (e3)) ### NotEqual 298 299
% 1.69/1.92 301. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 302. ((op (e0) (e2)) = (e2)) ((e2) != (op (e0) (e2))) ### Sym(=)
% 1.69/1.92 303. ((op (op (e3) (e0)) (e2)) != (op (e3) (op (e0) (e2)))) ((op (e0) (e2)) = (e2)) ((op (e3) (e0)) = (e3)) ### NotEqual 301 302
% 1.69/1.92 304. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 305. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 1.69/1.92 306. ((op (op (e3) (e0)) (e3)) != (op (e3) (op (e0) (e3)))) ((op (e0) (e3)) = (e3)) ((op (e3) (e0)) = (e3)) ### NotEqual 304 305
% 1.69/1.92 307. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 308. ((op (op (e3) (e1)) (e0)) != (op (e2) (e0))) ((op (e3) (e1)) = (e2)) ### NotEqual 307 52
% 1.69/1.92 309. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 1.69/1.92 310. ((op (e3) (op (e1) (e0))) != (op (e3) (e1))) ((op (e1) (e0)) = (e1)) ### NotEqual 70 309
% 1.69/1.92 311. ((e2) != (op (e3) (op (e1) (e0)))) ((op (e3) (e1)) = (e2)) ((op (e1) (e0)) = (e1)) ### Trans-sym 310 66
% 1.69/1.92 312. ((op (op (e3) (e1)) (e0)) != (op (e3) (op (e1) (e0)))) ((op (e2) (e0)) = (e2)) ((op (e1) (e0)) = (e1)) ((op (e3) (e1)) = (e2)) ### Trans 308 311
% 1.69/1.92 313. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 314. ((op (op (e3) (e1)) (e1)) != (op (e2) (e1))) ((op (e3) (e1)) = (e2)) ### NotEqual 313 56
% 1.69/1.92 315. ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (e0)) ### Axiom
% 1.69/1.92 316. ((op (e3) (op (e1) (e1))) != (op (e3) (e0))) ((op (e1) (e1)) = (e0)) ### NotEqual 70 315
% 1.69/1.92 317. ((e3) != (op (e3) (op (e1) (e1)))) ((op (e3) (e0)) = (e3)) ((op (e1) (e1)) = (e0)) ### Trans-sym 316 70
% 1.69/1.92 318. ((op (op (e3) (e1)) (e1)) != (op (e3) (op (e1) (e1)))) ((op (e2) (e1)) = (e3)) ((op (e1) (e1)) = (e0)) ((op (e3) (e0)) = (e3)) ((op (e3) (e1)) = (e2)) ### Trans 314 317
% 1.69/1.92 319. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 320. ((op (op (e3) (e1)) (e2)) != (op (e2) (e2))) ((op (e3) (e1)) = (e2)) ### NotEqual 319 66
% 1.69/1.92 321. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom
% 1.69/1.92 322. ((op (e3) (op (e1) (e2))) != (op (e3) (e3))) ((op (e1) (e2)) = (e3)) ### NotEqual 70 321
% 1.69/1.92 323. ((e0) != (op (e3) (op (e1) (e2)))) ((op (e3) (e3)) = (e0)) ((op (e1) (e2)) = (e3)) ### Trans-sym 322 52
% 1.69/1.92 324. ((op (op (e3) (e1)) (e2)) != (op (e3) (op (e1) (e2)))) ((op (e2) (e2)) = (e0)) ((op (e1) (e2)) = (e3)) ((op (e3) (e3)) = (e0)) ((op (e3) (e1)) = (e2)) ### Trans 320 323
% 1.69/1.92 325. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 326. ((op (op (e3) (e1)) (e3)) != (op (e2) (e3))) ((op (e3) (e1)) = (e2)) ### NotEqual 325 70
% 1.69/1.92 327. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom
% 1.69/1.92 328. ((op (e3) (op (e1) (e3))) != (op (e3) (e2))) ((op (e1) (e3)) = (e2)) ### NotEqual 70 327
% 1.69/1.92 329. ((e1) != (op (e3) (op (e1) (e3)))) ((op (e3) (e2)) = (e1)) ((op (e1) (e3)) = (e2)) ### Trans-sym 328 56
% 1.69/1.92 330. ((op (op (e3) (e1)) (e3)) != (op (e3) (op (e1) (e3)))) ((op (e2) (e3)) = (e1)) ((op (e1) (e3)) = (e2)) ((op (e3) (e2)) = (e1)) ((op (e3) (e1)) = (e2)) ### Trans 326 329
% 1.69/1.92 331. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 332. ((op (op (e3) (e2)) (e0)) != (op (e1) (e0))) ((op (e3) (e2)) = (e1)) ### NotEqual 331 52
% 1.69/1.92 333. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 1.69/1.92 334. ((op (e3) (op (e2) (e0))) != (op (e3) (e2))) ((op (e2) (e0)) = (e2)) ### NotEqual 70 333
% 1.69/1.92 335. ((e1) != (op (e3) (op (e2) (e0)))) ((op (e3) (e2)) = (e1)) ((op (e2) (e0)) = (e2)) ### Trans-sym 334 56
% 1.69/1.92 336. ((op (op (e3) (e2)) (e0)) != (op (e3) (op (e2) (e0)))) ((op (e1) (e0)) = (e1)) ((op (e2) (e0)) = (e2)) ((op (e3) (e2)) = (e1)) ### Trans 332 335
% 1.69/1.92 337. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 338. ((op (op (e3) (e2)) (e1)) != (op (e1) (e1))) ((op (e3) (e2)) = (e1)) ### NotEqual 337 56
% 1.69/1.92 339. ((op (e2) (e1)) = (e3)) ((op (e2) (e1)) != (e3)) ### Axiom
% 1.69/1.92 340. ((op (e3) (op (e2) (e1))) != (op (e3) (e3))) ((op (e2) (e1)) = (e3)) ### NotEqual 70 339
% 1.69/1.92 341. ((e0) != (op (e3) (op (e2) (e1)))) ((op (e3) (e3)) = (e0)) ((op (e2) (e1)) = (e3)) ### Trans-sym 340 52
% 1.69/1.92 342. ((op (op (e3) (e2)) (e1)) != (op (e3) (op (e2) (e1)))) ((op (e1) (e1)) = (e0)) ((op (e2) (e1)) = (e3)) ((op (e3) (e3)) = (e0)) ((op (e3) (e2)) = (e1)) ### Trans 338 341
% 1.69/1.92 343. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 344. ((op (op (e3) (e2)) (e2)) != (op (e1) (e2))) ((op (e3) (e2)) = (e1)) ### NotEqual 343 66
% 1.69/1.92 345. ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (e0)) ### Axiom
% 1.69/1.92 346. ((op (e3) (op (e2) (e2))) != (op (e3) (e0))) ((op (e2) (e2)) = (e0)) ### NotEqual 70 345
% 1.69/1.92 347. ((e3) != (op (e3) (op (e2) (e2)))) ((op (e3) (e0)) = (e3)) ((op (e2) (e2)) = (e0)) ### Trans-sym 346 70
% 1.69/1.92 348. ((op (op (e3) (e2)) (e2)) != (op (e3) (op (e2) (e2)))) ((op (e1) (e2)) = (e3)) ((op (e2) (e2)) = (e0)) ((op (e3) (e0)) = (e3)) ((op (e3) (e2)) = (e1)) ### Trans 344 347
% 1.69/1.92 349. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 350. ((op (op (e3) (e2)) (e3)) != (op (e1) (e3))) ((op (e3) (e2)) = (e1)) ### NotEqual 349 70
% 1.69/1.92 351. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom
% 1.69/1.92 352. ((op (e3) (op (e2) (e3))) != (op (e3) (e1))) ((op (e2) (e3)) = (e1)) ### NotEqual 70 351
% 1.69/1.92 353. ((e2) != (op (e3) (op (e2) (e3)))) ((op (e3) (e1)) = (e2)) ((op (e2) (e3)) = (e1)) ### Trans-sym 352 66
% 1.69/1.92 354. ((op (op (e3) (e2)) (e3)) != (op (e3) (op (e2) (e3)))) ((op (e1) (e3)) = (e2)) ((op (e2) (e3)) = (e1)) ((op (e3) (e1)) = (e2)) ((op (e3) (e2)) = (e1)) ### Trans 350 353
% 1.69/1.92 355. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 356. ((op (op (e3) (e3)) (e0)) != (op (e0) (e0))) ((op (e3) (e3)) = (e0)) ### NotEqual 355 52
% 1.69/1.92 357. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 1.69/1.92 358. ((op (e3) (op (e3) (e0))) != (op (e3) (e3))) ((op (e3) (e0)) = (e3)) ### NotEqual 70 357
% 1.69/1.92 359. ((e0) != (op (e3) (op (e3) (e0)))) ((op (e3) (e3)) = (e0)) ((op (e3) (e0)) = (e3)) ### Trans-sym 358 52
% 1.69/1.92 360. ((op (op (e3) (e3)) (e0)) != (op (e3) (op (e3) (e0)))) ((op (e0) (e0)) = (e0)) ((op (e3) (e0)) = (e3)) ((op (e3) (e3)) = (e0)) ### Trans 356 359
% 1.69/1.92 361. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 362. ((op (op (e3) (e3)) (e1)) != (op (e0) (e1))) ((op (e3) (e3)) = (e0)) ### NotEqual 361 56
% 1.69/1.92 363. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom
% 1.69/1.92 364. ((op (e3) (op (e3) (e1))) != (op (e3) (e2))) ((op (e3) (e1)) = (e2)) ### NotEqual 70 363
% 1.69/1.92 365. ((e1) != (op (e3) (op (e3) (e1)))) ((op (e3) (e2)) = (e1)) ((op (e3) (e1)) = (e2)) ### Trans-sym 364 56
% 1.69/1.92 366. ((op (op (e3) (e3)) (e1)) != (op (e3) (op (e3) (e1)))) ((op (e0) (e1)) = (e1)) ((op (e3) (e1)) = (e2)) ((op (e3) (e2)) = (e1)) ((op (e3) (e3)) = (e0)) ### Trans 362 365
% 1.69/1.92 367. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 368. ((op (op (e3) (e3)) (e2)) != (op (e0) (e2))) ((op (e3) (e3)) = (e0)) ### NotEqual 367 66
% 1.69/1.92 369. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom
% 1.69/1.92 370. ((op (e3) (op (e3) (e2))) != (op (e3) (e1))) ((op (e3) (e2)) = (e1)) ### NotEqual 70 369
% 1.69/1.92 371. ((e2) != (op (e3) (op (e3) (e2)))) ((op (e3) (e1)) = (e2)) ((op (e3) (e2)) = (e1)) ### Trans-sym 370 66
% 1.69/1.92 372. ((op (op (e3) (e3)) (e2)) != (op (e3) (op (e3) (e2)))) ((op (e0) (e2)) = (e2)) ((op (e3) (e2)) = (e1)) ((op (e3) (e1)) = (e2)) ((op (e3) (e3)) = (e0)) ### Trans 368 371
% 1.69/1.92 373. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 374. ((op (op (e3) (e3)) (e3)) != (op (e0) (e3))) ((op (e3) (e3)) = (e0)) ### NotEqual 373 70
% 1.69/1.92 375. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom
% 1.69/1.92 376. ((op (e3) (op (e3) (e3))) != (op (e3) (e0))) ((op (e3) (e3)) = (e0)) ### NotEqual 70 375
% 1.69/1.92 377. ((e3) != (op (e3) (op (e3) (e3)))) ((op (e3) (e0)) = (e3)) ((op (e3) (e3)) = (e0)) ### Trans-sym 376 70
% 1.69/1.92 378. ((op (op (e3) (e3)) (e3)) != (op (e3) (op (e3) (e3)))) ((op (e0) (e3)) = (e3)) ((op (e3) (e0)) = (e3)) ((op (e3) (e3)) = (e0)) ### Trans 374 377
% 1.69/1.92 379. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 380. ((op (unit) (e0)) != (op (e0) (e0))) ((unit) = (e0)) ### NotEqual 379 52
% 1.69/1.92 381. ((op (unit) (e0)) != (e0)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ### Trans 380 52
% 1.69/1.92 382. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 383. ((op (e0) (unit)) != (op (e0) (e0))) ((unit) = (e0)) ### NotEqual 52 382
% 1.69/1.92 384. ((op (e0) (unit)) != (e0)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ### Trans 383 52
% 1.69/1.92 385. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 386. ((op (unit) (e1)) != (op (e0) (e1))) ((unit) = (e0)) ### NotEqual 385 56
% 1.69/1.92 387. ((op (unit) (e1)) != (e1)) ((op (e0) (e1)) = (e1)) ((unit) = (e0)) ### Trans 386 56
% 1.69/1.92 388. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 389. ((op (e1) (unit)) != (op (e1) (e0))) ((unit) = (e0)) ### NotEqual 56 388
% 1.69/1.92 390. ((op (e1) (unit)) != (e1)) ((op (e1) (e0)) = (e1)) ((unit) = (e0)) ### Trans 389 56
% 1.69/1.92 391. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 392. ((op (unit) (e2)) != (op (e0) (e2))) ((unit) = (e0)) ### NotEqual 391 66
% 1.69/1.92 393. ((op (unit) (e2)) != (e2)) ((op (e0) (e2)) = (e2)) ((unit) = (e0)) ### Trans 392 66
% 1.69/1.92 394. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 395. ((op (e2) (unit)) != (op (e2) (e0))) ((unit) = (e0)) ### NotEqual 66 394
% 1.69/1.92 396. ((op (e2) (unit)) != (e2)) ((op (e2) (e0)) = (e2)) ((unit) = (e0)) ### Trans 395 66
% 1.69/1.92 397. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 398. ((op (unit) (e3)) != (op (e0) (e3))) ((unit) = (e0)) ### NotEqual 397 70
% 1.69/1.92 399. ((op (unit) (e3)) != (e3)) ((op (e0) (e3)) = (e3)) ((unit) = (e0)) ### Trans 398 70
% 1.69/1.92 400. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 401. ((op (e3) (unit)) != (op (e3) (e0))) ((unit) = (e0)) ### NotEqual 70 400
% 1.69/1.92 402. ((op (e3) (unit)) != (e3)) ((op (e3) (e0)) = (e3)) ((unit) = (e0)) ### Trans 401 70
% 1.69/1.92 403. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 1.69/1.92 404. (-. (((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ ((unit) = (e3)))))) ((unit) = (e0)) ### ConjTree 403
% 1.69/1.92 405. ((inv (e0)) = (e0)) ((inv (e0)) != (e0)) ### Axiom
% 1.69/1.92 406. ((op (e0) (inv (e0))) != (op (e0) (e0))) ((inv (e0)) = (e0)) ### NotEqual 52 405
% 1.69/1.92 407. ((unit) = (e0)) ((e0) != (unit)) ### Sym(=)
% 1.69/1.92 408. ((op (e0) (inv (e0))) != (unit)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ((inv (e0)) = (e0)) ### Trans 406 407
% 1.69/1.92 409. ((inv (e0)) = (e0)) ((inv (e0)) != (e0)) ### Axiom
% 1.69/1.92 410. ((op (inv (e0)) (e0)) != (op (e0) (e0))) ((inv (e0)) = (e0)) ### NotEqual 409 52
% 1.69/1.92 411. ((unit) = (e0)) ((e0) != (unit)) ### Sym(=)
% 1.69/1.92 412. ((op (inv (e0)) (e0)) != (unit)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ((inv (e0)) = (e0)) ### Trans 410 411
% 1.69/1.92 413. ((inv (e1)) = (e1)) ((inv (e1)) != (e1)) ### Axiom
% 1.69/1.92 414. ((op (e1) (inv (e1))) != (op (e1) (e1))) ((inv (e1)) = (e1)) ### NotEqual 56 413
% 1.69/1.92 415. ((unit) = (e0)) ((e0) != (unit)) ### Sym(=)
% 1.69/1.92 416. ((op (e1) (inv (e1))) != (unit)) ((op (e1) (e1)) = (e0)) ((unit) = (e0)) ((inv (e1)) = (e1)) ### Trans 414 415
% 1.69/1.92 417. ((inv (e1)) = (e1)) ((inv (e1)) != (e1)) ### Axiom
% 1.69/1.92 418. ((op (inv (e1)) (e1)) != (op (e1) (e1))) ((inv (e1)) = (e1)) ### NotEqual 417 56
% 1.69/1.92 419. ((unit) = (e0)) ((e0) != (unit)) ### Sym(=)
% 1.69/1.92 420. ((op (inv (e1)) (e1)) != (unit)) ((op (e1) (e1)) = (e0)) ((unit) = (e0)) ((inv (e1)) = (e1)) ### Trans 418 419
% 1.69/1.92 421. ((inv (e2)) = (e2)) ((inv (e2)) != (e2)) ### Axiom
% 1.69/1.92 422. ((op (e2) (inv (e2))) != (op (e2) (e2))) ((inv (e2)) = (e2)) ### NotEqual 66 421
% 1.69/1.92 423. ((unit) = (e0)) ((e0) != (unit)) ### Sym(=)
% 1.69/1.92 424. ((op (e2) (inv (e2))) != (unit)) ((op (e2) (e2)) = (e0)) ((unit) = (e0)) ((inv (e2)) = (e2)) ### Trans 422 423
% 1.69/1.92 425. ((inv (e2)) = (e2)) ((inv (e2)) != (e2)) ### Axiom
% 1.69/1.92 426. ((op (inv (e2)) (e2)) != (op (e2) (e2))) ((inv (e2)) = (e2)) ### NotEqual 425 66
% 1.69/1.92 427. ((unit) = (e0)) ((e0) != (unit)) ### Sym(=)
% 1.69/1.92 428. ((op (inv (e2)) (e2)) != (unit)) ((op (e2) (e2)) = (e0)) ((unit) = (e0)) ((inv (e2)) = (e2)) ### Trans 426 427
% 1.69/1.92 429. ((inv (e3)) = (e3)) ((inv (e3)) != (e3)) ### Axiom
% 1.69/1.92 430. ((op (e3) (inv (e3))) != (op (e3) (e3))) ((inv (e3)) = (e3)) ### NotEqual 70 429
% 1.69/1.92 431. ((unit) = (e0)) ((e0) != (unit)) ### Sym(=)
% 1.69/1.92 432. ((op (e3) (inv (e3))) != (unit)) ((op (e3) (e3)) = (e0)) ((unit) = (e0)) ((inv (e3)) = (e3)) ### Trans 430 431
% 1.69/1.92 433. ((inv (e3)) = (e3)) ((inv (e3)) != (e3)) ### Axiom
% 1.69/1.92 434. ((op (inv (e3)) (e3)) != (op (e3) (e3))) ((inv (e3)) = (e3)) ### NotEqual 433 70
% 1.69/1.92 435. ((unit) = (e0)) ((e0) != (unit)) ### Sym(=)
% 1.69/1.92 436. ((op (inv (e3)) (e3)) != (unit)) ((op (e3) (e3)) = (e0)) ((unit) = (e0)) ((inv (e3)) = (e3)) ### Trans 434 435
% 1.69/1.92 437. ((inv (e0)) = (e0)) ((inv (e0)) != (e0)) ### Axiom
% 1.69/1.92 438. (-. (((inv (e0)) = (e0)) \/ (((inv (e0)) = (e1)) \/ (((inv (e0)) = (e2)) \/ ((inv (e0)) = (e3)))))) ((inv (e0)) = (e0)) ### ConjTree 437
% 1.69/1.92 439. ((inv (e1)) = (e1)) ((inv (e1)) != (e1)) ### Axiom
% 1.69/1.92 440. (-. (((inv (e1)) = (e0)) \/ (((inv (e1)) = (e1)) \/ (((inv (e1)) = (e2)) \/ ((inv (e1)) = (e3)))))) ((inv (e1)) = (e1)) ### ConjTree 439
% 1.69/1.92 441. ((inv (e2)) = (e2)) ((inv (e2)) != (e2)) ### Axiom
% 1.69/1.92 442. (-. (((inv (e2)) = (e0)) \/ (((inv (e2)) = (e1)) \/ (((inv (e2)) = (e2)) \/ ((inv (e2)) = (e3)))))) ((inv (e2)) = (e2)) ### ConjTree 441
% 1.69/1.92 443. ((inv (e3)) = (e3)) ((inv (e3)) != (e3)) ### Axiom
% 1.69/1.92 444. (-. (((inv (e3)) = (e0)) \/ (((inv (e3)) = (e1)) \/ (((inv (e3)) = (e2)) \/ ((inv (e3)) = (e3)))))) ((inv (e3)) = (e3)) ### ConjTree 443
% 1.69/1.92 445. (-. (((((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0))))) \/ ((((op (e0) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e1))))) \/ ((((op (e0) (e0)) = (e2)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e2))))) \/ (((op (e0) (e0)) = (e3)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) = (e3)))))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ ((op (e1) (e0)) = (e3))))) /\ ((((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) /\ ((((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) /\ ((((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) /\ ((((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e2) (e1)) = (e3))))) /\ ((((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) /\ ((((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (op (e0) (e0)) (e0)) = (op (e0) (op (e0) (e0)))) /\ (((op (op (e0) (e0)) (e1)) = (op (e0) (op (e0) (e1)))) /\ (((op (op (e0) (e0)) (e2)) = (op (e0) (op (e0) (e2)))) /\ (((op (op (e0) (e0)) (e3)) = (op (e0) (op (e0) (e3)))) /\ (((op (op (e0) (e1)) (e0)) = (op (e0) (op (e1) (e0)))) /\ (((op (op (e0) (e1)) (e1)) = (op (e0) (op (e1) (e1)))) /\ (((op (op (e0) (e1)) (e2)) = (op (e0) (op (e1) (e2)))) /\ (((op (op (e0) (e1)) (e3)) = (op (e0) (op (e1) (e3)))) /\ (((op (op (e0) (e2)) (e0)) = (op (e0) (op (e2) (e0)))) /\ (((op (op (e0) (e2)) (e1)) = (op (e0) (op (e2) (e1)))) /\ (((op (op (e0) (e2)) (e2)) = (op (e0) (op (e2) (e2)))) /\ (((op (op (e0) (e2)) (e3)) = (op (e0) (op (e2) (e3)))) /\ (((op (op (e0) (e3)) (e0)) = (op (e0) (op (e3) (e0)))) /\ (((op (op (e0) (e3)) (e1)) = (op (e0) (op (e3) (e1)))) /\ (((op (op (e0) (e3)) (e2)) = (op (e0) (op (e3) (e2)))) /\ (((op (op (e0) (e3)) (e3)) = (op (e0) (op (e3) (e3)))) /\ (((op (op (e1) (e0)) (e0)) = (op (e1) (op (e0) (e0)))) /\ (((op (op (e1) (e0)) (e1)) = (op (e1) (op (e0) (e1)))) /\ (((op (op (e1) (e0)) (e2)) = (op (e1) (op (e0) (e2)))) /\ (((op (op (e1) (e0)) (e3)) = (op (e1) (op (e0) (e3)))) /\ (((op (op (e1) (e1)) (e0)) = (op (e1) (op (e1) (e0)))) /\ (((op (op (e1) (e1)) (e1)) = (op (e1) (op (e1) (e1)))) /\ (((op (op (e1) (e1)) (e2)) = (op (e1) (op (e1) (e2)))) /\ (((op (op (e1) (e1)) (e3)) = (op (e1) (op (e1) (e3)))) /\ (((op (op (e1) (e2)) (e0)) = (op (e1) (op (e2) (e0)))) /\ (((op (op (e1) (e2)) (e1)) = (op (e1) (op (e2) (e1)))) /\ (((op (op (e1) (e2)) (e2)) = (op (e1) (op (e2) (e2)))) /\ (((op (op (e1) (e2)) (e3)) = (op (e1) (op (e2) (e3)))) /\ (((op (op (e1) (e3)) (e0)) = (op (e1) (op (e3) (e0)))) /\ (((op (op (e1) (e3)) (e1)) = (op (e1) (op (e3) (e1)))) /\ (((op (op (e1) (e3)) (e2)) = (op (e1) (op (e3) (e2)))) /\ (((op (op (e1) (e3)) (e3)) = (op (e1) (op (e3) (e3)))) /\ (((op (op (e2) (e0)) (e0)) = (op (e2) (op (e0) (e0)))) /\ (((op (op (e2) (e0)) (e1)) = (op (e2) (op (e0) (e1)))) /\ (((op (op (e2) (e0)) (e2)) = (op (e2) (op (e0) (e2)))) /\ (((op (op (e2) (e0)) (e3)) = (op (e2) (op (e0) (e3)))) /\ (((op (op (e2) (e1)) (e0)) = (op (e2) (op (e1) (e0)))) /\ (((op (op (e2) (e1)) (e1)) = (op (e2) (op (e1) (e1)))) /\ (((op (op (e2) (e1)) (e2)) = (op (e2) (op (e1) (e2)))) /\ (((op (op (e2) (e1)) (e3)) = (op (e2) (op (e1) (e3)))) /\ (((op (op (e2) (e2)) (e0)) = (op (e2) (op (e2) (e0)))) /\ (((op (op (e2) (e2)) (e1)) = (op (e2) (op (e2) (e1)))) /\ (((op (op (e2) (e2)) (e2)) = (op (e2) (op (e2) (e2)))) /\ (((op (op (e2) (e2)) (e3)) = (op (e2) (op (e2) (e3)))) /\ (((op (op (e2) (e3)) (e0)) = (op (e2) (op (e3) (e0)))) /\ (((op (op (e2) (e3)) (e1)) = (op (e2) (op (e3) (e1)))) /\ (((op (op (e2) (e3)) (e2)) = (op (e2) (op (e3) (e2)))) /\ (((op (op (e2) (e3)) (e3)) = (op (e2) (op (e3) (e3)))) /\ (((op (op (e3) (e0)) (e0)) = (op (e3) (op (e0) (e0)))) /\ (((op (op (e3) (e0)) (e1)) = (op (e3) (op (e0) (e1)))) /\ (((op (op (e3) (e0)) (e2)) = (op (e3) (op (e0) (e2)))) /\ (((op (op (e3) (e0)) (e3)) = (op (e3) (op (e0) (e3)))) /\ (((op (op (e3) (e1)) (e0)) = (op (e3) (op (e1) (e0)))) /\ (((op (op (e3) (e1)) (e1)) = (op (e3) (op (e1) (e1)))) /\ (((op (op (e3) (e1)) (e2)) = (op (e3) (op (e1) (e2)))) /\ (((op (op (e3) (e1)) (e3)) = (op (e3) (op (e1) (e3)))) /\ (((op (op (e3) (e2)) (e0)) = (op (e3) (op (e2) (e0)))) /\ (((op (op (e3) (e2)) (e1)) = (op (e3) (op (e2) (e1)))) /\ (((op (op (e3) (e2)) (e2)) = (op (e3) (op (e2) (e2)))) /\ (((op (op (e3) (e2)) (e3)) = (op (e3) (op (e2) (e3)))) /\ (((op (op (e3) (e3)) (e0)) = (op (e3) (op (e3) (e0)))) /\ (((op (op (e3) (e3)) (e1)) = (op (e3) (op (e3) (e1)))) /\ (((op (op (e3) (e3)) (e2)) = (op (e3) (op (e3) (e2)))) /\ (((op (op (e3) (e3)) (e3)) = (op (e3) (op (e3) (e3)))) /\ (((op (unit) (e0)) = (e0)) /\ (((op (e0) (unit)) = (e0)) /\ (((op (unit) (e1)) = (e1)) /\ (((op (e1) (unit)) = (e1)) /\ (((op (unit) (e2)) = (e2)) /\ (((op (e2) (unit)) = (e2)) /\ (((op (unit) (e3)) = (e3)) /\ (((op (e3) (unit)) = (e3)) /\ ((((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ ((unit) = (e3))))) /\ (((op (e0) (inv (e0))) = (unit)) /\ (((op (inv (e0)) (e0)) = (unit)) /\ (((op (e1) (inv (e1))) = (unit)) /\ (((op (inv (e1)) (e1)) = (unit)) /\ (((op (e2) (inv (e2))) = (unit)) /\ (((op (inv (e2)) (e2)) = (unit)) /\ (((op (e3) (inv (e3))) = (unit)) /\ (((op (inv (e3)) (e3)) = (unit)) /\ ((((inv (e0)) = (e0)) \/ (((inv (e0)) = (e1)) \/ (((inv (e0)) = (e2)) \/ ((inv (e0)) = (e3))))) /\ ((((inv (e1)) = (e0)) \/ (((inv (e1)) = (e1)) \/ (((inv (e1)) = (e2)) \/ ((inv (e1)) = (e3))))) /\ ((((inv (e2)) = (e0)) \/ (((inv (e2)) = (e1)) \/ (((inv (e2)) = (e2)) \/ ((inv (e2)) = (e3))))) /\ (((inv (e3)) = (e0)) \/ (((inv (e3)) = (e1)) \/ (((inv (e3)) = (e2)) \/ ((inv (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ((inv (e3)) = (e3)) ((inv (e2)) = (e2)) ((inv (e1)) = (e1)) ((inv (e0)) = (e0)) ((unit) = (e0)) ((op (e3) (e2)) = (e1)) ((op (e3) (e1)) = (e2)) ((op (e3) (e0)) = (e3)) ((op (e2) (e3)) = (e1)) ((op (e2) (e1)) = (e3)) ((op (e2) (e0)) = (e2)) ((op (e1) (e3)) = (e2)) ((op (e1) (e2)) = (e3)) ((op (e1) (e0)) = (e1)) ((op (e0) (e3)) = (e3)) ((op (e0) (e2)) = (e2)) ((op (e0) (e1)) = (e1)) ((op (e3) (e3)) = (e0)) ((op (e2) (e2)) = (e0)) ((op (e1) (e1)) = (e0)) ((op (e0) (e0)) = (e0)) ### DisjTree 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 41 44 47 50 58 64 72 78 84 90 96 102 108 114 120 126 129 132 135 138 144 150 156 162 168 174 180 186 192 198 204 210 213 216 219 222 228 234 240 246 252 258 264 270 276 282 288 294 297 300 303 306 312 318 324 330 336 342 348 354 360 366 372 378 381 384 387 390 393 396 399 402 404 408 412 416 420 424 428 432 436 438 440 442 444
% 1.69/1.92 446. (((inv (e0)) = (e0)) /\ (((inv (e1)) = (e1)) /\ (((inv (e2)) = (e2)) /\ ((inv (e3)) = (e3))))) ((op (e0) (e0)) = (e0)) ((op (e1) (e1)) = (e0)) ((op (e2) (e2)) = (e0)) ((op (e3) (e3)) = (e0)) ((op (e0) (e1)) = (e1)) ((op (e0) (e2)) = (e2)) ((op (e0) (e3)) = (e3)) ((op (e1) (e0)) = (e1)) ((op (e1) (e2)) = (e3)) ((op (e1) (e3)) = (e2)) ((op (e2) (e0)) = (e2)) ((op (e2) (e1)) = (e3)) ((op (e2) (e3)) = (e1)) ((op (e3) (e0)) = (e3)) ((op (e3) (e1)) = (e2)) ((op (e3) (e2)) = (e1)) ((unit) = (e0)) (-. (((((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0))))) \/ ((((op (e0) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e1))))) \/ ((((op (e0) (e0)) = (e2)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e2))))) \/ (((op (e0) (e0)) = (e3)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) = (e3)))))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = 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(e3)) (e1)) = (op (e1) (op (e3) (e1)))) /\ (((op (op (e1) (e3)) (e2)) = (op (e1) (op (e3) (e2)))) /\ (((op (op (e1) (e3)) (e3)) = (op (e1) (op (e3) (e3)))) /\ (((op (op (e2) (e0)) (e0)) = (op (e2) (op (e0) (e0)))) /\ (((op (op (e2) (e0)) (e1)) = (op (e2) (op (e0) (e1)))) /\ (((op (op (e2) (e0)) (e2)) = (op (e2) (op (e0) (e2)))) /\ (((op (op (e2) (e0)) (e3)) = (op (e2) (op (e0) (e3)))) /\ (((op (op (e2) (e1)) (e0)) = (op (e2) (op (e1) (e0)))) /\ (((op (op (e2) (e1)) (e1)) = (op (e2) (op (e1) (e1)))) /\ (((op (op (e2) (e1)) (e2)) = (op (e2) (op (e1) (e2)))) /\ (((op (op (e2) (e1)) (e3)) = (op (e2) (op (e1) (e3)))) /\ (((op (op (e2) (e2)) (e0)) = (op (e2) (op (e2) (e0)))) /\ (((op (op (e2) (e2)) (e1)) = (op (e2) (op (e2) (e1)))) /\ (((op (op (e2) (e2)) (e2)) = (op (e2) (op (e2) (e2)))) /\ (((op (op (e2) (e2)) (e3)) = (op (e2) (op (e2) (e3)))) /\ (((op (op (e2) (e3)) (e0)) = (op (e2) (op (e3) (e0)))) /\ (((op (op (e2) (e3)) (e1)) = (op (e2) (op (e3) (e1)))) /\ (((op (op (e2) (e3)) (e2)) = (op (e2) (op (e3) (e2)))) /\ (((op (op (e2) (e3)) (e3)) = (op (e2) (op (e3) (e3)))) /\ (((op (op (e3) (e0)) (e0)) = (op (e3) (op (e0) (e0)))) /\ (((op (op (e3) (e0)) (e1)) = (op (e3) (op (e0) (e1)))) /\ (((op (op (e3) (e0)) (e2)) = (op (e3) (op (e0) (e2)))) /\ (((op (op (e3) (e0)) (e3)) = (op (e3) (op (e0) (e3)))) /\ (((op (op (e3) (e1)) (e0)) = (op (e3) (op (e1) (e0)))) /\ (((op (op (e3) (e1)) (e1)) = (op (e3) (op (e1) (e1)))) /\ (((op (op (e3) (e1)) (e2)) = (op (e3) (op (e1) (e2)))) /\ (((op (op (e3) (e1)) (e3)) = (op (e3) (op (e1) (e3)))) /\ (((op (op (e3) (e2)) (e0)) = (op (e3) (op (e2) (e0)))) /\ (((op (op (e3) (e2)) (e1)) = (op (e3) (op (e2) (e1)))) /\ (((op (op (e3) (e2)) (e2)) = (op (e3) (op (e2) (e2)))) /\ (((op (op (e3) (e2)) (e3)) = (op (e3) (op (e2) (e3)))) /\ (((op (op (e3) (e3)) (e0)) = (op (e3) (op (e3) (e0)))) /\ (((op (op (e3) (e3)) (e1)) = (op (e3) (op (e3) (e1)))) /\ (((op (op (e3) (e3)) (e2)) = (op (e3) (op (e3) (e2)))) /\ (((op (op (e3) (e3)) (e3)) = (op (e3) (op (e3) (e3)))) /\ (((op (unit) (e0)) = (e0)) /\ (((op (e0) (unit)) = (e0)) /\ (((op (unit) (e1)) = (e1)) /\ (((op (e1) (unit)) = (e1)) /\ (((op (unit) (e2)) = (e2)) /\ (((op (e2) (unit)) = (e2)) /\ (((op (unit) (e3)) = (e3)) /\ (((op (e3) (unit)) = (e3)) /\ ((((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ ((unit) = (e3))))) /\ (((op (e0) (inv (e0))) = (unit)) /\ (((op (inv (e0)) (e0)) = (unit)) /\ (((op (e1) (inv (e1))) = (unit)) /\ (((op (inv (e1)) (e1)) = (unit)) /\ (((op (e2) (inv (e2))) = (unit)) /\ (((op (inv (e2)) (e2)) = (unit)) /\ (((op (e3) (inv (e3))) = (unit)) /\ (((op (inv (e3)) (e3)) = (unit)) /\ ((((inv (e0)) = (e0)) \/ (((inv (e0)) = (e1)) \/ (((inv (e0)) = (e2)) \/ ((inv (e0)) = (e3))))) /\ ((((inv (e1)) = (e0)) \/ (((inv (e1)) = (e1)) \/ (((inv (e1)) = (e2)) \/ ((inv (e1)) = (e3))))) /\ ((((inv (e2)) = (e0)) \/ (((inv (e2)) = (e1)) \/ (((inv (e2)) = (e2)) \/ ((inv (e2)) = (e3))))) /\ (((inv (e3)) = (e0)) \/ (((inv (e3)) = (e1)) \/ (((inv (e3)) = (e2)) \/ ((inv (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ### ConjTree 445
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(((((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0))))) \/ ((((op (e0) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e1))))) \/ ((((op (e0) (e0)) = (e2)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e2))))) \/ (((op (e0) (e0)) = (e3)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) = (e3)))))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = 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(((op (op (e0) (e3)) (e0)) = (op (e0) (op (e3) (e0)))) /\ (((op (op (e0) (e3)) (e1)) = (op (e0) (op (e3) (e1)))) /\ (((op (op (e0) (e3)) (e2)) = (op (e0) (op (e3) (e2)))) /\ (((op (op (e0) (e3)) (e3)) = (op (e0) (op (e3) (e3)))) /\ (((op (op (e1) (e0)) (e0)) = (op (e1) (op (e0) (e0)))) /\ (((op (op (e1) (e0)) (e1)) = (op (e1) (op (e0) (e1)))) /\ (((op (op (e1) (e0)) (e2)) = (op (e1) (op (e0) (e2)))) /\ (((op (op (e1) (e0)) (e3)) = (op (e1) (op (e0) (e3)))) /\ (((op (op (e1) (e1)) (e0)) = (op (e1) (op (e1) (e0)))) /\ (((op (op (e1) (e1)) (e1)) = (op (e1) (op (e1) (e1)))) /\ (((op (op (e1) (e1)) (e2)) = (op (e1) (op (e1) (e2)))) /\ (((op (op (e1) (e1)) (e3)) = (op (e1) (op (e1) (e3)))) /\ (((op (op (e1) (e2)) (e0)) = (op (e1) (op (e2) (e0)))) /\ (((op (op (e1) (e2)) (e1)) = (op (e1) (op (e2) (e1)))) /\ (((op (op (e1) (e2)) (e2)) = (op (e1) (op (e2) (e2)))) /\ (((op (op (e1) (e2)) (e3)) = (op (e1) (op (e2) (e3)))) /\ (((op (op (e1) (e3)) (e0)) = (op (e1) (op (e3) (e0)))) /\ (((op (op (e1) (e3)) (e1)) = (op (e1) (op (e3) (e1)))) /\ (((op (op (e1) (e3)) (e2)) = (op (e1) (op (e3) (e2)))) /\ (((op (op (e1) (e3)) (e3)) = (op (e1) (op (e3) (e3)))) /\ (((op (op (e2) (e0)) (e0)) = (op (e2) (op (e0) (e0)))) /\ (((op (op (e2) (e0)) (e1)) = (op (e2) (op (e0) (e1)))) /\ (((op (op (e2) (e0)) (e2)) = (op (e2) (op (e0) (e2)))) /\ (((op (op (e2) (e0)) (e3)) = (op (e2) (op (e0) (e3)))) /\ (((op (op (e2) (e1)) (e0)) = (op (e2) (op (e1) (e0)))) /\ (((op (op (e2) (e1)) (e1)) = (op (e2) (op (e1) (e1)))) /\ (((op (op (e2) (e1)) (e2)) = (op (e2) (op (e1) (e2)))) /\ (((op (op (e2) (e1)) (e3)) = (op (e2) (op (e1) (e3)))) /\ (((op (op (e2) (e2)) (e0)) = (op (e2) (op (e2) (e0)))) /\ (((op (op (e2) (e2)) (e1)) = (op (e2) (op (e2) (e1)))) /\ (((op (op (e2) (e2)) (e2)) = (op (e2) (op (e2) (e2)))) /\ (((op (op (e2) (e2)) (e3)) = (op (e2) (op (e2) (e3)))) /\ (((op (op (e2) (e3)) (e0)) = (op (e2) (op (e3) (e0)))) /\ (((op (op (e2) (e3)) (e1)) = (op (e2) (op (e3) (e1)))) /\ (((op (op (e2) (e3)) (e2)) = (op (e2) (op (e3) (e2)))) /\ (((op (op (e2) (e3)) (e3)) = (op (e2) (op (e3) (e3)))) /\ (((op (op (e3) (e0)) (e0)) = (op (e3) (op (e0) (e0)))) /\ (((op (op (e3) (e0)) (e1)) = (op (e3) (op (e0) (e1)))) /\ (((op (op (e3) (e0)) (e2)) = (op (e3) (op (e0) (e2)))) /\ (((op (op (e3) (e0)) (e3)) = (op (e3) (op (e0) (e3)))) /\ (((op (op (e3) (e1)) (e0)) = (op (e3) (op (e1) (e0)))) /\ (((op (op (e3) (e1)) (e1)) = (op (e3) (op (e1) (e1)))) /\ (((op (op (e3) (e1)) (e2)) = (op (e3) (op (e1) (e2)))) /\ (((op (op (e3) (e1)) (e3)) = (op (e3) (op (e1) (e3)))) /\ (((op (op (e3) (e2)) (e0)) = (op (e3) (op (e2) (e0)))) /\ (((op (op (e3) (e2)) (e1)) = (op (e3) (op (e2) (e1)))) /\ (((op (op (e3) (e2)) (e2)) = (op (e3) (op (e2) (e2)))) /\ (((op (op (e3) (e2)) (e3)) = (op (e3) (op (e2) (e3)))) /\ (((op (op (e3) (e3)) (e0)) = (op (e3) (op (e3) (e0)))) /\ (((op (op (e3) (e3)) (e1)) = (op (e3) (op (e3) (e1)))) /\ (((op (op (e3) (e3)) (e2)) = (op (e3) (op (e3) (e2)))) /\ (((op (op (e3) (e3)) (e3)) = (op (e3) (op (e3) (e3)))) /\ (((op (unit) (e0)) = (e0)) /\ (((op (e0) (unit)) = (e0)) /\ (((op (unit) (e1)) = (e1)) /\ (((op (e1) (unit)) = (e1)) /\ (((op (unit) (e2)) = (e2)) /\ (((op (e2) (unit)) = (e2)) /\ (((op (unit) (e3)) = (e3)) /\ (((op (e3) (unit)) = (e3)) /\ ((((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ ((unit) = (e3))))) /\ (((op (e0) (inv (e0))) = (unit)) /\ (((op (inv (e0)) (e0)) = (unit)) /\ (((op (e1) (inv (e1))) = (unit)) /\ (((op (inv (e1)) (e1)) = (unit)) /\ (((op (e2) (inv (e2))) = (unit)) /\ (((op (inv (e2)) (e2)) = (unit)) /\ (((op (e3) (inv (e3))) = (unit)) /\ (((op (inv (e3)) (e3)) = (unit)) /\ ((((inv (e0)) = (e0)) \/ (((inv (e0)) = (e1)) \/ (((inv (e0)) = (e2)) \/ ((inv (e0)) = (e3))))) /\ ((((inv (e1)) = (e0)) \/ (((inv (e1)) = (e1)) \/ (((inv (e1)) = (e2)) \/ ((inv (e1)) = (e3))))) /\ ((((inv (e2)) = (e0)) \/ (((inv (e2)) = (e1)) \/ (((inv (e2)) = (e2)) \/ ((inv (e2)) = (e3))))) /\ (((inv (e3)) = (e0)) \/ (((inv (e3)) = (e1)) \/ (((inv (e3)) = (e2)) \/ ((inv (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ((unit) = (e0)) (((inv (e0)) = (e0)) /\ (((inv (e1)) = (e1)) /\ (((inv (e2)) = (e2)) /\ ((inv (e3)) = (e3))))) ### ConjTree 446
% 1.69/1.92 % SZS output end Proof
% 1.69/1.92 (* END-PROOF *)
%------------------------------------------------------------------------------