TSTP Solution File: ALG135+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : ALG135+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 : n027.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 18:05:33 EDT 2022
% Result : Unsatisfiable 3.79s 4.02s
% Output : Proof 3.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG135+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 8 15:15:11 EDT 2022
% 0.11/0.33 % CPUTime :
% 3.79/4.02 % SZS status Theorem
% 3.79/4.02 (* PROOF-FOUND *)
% 3.79/4.02 (* BEGIN-PROOF *)
% 3.79/4.02 % SZS output start Proof
% 3.79/4.02 1. ((op (e0) (e0)) != (e0)) ((op (e0) (e0)) = (e0)) ### Axiom
% 3.79/4.02 2. (((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) ### And 1
% 3.79/4.02 3. ((op (e0) (e1)) != (e0)) ((op (e0) (e1)) = (e0)) ### Axiom
% 3.79/4.02 4. (((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) ((op (e0) (e1)) != (e0)) ### And 3
% 3.79/4.02 5. ((op (e1) (e1)) != (e1)) ((op (e1) (e1)) = (e1)) ### Axiom
% 3.79/4.02 6. (((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) ### And 5
% 3.79/4.02 7. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.79/4.02 8. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.79/4.02 9. ((op (e0) (e3)) = (e0)) ((e0) != (op (e0) (e3))) ### Sym(=)
% 3.79/4.02 10. ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e2)) = (e0)) ((op (e0) (e3)) = (e0)) ### TransEq 7 8 9
% 3.79/4.02 11. (((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ### And 10
% 3.79/4.02 12. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.79/4.02 13. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.79/4.02 14. ((op (e1) (e0)) = (e1)) ((e1) != (op (e1) (e0))) ### Sym(=)
% 3.79/4.02 15. ((op (e1) (e0)) != (op (e1) (e3))) ((op (e1) (e3)) = (e1)) ((op (e1) (e0)) = (e1)) ### TransEq-sym 12 13 14
% 3.79/4.02 16. (((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e1) (e3))) ### And 15
% 3.79/4.02 17. ((op (e2) (e1)) != (op (e2) (e1))) ### Refl(=)
% 3.79/4.02 18. ((op (e2) (e1)) != (op (e2) (e1))) ### Refl(=)
% 3.79/4.02 19. ((op (e2) (e3)) = (e2)) ((e2) != (op (e2) (e3))) ### Sym(=)
% 3.79/4.02 20. ((op (e2) (e1)) != (op (e2) (e3))) ((op (e2) (e1)) = (e2)) ((op (e2) (e3)) = (e2)) ### TransEq 17 18 19
% 3.79/4.02 21. (((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e3))) ### And 20
% 3.79/4.02 22. ((op (e3) (e3)) != (e3)) ((op (e3) (e3)) = (e3)) ### Axiom
% 3.79/4.02 23. (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3))) ### And 22
% 3.79/4.02 24. ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e2) (e1)) = (e2)) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e1) (e0)) = (e1)) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e2)) = (e0)) ### DisjTree 11 16 21 23
% 3.79/4.02 25. (((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 24
% 3.79/4.02 26. ((op (e1) (e2)) != (e1)) ((op (e1) (e2)) = (e1)) ### Axiom
% 3.79/4.02 27. (((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) ((op (e1) (e2)) != (e1)) ### And 26
% 3.79/4.02 28. ((op (e2) (e2)) != (e2)) ((op (e2) (e2)) = (e2)) ### Axiom
% 3.79/4.02 29. (((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) ### And 28
% 3.79/4.02 30. ((op (e1) (e0)) != (op (e1) (e0))) ### Refl(=)
% 3.79/4.02 31. ((op (e1) (e0)) != (op (e1) (e0))) ### Refl(=)
% 3.79/4.02 32. ((op (e0) (e0)) = (e1)) ((e1) != (op (e0) (e0))) ### Sym(=)
% 3.79/4.02 33. ((op (e0) (e0)) != (op (e1) (e0))) ((op (e1) (e0)) = (e1)) ((op (e0) (e0)) = (e1)) ### TransEq-sym 30 31 32
% 3.79/4.02 34. ((op (e2) (e0)) = (e1)) ((e1) != (op (e2) (e0))) ### Sym(=)
% 3.79/4.02 35. ((op (e2) (e0)) = (e1)) ((e1) != (op (e2) (e0))) ### Sym(=)
% 3.79/4.02 36. ((e0) != (e0)) ### NotEqual
% 3.79/4.02 37. ((e0) != (e1)) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) = (e1)) ### TransEq-sym 34 35 36
% 3.79/4.02 38. ((op (e2) (e1)) = (e1)) ((e1) != (op (e2) (e1))) ### Sym(=)
% 3.79/4.02 39. ((op (e2) (e1)) = (e1)) ((e1) != (op (e2) (e1))) ### Sym(=)
% 3.79/4.02 40. ((e2) != (e2)) ### NotEqual
% 3.79/4.02 41. ((e1) != (e2)) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) = (e1)) ### TransEq 38 39 40
% 3.79/4.02 42. ((op (e1) (e0)) != (op (e1) (e0))) ### Refl(=)
% 3.79/4.02 43. ((op (e1) (e0)) != (op (e1) (e0))) ### Refl(=)
% 3.79/4.02 44. ((op (e3) (e0)) = (e1)) ((e1) != (op (e3) (e0))) ### Sym(=)
% 3.79/4.02 45. ((op (e1) (e0)) != (op (e3) (e0))) ((op (e1) (e0)) = (e1)) ((op (e3) (e0)) = (e1)) ### TransEq 42 43 44
% 3.79/4.02 46. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.79/4.02 47. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.79/4.02 48. ((op (e3) (e1)) = (e1)) ((e1) != (op (e3) (e1))) ### Sym(=)
% 3.79/4.02 49. ((op (e0) (e1)) != (op (e3) (e1))) ((op (e0) (e1)) = (e1)) ((op (e3) (e1)) = (e1)) ### TransEq 46 47 48
% 3.79/4.02 50. ((op (e3) (e2)) = (e1)) ((e1) != (op (e3) (e2))) ### Sym(=)
% 3.79/4.02 51. ((op (e3) (e2)) = (e1)) ((e1) != (op (e3) (e2))) ### Sym(=)
% 3.79/4.02 52. ((e3) != (e3)) ### NotEqual
% 3.79/4.02 53. ((e1) != (e3)) ((op (e3) (e2)) = (e3)) ((op (e3) (e2)) = (e1)) ### TransEq 50 51 52
% 3.79/4.02 54. ((op (e0) (e3)) = (e2)) ((e2) != (op (e0) (e3))) ### Sym(=)
% 3.79/4.02 55. ((op (e0) (e3)) = (e2)) ((e2) != (op (e0) (e3))) ### Sym(=)
% 3.79/4.02 56. ((e0) != (e2)) ((op (e0) (e3)) = (e0)) ((op (e0) (e3)) = (e2)) ### TransEq-sym 54 55 36
% 3.79/4.02 57. ((op (e0) (e0)) = (e3)) ((op (e0) (e0)) != (e3)) ### Axiom
% 3.79/4.02 58. ((op (e0) (e0)) = (e3)) ((op (e0) (e0)) != (e3)) ### Axiom
% 3.79/4.02 59. ((op (op (e0) (e0)) (op (e0) (e0))) != (op (e3) (e3))) ((op (e0) (e0)) = (e3)) ### NotEqual 57 58
% 3.79/4.02 60. ((e1) != (e1)) ### NotEqual
% 3.79/4.02 61. ((e1) != (op (op (e0) (e0)) (op (e0) (e0)))) ((op (e3) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) ### Trans-sym 59 60
% 3.79/4.02 62. ((op (op (e0) (e0)) (op (e0) (e0))) != (e1)) ((op (e3) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) ### Trans 59 60
% 3.79/4.02 63. ((op (e0) (e0)) = (e3)) ((op (e0) (e0)) != (e3)) ### Axiom
% 3.79/4.02 64. ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) != (op (e1) (e3))) ((op (e0) (e0)) = (e3)) ((op (e3) (e3)) = (e1)) ### NotEqual 62 63
% 3.79/4.02 65. ((e2) != (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) ((op (e1) (e3)) = (e2)) ((op (e3) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) ### Trans-sym 64 40
% 3.79/4.02 66. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 3.79/4.02 67. (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e1) (e3)) = (e2)) ((op (e0) (e0)) = (e3)) ((op (e3) (e3)) = (e1)) ### DisjTree 61 65 66
% 3.79/4.02 68. ((op (e2) (e3)) != (e2)) ((op (e2) (e3)) = (e2)) ### Axiom
% 3.79/4.02 69. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 3.79/4.02 70. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 3.79/4.02 71. ((op (op (e3) (e3)) (op (e3) (e3))) != (op (e2) (e2))) ((op (e3) (e3)) = (e2)) ### NotEqual 69 70
% 3.79/4.02 72. ((e1) != (op (op (e3) (e3)) (op (e3) (e3)))) ((op (e2) (e2)) = (e1)) ((op (e3) (e3)) = (e2)) ### Trans-sym 71 60
% 3.79/4.02 73. ((op (op (e3) (e3)) (op (e3) (e3))) != (e1)) ((op (e2) (e2)) = (e1)) ((op (e3) (e3)) = (e2)) ### Trans 71 60
% 3.79/4.02 74. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 3.79/4.02 75. ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) != (op (e1) (e2))) ((op (e3) (e3)) = (e2)) ((op (e2) (e2)) = (e1)) ### NotEqual 73 74
% 3.79/4.02 76. ((e0) != (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) ((op (e1) (e2)) = (e0)) ((op (e2) (e2)) = (e1)) ((op (e3) (e3)) = (e2)) ### Trans-sym 75 36
% 3.79/4.02 77. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 3.79/4.02 78. (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e1) (e2)) = (e0)) ((op (e3) (e3)) = (e2)) ((op (e2) (e2)) = (e1)) ### DisjTree 72 76 77
% 3.79/4.02 79. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e2) (e2)) = (e1)) ((op (e1) (e2)) = (e0)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e3) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) = (e0)) ((e0) != (e2)) ### DisjTree 56 67 68 78
% 3.79/4.02 80. (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) ((op (e0) (e3)) = (e0)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e1) (e2)) = (e0)) ((op (e2) (e2)) = (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e3) (e2)) = (e3)) ((e1) != (e3)) ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e3) (e0))) ### DisjTree 45 49 53 79
% 3.79/4.02 81. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.79/4.02 82. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.79/4.02 83. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=)
% 3.79/4.02 84. ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e1)) ((op (e3) (e3)) = (e1)) ### TransEq 81 82 83
% 3.79/4.02 85. (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e2)) = (e3)) ((e1) != (e3)) ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e3) (e0))) ### DisjTree 45 49 53 84
% 3.79/4.02 86. (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e1) (e0)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e0) (e1)) = (e1)) ((e1) != (e3)) ((op (e3) (e2)) = (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e2)) = (e0)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e0) (e0)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) = (e0)) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((op (e2) (e0)) = (e0)) ((e0) != (e1)) ### DisjTree 37 41 80 85
% 3.79/4.02 87. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.79/4.02 88. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.79/4.02 89. ((op (e2) (e2)) = (e0)) ((e0) != (op (e2) (e2))) ### Sym(=)
% 3.79/4.02 90. ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) = (e0)) ((op (e2) (e2)) = (e0)) ### TransEq 87 88 89
% 3.79/4.02 91. ((op (e3) (e2)) = (e0)) ((e0) != (op (e3) (e2))) ### Sym(=)
% 3.79/4.02 92. ((op (e3) (e2)) = (e0)) ((e0) != (op (e3) (e2))) ### Sym(=)
% 3.79/4.02 93. ((e0) != (e3)) ((op (e3) (e2)) = (e3)) ((op (e3) (e2)) = (e0)) ### TransEq 91 92 52
% 3.79/4.02 94. (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e1)) ((op (e2) (e0)) = (e0)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e3) (e2)) = (e3)) ((e1) != (e3)) ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e3)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ### DisjTree 10 86 90 93
% 3.79/4.02 95. ((op (e2) (e1)) = (e0)) ((e0) != (op (e2) (e1))) ### Sym(=)
% 3.79/4.02 96. ((op (e2) (e1)) = (e0)) ((e0) != (op (e2) (e1))) ### Sym(=)
% 3.79/4.02 97. ((e0) != (e2)) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) = (e0)) ### TransEq 95 96 40
% 3.79/4.02 98. ((op (e2) (e3)) != (e2)) ((op (e2) (e3)) = (e2)) ### Axiom
% 3.79/4.02 99. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.79/4.02 100. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.79/4.02 101. ((op (e2) (e2)) = (e0)) ((e0) != (op (e2) (e2))) ### Sym(=)
% 3.79/4.02 102. ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) = (e0)) ((op (e2) (e2)) = (e0)) ### TransEq 99 100 101
% 3.79/4.02 103. ((e0) != (op (op (e3) (e3)) (op (e3) (e3)))) ((op (e2) (e2)) = (e0)) ((op (e3) (e3)) = (e2)) ### Trans-sym 71 36
% 3.79/4.02 104. ((op (op (e3) (e3)) (op (e3) (e3))) != (e0)) ((op (e2) (e2)) = (e0)) ((op (e3) (e3)) = (e2)) ### Trans 71 36
% 3.79/4.02 105. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 3.79/4.02 106. ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) != (op (e0) (e2))) ((op (e3) (e3)) = (e2)) ((op (e2) (e2)) = (e0)) ### NotEqual 104 105
% 3.79/4.02 107. ((e1) != (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) ((op (e0) (e2)) = (e1)) ((op (e2) (e2)) = (e0)) ((op (e3) (e3)) = (e2)) ### Trans-sym 106 60
% 3.79/4.02 108. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 3.79/4.02 109. (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e2)) = (e1)) ((op (e3) (e3)) = (e2)) ((op (e2) (e2)) = (e0)) ### DisjTree 103 107 108
% 3.79/4.02 110. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.79/4.02 111. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.79/4.02 112. ((op (e2) (e2)) = (e0)) ((e0) != (op (e2) (e2))) ### Sym(=)
% 3.79/4.02 113. ((op (e1) (e2)) != (op (e2) (e2))) ((op (e1) (e2)) = (e0)) ((op (e2) (e2)) = (e0)) ### TransEq 110 111 112
% 3.79/4.02 114. ((op (e1) (e2)) != (e1)) ((op (e1) (e2)) = (e1)) ### Axiom
% 3.79/4.02 115. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.79/4.02 116. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.79/4.02 117. ((op (e1) (e2)) = (e2)) ((e2) != (op (e1) (e2))) ### Sym(=)
% 3.79/4.02 118. ((op (e0) (e2)) != (op (e1) (e2))) ((op (e0) (e2)) = (e2)) ((op (e1) (e2)) = (e2)) ### TransEq 115 116 117
% 3.79/4.02 119. ((op (e3) (e2)) != (op (e3) (e2))) ### Refl(=)
% 3.79/4.02 120. ((op (e3) (e2)) != (op (e3) (e2))) ### Refl(=)
% 3.79/4.02 121. ((op (e1) (e2)) = (e3)) ((e3) != (op (e1) (e2))) ### Sym(=)
% 3.79/4.02 122. ((op (e1) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) ((op (e1) (e2)) = (e3)) ### TransEq-sym 119 120 121
% 3.79/4.02 123. (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (e1)) ((op (e2) (e2)) = (e0)) ((op (e1) (e2)) != (op (e2) (e2))) ### DisjTree 113 114 118 122
% 3.79/4.02 124. ((op (e3) (e2)) != (op (e3) (e2))) ### Refl(=)
% 3.79/4.02 125. ((op (e3) (e2)) != (op (e3) (e2))) ### Refl(=)
% 3.79/4.02 126. ((op (e0) (e2)) = (e3)) ((e3) != (op (e0) (e2))) ### Sym(=)
% 3.79/4.02 127. ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) = (e3)) ### TransEq-sym 124 125 126
% 3.79/4.02 128. (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e1) (e2)) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e3) (e3)) = (e2)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) = (e0)) ((op (e0) (e2)) != (op (e2) (e2))) ### DisjTree 102 109 123 127
% 3.79/4.02 129. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e2) (e2)) = (e0)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (e1)) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e2) (e3)) != (e2)) ((op (e3) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) = (e0)) ((e0) != (e2)) ### DisjTree 56 67 98 128
% 3.85/4.02 130. (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) ((op (e0) (e3)) = (e0)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) ((op (e2) (e3)) != (e2)) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e1) (e2)) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) = (e0)) ((op (e0) (e2)) != (op (e2) (e2))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e3) (e2)) = (e3)) ((e1) != (e3)) ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e3) (e0))) ### DisjTree 45 49 53 129
% 3.85/4.02 131. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.02 132. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.02 133. ((op (e2) (e3)) = (e0)) ((e0) != (op (e2) (e3))) ### Sym(=)
% 3.85/4.02 134. ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) = (e0)) ((op (e2) (e3)) = (e0)) ### TransEq 131 132 133
% 3.85/4.02 135. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (e1)) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e3)) = (e0)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e1) (e0)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e0) (e1)) = (e1)) ((e1) != (e3)) ((op (e3) (e2)) = (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e0) (e0)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((e0) != (e1)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ### DisjTree 94 97 130 134
% 3.85/4.02 136. ((op (e0) (e1)) = (e3)) ((e3) != (op (e0) (e1))) ### Sym(=)
% 3.85/4.02 137. ((op (e0) (e1)) = (e3)) ((e3) != (op (e0) (e1))) ### Sym(=)
% 3.85/4.02 138. ((e1) != (e3)) ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) = (e3)) ### TransEq-sym 136 137 60
% 3.85/4.02 139. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.02 140. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.02 141. ((e0) != (e3)) ((op (e0) (e3)) = (e0)) ((op (e0) (e3)) = (e3)) ### TransEq-sym 139 140 36
% 3.85/4.02 142. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e1)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e3) (e2)) = (e3)) ((e1) != (e3)) ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e3)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e1) (e2)) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ### DisjTree 135 138 127 141
% 3.85/4.02 143. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.02 144. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.02 145. ((op (e2) (e2)) = (e1)) ((e1) != (op (e2) (e2))) ### Sym(=)
% 3.85/4.02 146. ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) = (e1)) ((op (e2) (e2)) = (e1)) ### TransEq 143 144 145
% 3.85/4.02 147. ((op (e2) (e1)) != (op (e2) (e1))) ### Refl(=)
% 3.85/4.02 148. ((op (e2) (e1)) != (op (e2) (e1))) ### Refl(=)
% 3.85/4.02 149. ((op (e2) (e2)) = (e2)) ((e2) != (op (e2) (e2))) ### Sym(=)
% 3.85/4.02 150. ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e1)) = (e2)) ((op (e2) (e2)) = (e2)) ### TransEq 147 148 149
% 3.85/4.02 151. ((op (e3) (e2)) != (op (e3) (e2))) ### Refl(=)
% 3.85/4.02 152. ((op (e3) (e2)) != (op (e3) (e2))) ### Refl(=)
% 3.85/4.02 153. ((op (e2) (e2)) = (e3)) ((e3) != (op (e2) (e2))) ### Sym(=)
% 3.85/4.02 154. ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) ((op (e2) (e2)) = (e3)) ### TransEq-sym 151 152 153
% 3.85/4.02 155. (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e0) (e2)) = (e1)) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) != (op (e2) (e2))) ### DisjTree 90 146 150 154
% 3.85/4.02 156. ((op (e0) (e3)) = (e1)) ((e1) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.02 157. ((op (e0) (e3)) = (e1)) ((e1) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.02 158. ((e0) != (e1)) ((op (e0) (e3)) = (e0)) ((op (e0) (e3)) = (e1)) ### TransEq-sym 156 157 36
% 3.85/4.02 159. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.02 160. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.02 161. ((op (e3) (e3)) = (e0)) ((e0) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.02 162. ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) = (e0)) ((op (e3) (e3)) = (e0)) ### TransEq 159 160 161
% 3.85/4.02 163. ((op (e3) (e2)) != (op (e3) (e2))) ### Refl(=)
% 3.85/4.02 164. ((op (e3) (e2)) != (op (e3) (e2))) ### Refl(=)
% 3.85/4.02 165. ((op (e3) (e3)) = (e3)) ((e3) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.02 166. ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e2)) = (e3)) ((op (e3) (e3)) = (e3)) ### TransEq 163 164 165
% 3.85/4.02 167. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e2) (e2)) = (e0)) ((op (e0) (e2)) = (e1)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) = (e0)) ((op (e0) (e3)) != (op (e3) (e3))) ### DisjTree 162 84 109 166
% 3.85/4.02 168. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.02 169. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.02 170. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.02 171. ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e1)) ((op (e3) (e3)) = (e1)) ### TransEq 168 169 170
% 3.85/4.02 172. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) = (e1)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e2)) = (e1)) ((op (e2) (e2)) = (e0)) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e2)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e0) (e3)) = (e0)) ((e0) != (e1)) ### DisjTree 158 15 167 171
% 3.85/4.02 173. ((op (e2) (e3)) != (e2)) ((op (e2) (e3)) = (e2)) ### Axiom
% 3.85/4.02 174. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e2) (e2)) = (e0)) ((op (e0) (e2)) = (e1)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e3) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) = (e0)) ((e0) != (e2)) ### DisjTree 56 67 173 109
% 3.85/4.02 175. (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) ((op (e2) (e3)) != (e2)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e1) != (e3)) ((e0) != (e1)) ((op (e0) (e3)) = (e0)) ((op (e1) (e0)) != (op (e1) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e2) (e2)) = (e0)) ((op (e0) (e2)) = (e1)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e3) (e0))) ### DisjTree 45 172 53 174
% 3.85/4.02 176. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e1) (e0)) = (e1)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e0) (e3)) = (e0)) ((e0) != (e1)) ((e1) != (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e2) (e3)) != (e2)) ((op (e0) (e0)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) = (e1)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e1)) = (e2)) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ### DisjTree 155 97 175 134
% 3.85/4.02 177. ((op (e1) (e0)) != (op (e1) (e0))) ### Refl(=)
% 3.85/4.02 178. ((op (e1) (e0)) != (op (e1) (e0))) ### Refl(=)
% 3.85/4.02 179. ((op (e1) (e1)) = (e1)) ((e1) != (op (e1) (e1))) ### Sym(=)
% 3.85/4.02 180. ((op (e1) (e0)) != (op (e1) (e1))) ((op (e1) (e0)) = (e1)) ((op (e1) (e1)) = (e1)) ### TransEq 177 178 179
% 3.85/4.02 181. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e3)) = (e0)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e1) (e0)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e0) (e1)) = (e1)) ((e1) != (e3)) ((op (e3) (e2)) = (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((op (e2) (e0)) = (e0)) ((e0) != (e1)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ### DisjTree 94 138 127 141
% 3.85/4.02 182. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e1)) ((op (e2) (e0)) = (e0)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e3) (e2)) = (e3)) ((e1) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e3)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e1) (e0)) = (e1)) ((op (e0) (e0)) != (op (e1) (e0))) ### DisjTree 33 181 155 158
% 3.85/4.03 183. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e1) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e2)) = (e1)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e1)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e0)) != (op (e1) (e0))) ((op (e1) (e0)) = (e1)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e3)) = (e0)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e0) (e1)) != (op (e3) (e1))) ((e1) != (e3)) ((op (e3) (e2)) = (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((e0) != (e1)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e2) (e2))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ### DisjTree 182 97 172 134
% 3.85/4.03 184. (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e1)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e3) (e2)) = (e3)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e3)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e1) (e0))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e2)) = (e1)) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e1) (e1))) ((op (e0) (e1)) = (e3)) ((e1) != (e3)) ### DisjTree 138 180 41 183
% 3.85/4.03 185. ((op (e1) (e0)) != (op (e1) (e1))) ((e1) != (e2)) ((op (e0) (e0)) != (op (e1) (e0))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((e0) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e0) (e2)) = (e1)) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e2) (e3)) != (e2)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e1) != (e3)) ((e0) != (e1)) ((op (e0) (e3)) = (e0)) ((op (e1) (e0)) != (op (e1) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ### DisjTree 176 184 127 141
% 3.85/4.03 186. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (e1)) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e3)) = (e0)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e0) (e1)) != (op (e3) (e1))) ((e1) != (e3)) ((op (e3) (e2)) = (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((e0) != (e1)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e1) (e0)) = (e1)) ((op (e0) (e0)) != (op (e1) (e0))) ### DisjTree 33 142 185 158
% 3.85/4.03 187. (((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) ((op (e0) (e0)) != (op (e1) (e0))) ((op (e1) (e0)) = (e1)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e1)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e3) (e2)) = (e3)) ((e1) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e1) (e2)) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e1) (e0)) != (op (e1) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ### And 186
% 3.85/4.03 188. ((op (e2) (e3)) != (e2)) ((op (e2) (e3)) = (e2)) ### Axiom
% 3.85/4.03 189. (((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) ((op (e2) (e3)) != (e2)) ### And 188
% 3.85/4.03 190. ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (e1)) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e0) (e1)) != (op (e3) (e1))) ((e1) != (e3)) ((op (e3) (e2)) = (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((e0) != (e1)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e1) (e0)) = (e1)) ((op (e0) (e0)) != (op (e1) (e0))) ### DisjTree 187 16 189 23
% 3.85/4.03 191. (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2))) ((op (e0) (e0)) != (op (e1) (e0))) ((op (e1) (e0)) = (e1)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e1)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e1) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e1) (e2)) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e1) (e0)) != (op (e1) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 190
% 3.85/4.03 192. ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e0) (e1)) != (op (e3) (e1))) ((e1) != (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e1) != (e2)) ((e0) != (e1)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e1) (e0))) ((op (e1) (e2)) != (e1)) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e2) (e1)) = (e2)) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e1) (e0)) = (e1)) ((op (e0) (e2)) != (op (e0) (e3))) ### DisjTree 25 27 29 191
% 3.85/4.03 193. (((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e2) (e1)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e0) (e0)) != (op (e1) (e0))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e1)) ((e1) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e1) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e1)) != (op (e2) (e2))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ### And 192
% 3.85/4.03 194. ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) = (e1)) ### Axiom
% 3.85/4.03 195. (((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) ((op (e1) (e3)) != (e1)) ### And 194
% 3.85/4.03 196. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.03 197. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.03 198. ((op (e0) (e0)) = (e0)) ((e0) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.03 199. ((op (e0) (e0)) != (op (e0) (e2))) ((op (e0) (e2)) = (e0)) ((op (e0) (e0)) = (e0)) ### TransEq-sym 196 197 198
% 3.85/4.03 200. ((op (e1) (e0)) = (e0)) ((e0) != (op (e1) (e0))) ### Sym(=)
% 3.85/4.03 201. ((op (e1) (e0)) = (e0)) ((e0) != (op (e1) (e0))) ### Sym(=)
% 3.85/4.03 202. ((e0) != (e1)) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) = (e0)) ### TransEq 200 201 60
% 3.85/4.03 203. ((op (e2) (e0)) = (e3)) ((e3) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.03 204. ((op (e2) (e0)) = (e3)) ((e3) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.03 205. ((e0) != (e3)) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) = (e3)) ### TransEq-sym 203 204 36
% 3.85/4.03 206. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.03 207. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.03 208. ((op (e2) (e1)) = (e3)) ((e3) != (op (e2) (e1))) ### Sym(=)
% 3.85/4.03 209. ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) = (e3)) ### TransEq-sym 206 207 208
% 3.85/4.03 210. ((op (e0) (e2)) = (e3)) ((e3) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.03 211. ((op (e0) (e2)) = (e3)) ((e3) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.03 212. ((e0) != (e3)) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) = (e3)) ### TransEq-sym 210 211 36
% 3.85/4.03 213. ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (e2)) ### Axiom
% 3.85/4.03 214. ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (e2)) ### Axiom
% 3.85/4.03 215. ((op (op (e0) (e0)) (op (e0) (e0))) != (op (e2) (e2))) ((op (e0) (e0)) = (e2)) ### NotEqual 213 214
% 3.85/4.03 216. ((e1) != (op (op (e0) (e0)) (op (e0) (e0)))) ((op (e2) (e2)) = (e1)) ((op (e0) (e0)) = (e2)) ### Trans-sym 215 60
% 3.85/4.03 217. ((op (op (e0) (e0)) (op (e0) (e0))) != (e1)) ((op (e2) (e2)) = (e1)) ((op (e0) (e0)) = (e2)) ### Trans 215 60
% 3.85/4.03 218. ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (e2)) ### Axiom
% 3.85/4.03 219. ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) != (op (e1) (e2))) ((op (e0) (e0)) = (e2)) ((op (e2) (e2)) = (e1)) ### NotEqual 217 218
% 3.85/4.03 220. ((e3) != (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) ((op (e1) (e2)) = (e3)) ((op (e2) (e2)) = (e1)) ((op (e0) (e0)) = (e2)) ### Trans-sym 219 52
% 3.85/4.03 221. ((op (e0) (e0)) = (e2)) ((e2) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.03 222. (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e1) (e2)) = (e3)) ((op (e0) (e0)) = (e2)) ((op (e2) (e2)) = (e1)) ### DisjTree 216 220 221
% 3.85/4.03 223. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.03 224. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.03 225. ((op (e2) (e2)) = (e2)) ((e2) != (op (e2) (e2))) ### Sym(=)
% 3.85/4.03 226. ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) = (e2)) ### TransEq-sym 223 224 225
% 3.85/4.03 227. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.03 228. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.03 229. ((op (e3) (e3)) = (e0)) ((e0) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.03 230. ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) = (e0)) ((op (e3) (e3)) = (e0)) ### TransEq 227 228 229
% 3.85/4.03 231. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 3.85/4.03 232. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 3.85/4.03 233. ((op (op (e2) (e2)) (op (e2) (e2))) != (op (e3) (e3))) ((op (e2) (e2)) = (e3)) ### NotEqual 231 232
% 3.85/4.03 234. ((e1) != (op (op (e2) (e2)) (op (e2) (e2)))) ((op (e3) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) ### Trans-sym 233 60
% 3.85/4.03 235. ((op (op (e2) (e2)) (op (e2) (e2))) != (e1)) ((op (e3) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) ### Trans 233 60
% 3.85/4.03 236. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 3.85/4.03 237. ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) != (op (e1) (e3))) ((op (e2) (e2)) = (e3)) ((op (e3) (e3)) = (e1)) ### NotEqual 235 236
% 3.85/4.03 238. ((e0) != (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) ((op (e1) (e3)) = (e0)) ((op (e3) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) ### Trans-sym 237 36
% 3.85/4.03 239. ((op (e2) (e2)) = (e3)) ((e3) != (op (e2) (e2))) ### Sym(=)
% 3.85/4.03 240. (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) = (e0)) ((op (e2) (e2)) = (e3)) ((op (e3) (e3)) = (e1)) ### DisjTree 234 238 239
% 3.85/4.03 241. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.03 242. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.03 243. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.03 244. ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e3)) = (e2)) ### TransEq 241 242 243
% 3.85/4.03 245. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.03 246. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.03 247. ((op (e3) (e3)) = (e3)) ((e3) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.03 248. ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) ((op (e3) (e3)) = (e3)) ### TransEq 245 246 247
% 3.85/4.03 249. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e2)) = (e3)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (op (e3) (e3))) ### DisjTree 230 240 244 248
% 3.85/4.03 250. (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) = (e0)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e0) (e0)) = (e2)) ((op (e1) (e2)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) != (op (e2) (e2))) ### DisjTree 90 222 226 249
% 3.85/4.03 251. ((op (e3) (e2)) != (e3)) ((op (e3) (e2)) = (e3)) ### Axiom
% 3.85/4.03 252. (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) = (e0)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e0) (e2)) = (e0)) ((e0) != (e3)) ### DisjTree 212 250 249 251
% 3.85/4.03 253. ((op (e2) (e3)) = (e0)) ((e0) != (op (e2) (e3))) ### Sym(=)
% 3.85/4.03 254. ((op (e2) (e3)) = (e0)) ((e0) != (op (e2) (e3))) ### Sym(=)
% 3.85/4.03 255. ((e0) != (e2)) ((op (e2) (e3)) = (e2)) ((op (e2) (e3)) = (e0)) ### TransEq 253 254 40
% 3.85/4.03 256. ((e0) != (op (op (e2) (e2)) (op (e2) (e2)))) ((op (e3) (e3)) = (e0)) ((op (e2) (e2)) = (e3)) ### Trans-sym 233 36
% 3.85/4.03 257. ((op (op (e2) (e2)) (op (e2) (e2))) != (e0)) ((op (e3) (e3)) = (e0)) ((op (e2) (e2)) = (e3)) ### Trans 233 36
% 3.85/4.03 258. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 3.85/4.03 259. ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) != (op (e0) (e3))) ((op (e2) (e2)) = (e3)) ((op (e3) (e3)) = (e0)) ### NotEqual 257 258
% 3.85/4.03 260. ((e1) != (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) ((op (e0) (e3)) = (e1)) ((op (e3) (e3)) = (e0)) ((op (e2) (e2)) = (e3)) ### Trans-sym 259 60
% 3.85/4.03 261. ((op (e2) (e2)) = (e3)) ((e3) != (op (e2) (e2))) ### Sym(=)
% 3.85/4.03 262. (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e0) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) ((op (e3) (e3)) = (e0)) ### DisjTree 256 260 261
% 3.85/4.03 263. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e2) (e2)) = (e3)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) ((e0) != (e3)) ((op (e0) (e2)) = (e0)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e0) (e0)) = (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e3) (e2)) != (e3)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e3)) = (e1)) ((e0) != (e1)) ### DisjTree 158 252 255 262
% 3.85/4.03 264. ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) = (e1)) ### Axiom
% 3.85/4.03 265. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.03 266. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.03 267. ((op (e1) (e3)) = (e2)) ((e2) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.03 268. ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) ((op (e1) (e3)) = (e2)) ### TransEq-sym 265 266 267
% 3.85/4.03 269. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.03 270. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.03 271. ((op (e2) (e3)) = (e3)) ((e3) != (op (e2) (e3))) ### Sym(=)
% 3.85/4.03 272. ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) = (e3)) ((op (e2) (e3)) = (e3)) ### TransEq 269 270 271
% 3.85/4.03 273. (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e2) (e3)) = (e3)) ((op (e2) (e3)) = (e2)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (e1)) ((op (e3) (e3)) = (e0)) ((op (e1) (e3)) != (op (e3) (e3))) ### DisjTree 230 264 268 272
% 3.85/4.03 274. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) = (e3)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((e0) != (e2)) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) = (e0)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e1) (e2)) = (e3)) ((op (e0) (e0)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ### DisjTree 10 250 255 273
% 3.85/4.03 275. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) = (e3)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((e0) != (e2)) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e2)) = (e3)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ### DisjTree 10 249 255 273
% 3.85/4.03 276. ((op (e3) (e2)) != (e3)) ((op (e3) (e2)) = (e3)) ### Axiom
% 3.85/4.03 277. (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e0) (e0)) = (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e2)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e2) (e3)) = (e3)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (e1)) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e0) (e2)) = (e0)) ((e0) != (e3)) ### DisjTree 212 274 275 276
% 3.85/4.03 278. (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) ((e0) != (e1)) ((op (e0) (e3)) = (e1)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e0) (e2)) = (e0)) ((e0) != (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) = (e0)) ((e0) != (e3)) ### DisjTree 205 209 263 277
% 3.85/4.03 279. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.03 280. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.03 281. ((op (e1) (e0)) = (e0)) ((e0) != (op (e1) (e0))) ### Sym(=)
% 3.85/4.03 282. ((op (e1) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) = (e0)) ((op (e1) (e0)) = (e0)) ### TransEq-sym 279 280 281
% 3.85/4.03 283. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 3.85/4.03 284. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 3.85/4.03 285. ((op (op (e3) (e3)) (op (e3) (e3))) != (op (e1) (e1))) ((op (e3) (e3)) = (e1)) ### NotEqual 283 284
% 3.85/4.03 286. ((e0) != (op (op (e3) (e3)) (op (e3) (e3)))) ((op (e1) (e1)) = (e0)) ((op (e3) (e3)) = (e1)) ### Trans-sym 285 36
% 3.85/4.03 287. ((op (op (e3) (e3)) (op (e3) (e3))) != (e0)) ((op (e1) (e1)) = (e0)) ((op (e3) (e3)) = (e1)) ### Trans 285 36
% 3.85/4.03 288. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 3.85/4.03 289. ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) != (op (e0) (e1))) ((op (e3) (e3)) = (e1)) ((op (e1) (e1)) = (e0)) ### NotEqual 287 288
% 3.85/4.03 290. ((e2) != (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) ((op (e0) (e1)) = (e2)) ((op (e1) (e1)) = (e0)) ((op (e3) (e3)) = (e1)) ### Trans-sym 289 40
% 3.85/4.03 291. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.03 292. (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e1)) = (e2)) ((op (e3) (e3)) = (e1)) ((op (e1) (e1)) = (e0)) ### DisjTree 286 290 291
% 3.85/4.03 293. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e1)) = (e0)) ((op (e0) (e1)) = (e2)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (op (e3) (e3))) ### DisjTree 230 292 244 248
% 3.85/4.03 294. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e2) (e2)) = (e3)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e1)) = (e2)) ((op (e1) (e1)) = (e0)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e3)) = (e1)) ((e0) != (e1)) ### DisjTree 158 293 255 262
% 3.85/4.03 295. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) = (e3)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((e0) != (e2)) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e1)) = (e2)) ((op (e1) (e1)) = (e0)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ### DisjTree 10 293 255 273
% 3.85/4.03 296. (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e2)) = (e0)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (e1)) ((e0) != (e1)) ((op (e0) (e3)) = (e1)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e1)) = (e0)) ((op (e0) (e1)) = (e2)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e3)) != (op (e3) (e3))) ((e0) != (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) = (e0)) ((e0) != (e3)) ### DisjTree 205 209 294 295
% 3.85/4.03 297. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.03 298. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.03 299. ((op (e1) (e2)) = (e0)) ((e0) != (op (e1) (e2))) ### Sym(=)
% 3.85/4.03 300. ((op (e0) (e2)) != (op (e1) (e2))) ((op (e0) (e2)) = (e0)) ((op (e1) (e2)) = (e0)) ### TransEq 297 298 299
% 3.85/4.03 301. ((op (e0) (e1)) != (e0)) ((op (e0) (e1)) = (e0)) ### Axiom
% 3.85/4.03 302. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.03 303. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.03 304. ((op (e2) (e1)) = (e0)) ((e0) != (op (e2) (e1))) ### Sym(=)
% 3.85/4.03 305. ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) = (e0)) ((op (e2) (e1)) = (e0)) ### TransEq 302 303 304
% 3.85/4.03 306. ((op (e3) (e1)) = (e0)) ((e0) != (op (e3) (e1))) ### Sym(=)
% 3.85/4.03 307. ((op (e3) (e1)) = (e0)) ((e0) != (op (e3) (e1))) ### Sym(=)
% 3.85/4.03 308. ((e0) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) = (e0)) ### TransEq 306 307 52
% 3.85/4.03 309. (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) = (e0)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e1)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e1)) != (e0)) ### DisjTree 301 293 305 308
% 3.85/4.03 310. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e1)) != (e0)) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) ((e0) != (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e1)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e3)) = (e1)) ((e0) != (e1)) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e0)) = (e0)) ((op (e1) (e0)) != (op (e2) (e0))) ### DisjTree 282 296 300 309
% 3.85/4.03 311. ((op (e0) (e2)) = (e2)) ((e2) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.03 312. ((op (e0) (e2)) = (e2)) ((e2) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.03 313. ((e0) != (e2)) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) = (e2)) ### TransEq-sym 311 312 36
% 3.85/4.03 314. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.03 315. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.03 316. ((op (e0) (e3)) = (e2)) ((e2) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.03 317. ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) ((op (e0) (e3)) = (e2)) ### TransEq-sym 314 315 316
% 3.85/4.03 318. (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e2) (e0))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e0) (e1)) != (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) = (e0)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) ((op (e0) (e2)) = (e0)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e3) (e2)) != (e3)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e3)) = (e1)) ((e0) != (e1)) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (e1)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ### DisjTree 278 310 313 317
% 3.85/4.03 319. ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) = (e1)) ### Axiom
% 3.85/4.03 320. ((op (e2) (e3)) = (e1)) ((e1) != (op (e2) (e3))) ### Sym(=)
% 3.85/4.03 321. ((op (e2) (e3)) = (e1)) ((e1) != (op (e2) (e3))) ### Sym(=)
% 3.85/4.03 322. ((e1) != (e2)) ((op (e2) (e3)) = (e2)) ((op (e2) (e3)) = (e1)) ### TransEq 320 321 40
% 3.85/4.03 323. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.03 324. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.03 325. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.03 326. ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) = (e1)) ((op (e3) (e3)) = (e1)) ### TransEq 323 324 325
% 3.85/4.03 327. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.03 328. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.03 329. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.03 330. ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) = (e1)) ((op (e3) (e3)) = (e1)) ### TransEq 327 328 329
% 3.85/4.03 331. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.03 332. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.03 333. ((op (e1) (e3)) = (e3)) ((e3) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.03 334. ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e3)) = (e3)) ((op (e1) (e3)) = (e3)) ### TransEq 331 332 333
% 3.85/4.03 335. (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e2) (e3)) = (e2)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ### DisjTree 240 330 268 334
% 3.85/4.03 336. (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e2)) = (e3)) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e3) (e3)) = (e1)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ### DisjTree 10 326 317 335
% 3.85/4.03 337. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e2) (e2)) = (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) ((e0) != (e1)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e0) (e2)) = (e0)) ((e0) != (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) = (e0)) ((e0) != (e3)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e1)) != (e0)) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ### DisjTree 318 319 322 336
% 3.85/4.03 338. ((op (e0) (e0)) = (e2)) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e2) (e0))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e0) (e1)) != (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) ((op (e0) (e2)) = (e0)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e3) (e2)) != (e3)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((e0) != (e1)) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (e1)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e1) != (e2)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) = (e0)) ((e0) != (e3)) ### DisjTree 205 209 337 277
% 3.85/4.03 339. ((op (e0) (e1)) = (e2)) ((e2) != (op (e0) (e1))) ### Sym(=)
% 3.85/4.03 340. ((op (e0) (e1)) = (e2)) ((e2) != (op (e0) (e1))) ### Sym(=)
% 3.85/4.03 341. ((e1) != (e2)) ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) = (e2)) ### TransEq-sym 339 340 60
% 3.85/4.03 342. ((op (e0) (e1)) = (e1)) ((e0) != (e3)) ((op (e2) (e0)) = (e0)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) ((e0) != (e1)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e0) (e2)) = (e0)) ((e0) != (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e1)) != (e0)) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ### DisjTree 338 341 313 317
% 3.85/4.03 343. ((op (e0) (e2)) = (e1)) ((e1) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.03 344. ((op (e0) (e2)) = (e1)) ((e1) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.03 345. ((e0) != (e1)) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) = (e1)) ### TransEq-sym 343 344 36
% 3.85/4.03 346. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e2) (e0))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e0) (e1)) != (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) ((op (e0) (e2)) = (e0)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e3) (e2)) != (e3)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((e0) != (e1)) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (e1)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e1) != (e2)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) = (e0)) ((e0) != (e3)) ((op (e1) (e0)) = (e1)) ((op (e0) (e0)) != (op (e1) (e0))) ### DisjTree 33 342 345 318
% 3.85/4.03 347. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.03 348. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.03 349. ((op (e3) (e3)) = (e0)) ((e0) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.03 350. ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e0)) = (e0)) ((op (e3) (e3)) = (e0)) ### TransEq 347 348 349
% 3.85/4.03 351. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) = (e1)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e0)) = (e0)) ((op (e3) (e0)) != (op (e3) (e3))) ### DisjTree 350 326 244 248
% 3.85/4.03 352. ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) = (e1)) ### Axiom
% 3.85/4.03 353. (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e3) (e3)) = (e1)) ((op (e1) (e3)) = (e0)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e0) (e0)) = (e2)) ((op (e1) (e2)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e2) (e2))) ### DisjTree 102 222 226 240
% 3.85/4.03 354. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) = (e0)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e1) (e2)) = (e3)) ((op (e0) (e0)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) = (e0)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((e1) != (e2)) ((op (e1) (e3)) != (e1)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e0)) = (e0)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ### DisjTree 351 352 322 353
% 3.85/4.03 355. ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) = (e1)) ### Axiom
% 3.85/4.03 356. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e2)) = (e3)) ((op (e1) (e3)) = (e0)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e1) != (e2)) ((op (e1) (e3)) != (e1)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e0)) = (e0)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ### DisjTree 351 355 322 240
% 3.85/4.03 357. ((op (e3) (e2)) != (e3)) ((op (e3) (e2)) = (e3)) ### Axiom
% 3.85/4.03 358. (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e0)) = (e0)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e1) (e3)) != (e1)) ((e1) != (e2)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) = (e0)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e0) (e0)) = (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e0) (e2)) != (op (e2) (e2))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) = (e0)) ((e0) != (e3)) ### DisjTree 212 354 356 357
% 3.85/4.03 359. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((e0) != (e2)) ((e0) != (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((e1) != (e2)) ((op (e1) (e3)) != (e1)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e0)) = (e0)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (e3)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ### DisjTree 10 358 255 350
% 3.85/4.03 360. (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e1)) = (e1)) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e2)) = (e0)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e0)) = (e0)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e1) (e3)) != (e1)) ((e1) != (e2)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e0) (e2)) != (op (e2) (e2))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e3)) ((e0) != (e2)) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ### DisjTree 359 341 313 317
% 3.85/4.03 361. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((e0) != (e1)) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((e0) != (e2)) ((e0) != (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((e1) != (e2)) ((op (e1) (e3)) != (e1)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e0)) = (e0)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e3)) = (e2)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e1)) = (e3)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (e3)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e1) (e0)) = (e1)) ((op (e0) (e0)) != (op (e1) (e0))) ### DisjTree 33 360 345 351
% 3.85/4.03 362. (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e0)) != (op (e1) (e0))) ((e0) != (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((e0) != (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e1)) != (e0)) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) = (e1)) ((e0) != (e1)) ((op (e0) (e2)) = (e0)) ((op (e0) (e0)) != (op (e0) (e2))) ### DisjTree 199 202 346 361
% 3.85/4.03 363. (((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) ((op (e0) (e0)) != (op (e0) (e2))) ((op (e0) (e2)) = (e0)) ((e0) != (e1)) ((op (e1) (e0)) = (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e2) (e0))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e0) (e1)) != (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e0) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (e1)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e1) != (e2)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((e0) != (e3)) ((op (e0) (e0)) != (op (e1) (e0))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ### And 362
% 3.85/4.03 364. ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e0)) != (op (e1) (e0))) ((e0) != (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e0)) != (op (e2) (e2))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((e0) != (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e1)) != (e0)) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) = (e1)) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) ((op (e1) (e3)) != (e1)) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e2)) = (e0)) ### DisjTree 11 195 363 23
% 3.85/4.03 365. (((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e1) (e3)) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) ((op (e1) (e0)) = (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e2) (e0))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e0) (e1)) != (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e1) != (e2)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((e0) != (e3)) ((op (e0) (e0)) != (op (e1) (e0))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 364
% 3.85/4.03 366. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.03 367. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.03 368. ((op (e1) (e0)) = (e1)) ((e1) != (op (e1) (e0))) ### Sym(=)
% 3.85/4.03 369. ((op (e1) (e0)) != (op (e1) (e2))) ((op (e1) (e2)) = (e1)) ((op (e1) (e0)) = (e1)) ### TransEq-sym 366 367 368
% 3.85/4.03 370. (((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (op (e1) (e2))) ### And 369
% 3.85/4.03 371. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.03 372. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.03 373. ((op (e3) (e2)) = (e3)) ((e3) != (op (e3) (e2))) ### Sym(=)
% 3.85/4.03 374. ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((op (e3) (e2)) = (e3)) ### TransEq 371 372 373
% 3.85/4.03 375. (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e2))) ### And 374
% 3.85/4.03 376. ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e1) (e0)) != (op (e1) (e2))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e0)) != (op (e1) (e0))) ((e0) != (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e0)) != (op (e2) (e2))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((e0) != (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e1)) != (e0)) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) = (e1)) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) ((op (e1) (e3)) != (e1)) ((op (e0) (e2)) != (op (e0) (e3))) ### DisjTree 365 370 29 375
% 3.85/4.03 377. (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) ((op (e1) (e0)) = (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e2) (e0))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e0) (e1)) != (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((e0) != (e2)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e1) != (e2)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) != (op (e3) (e1))) ((e0) != (e3)) ((op (e0) (e0)) != (op (e1) (e0))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e1) (e0)) != (op (e1) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ### And 376
% 3.85/4.03 378. ((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e1) (e0)) != (op (e1) (e2))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e0)) != (op (e2) (e0))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e0)) != (op (e0) (e2))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e0) (e1)) != (op (e3) (e1))) ((e1) != (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e1) != (e2)) ((e0) != (e1)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e1) (e0))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e1) (e0)) = (e1)) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e0) (e1)) != (e0)) ### DisjTree 4 6 193 377
% 3.85/4.03 379. (((op (e1) (e0)) = (e1)) /\ ((op (e0) (e1)) != (e0))) ((op (e0) (e2)) != (op (e0) (e3))) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e2) (e1)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e0) (e0)) != (op (e1) (e0))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((e0) != (e1)) ((e1) != (e2)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e2)) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e1) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e0) (e2)) != (op (e2) (e2))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e1)) != (op (e2) (e2))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e1) (e0)) != (op (e2) (e0))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((op (e1) (e0)) != (op (e1) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) ### And 378
% 3.85/4.03 380. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.03 381. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.03 382. ((op (e0) (e1)) = (e0)) ((e0) != (op (e0) (e1))) ### Sym(=)
% 3.85/4.03 383. ((op (e0) (e1)) != (op (e0) (e2))) ((op (e0) (e2)) = (e0)) ((op (e0) (e1)) = (e0)) ### TransEq-sym 380 381 382
% 3.85/4.03 384. (((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) != (op (e0) (e2))) ### And 383
% 3.85/4.03 385. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.03 386. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.03 387. ((op (e0) (e3)) = (e0)) ((e0) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.03 388. ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e1)) = (e0)) ((op (e0) (e3)) = (e0)) ### TransEq 385 386 387
% 3.85/4.03 389. (((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) != (op (e0) (e3))) ### And 388
% 3.85/4.04 390. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.04 391. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.04 392. ((op (e1) (e3)) = (e1)) ((e1) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.04 393. ((op (e1) (e2)) != (op (e1) (e3))) ((op (e1) (e2)) = (e1)) ((op (e1) (e3)) = (e1)) ### TransEq 390 391 392
% 3.85/4.04 394. (((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) != (op (e1) (e3))) ### And 393
% 3.85/4.04 395. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.04 396. ((op (e2) (e3)) != (op (e2) (e3))) ### Refl(=)
% 3.85/4.04 397. ((op (e2) (e0)) = (e2)) ((e2) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.04 398. ((op (e2) (e0)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) ((op (e2) (e0)) = (e2)) ### TransEq-sym 395 396 397
% 3.85/4.04 399. (((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e2) (e3))) ### And 398
% 3.85/4.04 400. ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e0)) != (op (e2) (e3))) ((op (e2) (e0)) = (e2)) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e1) (e2)) = (e1)) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e1)) = (e0)) ### DisjTree 389 394 399 23
% 3.85/4.04 401. (((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 400
% 3.85/4.04 402. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.04 403. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.04 404. ((op (e0) (e0)) = (e0)) ((e0) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.04 405. ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e1)) = (e0)) ((op (e0) (e0)) = (e0)) ### TransEq-sym 402 403 404
% 3.85/4.04 406. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.04 407. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.04 408. ((e1) != (e3)) ((op (e0) (e0)) = (e1)) ((op (e0) (e0)) = (e3)) ### TransEq-sym 406 407 60
% 3.85/4.04 409. ((op (e0) (e1)) = (e3)) ((e3) != (op (e0) (e1))) ### Sym(=)
% 3.85/4.04 410. ((op (e0) (e1)) = (e3)) ((e3) != (op (e0) (e1))) ### Sym(=)
% 3.85/4.04 411. ((e0) != (e3)) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) = (e3)) ### TransEq-sym 409 410 36
% 3.85/4.04 412. ((op (e1) (e0)) = (e3)) ((e3) != (op (e1) (e0))) ### Sym(=)
% 3.85/4.04 413. ((op (e1) (e0)) = (e3)) ((e3) != (op (e1) (e0))) ### Sym(=)
% 3.85/4.04 414. ((e0) != (e3)) ((op (e1) (e0)) = (e0)) ((op (e1) (e0)) = (e3)) ### TransEq-sym 412 413 36
% 3.85/4.04 415. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.04 416. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.04 417. ((op (e1) (e1)) = (e0)) ((e0) != (op (e1) (e1))) ### Sym(=)
% 3.85/4.04 418. ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e1)) = (e0)) ((op (e1) (e1)) = (e0)) ### TransEq 415 416 417
% 3.85/4.04 419. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.04 420. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.04 421. ((op (e0) (e0)) = (e1)) ((e1) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.04 422. ((op (e0) (e0)) != (op (e0) (e2))) ((op (e0) (e2)) = (e1)) ((op (e0) (e0)) = (e1)) ### TransEq-sym 419 420 421
% 3.85/4.04 423. ((op (e1) (e2)) = (e0)) ((e0) != (op (e1) (e2))) ### Sym(=)
% 3.85/4.04 424. ((op (e1) (e2)) = (e0)) ((e0) != (op (e1) (e2))) ### Sym(=)
% 3.85/4.04 425. ((e0) != (e1)) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) = (e0)) ### TransEq 423 424 60
% 3.85/4.04 426. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.04 427. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.04 428. ((e2) != (e3)) ((op (e0) (e3)) = (e2)) ((op (e0) (e3)) = (e3)) ### TransEq-sym 426 427 40
% 3.85/4.04 429. ((op (e1) (e3)) = (e2)) ((e2) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.04 430. ((op (e1) (e3)) = (e2)) ((e2) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.04 431. ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e1) (e3)) = (e2)) ### TransEq-sym 429 430 60
% 3.85/4.04 432. ((op (e2) (e3)) != (e2)) ((op (e2) (e3)) = (e2)) ### Axiom
% 3.85/4.04 433. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e2) (e2)) = (e1)) ((op (e1) (e2)) = (e0)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((op (e0) (e3)) = (e3)) ((e2) != (e3)) ### DisjTree 428 431 432 78
% 3.85/4.04 434. (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e3) (e2)) = (e3)) ((e1) != (e3)) ((e2) != (e3)) ((op (e0) (e3)) = (e3)) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e2)) = (e0)) ((e0) != (e1)) ((op (e0) (e0)) = (e1)) ((op (e0) (e0)) != (op (e0) (e2))) ### DisjTree 422 425 433 53
% 3.85/4.04 435. ((op (e1) (e3)) = (e0)) ((e0) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.04 436. ((op (e1) (e3)) = (e0)) ((e0) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.04 437. ((e0) != (e1)) ((op (e1) (e3)) = (e1)) ((op (e1) (e3)) = (e0)) ### TransEq 435 436 60
% 3.85/4.04 438. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((op (e0) (e0)) = (e1)) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((op (e0) (e3)) = (e3)) ((e2) != (e3)) ((e1) != (e3)) ((op (e3) (e2)) = (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e1) (e0)) = (e3)) ((e0) != (e3)) ### DisjTree 414 418 434 437
% 3.85/4.04 439. ((op (e2) (e0)) = (e3)) ((e3) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.04 440. ((op (e2) (e0)) = (e3)) ((e3) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.04 441. ((e2) != (e3)) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) = (e3)) ### TransEq-sym 439 440 40
% 3.85/4.04 442. ((op (e3) (e0)) = (e0)) ((e0) != (op (e3) (e0))) ### Sym(=)
% 3.85/4.04 443. ((op (e3) (e0)) = (e0)) ((e0) != (op (e3) (e0))) ### Sym(=)
% 3.85/4.04 444. ((e0) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) = (e0)) ### TransEq 442 443 52
% 3.85/4.04 445. (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e0)) = (e0)) ((op (e2) (e0)) = (e2)) ((e0) != (e3)) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e1)) = (e0)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e3) (e2)) = (e3)) ((e2) != (e3)) ((op (e0) (e3)) = (e3)) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) = (e1)) ((e1) != (e3)) ### DisjTree 408 438 441 444
% 3.85/4.04 446. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e2) (e0)) = (e2)) ((op (e3) (e0)) = (e0)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e1)) = (e0)) ((e0) != (e3)) ((op (e0) (e0)) = (e1)) ((e1) != (e3)) ### DisjTree 408 411 127 445
% 3.85/4.04 447. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.04 448. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.04 449. ((op (e0) (e0)) = (e1)) ((e1) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.04 450. ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e1)) = (e1)) ((op (e0) (e0)) = (e1)) ### TransEq-sym 447 448 449
% 3.85/4.04 451. ((op (e1) (e0)) != (e1)) ((op (e1) (e0)) = (e1)) ### Axiom
% 3.85/4.04 452. ((op (e2) (e0)) = (e1)) ((e1) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.04 453. ((op (e2) (e0)) = (e1)) ((e1) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.04 454. ((e1) != (e2)) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) = (e1)) ### TransEq 452 453 40
% 3.85/4.04 455. ((op (e3) (e0)) = (e1)) ((e1) != (op (e3) (e0))) ### Sym(=)
% 3.85/4.04 456. ((op (e3) (e0)) = (e1)) ((e1) != (op (e3) (e0))) ### Sym(=)
% 3.85/4.04 457. ((e0) != (e1)) ((op (e3) (e0)) = (e0)) ((op (e3) (e0)) = (e1)) ### TransEq-sym 455 456 36
% 3.85/4.04 458. (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e3) (e0)) = (e0)) ((e0) != (e1)) ((op (e2) (e0)) = (e2)) ((e1) != (e2)) ((op (e1) (e0)) != (e1)) ((op (e0) (e1)) = (e1)) ((op (e0) (e0)) != (op (e0) (e1))) ### DisjTree 450 451 454 457
% 3.85/4.04 459. ((op (e1) (e0)) != (e1)) ((op (e1) (e0)) = (e1)) ### Axiom
% 3.85/4.04 460. (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e3) (e0)) = (e0)) ((e0) != (e1)) ((op (e2) (e0)) = (e2)) ((e1) != (e2)) ((op (e1) (e0)) != (e1)) ((op (e0) (e2)) = (e1)) ((op (e0) (e0)) != (op (e0) (e2))) ### DisjTree 422 459 454 457
% 3.85/4.04 461. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.04 462. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.04 463. ((op (e0) (e3)) = (e1)) ((e1) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.04 464. ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) = (e1)) ((op (e0) (e3)) = (e1)) ### TransEq-sym 461 462 463
% 3.85/4.04 465. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e0)) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((e1) != (e3)) ((e0) != (e3)) ((op (e0) (e1)) = (e0)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e0)) = (e0)) ((op (e2) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ### DisjTree 446 458 460 464
% 3.85/4.04 466. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.04 467. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.04 468. ((op (e3) (e1)) = (e0)) ((e0) != (op (e3) (e1))) ### Sym(=)
% 3.85/4.04 469. ((op (e0) (e1)) != (op (e3) (e1))) ((op (e0) (e1)) = (e0)) ((op (e3) (e1)) = (e0)) ### TransEq 466 467 468
% 3.85/4.04 470. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom
% 3.85/4.04 471. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom
% 3.85/4.04 472. ((op (op (e1) (e1)) (op (e1) (e1))) != (op (e3) (e3))) ((op (e1) (e1)) = (e3)) ### NotEqual 470 471
% 3.85/4.04 473. ((e0) != (op (op (e1) (e1)) (op (e1) (e1)))) ((op (e3) (e3)) = (e0)) ((op (e1) (e1)) = (e3)) ### Trans-sym 472 36
% 3.85/4.04 474. ((op (op (e1) (e1)) (op (e1) (e1))) != (e0)) ((op (e3) (e3)) = (e0)) ((op (e1) (e1)) = (e3)) ### Trans 472 36
% 3.85/4.04 475. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom
% 3.85/4.04 476. ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) != (op (e0) (e3))) ((op (e1) (e1)) = (e3)) ((op (e3) (e3)) = (e0)) ### NotEqual 474 475
% 3.85/4.04 477. ((e2) != (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) ((op (e0) (e3)) = (e2)) ((op (e3) (e3)) = (e0)) ((op (e1) (e1)) = (e3)) ### Trans-sym 476 40
% 3.85/4.04 478. ((op (e1) (e1)) = (e3)) ((e3) != (op (e1) (e1))) ### Sym(=)
% 3.85/4.04 479. (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e3)) = (e2)) ((op (e1) (e1)) = (e3)) ((op (e3) (e3)) = (e0)) ### DisjTree 473 477 478
% 3.85/4.04 480. ((op (e2) (e3)) != (e2)) ((op (e2) (e3)) = (e2)) ### Axiom
% 3.85/4.04 481. ((e2) != (op (op (e1) (e1)) (op (e1) (e1)))) ((op (e3) (e3)) = (e2)) ((op (e1) (e1)) = (e3)) ### Trans-sym 472 40
% 3.85/4.04 482. ((op (op (e1) (e1)) (op (e1) (e1))) != (e2)) ((op (e3) (e3)) = (e2)) ((op (e1) (e1)) = (e3)) ### Trans 472 40
% 3.85/4.04 483. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom
% 3.85/4.04 484. ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) != (op (e2) (e3))) ((op (e1) (e1)) = (e3)) ((op (e3) (e3)) = (e2)) ### NotEqual 482 483
% 3.85/4.04 485. ((e0) != (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) ((op (e2) (e3)) = (e0)) ((op (e3) (e3)) = (e2)) ((op (e1) (e1)) = (e3)) ### Trans-sym 484 36
% 3.85/4.04 486. ((op (e1) (e1)) = (e3)) ((e3) != (op (e1) (e1))) ### Sym(=)
% 3.85/4.04 487. (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e2) (e3)) = (e0)) ((op (e1) (e1)) = (e3)) ((op (e3) (e3)) = (e2)) ### DisjTree 481 485 486
% 3.85/4.04 488. ((e2) != (op (op (e0) (e0)) (op (e0) (e0)))) ((op (e3) (e3)) = (e2)) ((op (e0) (e0)) = (e3)) ### Trans-sym 59 40
% 3.85/4.04 489. ((op (op (e0) (e0)) (op (e0) (e0))) != (e2)) ((op (e3) (e3)) = (e2)) ((op (e0) (e0)) = (e3)) ### Trans 59 40
% 3.85/4.04 490. ((op (e0) (e0)) = (e3)) ((op (e0) (e0)) != (e3)) ### Axiom
% 3.85/4.04 491. ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) != (op (e2) (e3))) ((op (e0) (e0)) = (e3)) ((op (e3) (e3)) = (e2)) ### NotEqual 489 490
% 3.85/4.04 492. ((e1) != (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) ((op (e2) (e3)) = (e1)) ((op (e3) (e3)) = (e2)) ((op (e0) (e0)) = (e3)) ### Trans-sym 491 60
% 3.85/4.04 493. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.04 494. (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e2) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) ((op (e3) (e3)) = (e2)) ### DisjTree 488 492 493
% 3.85/4.04 495. ((op (e2) (e3)) != (e2)) ((op (e2) (e3)) = (e2)) ### Axiom
% 3.85/4.04 496. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.04 497. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.04 498. ((op (e2) (e3)) = (e3)) ((e3) != (op (e2) (e3))) ### Sym(=)
% 3.85/4.04 499. ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) = (e3)) ((op (e2) (e3)) = (e3)) ### TransEq 496 497 498
% 3.85/4.04 500. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (e2)) ((op (e0) (e0)) = (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e3)) = (e2)) ((op (e1) (e1)) = (e3)) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ### DisjTree 487 494 495 499
% 3.85/4.04 501. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) = (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((op (e3) (e3)) = (e0)) ((op (e1) (e1)) = (e3)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ### DisjTree 479 431 480 500
% 3.85/4.04 502. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e1)) = (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e0)) = (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e2) (e0)) = (e2)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e1)) = (e0)) ((e0) != (e3)) ((e1) != (e3)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e1) (e0)) != (e1)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ### DisjTree 465 469 93 501
% 3.85/4.04 503. (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e0)) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((e1) != (e3)) ((op (e0) (e1)) = (e0)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) = (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e1) (e0)) = (e0)) ((e0) != (e3)) ### DisjTree 414 502 122 334
% 3.85/4.04 504. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.04 505. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.04 506. ((op (e3) (e2)) = (e3)) ((e3) != (op (e3) (e2))) ### Sym(=)
% 3.85/4.04 507. ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e0)) = (e3)) ((op (e3) (e2)) = (e3)) ### TransEq 504 505 506
% 3.85/4.04 508. ((op (e3) (e0)) != (op (e3) (e2))) ((op (e0) (e0)) = (e1)) ((e0) != (e3)) ((op (e1) (e0)) = (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e2) (e0)) = (e2)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e1)) = (e0)) ((e1) != (e3)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e1) (e0)) != (e1)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ### DisjTree 503 438 441 507
% 3.85/4.04 509. (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e0)) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e1) (e0)) = (e0)) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e1)) = (e0)) ((e0) != (e3)) ((op (e0) (e0)) = (e1)) ((e1) != (e3)) ### DisjTree 408 411 127 508
% 3.85/4.04 510. ((op (e1) (e0)) != (e1)) ((op (e1) (e0)) = (e1)) ### Axiom
% 3.85/4.04 511. ((op (e3) (e0)) = (e1)) ((e1) != (op (e3) (e0))) ### Sym(=)
% 3.85/4.04 512. ((op (e3) (e0)) = (e1)) ((e1) != (op (e3) (e0))) ### Sym(=)
% 3.85/4.04 513. ((e1) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) = (e1)) ### TransEq 511 512 52
% 3.85/4.04 514. ((op (e3) (e0)) = (e1)) ((e0) != (e3)) ((op (e1) (e0)) = (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e2) (e0)) = (e2)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e1)) = (e0)) ((e1) != (e3)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e1) (e0)) != (e1)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ### DisjTree 503 414 441 513
% 3.85/4.04 515. ((op (e1) (e3)) = (e3)) ((e3) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.04 516. ((op (e1) (e3)) = (e3)) ((e3) != (op (e1) (e3))) ### Sym(=)
% 3.85/4.04 517. ((e1) != (e3)) ((op (e1) (e3)) = (e1)) ((op (e1) (e3)) = (e3)) ### TransEq-sym 515 516 60
% 3.85/4.04 518. (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e2) (e3)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e3) (e3)) = (e0)) ((op (e1) (e1)) = (e3)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e3)) = (e1)) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) != (op (e0) (e3))) ### DisjTree 388 464 479 499
% 3.85/4.04 519. (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e1) (e1)) = (e3)) ((op (e3) (e3)) = (e0)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e0)) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((e1) != (e3)) ((op (e0) (e1)) = (e0)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e1) (e0)) = (e0)) ((e0) != (e3)) ((op (e3) (e0)) = (e1)) ### DisjTree 514 517 518 166
% 3.85/4.04 520. ((op (e3) (e0)) = (e1)) ((op (e1) (e0)) = (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e1) (e1)) = (e3)) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e2) (e0)) = (e2)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e1)) = (e0)) ((e0) != (e3)) ((e1) != (e3)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e1) (e0)) != (e1)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ### DisjTree 465 469 93 519
% 3.85/4.04 521. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e0)) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((e1) != (e3)) ((op (e0) (e1)) = (e0)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) = (e1)) ((op (e1) (e0)) = (e0)) ((e0) != (e3)) ### DisjTree 414 520 122 517
% 3.85/4.04 522. ((e0) != (e3)) ((op (e1) (e0)) = (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e1)) = (e0)) ((e1) != (e3)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e2) (e0)) = (e2)) ((e1) != (e2)) ((op (e1) (e0)) != (e1)) ((op (e0) (e1)) = (e1)) ((op (e0) (e0)) != (op (e0) (e1))) ### DisjTree 450 510 454 521
% 3.85/4.04 523. ((op (e1) (e0)) != (e1)) ((op (e1) (e0)) = (e1)) ### Axiom
% 3.85/4.04 524. ((e0) != (e3)) ((op (e1) (e0)) = (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e1)) = (e0)) ((e1) != (e3)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e2) (e0)) = (e2)) ((e1) != (e2)) ((op (e1) (e0)) != (e1)) ((op (e0) (e2)) = (e1)) ((op (e0) (e0)) != (op (e0) (e2))) ### DisjTree 422 523 454 521
% 3.85/4.04 525. (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e3)) ((e0) != (e3)) ((op (e0) (e1)) = (e0)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e1) (e0)) = (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e2) (e0)) = (e2)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e1) (e0)) != (e1)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ### DisjTree 509 522 524 464
% 3.85/4.04 526. ((op (e2) (e0)) = (e0)) ((e0) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.04 527. ((op (e2) (e0)) = (e0)) ((e0) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.04 528. ((e0) != (e2)) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) = (e0)) ### TransEq 526 527 40
% 3.85/4.04 529. (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((e0) != (e2)) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e0)) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((e0) != (e3)) ((e1) != (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e1)) = (e0)) ((op (e0) (e0)) != (op (e0) (e1))) ### DisjTree 405 525 528 465
% 3.85/4.04 530. (((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e1)) = (e0)) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e3)) ((e0) != (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e3)) != (e2)) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e2) (e0)) = (e2)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e1) (e0)) != (e1)) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((e0) != (e2)) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ### And 529
% 3.85/4.04 531. ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e0)) != (op (e2) (e3))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((e0) != (e2)) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e0)) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) ((op (e2) (e3)) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((e0) != (e3)) ((e1) != (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e1)) = (e0)) ### DisjTree 389 530 399 23
% 3.85/4.04 532. (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2))) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e3)) ((e0) != (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e2) (e0)) = (e2)) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e1) (e0)) != (e1)) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((e0) != (e2)) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 531
% 3.85/4.04 533. ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((e0) != (e2)) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e0)) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((e0) != (e3)) ((e1) != (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e1))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e0)) != (op (e2) (e3))) ((op (e2) (e0)) = (e2)) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e1)) != (op (e0) (e2))) ((op (e0) (e1)) = (e0)) ### DisjTree 384 401 29 532
% 3.85/4.04 534. (((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) ((op (e0) (e1)) != (op (e0) (e2))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e0) (e0)) != (op (e0) (e1))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e3)) ((e0) != (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((e0) != (e2)) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ### And 533
% 3.85/4.04 535. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.04 536. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.04 537. ((op (e2) (e1)) = (e2)) ((e2) != (op (e2) (e1))) ### Sym(=)
% 3.85/4.04 538. ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) = (e2)) ((op (e2) (e1)) = (e2)) ### TransEq 535 536 537
% 3.85/4.04 539. (((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e2) (e1))) ### And 538
% 3.85/4.04 540. ((op (e0) (e2)) != (e0)) ((op (e0) (e2)) = (e0)) ### Axiom
% 3.85/4.04 541. (((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) ((op (e0) (e2)) != (e0)) ### And 540
% 3.85/4.04 542. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.04 543. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.04 544. ((op (e0) (e0)) = (e2)) ((e2) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.04 545. ((op (e0) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) = (e2)) ((op (e0) (e0)) = (e2)) ### TransEq-sym 542 543 544
% 3.85/4.04 546. ((op (e0) (e2)) != (e0)) ((op (e0) (e2)) = (e0)) ### Axiom
% 3.85/4.04 547. ((op (e3) (e1)) = (e1)) ((e1) != (op (e3) (e1))) ### Sym(=)
% 3.85/4.04 548. ((op (e3) (e1)) = (e1)) ((e1) != (op (e3) (e1))) ### Sym(=)
% 3.85/4.04 549. ((e1) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) = (e1)) ### TransEq 547 548 52
% 3.85/4.04 550. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.04 551. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.04 552. ((op (e3) (e2)) = (e1)) ((e1) != (op (e3) (e2))) ### Sym(=)
% 3.85/4.04 553. ((op (e1) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) = (e1)) ((op (e3) (e2)) = (e1)) ### TransEq 550 551 552
% 3.85/4.04 554. ((op (e0) (e2)) != (e0)) ((op (e0) (e2)) = (e0)) ### Axiom
% 3.85/4.04 555. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.04 556. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.04 557. ((op (e0) (e2)) = (e1)) ((e1) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.04 558. ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) = (e1)) ((op (e0) (e2)) = (e1)) ### TransEq-sym 555 556 557
% 3.85/4.04 559. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.04 560. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.04 561. ((op (e3) (e2)) = (e0)) ((e0) != (op (e3) (e2))) ### Sym(=)
% 3.85/4.04 562. ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e0)) = (e0)) ((op (e3) (e2)) = (e0)) ### TransEq 559 560 561
% 3.85/4.04 563. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.04 564. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 3.85/4.04 565. ((op (e3) (e2)) = (e2)) ((e2) != (op (e3) (e2))) ### Sym(=)
% 3.85/4.04 566. ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e2)) ((op (e3) (e2)) = (e2)) ### TransEq 563 564 565
% 3.85/4.04 567. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) = (e0)) ((op (e3) (e0)) != (op (e3) (e2))) ### DisjTree 562 553 566 374
% 3.85/4.04 568. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.04 569. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.04 570. ((op (e1) (e1)) = (e1)) ((e1) != (op (e1) (e1))) ### Sym(=)
% 3.85/4.04 571. ((op (e1) (e1)) != (op (e1) (e2))) ((op (e1) (e2)) = (e1)) ((op (e1) (e1)) = (e1)) ### TransEq-sym 568 569 570
% 3.85/4.04 572. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 3.85/4.04 573. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 3.85/4.04 574. ((op (op (e1) (e1)) (op (e1) (e1))) != (op (e2) (e2))) ((op (e1) (e1)) = (e2)) ### NotEqual 572 573
% 3.85/4.04 575. ((e0) != (op (op (e1) (e1)) (op (e1) (e1)))) ((op (e2) (e2)) = (e0)) ((op (e1) (e1)) = (e2)) ### Trans-sym 574 36
% 3.85/4.04 576. ((op (op (e1) (e1)) (op (e1) (e1))) != (e0)) ((op (e2) (e2)) = (e0)) ((op (e1) (e1)) = (e2)) ### Trans 574 36
% 3.85/4.04 577. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 3.85/4.04 578. ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) != (op (e0) (e2))) ((op (e1) (e1)) = (e2)) ((op (e2) (e2)) = (e0)) ### NotEqual 576 577
% 3.85/4.04 579. ((e3) != (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) ((op (e0) (e2)) = (e3)) ((op (e2) (e2)) = (e0)) ((op (e1) (e1)) = (e2)) ### Trans-sym 578 52
% 3.85/4.04 580. ((op (e1) (e1)) = (e2)) ((e2) != (op (e1) (e1))) ### Sym(=)
% 3.85/4.04 581. (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e2)) = (e3)) ((op (e1) (e1)) = (e2)) ((op (e2) (e2)) = (e0)) ### DisjTree 575 579 580
% 3.85/4.04 582. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.04 583. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.04 584. ((op (e1) (e1)) = (e3)) ((e3) != (op (e1) (e1))) ### Sym(=)
% 3.85/4.04 585. ((op (e1) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) ((op (e1) (e1)) = (e3)) ### TransEq-sym 582 583 584
% 3.85/4.04 586. (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e3) (e1)) = (e3)) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e2)) = (e0)) ((op (e0) (e2)) = (e3)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e2)) = (e1)) ((op (e1) (e1)) != (op (e1) (e2))) ((op (e3) (e3)) = (e1)) ((op (e0) (e1)) = (e2)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ### DisjTree 292 571 581 585
% 3.85/4.04 587. (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e1)) = (e2)) ((op (e3) (e3)) = (e1)) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e2) (e2)) = (e0)) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e0)) = (e0)) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e1) (e2)) = (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e0) (e2)) != (e0)) ### DisjTree 554 558 567 586
% 3.85/4.04 588. (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (e0)) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e2)) = (e0)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e1) (e2))) ((op (e0) (e1)) = (e2)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((e1) != (e3)) ((op (e3) (e0)) = (e0)) ((e0) != (e1)) ### DisjTree 457 549 553 587
% 3.85/4.04 589. (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((op (e3) (e0)) = (e0)) ((e1) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e0) (e1)) = (e2)) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e1) (e2)) = (e1)) ((e0) != (e1)) ((op (e0) (e2)) != (e0)) ### DisjTree 546 425 588 562
% 3.85/4.04 590. ((op (e0) (e0)) != (op (e0) (e0))) ### Refl(=)
% 3.85/4.04 591. ((op (e0) (e0)) != (op (e0) (e0))) ### Refl(=)
% 3.85/4.04 592. ((op (e3) (e0)) = (e1)) ((e1) != (op (e3) (e0))) ### Sym(=)
% 3.85/4.04 593. ((op (e0) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) = (e1)) ((op (e3) (e0)) = (e1)) ### TransEq 590 591 592
% 3.85/4.04 594. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.04 595. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 3.85/4.04 596. ((op (e3) (e0)) = (e2)) ((e2) != (op (e3) (e0))) ### Sym(=)
% 3.85/4.04 597. ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) = (e2)) ((op (e3) (e0)) = (e2)) ### TransEq 594 595 596
% 3.85/4.04 598. ((op (e3) (e0)) != (e3)) ((op (e3) (e0)) = (e3)) ### Axiom
% 3.85/4.04 599. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e0)) != (e3)) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) = (e1)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e0) (e2)) != (e0)) ((e0) != (e1)) ((op (e1) (e2)) = (e1)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e1) (e2))) ((op (e0) (e1)) = (e2)) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((e1) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ### DisjTree 589 593 597 598
% 3.85/4.04 600. ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) = (e1)) ### Axiom
% 3.85/4.04 601. ((op (e3) (e1)) = (e2)) ((e2) != (op (e3) (e1))) ### Sym(=)
% 3.85/4.04 602. ((op (e3) (e1)) = (e2)) ((e2) != (op (e3) (e1))) ### Sym(=)
% 3.85/4.04 603. ((e2) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e3) (e1)) = (e2)) ### TransEq 601 602 52
% 3.85/4.04 604. (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e0) (e0)) = (e3)) ((op (e2) (e3)) = (e1)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((e2) != (e3)) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e3) (e0))) ### DisjTree 597 603 566 494
% 3.85/4.04 605. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) = (e3)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e2)) ((op (e0) (e0)) = (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) = (e0)) ((op (e0) (e3)) != (op (e2) (e3))) ### DisjTree 134 494 244 272
% 3.85/4.04 606. ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) = (e1)) ### Axiom
% 3.85/4.04 607. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.04 608. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.04 609. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.04 610. ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) = (e2)) ((op (e3) (e3)) = (e2)) ### TransEq 607 608 609
% 3.85/4.04 611. (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e2) (e3)) = (e3)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e3) (e3)) = (e2)) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (e1)) ((op (e3) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ### DisjTree 240 606 610 272
% 3.85/4.04 612. (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e2)) = (e3)) ((op (e3) (e3)) = (e1)) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) = (e3)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((e2) != (e3)) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e3) (e0))) ### DisjTree 597 603 566 611
% 3.85/4.04 613. (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) = (e2)) ((e2) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e2)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (e1)) ((op (e3) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) ((op (e3) (e3)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) = (e0)) ((e0) != (e3)) ### DisjTree 141 605 612 248
% 3.85/4.04 614. ((e0) != (e3)) ((op (e0) (e3)) = (e0)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e0)) = (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e2)) = (e3)) ((op (e3) (e3)) = (e1)) ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((e2) != (e3)) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e3) (e0))) ### DisjTree 597 603 566 613
% 3.85/4.04 615. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e2) (e2)) = (e3)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) = (e2)) ((e2) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e2)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e3)) != (e1)) ((op (e0) (e3)) = (e0)) ((e0) != (e1)) ### DisjTree 158 600 604 614
% 3.85/4.04 616. ((op (e0) (e2)) = (e3)) ((e3) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.04 617. ((op (e0) (e2)) = (e3)) ((e3) != (op (e0) (e2))) ### Sym(=)
% 3.85/4.04 618. ((e2) != (e3)) ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) = (e3)) ### TransEq-sym 616 617 40
% 3.85/4.04 619. ((op (e1) (e2)) = (e3)) ((e3) != (op (e1) (e2))) ### Sym(=)
% 3.85/4.04 620. ((op (e1) (e2)) = (e3)) ((e3) != (op (e1) (e2))) ### Sym(=)
% 3.85/4.04 621. ((e1) != (e3)) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) = (e3)) ### TransEq-sym 619 620 60
% 3.85/4.04 622. ((op (e1) (e3)) != (e1)) ((op (e1) (e3)) = (e1)) ### Axiom
% 3.85/4.04 623. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e2) (e3)) = (e3)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e2) (e2)) = (e3)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) = (e2)) ((e2) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e2)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e3)) != (e1)) ((op (e0) (e3)) = (e0)) ((e0) != (e1)) ### DisjTree 158 622 604 612
% 3.85/4.04 624. (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) ((e0) != (e1)) ((op (e0) (e3)) = (e0)) ((op (e1) (e3)) != (e1)) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e0) (e0)) = (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (op (e3) (e0))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) = (e3)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e1) (e2)) = (e1)) ((e1) != (e3)) ((op (e0) (e2)) = (e2)) ((e2) != (e3)) ### DisjTree 618 621 623 374
% 3.85/4.04 625. (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e1) != (e3)) ((op (e1) (e2)) = (e1)) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((e0) != (e1)) ((op (e0) (e3)) = (e0)) ((op (e1) (e3)) != (e1)) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e0) (e0)) = (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e2) (e0)) != (op (e3) (e0))) ((e0) != (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) = (e2)) ((e2) != (e3)) ### DisjTree 441 209 615 624
% 3.85/4.04 626. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.04 627. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 3.85/4.04 628. ((op (e0) (e1)) = (e3)) ((e3) != (op (e0) (e1))) ### Sym(=)
% 3.85/4.04 629. ((op (e0) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) ((op (e0) (e1)) = (e3)) ### TransEq-sym 626 627 628
% 3.85/4.04 630. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e2) (e0)) = (e2)) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) = (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((e0) != (e3)) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e2)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e3)) != (e1)) ((op (e0) (e3)) = (e0)) ((e0) != (e1)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e1) (e2)) = (e1)) ((e1) != (e3)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ### DisjTree 625 629 618 141
% 3.85/4.04 631. (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((e0) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e3)) = (e0)) ((op (e1) (e3)) != (e1)) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e1) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e1) (e2)) = (e1)) ((e0) != (e1)) ((op (e0) (e2)) != (e0)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) = (e1)) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) != (e3)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ### DisjTree 545 599 630 56
% 3.85/4.04 632. (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((e0) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e1) != (e3)) ((op (e1) (e2)) = (e1)) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((e0) != (e1)) ((op (e0) (e3)) = (e0)) ((op (e1) (e3)) != (e1)) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e2) (e0)) != (op (e3) (e0))) ((e0) != (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) = (e3)) ((op (e2) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) = (e1)) ((e1) != (e2)) ((op (e2) (e0)) = (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ### DisjTree 545 341 630 56
% 3.85/4.04 633. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((e1) != (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) = (e2)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e3) (e0)) != (e3)) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e0) (e2)) != (e0)) ((e0) != (e1)) ((op (e1) (e2)) = (e1)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((e1) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e2) (e1)) != (op (e3) (e1))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((e0) != (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e3)) != (e1)) ((op (e0) (e3)) = (e0)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e0) != (e2)) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ### DisjTree 631 632 558 158
% 3.85/4.05 634. (((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((e0) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e1) (e3)) != (e1)) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e1) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e1) (e2)) = (e1)) ((e0) != (e1)) ((op (e0) (e2)) != (e0)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ((e1) != (e2)) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ### And 633
% 3.85/4.05 635. ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e0)) != (op (e2) (e3))) ((op (e1) (e2)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((e1) != (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) = (e2)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e0) (e2)) != (e0)) ((e0) != (e1)) ((op (e1) (e2)) = (e1)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((e1) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e2) (e1)) != (op (e3) (e1))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((e0) != (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e3)) != (e1)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e0) != (e2)) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ### DisjTree 634 394 399 23
% 3.85/4.05 636. (((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((e0) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e1) (e3)) != (e1)) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e1) != (e3)) ((op (e3) (e1)) = (e3)) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e1)) ((op (e0) (e2)) != (e0)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ((e1) != (e2)) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e2) (e0)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 635
% 3.85/4.05 637. ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e0)) != (op (e2) (e3))) ((op (e1) (e2)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((e1) != (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) = (e2)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) != (op (e3) (e0))) ((e0) != (e1)) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e3)) ((e1) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e2) (e1)) != (op (e3) (e1))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((e0) != (e3)) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e3)) != (e1)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((e0) != (e2)) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e2)) != (e0)) ### DisjTree 541 636 29 375
% 3.85/4.05 638. (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1))) ((op (e0) (e2)) != (e0)) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((e0) != (e2)) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((e0) != (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) != (op (e3) (e1))) ((e2) != (e3)) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e1) != (e3)) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) = (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ((e1) != (e2)) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e2) (e0)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ### And 637
% 3.85/4.05 639. ((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) ((op (e0) (e0)) != (op (e2) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((op (e2) (e1)) != (op (e3) (e1))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e2)) != (e0)) ((op (e2) (e0)) != (op (e2) (e1))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((e0) != (e2)) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) ((e1) != (e2)) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((e0) != (e3)) ((e1) != (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e1))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e0)) != (op (e2) (e3))) ((op (e2) (e0)) = (e2)) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e1)) != (op (e0) (e2))) ### DisjTree 534 6 539 638
% 3.85/4.05 640. (((op (e2) (e0)) = (e2)) /\ ((op (e0) (e2)) != (e0))) ((op (e0) (e1)) != (op (e0) (e2))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e2) (e0)) != (op (e2) (e3))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e0) (e0)) != (op (e0) (e1))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((e1) != (e3)) ((e0) != (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e0)) != (op (e0) (e2))) ((e0) != (e1)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e2)) != (op (e3) (e2))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) ((e0) != (e2)) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e1)) != (op (e3) (e1))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e2) (e0))) ((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) ### And 639
% 3.85/4.05 641. ((op (e0) (e3)) != (e0)) ((op (e0) (e3)) = (e0)) ### Axiom
% 3.85/4.05 642. (((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) ((op (e0) (e3)) != (e0)) ### And 641
% 3.85/4.05 643. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.05 644. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.05 645. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.05 646. ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) = (e3)) ### TransEq-sym 643 644 645
% 3.85/4.05 647. ((op (e1) (e0)) = (e2)) ((e2) != (op (e1) (e0))) ### Sym(=)
% 3.85/4.05 648. ((op (e1) (e0)) = (e2)) ((e2) != (op (e1) (e0))) ### Sym(=)
% 3.85/4.05 649. ((e0) != (e2)) ((op (e1) (e0)) = (e0)) ((op (e1) (e0)) = (e2)) ### TransEq-sym 647 648 36
% 3.85/4.05 650. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.05 651. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 3.85/4.05 652. ((op (e2) (e1)) = (e0)) ((e0) != (op (e2) (e1))) ### Sym(=)
% 3.85/4.05 653. ((op (e0) (e1)) != (op (e2) (e1))) ((op (e0) (e1)) = (e0)) ((op (e2) (e1)) = (e0)) ### TransEq 650 651 652
% 3.85/4.05 654. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e2) (e3)) = (e2)) ((e0) != (e2)) ((op (e1) (e1)) = (e2)) ((op (e0) (e2)) = (e3)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e1) (e0)) = (e0)) ((op (e1) (e0)) != (op (e2) (e0))) ### DisjTree 282 653 581 255
% 3.85/4.05 655. ((op (e1) (e2)) = (e2)) ((e2) != (op (e1) (e2))) ### Sym(=)
% 3.85/4.05 656. ((op (e1) (e2)) = (e2)) ((e2) != (op (e1) (e2))) ### Sym(=)
% 3.85/4.05 657. ((e1) != (e2)) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) = (e2)) ### TransEq-sym 655 656 60
% 3.85/4.05 658. (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e2)) = (e1)) ((e1) != (e2)) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e0) (e1)) = (e0)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e2)) = (e3)) ((op (e2) (e3)) = (e2)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e1) (e0)) = (e0)) ((e0) != (e2)) ### DisjTree 649 654 657 268
% 3.85/4.05 659. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.05 660. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 3.85/4.05 661. ((e1) != (e3)) ((op (e0) (e3)) = (e1)) ((op (e0) (e3)) = (e3)) ### TransEq-sym 659 660 60
% 3.85/4.05 662. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e2)) = (e3)) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((e1) != (e2)) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e3)) = (e3)) ((e1) != (e3)) ### DisjTree 661 393 322 335
% 3.85/4.05 663. ((op (e3) (e2)) != (e3)) ((op (e3) (e2)) = (e3)) ### Axiom
% 3.85/4.05 664. (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) ((op (e0) (e3)) = (e3)) ((op (e1) (e2)) != (op (e1) (e3))) ((e1) != (e2)) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e1) (e2)) = (e1)) ((e1) != (e3)) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e1) (e0)) = (e0)) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e0) (e1)) = (e0)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) = (e2)) ((e0) != (e2)) ((op (e2) (e3)) = (e2)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ### DisjTree 654 621 662 663
% 3.85/4.05 665. (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e2) (e3)) = (e2)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e1)) = (e0)) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e1) (e0)) != (op (e2) (e0))) ((e1) != (e3)) ((op (e1) (e2)) = (e1)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((e1) != (e2)) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e3)) = (e3)) ((op (e3) (e2)) != (e3)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e1) (e0)) = (e0)) ((e0) != (e2)) ### DisjTree 649 664 657 268
% 3.85/4.05 666. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (e3)) ((op (e1) (e2)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e1) != (e3)) ((e0) != (e2)) ((op (e1) (e0)) = (e0)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e2) (e3)) = (e2)) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e1) (e0)) != (op (e2) (e0))) ((e1) != (e2)) ((op (e1) (e2)) = (e1)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e0) (e1)) = (e0)) ((e0) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ### DisjTree 646 411 658 665
% 3.85/4.05 667. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.05 668. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 3.85/4.05 669. ((op (e0) (e0)) = (e1)) ((e1) != (op (e0) (e0))) ### Sym(=)
% 3.85/4.05 670. ((op (e0) (e0)) != (op (e0) (e3))) ((op (e0) (e3)) = (e1)) ((op (e0) (e0)) = (e1)) ### TransEq-sym 667 668 669
% 3.85/4.05 671. ((op (e1) (e0)) != (e1)) ((op (e1) (e0)) = (e1)) ### Axiom
% 3.85/4.05 672. (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((op (e3) (e0)) = (e3)) ((e1) != (e3)) ((op (e2) (e0)) = (e0)) ((e0) != (e1)) ((op (e1) (e0)) != (e1)) ((op (e0) (e3)) = (e1)) ((op (e0) (e0)) != (op (e0) (e3))) ### DisjTree 670 671 37 513
% 3.85/4.05 673. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.05 674. ((op (e1) (e2)) != (op (e1) (e2))) ### Refl(=)
% 3.85/4.05 675. ((op (e2) (e2)) = (e1)) ((e1) != (op (e2) (e2))) ### Sym(=)
% 3.85/4.05 676. ((op (e1) (e2)) != (op (e2) (e2))) ((op (e1) (e2)) = (e1)) ((op (e2) (e2)) = (e1)) ### TransEq 673 674 675
% 3.85/4.05 677. (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e3) (e3)) = (e1)) ((op (e1) (e3)) = (e0)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) != (op (e2) (e2))) ### DisjTree 90 676 226 240
% 3.85/4.05 678. (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) = (e0)) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e1) (e2)) = (e1)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) = (e2)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e3)) = (e1)) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ### DisjTree 677 330 268 334
% 3.85/4.05 679. ((op (e0) (e3)) != (e0)) ((op (e0) (e3)) = (e0)) ### Axiom
% 3.85/4.05 680. (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e1) (e3)) = (e3)) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e2) (e3)) = (e2)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e3) (e3)) = (e1)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (e0)) ### DisjTree 679 326 317 334
% 3.85/4.05 681. ((op (e0) (e3)) != (e0)) ((op (e0) (e3)) = (e0)) ### Axiom
% 3.85/4.05 682. (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e2) (e3)) = (e3)) ((op (e2) (e3)) = (e2)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e3) (e3)) = (e1)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (e0)) ### DisjTree 681 326 317 499
% 3.85/4.05 683. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.05 684. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.05 685. ((op (e3) (e3)) = (e3)) ((e3) != (op (e3) (e3))) ### Sym(=)
% 3.85/4.05 686. ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e0)) = (e3)) ((op (e3) (e3)) = (e3)) ### TransEq 683 684 685
% 3.85/4.05 687. (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e3)) != (e0)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e3) (e3)) = (e1)) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e3)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ### DisjTree 678 680 682 686
% 3.85/4.05 688. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (e0)) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e3)) = (e2)) ((e1) != (e2)) ((op (e1) (e2)) = (e1)) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e3))) ((op (e1) (e0)) != (e1)) ((e0) != (e1)) ((op (e2) (e0)) = (e0)) ((e1) != (e3)) ((op (e3) (e0)) = (e3)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ### DisjTree 672 393 322 687
% 3.85/4.05 689. (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((e0) != (e1)) ((op (e1) (e0)) != (e1)) ((op (e0) (e0)) != (op (e0) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e3)) != (e0)) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) ((e0) != (e3)) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e2)) = (e1)) ((e1) != (e2)) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e1)) != (op (e2) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e2) (e3)) = (e2)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((e0) != (e2)) ((e1) != (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e3) (e2)) != (e3)) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) = (e0)) ((op (e0) (e0)) != (op (e0) (e1))) ### DisjTree 405 666 688 444
% 3.85/4.05 690. (((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e1)) = (e0)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e1) != (e3)) ((e0) != (e2)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e1) (e0)) != (op (e2) (e0))) ((e1) != (e2)) ((op (e1) (e2)) = (e1)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((e0) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (e0)) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e3))) ((op (e1) (e0)) != (e1)) ((e0) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ### And 689
% 3.85/4.05 691. ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((e0) != (e1)) ((op (e1) (e0)) != (e1)) ((op (e0) (e0)) != (op (e0) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) ((e0) != (e3)) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e1) (e3)) != (op (e2) (e3))) ((e1) != (e2)) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e1)) != (op (e2) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((e0) != (e2)) ((e1) != (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e1)) = (e0)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e1) (e2)) = (e1)) ((op (e0) (e3)) != (e0)) ### DisjTree 642 394 690 23
% 3.85/4.05 692. (((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) ((op (e0) (e3)) != (e0)) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e1)) = (e0)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e1) != (e3)) ((e0) != (e2)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e1) (e0)) != (op (e2) (e0))) ((e1) != (e2)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((e0) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e3))) ((op (e1) (e0)) != (e1)) ((e0) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 691
% 3.85/4.05 693. (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2))) ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (op (e3) (e2))) ### And 507
% 3.85/4.05 694. ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((e0) != (e1)) ((op (e1) (e0)) != (e1)) ((op (e0) (e0)) != (op (e0) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) ((e0) != (e3)) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e1) (e3)) != (op (e2) (e3))) ((e1) != (e2)) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e1)) != (op (e2) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((e0) != (e2)) ((e1) != (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e3)) != (e0)) ((op (e0) (e1)) != (op (e0) (e2))) ((op (e0) (e1)) = (e0)) ### DisjTree 384 692 29 693
% 3.85/4.05 695. (((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) ((op (e0) (e1)) != (op (e0) (e2))) ((op (e0) (e3)) != (e0)) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e1) != (e3)) ((e0) != (e2)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e1) (e0)) != (op (e2) (e0))) ((e1) != (e2)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((e0) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e3))) ((e0) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ### And 694
% 3.85/4.05 696. ((op (e2) (e2)) = (e1)) ((op (e2) (e2)) != (e1)) ### Axiom
% 3.85/4.05 697. ((op (e2) (e2)) = (e1)) ((op (e2) (e2)) != (e1)) ### Axiom
% 3.85/4.05 698. ((op (op (e2) (e2)) (op (e2) (e2))) != (op (e1) (e1))) ((op (e2) (e2)) = (e1)) ### NotEqual 696 697
% 3.85/4.05 699. ((e0) != (op (op (e2) (e2)) (op (e2) (e2)))) ((op (e1) (e1)) = (e0)) ((op (e2) (e2)) = (e1)) ### Trans-sym 698 36
% 3.85/4.05 700. ((op (op (e2) (e2)) (op (e2) (e2))) != (e0)) ((op (e1) (e1)) = (e0)) ((op (e2) (e2)) = (e1)) ### Trans 698 36
% 3.85/4.05 701. ((op (e2) (e2)) = (e1)) ((op (e2) (e2)) != (e1)) ### Axiom
% 3.85/4.05 702. ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) != (op (e0) (e1))) ((op (e2) (e2)) = (e1)) ((op (e1) (e1)) = (e0)) ### NotEqual 700 701
% 3.85/4.05 703. ((e3) != (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) ((op (e0) (e1)) = (e3)) ((op (e1) (e1)) = (e0)) ((op (e2) (e2)) = (e1)) ### Trans-sym 702 52
% 3.85/4.05 704. ((op (e2) (e2)) = (e1)) ((e1) != (op (e2) (e2))) ### Sym(=)
% 3.85/4.05 705. (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e1)) = (e3)) ((op (e2) (e2)) = (e1)) ((op (e1) (e1)) = (e0)) ### DisjTree 699 703 704
% 3.85/4.05 706. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.05 707. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 3.85/4.05 708. ((op (e2) (e3)) = (e1)) ((e1) != (op (e2) (e3))) ### Sym(=)
% 3.85/4.05 709. ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) = (e1)) ### TransEq 706 707 708
% 3.85/4.05 710. (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e3)) = (e1)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e1)) = (e0)) ((op (e0) (e1)) = (e3)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((op (e2) (e0)) = (e0)) ((e0) != (e1)) ### DisjTree 37 41 705 709
% 3.85/4.05 711. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e1) (e2))) ((e0) != (e1)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e1)) = (e3)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e0)) = (e0)) ((op (e1) (e0)) != (op (e2) (e0))) ### DisjTree 282 710 300 437
% 3.85/4.05 712. ((op (e0) (e0)) != (op (e0) (e0))) ### Refl(=)
% 3.85/4.05 713. ((op (e0) (e0)) != (op (e0) (e0))) ### Refl(=)
% 3.85/4.05 714. ((op (e2) (e0)) = (e1)) ((e1) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.05 715. ((op (e0) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) = (e1)) ((op (e2) (e0)) = (e1)) ### TransEq 712 713 714
% 3.85/4.05 716. ((op (e2) (e0)) != (e2)) ((op (e2) (e0)) = (e2)) ### Axiom
% 3.85/4.05 717. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.05 718. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.85/4.05 719. ((op (e2) (e0)) = (e3)) ((e3) != (op (e2) (e0))) ### Sym(=)
% 3.85/4.05 720. ((op (e2) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) ((op (e2) (e0)) = (e3)) ### TransEq-sym 717 718 719
% 3.85/4.05 721. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e3) (e0)) = (e3)) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (e2)) ((op (e0) (e0)) = (e1)) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e1) (e0)) != (op (e2) (e0))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e3)) = (e1)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e0) (e1)) = (e3)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((e0) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e0) (e2)) = (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ### DisjTree 711 715 716 720
% 3.85/4.05 722. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e3) (e3)) = (e2)) ((op (e1) (e1)) = (e3)) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ### DisjTree 487 709 20 499
% 3.85/4.05 723. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e1)) = (e3)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((op (e0) (e3)) = (e3)) ((e2) != (e3)) ### DisjTree 428 431 20 722
% 3.85/4.05 724. ((op (e2) (e1)) = (e3)) ((e3) != (op (e2) (e1))) ### Sym(=)
% 3.85/4.05 725. ((op (e2) (e1)) = (e3)) ((e3) != (op (e2) (e1))) ### Sym(=)
% 3.85/4.05 726. ((e2) != (e3)) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) = (e3)) ### TransEq-sym 724 725 40
% 3.85/4.05 727. ((op (e3) (e1)) != (e3)) ((op (e3) (e1)) = (e3)) ### Axiom
% 3.85/4.05 728. (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((op (e3) (e1)) != (e3)) ((e2) != (e3)) ((op (e0) (e3)) = (e3)) ((op (e2) (e1)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e1) (e2))) ((e0) != (e1)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) = (e1)) ((op (e2) (e0)) != (e2)) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ### DisjTree 721 723 726 727
% 3.85/4.05 729. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e3))) ((e2) != (e3)) ((op (e3) (e1)) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((e0) != (e3)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e1) (e2))) ((e0) != (e1)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) = (e1)) ((op (e2) (e0)) != (e2)) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ### DisjTree 646 721 212 728
% 3.85/4.05 730. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) = (e2)) ((e2) != (e3)) ((op (e0) (e2)) = (e0)) ((e0) != (e3)) ((op (e0) (e1)) = (e1)) ((e1) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ### DisjTree 646 138 212 428
% 3.85/4.05 731. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e1)) = (e3)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) = (e3)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) ((e1) != (e3)) ((op (e0) (e1)) = (e1)) ((e0) != (e3)) ((op (e0) (e2)) = (e0)) ((e2) != (e3)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ### DisjTree 730 431 20 722
% 3.85/4.05 732. ((op (e3) (e1)) != (e3)) ((op (e3) (e1)) = (e3)) ### Axiom
% 3.85/4.05 733. (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((op (e3) (e1)) != (e3)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((e2) != (e3)) ((op (e0) (e2)) = (e0)) ((e0) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((e1) != (e2)) ((op (e1) (e3)) = (e1)) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e2) (e1)) = (e2)) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e0) (e1)) = (e1)) ((e1) != (e3)) ### DisjTree 138 731 726 732
% 3.88/4.05 734. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) ((e1) != (e2)) ((e2) != (e3)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e3) (e1)) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e2)) = (e0)) ((e0) != (e3)) ((op (e0) (e1)) = (e1)) ((e1) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ### DisjTree 646 138 212 733
% 3.88/4.05 735. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((e1) != (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e1) (e0)) != (op (e2) (e0))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e3)) = (e1)) ((op (e1) (e3)) != (op (e2) (e3))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((e0) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e0) (e2)) = (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((e0) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((op (e3) (e1)) != (e3)) ((e2) != (e3)) ((op (e2) (e1)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ### DisjTree 729 734 345 464
% 3.88/4.05 736. (((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e3))) ((e2) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((e0) != (e3)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (op (e1) (e2))) ((e0) != (e1)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) != (e2)) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((e1) != (e3)) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ### And 735
% 3.88/4.05 737. ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((e1) != (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (e2)) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e1) (e0)) != (op (e2) (e0))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e3)) != (op (e2) (e3))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((e0) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e0) (e2)) = (e0)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((e0) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((e2) != (e3)) ((op (e2) (e1)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (e0)) ### DisjTree 642 736 21 23
% 3.88/4.05 738. (((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) ((op (e0) (e3)) != (e0)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e3))) ((e2) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((e0) != (e3)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) ((e0) != (e1)) ((e1) != (e2)) ((op (e2) (e1)) = (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((e1) != (e3)) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 737
% 3.88/4.05 739. ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e1) (e2)) != (e1)) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e0) (e3)) != (op (e1) (e3))) ((e1) != (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e1) (e0)) != (op (e2) (e0))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e3)) != (op (e2) (e3))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e2) (e1)) = (e2)) ((e1) != (e2)) ((e0) != (e1)) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((e0) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((e2) != (e3)) ((op (e2) (e1)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (e0)) ### DisjTree 738 27 29 693
% 3.88/4.05 740. (((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) ((op (e0) (e3)) != (e0)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e3))) ((e2) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((e0) != (e3)) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) ((e0) != (e1)) ((e1) != (e2)) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e3) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((e1) != (e3)) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ### And 739
% 3.88/4.05 741. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.88/4.05 742. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 3.88/4.05 743. ((op (e3) (e1)) = (e3)) ((e3) != (op (e3) (e1))) ### Sym(=)
% 3.88/4.05 744. ((op (e3) (e0)) != (op (e3) (e1))) ((op (e3) (e0)) = (e3)) ((op (e3) (e1)) = (e3)) ### TransEq 741 742 743
% 3.88/4.05 745. (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1))) ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (op (e3) (e1))) ### And 744
% 3.88/4.05 746. ((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) != (op (e2) (e0))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e2)) != (op (e1) (e2))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((e2) != (e3)) ((op (e2) (e1)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) ((e0) != (e1)) ((op (e0) (e0)) != (op (e0) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e3)) ((e0) != (e3)) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e1) (e3)) != (op (e2) (e3))) ((e1) != (e2)) ((op (e1) (e0)) != (op (e2) (e0))) ((op (e0) (e1)) != (op (e2) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((e0) != (e2)) ((e1) != (e3)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e3)) != (e0)) ((op (e0) (e1)) != (op (e0) (e2))) ### DisjTree 695 6 740 745
% 3.88/4.05 747. (((op (e3) (e0)) = (e3)) /\ ((op (e0) (e3)) != (e0))) ((op (e0) (e1)) != (op (e0) (e2))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e1) (e3))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((e1) != (e3)) ((e0) != (e2)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e1) (e0)) != (op (e2) (e0))) ((e1) != (e2)) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((e0) != (e3)) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e0)) != (op (e3) (e3))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e3))) ((e0) != (e1)) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e3))) ((e2) != (e3)) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e0) (e2)) != (op (e1) (e2))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e3) (e0)) != (op (e3) (e1))) ((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) ### And 746
% 3.88/4.05 748. ((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e0)) = (e1)) /\ ((op (e0) (e1)) != (e0))) \/ ((((op (e2) (e0)) = (e2)) /\ ((op (e0) (e2)) != (e0))) \/ (((op (e3) (e0)) = (e3)) /\ ((op (e0) (e3)) != (e0)))))) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e3))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e0) (e0)) != (op (e2) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e1) (e2))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((e2) != (e3)) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e2) (e0)) != (op (e2) (e3))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e1)) != (op (e0) (e2))) ((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e1) (e0)) != (op (e1) (e2))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e0)) != (op (e2) (e0))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e0)) != (op (e0) (e2))) ((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e0) (e1)) != (op (e3) (e1))) ((e1) != (e3)) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. 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% 3.88/4.06 749. 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(((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((e2) != (e3)) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) ((op (e1) (e1)) != (op (e1) (e2))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e2) (e0))) ((op (e0) (e1)) != (op (e2) (e1))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e0) (e0)) != (op (e0) (e3))) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e3) (e0)) != (op (e3) (e1))) ### ConjTree 748
% 3.88/4.06 750. (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e3))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) ((op (e0) (e1)) != (op (e2) (e1))) ((op (e0) (e0)) != (op (e2) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e1) (e2))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e2) (e0)) != (op (e2) (e3))) ((op (e1) (e2)) != (op (e1) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e1)) != (op (e0) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e1) (e0)) != (op (e1) (e2))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e2) (e1)) != (op (e3) (e1))) ((op (e0) (e3)) != (op (e1) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) ((op (e1) (e3)) != (op (e2) (e3))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e3)) != (op (e3) (e3))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) ((op (e2) (e0)) != (op (e2) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e0)) != (op (e2) (e0))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) ((op (e0) (e0)) != (op (e0) (e2))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e3) (e3))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e2)) != (op (e2) (e2))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) ((op (e1) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e1) (e2))) ((op (e1) (e2)) != (op (e2) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e0)) != (op (e3) (e0))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((op (e0) (e0)) != (op (e1) (e0))) ((op (e2) (e1)) != (op (e2) (e3))) ((op (e1) (e0)) != (op (e1) (e3))) ((op (e0) (e2)) != (op (e0) (e3))) (((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e0)) = (e1)) /\ ((op (e0) (e1)) != (e0))) \/ ((((op (e2) (e0)) = (e2)) /\ ((op (e0) (e2)) != (e0))) \/ (((op (e3) (e0)) = (e3)) /\ ((op (e0) (e3)) != (e0)))))) /\ (((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) /\ (((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) /\ ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3))))))))) ### ConjTree 749
% 3.88/4.06 751. 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(((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) ### ConjTree 750
% 3.88/4.06 752. 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(((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e0)) = (e1)) /\ ((op (e0) (e1)) != (e0))) \/ ((((op (e2) (e0)) = (e2)) /\ ((op (e0) (e2)) != (e0))) \/ (((op (e3) (e0)) = (e3)) /\ ((op (e0) (e3)) != (e0)))))) /\ (((((op (e0) (e1)) = (e0)) /\ ((op (e1) (e0)) != (e1))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e1)) = (e2)) /\ ((op (e1) (e2)) != (e1))) \/ (((op (e3) (e1)) = (e3)) /\ ((op (e1) (e3)) != (e1)))))) /\ (((((op (e0) (e2)) = (e0)) /\ ((op (e2) (e0)) != (e2))) \/ ((((op (e1) (e2)) = (e1)) /\ ((op (e2) (e1)) != (e2))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e2)) = (e3)) /\ ((op (e2) (e3)) != (e2)))))) /\ ((((op (e0) (e3)) = (e0)) /\ ((op (e3) (e0)) != (e3))) \/ ((((op (e1) (e3)) = (e1)) /\ ((op (e3) (e1)) != (e3))) \/ ((((op (e2) (e3)) = (e2)) /\ ((op (e3) (e2)) != (e3))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3))))))))) (((op (e0) (e0)) != (op (e1) (e0))) /\ (((op (e0) (e0)) != (op (e2) (e0))) /\ (((op (e0) (e0)) != (op (e3) (e0))) /\ (((op (e1) (e0)) != (op (e2) (e0))) /\ (((op (e1) (e0)) != (op (e3) (e0))) /\ (((op (e2) (e0)) != (op (e3) (e0))) /\ (((op (e0) (e1)) != (op (e1) (e1))) /\ (((op (e0) (e1)) != (op (e2) (e1))) /\ (((op (e0) (e1)) != (op (e3) (e1))) /\ (((op (e1) (e1)) != (op (e2) (e1))) /\ (((op (e1) (e1)) != (op (e3) (e1))) /\ (((op (e2) (e1)) != (op (e3) (e1))) /\ (((op (e0) (e2)) != (op (e1) (e2))) /\ (((op (e0) (e2)) != (op (e2) (e2))) /\ (((op (e0) (e2)) != (op (e3) (e2))) /\ (((op (e1) (e2)) != (op (e2) (e2))) /\ (((op (e1) (e2)) != (op (e3) (e2))) /\ (((op (e2) (e2)) != (op (e3) (e2))) /\ (((op (e0) (e3)) != (op (e1) (e3))) /\ (((op (e0) (e3)) != (op (e2) (e3))) /\ (((op (e0) (e3)) != (op (e3) (e3))) /\ (((op (e1) (e3)) != (op (e2) (e3))) /\ (((op (e1) (e3)) != (op (e3) (e3))) /\ (((op (e2) (e3)) != (op (e3) (e3))) /\ (((op (e0) (e0)) != (op (e0) (e1))) /\ (((op (e0) (e0)) != (op (e0) (e2))) /\ (((op (e0) (e0)) != (op (e0) (e3))) /\ (((op (e0) (e1)) != (op (e0) (e2))) /\ (((op (e0) (e1)) != (op (e0) (e3))) /\ (((op (e0) (e2)) != (op (e0) (e3))) /\ (((op (e1) (e0)) != (op (e1) (e1))) /\ (((op (e1) (e0)) != (op (e1) (e2))) /\ (((op (e1) (e0)) != (op (e1) (e3))) /\ (((op (e1) (e1)) != (op (e1) (e2))) /\ (((op (e1) (e1)) != (op (e1) (e3))) /\ (((op (e1) (e2)) != (op (e1) (e3))) /\ (((op (e2) (e0)) != (op (e2) (e1))) /\ (((op (e2) (e0)) != (op (e2) (e2))) /\ (((op (e2) (e0)) != (op (e2) (e3))) /\ (((op (e2) (e1)) != (op (e2) (e2))) /\ (((op (e2) (e1)) != (op (e2) (e3))) /\ (((op (e2) (e2)) != (op (e2) (e3))) /\ (((op (e3) (e0)) != (op (e3) (e1))) /\ (((op (e3) (e0)) != (op (e3) (e2))) /\ (((op (e3) (e0)) != (op (e3) (e3))) /\ (((op (e3) (e1)) != (op (e3) (e2))) /\ (((op (e3) (e1)) != (op (e3) (e3))) /\ ((op (e3) (e2)) != (op (e3) (e3)))))))))))))))))))))))))))))))))))))))))))))))))) ### ConjTree 751
% 3.88/4.06 753. 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(((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ (((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ (((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ (((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (-. (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ (((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ ((op (e0) (e3)) = (e0))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) /\ ((((op (e1) (e0)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ ((op (e1) (e3)) = (e1))))) /\ ((((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) /\ ((((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) /\ ((((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) /\ ((((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) /\ ((((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) /\ ((((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) /\ ((((op (e2) (e0)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e3)) = (e2))))) /\ ((((op (e0) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e2))))) /\ ((((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e3) (e0)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))) ### ConjTree 752
% 3.88/4.06 % SZS output end Proof
% 3.88/4.06 (* END-PROOF *)
%------------------------------------------------------------------------------