TSTP Solution File: ALG139+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : ALG139+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 : n017.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 18:05:36 EDT 2022
% Result : Unsatisfiable 2.77s 2.97s
% Output : Proof 2.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG139+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 06:15:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.77/2.97 % SZS status Theorem
% 2.77/2.97 (* PROOF-FOUND *)
% 2.77/2.97 (* BEGIN-PROOF *)
% 2.77/2.97 % SZS output start Proof
% 2.77/2.97 1. ((op (e0) (e0)) != (e0)) ((op (e0) (e0)) = (e0)) ### Axiom
% 2.77/2.97 2. (((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) ### And 1
% 2.77/2.97 3. ((op (e0) (e0)) != (e1)) ((op (e0) (e0)) = (e1)) ### Axiom
% 2.77/2.97 4. (((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) ((op (e0) (e0)) != (e1)) ### And 3
% 2.77/2.97 5. ((op (e1) (e1)) != (e1)) ((op (e1) (e1)) = (e1)) ### Axiom
% 2.77/2.97 6. (((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) ### And 5
% 2.77/2.97 7. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.97 8. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.97 9. ((e2) != (e2)) ### NotEqual
% 2.77/2.97 10. ((e2) != (e3)) ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) = (e3)) ### TransEq-sym 7 8 9
% 2.77/2.97 11. (((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) ((op (e0) (e0)) = (e2)) ((e2) != (e3)) ### And 10
% 2.77/2.97 12. ((op (e1) (e1)) = (e0)) ((e0) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.97 13. ((op (e1) (e1)) = (e0)) ((e0) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.97 14. ((e3) != (e3)) ### NotEqual
% 2.77/2.97 15. ((e0) != (e3)) ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) = (e0)) ### TransEq 12 13 14
% 2.77/2.97 16. (((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) ((op (e1) (e1)) = (e0)) ((e0) != (e3)) ### And 15
% 2.77/2.97 17. ((op (e2) (e2)) = (e3)) ((e3) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.97 18. ((op (e2) (e2)) = (e3)) ((e3) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.97 19. ((e1) != (e1)) ### NotEqual
% 2.77/2.97 20. ((e1) != (e3)) ((op (e2) (e2)) = (e1)) ((op (e2) (e2)) = (e3)) ### TransEq-sym 17 18 19
% 2.77/2.97 21. (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) ((op (e2) (e2)) = (e1)) ((e1) != (e3)) ### And 20
% 2.77/2.97 22. ((op (e3) (e3)) != (e3)) ((op (e3) (e3)) = (e3)) ### Axiom
% 2.77/2.97 23. (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3))) ### And 22
% 2.77/2.97 24. ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e1) != (e3)) ((op (e2) (e2)) = (e1)) ((e0) != (e3)) ((op (e1) (e1)) = (e0)) ((e2) != (e3)) ((op (e0) (e0)) = (e2)) ### DisjTree 11 16 21 23
% 2.77/2.97 25. (((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) ((e2) != (e3)) ((op (e1) (e1)) = (e0)) ((e0) != (e3)) ((op (e2) (e2)) = (e1)) ((e1) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 24
% 2.77/2.97 26. ((op (e1) (e1)) != (e2)) ((op (e1) (e1)) = (e2)) ### Axiom
% 2.77/2.97 27. (((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) ((op (e1) (e1)) != (e2)) ### And 26
% 2.77/2.97 28. ((op (e2) (e2)) != (e2)) ((op (e2) (e2)) = (e2)) ### Axiom
% 2.77/2.97 29. (((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) ### And 28
% 2.77/2.97 30. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 2.77/2.97 31. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 2.77/2.97 32. ((op (e2) (e0)) = (e0)) ((e0) != (op (e2) (e0))) ### Sym(=)
% 2.77/2.97 33. ((op (e2) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) = (e0)) ((op (e2) (e0)) = (e0)) ### TransEq-sym 30 31 32
% 2.77/2.97 34. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.97 35. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.97 36. ((op (e3) (e1)) = (e0)) ((e0) != (op (e3) (e1))) ### Sym(=)
% 2.77/2.97 37. ((op (e1) (e1)) != (op (e3) (e1))) ((op (e1) (e1)) = (e0)) ((op (e3) (e1)) = (e0)) ### TransEq 34 35 36
% 2.77/2.97 38. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 2.77/2.97 39. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 2.77/2.97 40. ((op (e3) (e2)) = (e0)) ((e0) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.97 41. ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e0)) = (e0)) ((op (e3) (e2)) = (e0)) ### TransEq 38 39 40
% 2.77/2.97 42. ((op (e0) (e0)) = (e3)) ((op (e0) (e0)) != (e3)) ### Axiom
% 2.77/2.97 43. ((e0) != (e0)) ### NotEqual
% 2.77/2.97 44. ((op (op (e0) (e0)) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) = (e3)) ### NotEqual 42 43
% 2.77/2.97 45. ((e1) != (op (op (e0) (e0)) (e0))) ((op (e3) (e0)) = (e1)) ((op (e0) (e0)) = (e3)) ### Trans-sym 44 19
% 2.77/2.97 46. ((op (e0) (e0)) = (e3)) ((op (e0) (e0)) != (e3)) ### Axiom
% 2.77/2.97 47. ((op (e0) (e0)) = (e3)) ((op (e0) (e0)) != (e3)) ### Axiom
% 2.77/2.97 48. ((op (op (e0) (e0)) (op (e0) (e0))) != (op (e3) (e3))) ((op (e0) (e0)) = (e3)) ### NotEqual 46 47
% 2.77/2.97 49. ((e2) != (op (op (e0) (e0)) (op (e0) (e0)))) ((op (e3) (e3)) = (e2)) ((op (e0) (e0)) = (e3)) ### Trans-sym 48 9
% 2.77/2.97 50. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.97 51. (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e3)) = (e2)) ((op (e0) (e0)) = (e3)) ((op (e3) (e0)) = (e1)) ### DisjTree 45 49 50
% 2.77/2.97 52. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.97 53. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.97 54. ((op (e3) (e0)) = (e2)) ((e2) != (op (e3) (e0))) ### Sym(=)
% 2.77/2.97 55. ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e3)) = (e2)) ((op (e3) (e0)) = (e2)) ### TransEq-sym 52 53 54
% 2.77/2.97 56. ((op (e0) (e0)) != (op (e0) (e0))) ### Refl(=)
% 2.77/2.97 57. ((op (e0) (e0)) != (op (e0) (e0))) ### Refl(=)
% 2.77/2.97 58. ((op (e3) (e0)) = (e3)) ((e3) != (op (e3) (e0))) ### Sym(=)
% 2.77/2.97 59. ((op (e0) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) = (e3)) ((op (e3) (e0)) = (e3)) ### TransEq 56 57 58
% 2.77/2.97 60. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e0)) = (e3)) ((op (e3) (e3)) = (e2)) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e2)) = (e0)) ((op (e3) (e0)) != (op (e3) (e2))) ### DisjTree 41 51 55 59
% 2.77/2.97 61. ((op (e3) (e3)) != (e0)) ((op (e3) (e3)) = (e0)) ### Axiom
% 2.77/2.97 62. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e3)) != (e0)) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e3)) = (e2)) ((op (e0) (e0)) = (e3)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) != (op (e3) (e0))) ### DisjTree 33 37 60 61
% 2.77/2.97 63. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.97 64. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.97 65. ((op (e2) (e1)) = (e0)) ((e0) != (op (e2) (e1))) ### Sym(=)
% 2.77/2.97 66. ((op (e1) (e1)) != (op (e2) (e1))) ((op (e1) (e1)) = (e0)) ((op (e2) (e1)) = (e0)) ### TransEq 63 64 65
% 2.77/2.97 67. ((op (e2) (e2)) = (e1)) ((e1) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.97 68. ((op (e2) (e2)) = (e1)) ((e1) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.97 69. ((e0) != (e1)) ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) = (e1)) ### TransEq-sym 67 68 43
% 2.77/2.97 70. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 2.77/2.97 71. ((op (op (e3) (e3)) (e3)) != (op (e2) (e3))) ((op (e3) (e3)) = (e2)) ### NotEqual 70 14
% 2.77/2.97 72. ((e0) != (op (op (e3) (e3)) (e3))) ((op (e2) (e3)) = (e0)) ((op (e3) (e3)) = (e2)) ### Trans-sym 71 43
% 2.77/2.97 73. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 2.77/2.97 74. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 2.77/2.97 75. ((op (op (e3) (e3)) (op (e3) (e3))) != (op (e2) (e2))) ((op (e3) (e3)) = (e2)) ### NotEqual 73 74
% 2.77/2.97 76. ((e1) != (op (op (e3) (e3)) (op (e3) (e3)))) ((op (e2) (e2)) = (e1)) ((op (e3) (e3)) = (e2)) ### Trans-sym 75 19
% 2.77/2.97 77. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.97 78. (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) = (e1)) ((op (e3) (e3)) = (e2)) ((op (e2) (e3)) = (e0)) ### DisjTree 72 76 77
% 2.77/2.97 79. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) = (e1)) ((e0) != (e1)) ((op (e1) (e1)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e1) (e1)) = (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e0)) = (e3)) ((op (e3) (e3)) = (e2)) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e3)) != (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ### DisjTree 62 66 69 78
% 2.77/2.97 80. (((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e3)) = (e2)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e2) (e1))) ((e0) != (e1)) ((op (e2) (e2)) = (e1)) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (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))))) ### And 79
% 2.77/2.97 81. ((op (e2) (e2)) != (e3)) ((op (e2) (e2)) = (e3)) ### Axiom
% 2.77/2.97 82. (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) ((op (e2) (e2)) != (e3)) ### And 81
% 2.77/2.97 83. ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e2) (e2)) != (e3)) ((e0) != (e3)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) = (e1)) ((e0) != (e1)) ((op (e1) (e1)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e1) (e1)) = (e0)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e3)) = (e2)) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ### DisjTree 80 16 82 23
% 2.77/2.97 84. (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e2) (e1))) ((e0) != (e1)) ((op (e2) (e2)) = (e1)) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (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))))) ((e0) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 83
% 2.77/2.97 85. ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((e0) != (e1)) ((op (e1) (e1)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) != (op (e3) (e3))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e1) (e1)) != (e2)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e1) != (e3)) ((op (e2) (e2)) = (e1)) ((e0) != (e3)) ((op (e1) (e1)) = (e0)) ((e2) != (e3)) ### DisjTree 25 27 29 84
% 2.77/2.97 86. (((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) ((e2) != (e3)) ((op (e1) (e1)) = (e0)) ((e0) != (e3)) ((e1) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e2) (e1))) ((e0) != (e1)) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (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)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ### And 85
% 2.77/2.97 87. ((op (e1) (e1)) != (e3)) ((op (e1) (e1)) = (e3)) ### Axiom
% 2.77/2.97 88. (((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) ((op (e1) (e1)) != (e3)) ### And 87
% 2.77/2.97 89. ((op (e0) (e0)) != (op (e0) (e0))) ### Refl(=)
% 2.77/2.97 90. ((op (e0) (e0)) != (op (e0) (e0))) ### Refl(=)
% 2.77/2.97 91. ((op (e0) (e1)) = (e2)) ((e2) != (op (e0) (e1))) ### Sym(=)
% 2.77/2.97 92. ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e0)) = (e2)) ((op (e0) (e1)) = (e2)) ### TransEq 89 90 91
% 2.77/2.97 93. ((op (e1) (e1)) = (e0)) ((e0) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.97 94. ((op (e1) (e1)) = (e0)) ((e0) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.97 95. ((e0) != (e2)) ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) = (e0)) ### TransEq 93 94 9
% 2.77/2.97 96. ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (e2)) ### Axiom
% 2.77/2.97 97. ((op (op (e0) (e0)) (e0)) != (op (e2) (e0))) ((op (e0) (e0)) = (e2)) ### NotEqual 96 43
% 2.77/2.97 98. ((e1) != (op (op (e0) (e0)) (e0))) ((op (e2) (e0)) = (e1)) ((op (e0) (e0)) = (e2)) ### Trans-sym 97 19
% 2.77/2.97 99. ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (e2)) ### Axiom
% 2.77/2.97 100. ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (e2)) ### Axiom
% 2.77/2.97 101. ((op (op (e0) (e0)) (op (e0) (e0))) != (op (e2) (e2))) ((op (e0) (e0)) = (e2)) ### NotEqual 99 100
% 2.77/2.97 102. ((e3) != (op (op (e0) (e0)) (op (e0) (e0)))) ((op (e2) (e2)) = (e3)) ((op (e0) (e0)) = (e2)) ### Trans-sym 101 14
% 2.77/2.97 103. ((op (e0) (e0)) = (e2)) ((e2) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.97 104. (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) = (e3)) ((op (e0) (e0)) = (e2)) ((op (e2) (e0)) = (e1)) ### DisjTree 98 102 103
% 2.77/2.98 105. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 2.77/2.98 106. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 2.77/2.98 107. ((op (e2) (e1)) = (e1)) ((e1) != (op (e2) (e1))) ### Sym(=)
% 2.77/2.98 108. ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) = (e1)) ((op (e2) (e1)) = (e1)) ### TransEq 105 106 107
% 2.77/2.98 109. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 2.77/2.98 110. ((op (e2) (e0)) != (op (e2) (e0))) ### Refl(=)
% 2.77/2.98 111. ((op (e2) (e1)) = (e2)) ((e2) != (op (e2) (e1))) ### Sym(=)
% 2.77/2.98 112. ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) = (e2)) ((op (e2) (e1)) = (e2)) ### TransEq 109 110 111
% 2.77/2.98 113. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 114. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 115. ((op (e2) (e0)) = (e3)) ((e3) != (op (e2) (e0))) ### Sym(=)
% 2.77/2.98 116. ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e2)) = (e3)) ((op (e2) (e0)) = (e3)) ### TransEq-sym 113 114 115
% 2.77/2.98 117. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e2)) = (e3)) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e1)) = (e2)) ((op (e2) (e1)) = (e1)) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e3) (e0)) = (e0)) ((op (e2) (e0)) != (op (e3) (e0))) ### DisjTree 33 108 112 116
% 2.77/2.98 118. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 2.77/2.98 119. ((op (op (e2) (e2)) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) = (e3)) ### NotEqual 118 9
% 2.77/2.98 120. ((e0) != (op (op (e2) (e2)) (e2))) ((op (e3) (e2)) = (e0)) ((op (e2) (e2)) = (e3)) ### Trans-sym 119 43
% 2.77/2.98 121. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 2.77/2.98 122. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 2.77/2.98 123. ((op (op (e2) (e2)) (op (e2) (e2))) != (op (e3) (e3))) ((op (e2) (e2)) = (e3)) ### NotEqual 121 122
% 2.77/2.98 124. ((e1) != (op (op (e2) (e2)) (op (e2) (e2)))) ((op (e3) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) ### Trans-sym 123 19
% 2.77/2.98 125. ((op (e2) (e2)) = (e3)) ((e3) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.98 126. (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e3)) = (e1)) ((op (e2) (e2)) = (e3)) ((op (e3) (e2)) = (e0)) ### DisjTree 120 124 125
% 2.77/2.98 127. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.98 128. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.98 129. ((e0) != (e1)) ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) = (e1)) ### TransEq-sym 127 128 43
% 2.77/2.98 130. (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((op (e3) (e3)) = (e0)) ((e0) != (e1)) ### And 129
% 2.77/2.98 131. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((e0) != (e1)) (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((op (e3) (e3)) = (e1)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e1)) = (e0)) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e1)) = (e1)) ((op (e2) (e1)) = (e2)) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e2)) = (e3)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ### DisjTree 117 37 126 130
% 2.77/2.98 132. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 133. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 134. ((op (e2) (e3)) = (e1)) ((e1) != (op (e2) (e3))) ### Sym(=)
% 2.77/2.98 135. ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e1)) ((op (e2) (e3)) = (e1)) ### TransEq-sym 132 133 134
% 2.77/2.98 136. (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((e1) != (e3)) (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e1)) = (e2)) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e1) (e1)) = (e0)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e3)) = (e1)) (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((e0) != (e1)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e0) (e0)) = (e2)) ((op (e2) (e2)) = (e3)) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ### DisjTree 104 131 21 135
% 2.77/2.98 137. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 138. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 139. ((op (e3) (e2)) = (e1)) ((e1) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 140. ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e3)) = (e1)) ((op (e3) (e2)) = (e1)) ### TransEq-sym 137 138 139
% 2.77/2.98 141. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 2.77/2.98 142. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 2.77/2.98 143. ((op (e3) (e2)) = (e2)) ((e2) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 144. ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e1)) = (e2)) ((op (e3) (e2)) = (e2)) ### TransEq 141 142 143
% 2.77/2.98 145. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 146. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 147. ((op (e3) (e2)) = (e3)) ((e3) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 148. ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) = (e3)) ((op (e3) (e2)) = (e3)) ### TransEq 145 146 147
% 2.77/2.98 149. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e2) (e2)) = (e3)) ((op (e3) (e3)) = (e1)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ### DisjTree 126 140 144 148
% 2.77/2.98 150. (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) ((op (e2) (e2)) = (e3)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((e0) != (e1)) (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((op (e3) (e3)) = (e1)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) ((e1) != (e3)) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e1)) = (e0)) ((e0) != (e2)) ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (op (e0) (e1))) ### DisjTree 92 95 136 149
% 2.77/2.98 151. ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e0)) = (e2)) ((e0) != (e2)) ((op (e1) (e1)) = (e0)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((e1) != (e3)) (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e3)) = (e1)) (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((e0) != (e1)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ### And 150
% 2.77/2.98 152. ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((e0) != (e1)) (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((op (e3) (e3)) = (e1)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((e1) != (e3)) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e1)) = (e0)) ((e0) != (e2)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e1)) != (e3)) ((e2) != (e3)) ((op (e0) (e0)) = (e2)) ### DisjTree 11 88 151 23
% 2.77/2.98 153. (((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) ((e2) != (e3)) ((op (e1) (e1)) != (e3)) ((op (e0) (e0)) != (op (e0) (e1))) ((e0) != (e2)) ((op (e1) (e1)) = (e0)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((e1) != (e3)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e3)) = (e1)) (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((e0) != (e1)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 152
% 2.77/2.98 154. (((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) ((op (e1) (e1)) = (e0)) ((e0) != (e2)) ### And 95
% 2.77/2.98 155. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.98 156. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.98 157. ((e1) != (e2)) ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) = (e2)) ### TransEq-sym 155 156 19
% 2.77/2.98 158. (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3))) ((op (e3) (e3)) = (e1)) ((e1) != (e2)) ### And 157
% 2.77/2.98 159. ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ((e1) != (e2)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((e0) != (e1)) (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((op (e3) (e3)) = (e1)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((e1) != (e3)) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e1) (e1)) = (e0)) ((e0) != (e2)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e1) (e1)) != (e3)) ((e2) != (e3)) ### DisjTree 153 154 29 158
% 2.77/2.98 160. ((e2) != (e3)) ((op (e0) (e0)) != (op (e0) (e1))) ((e0) != (e2)) ((op (e1) (e1)) = (e0)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) ((e1) != (e3)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((e0) != (e1)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e1) != (e2)) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ### And 159
% 2.77/2.98 161. ((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) ((e1) != (e2)) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((e0) != (e2)) ((op (e0) (e0)) != (op (e0) (e1))) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((e0) != (e1)) ((op (e1) (e1)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) != (op (e3) (e3))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e1) != (e3)) ((e0) != (e3)) ((op (e1) (e1)) = (e0)) ((e2) != (e3)) ((op (e0) (e0)) != (e1)) ### DisjTree 4 6 86 160
% 2.77/2.98 162. (((op (e1) (e1)) = (e0)) /\ ((op (e0) (e0)) != (e1))) ((e2) != (e3)) ((e0) != (e3)) ((e1) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e2) (e1))) ((e0) != (e1)) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (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)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ((op (e0) (e0)) != (op (e0) (e1))) ((e0) != (e2)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e1))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((e1) != (e2)) ((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) ### And 161
% 2.77/2.98 163. ((op (e0) (e0)) = (e2)) ((e2) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.98 164. ((op (e0) (e0)) = (e2)) ((e2) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.98 165. ((e1) != (e2)) ((op (e0) (e0)) = (e1)) ((op (e0) (e0)) = (e2)) ### TransEq-sym 163 164 19
% 2.77/2.98 166. (((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) ((op (e0) (e0)) = (e1)) ((e1) != (e2)) ### And 165
% 2.77/2.98 167. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.98 168. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.98 169. ((e1) != (e3)) ((op (e0) (e0)) = (e1)) ((op (e0) (e0)) = (e3)) ### TransEq-sym 167 168 19
% 2.77/2.98 170. (((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) ((op (e0) (e0)) = (e1)) ((e1) != (e3)) ### And 169
% 2.77/2.98 171. ((op (e1) (e1)) = (e3)) ((e3) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.98 172. ((op (e1) (e1)) = (e3)) ((e3) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.98 173. ((e2) != (e3)) ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) = (e3)) ### TransEq-sym 171 172 9
% 2.77/2.98 174. (((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) ((op (e1) (e1)) = (e2)) ((e2) != (e3)) ### And 173
% 2.77/2.98 175. ((op (e2) (e2)) = (e0)) ((e0) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.98 176. ((op (e2) (e2)) = (e0)) ((e0) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.98 177. ((e0) != (e3)) ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) = (e0)) ### TransEq 175 176 14
% 2.77/2.98 178. (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) ((op (e2) (e2)) = (e0)) ((e0) != (e3)) ### And 177
% 2.77/2.98 179. ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e0) != (e3)) ((op (e2) (e2)) = (e0)) ((e2) != (e3)) ((op (e1) (e1)) = (e2)) ((e1) != (e3)) ((op (e0) (e0)) = (e1)) ### DisjTree 170 174 178 23
% 2.77/2.98 180. (((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) ((op (e0) (e0)) = (e1)) ((e1) != (e3)) ((e2) != (e3)) ((op (e2) (e2)) = (e0)) ((e0) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 179
% 2.77/2.98 181. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.98 182. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.98 183. ((op (e0) (e1)) = (e3)) ((e3) != (op (e0) (e1))) ### Sym(=)
% 2.77/2.98 184. ((op (e0) (e1)) != (op (e1) (e1))) ((op (e1) (e1)) = (e3)) ((op (e0) (e1)) = (e3)) ### TransEq-sym 181 182 183
% 2.77/2.98 185. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom
% 2.77/2.98 186. ((op (op (e1) (e1)) (e1)) != (op (e3) (e1))) ((op (e1) (e1)) = (e3)) ### NotEqual 185 19
% 2.77/2.98 187. ((e0) != (op (op (e1) (e1)) (e1))) ((op (e3) (e1)) = (e0)) ((op (e1) (e1)) = (e3)) ### Trans-sym 186 43
% 2.77/2.98 188. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom
% 2.77/2.98 189. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom
% 2.77/2.98 190. ((op (op (e1) (e1)) (op (e1) (e1))) != (op (e3) (e3))) ((op (e1) (e1)) = (e3)) ### NotEqual 188 189
% 2.77/2.98 191. ((e2) != (op (op (e1) (e1)) (op (e1) (e1)))) ((op (e3) (e3)) = (e2)) ((op (e1) (e1)) = (e3)) ### Trans-sym 190 9
% 2.77/2.98 192. ((op (e1) (e1)) = (e3)) ((e3) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.98 193. (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e3) (e3)) = (e2)) ((op (e1) (e1)) = (e3)) ((op (e3) (e1)) = (e0)) ### DisjTree 187 191 192
% 2.77/2.98 194. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 195. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 196. ((op (e3) (e2)) = (e0)) ((e0) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 197. ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) = (e0)) ((op (e3) (e2)) = (e0)) ### TransEq 194 195 196
% 2.77/2.98 198. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 2.77/2.98 199. ((op (e3) (e1)) != (op (e3) (e1))) ### Refl(=)
% 2.77/2.98 200. ((op (e3) (e2)) = (e1)) ((e1) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 201. ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e1)) = (e1)) ((op (e3) (e2)) = (e1)) ### TransEq 198 199 200
% 2.77/2.98 202. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 203. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 204. ((op (e3) (e2)) = (e2)) ((e2) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 205. ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e3)) = (e2)) ((op (e3) (e2)) = (e2)) ### TransEq-sym 202 203 204
% 2.77/2.98 206. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 2.77/2.98 207. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 2.77/2.98 208. ((op (e3) (e2)) = (e3)) ((e3) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 209. ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e3)) ((op (e3) (e2)) = (e3)) ### TransEq 206 207 208
% 2.77/2.98 210. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) = (e3)) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e3)) = (e2)) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) = (e1)) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (op (e3) (e2))) ### DisjTree 197 201 205 209
% 2.77/2.98 211. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 212. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 213. ((op (e3) (e1)) = (e2)) ((e2) != (op (e3) (e1))) ### Sym(=)
% 2.77/2.98 214. ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e3)) = (e2)) ((op (e3) (e1)) = (e2)) ### TransEq-sym 211 212 213
% 2.77/2.98 215. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.98 216. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.98 217. ((op (e3) (e1)) = (e3)) ((e3) != (op (e3) (e1))) ### Sym(=)
% 2.77/2.98 218. ((op (e1) (e1)) != (op (e3) (e1))) ((op (e1) (e1)) = (e3)) ((op (e3) (e1)) = (e3)) ### TransEq 215 216 217
% 2.77/2.98 219. (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) = (e0)) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e3)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e1) (e1)) = (e3)) ((op (e3) (e3)) = (e2)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ### DisjTree 193 210 214 218
% 2.77/2.98 220. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 2.77/2.98 221. ((op (e0) (e3)) = (e3)) ((e3) != (op (e0) (e3))) ### Sym(=)
% 2.77/2.98 222. ((e1) != (e3)) ((op (e0) (e3)) = (e1)) ((op (e0) (e3)) = (e3)) ### TransEq-sym 220 221 19
% 2.77/2.98 223. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 224. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 225. ((op (e2) (e3)) = (e0)) ((e0) != (op (e2) (e3))) ### Sym(=)
% 2.77/2.98 226. ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e2)) = (e0)) ((op (e2) (e3)) = (e0)) ### TransEq 223 224 225
% 2.77/2.98 227. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 2.77/2.98 228. ((op (e1) (e3)) != (op (e1) (e3))) ### Refl(=)
% 2.77/2.98 229. ((op (e2) (e3)) = (e1)) ((e1) != (op (e2) (e3))) ### Sym(=)
% 2.77/2.98 230. ((op (e1) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) = (e1)) ((op (e2) (e3)) = (e1)) ### TransEq 227 228 229
% 2.77/2.98 231. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 232. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 233. ((op (e2) (e3)) = (e2)) ((e2) != (op (e2) (e3))) ### Sym(=)
% 2.77/2.98 234. ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e2)) ((op (e2) (e3)) = (e2)) ### TransEq-sym 231 232 233
% 2.77/2.98 235. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 2.77/2.98 236. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 2.77/2.98 237. ((op (e2) (e3)) = (e3)) ((e3) != (op (e2) (e3))) ### Sym(=)
% 2.77/2.98 238. ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) = (e3)) ((op (e2) (e3)) = (e3)) ### TransEq 235 236 237
% 2.77/2.98 239. (((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 (e3) (e3)) = (e2)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) = (e1)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (op (e2) (e3))) ### DisjTree 226 230 234 238
% 2.77/2.98 240. ((e1) != (op (op (e3) (e3)) (e3))) ((op (e2) (e3)) = (e1)) ((op (e3) (e3)) = (e2)) ### Trans-sym 71 19
% 2.77/2.98 241. ((e0) != (op (op (e3) (e3)) (op (e3) (e3)))) ((op (e2) (e2)) = (e0)) ((op (e3) (e3)) = (e2)) ### Trans-sym 75 43
% 2.77/2.98 242. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.98 243. (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) = (e0)) ((op (e3) (e3)) = (e2)) ((op (e2) (e3)) = (e1)) ### DisjTree 240 241 242
% 2.77/2.98 244. ((op (e3) (e3)) != (e1)) ((op (e3) (e3)) = (e1)) ### Axiom
% 2.77/2.98 245. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) ((op (e3) (e3)) != (e1)) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e2)) = (e0)) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e2)) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) = (e3)) ((e1) != (e3)) ### DisjTree 222 239 243 244
% 2.77/2.98 246. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e3) (e3)) != (e1)) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e3) (e3)) = (e2)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) = (e3)) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e0)) = (e1)) ((e1) != (e3)) ### DisjTree 169 184 219 245
% 2.77/2.98 247. (((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) ((e1) != (e3)) ((op (e0) (e0)) = (e1)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) = (e0)) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e3)) = (e2)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ### And 246
% 2.77/2.98 248. ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e0) != (e3)) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e3) (e3)) = (e2)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) = (e0)) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((e1) != (e3)) ((op (e0) (e0)) = (e1)) ### DisjTree 170 247 178 23
% 2.77/2.98 249. (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3))) ((op (e0) (e0)) = (e1)) ((e1) != (e3)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) = (e0)) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((e0) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 248
% 2.77/2.98 250. ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e0) != (e3)) ((op (e2) (e2)) = (e0)) ((e2) != (e3)) ((e1) != (e3)) ((e1) != (e2)) ((op (e0) (e0)) = (e1)) ### DisjTree 166 180 29 249
% 2.77/2.98 251. (((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) ((e1) != (e2)) ((e1) != (e3)) ((e2) != (e3)) ((op (e2) (e2)) = (e0)) ((e0) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ### And 250
% 2.77/2.98 252. (((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) ((op (e2) (e2)) = (e0)) ((e0) != (e1)) ### And 69
% 2.77/2.98 253. ((op (e0) (e0)) != (e2)) ((op (e0) (e0)) = (e2)) ### Axiom
% 2.77/2.98 254. (((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) ((op (e0) (e0)) != (e2)) ### And 253
% 2.77/2.98 255. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 2.77/2.98 256. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 2.77/2.98 257. ((op (e0) (e1)) = (e0)) ((e0) != (op (e0) (e1))) ### Sym(=)
% 2.77/2.98 258. ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e3)) = (e0)) ((op (e0) (e1)) = (e0)) ### TransEq-sym 255 256 257
% 2.77/2.98 259. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 260. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 2.77/2.98 261. ((op (e2) (e1)) = (e0)) ((e0) != (op (e2) (e1))) ### Sym(=)
% 2.77/2.98 262. ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) = (e0)) ((op (e2) (e1)) = (e0)) ### TransEq-sym 259 260 261
% 2.77/2.98 263. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 2.77/2.98 264. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 2.77/2.98 265. ((op (e3) (e1)) = (e0)) ((e0) != (op (e3) (e1))) ### Sym(=)
% 2.77/2.98 266. ((op (e3) (e0)) != (op (e3) (e1))) ((op (e3) (e0)) = (e0)) ((op (e3) (e1)) = (e0)) ### TransEq 263 264 265
% 2.77/2.98 267. (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ((op (e3) (e0)) = (e0)) ((op (e3) (e0)) != (op (e3) (e1))) ((op (e2) (e2)) = (e0)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e1) (e1)) = (e2)) ((e0) != (e2)) ((op (e0) (e3)) = (e0)) ((op (e0) (e1)) != (op (e0) (e3))) ### DisjTree 258 95 262 266
% 2.77/2.98 268. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 269. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 270. ((op (e3) (e0)) = (e1)) ((e1) != (op (e3) (e0))) ### Sym(=)
% 2.77/2.98 271. ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e3)) = (e1)) ((op (e3) (e0)) = (e1)) ### TransEq-sym 268 269 270
% 2.77/2.98 272. ((e2) != (op (op (e0) (e0)) (e0))) ((op (e3) (e0)) = (e2)) ((op (e0) (e0)) = (e3)) ### Trans-sym 44 9
% 2.77/2.98 273. ((e1) != (op (op (e0) (e0)) (op (e0) (e0)))) ((op (e3) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) ### Trans-sym 48 19
% 2.77/2.98 274. ((op (e0) (e0)) = (e3)) ((e3) != (op (e0) (e0))) ### Sym(=)
% 2.77/2.98 275. (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e3)) = (e1)) ((op (e0) (e0)) = (e3)) ((op (e3) (e0)) = (e2)) ### DisjTree 272 273 274
% 2.77/2.98 276. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e0) (e0)) = (e3)) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e3)) = (e1)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e0) (e3)) = (e0)) ((e0) != (e2)) ((op (e1) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) = (e0)) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) ### DisjTree 267 271 275 59
% 2.77/2.98 277. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 2.77/2.98 278. ((op (op (e3) (e3)) (e3)) != (op (e1) (e3))) ((op (e3) (e3)) = (e1)) ### NotEqual 277 14
% 2.77/2.98 279. ((e0) != (op (op (e3) (e3)) (e3))) ((op (e1) (e3)) = (e0)) ((op (e3) (e3)) = (e1)) ### Trans-sym 278 43
% 2.77/2.98 280. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 2.77/2.98 281. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 2.77/2.98 282. ((op (op (e3) (e3)) (op (e3) (e3))) != (op (e1) (e1))) ((op (e3) (e3)) = (e1)) ### NotEqual 280 281
% 2.77/2.98 283. ((e2) != (op (op (e3) (e3)) (op (e3) (e3)))) ((op (e1) (e1)) = (e2)) ((op (e3) (e3)) = (e1)) ### Trans-sym 282 9
% 2.77/2.98 284. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.98 285. (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e1) (e1)) = (e2)) ((op (e3) (e3)) = (e1)) ((op (e1) (e3)) = (e0)) ### DisjTree 279 283 284
% 2.77/2.98 286. ((op (e3) (e3)) != (e0)) ((op (e3) (e3)) = (e0)) ### Axiom
% 2.77/2.98 287. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e3)) != (e0)) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (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 (e3) (e0)) != (op (e3) (e1))) ((op (e2) (e2)) = (e0)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e1) (e1)) = (e2)) ((e0) != (e2)) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e3)) = (e1)) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) = (e3)) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ### DisjTree 276 285 226 286
% 2.77/2.98 288. (((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e3)) = (e1)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((e0) != (e2)) ((op (e1) (e1)) = (e2)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) = (e0)) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ### And 287
% 2.77/2.98 289. ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e0) != (e3)) ((e2) != (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (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 (e3) (e0)) != (op (e3) (e1))) ((op (e2) (e2)) = (e0)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e1) (e1)) = (e2)) ((e0) != (e2)) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e3)) = (e1)) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ### DisjTree 288 174 178 23
% 2.77/2.98 290. (((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e3)) = (e1)) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((e0) != (e2)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) = (e0)) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((e2) != (e3)) ((e0) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 289
% 2.77/2.98 291. ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ((e1) != (e2)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e0) != (e3)) ((e2) != (e3)) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (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 (e3) (e0)) != (op (e3) (e1))) ((op (e2) (e2)) = (e0)) ((op (e2) (e1)) != (op (e2) (e2))) ((e0) != (e2)) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e3) (e3)) = (e1)) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (e2)) ### DisjTree 254 290 29 158
% 2.77/2.98 292. (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3))) ((op (e0) (e0)) != (e2)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((e0) != (e2)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e2) (e2)) = (e0)) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (e3))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((e2) != (e3)) ((e0) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e1) != (e2)) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ### And 291
% 2.77/2.98 293. ((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (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 (e3) (e0)) != (op (e3) (e1))) ((op (e2) (e1)) != (op (e2) (e2))) ((e0) != (e2)) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e3) (e0)) != (op (e3) (e3))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (e2)) ((e0) != (e1)) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e0) != (e3)) ((op (e2) (e2)) = (e0)) ((e2) != (e3)) ((e1) != (e3)) ((e1) != (e2)) ### DisjTree 251 6 252 292
% 2.77/2.98 294. (((op (e2) (e2)) = (e0)) /\ ((op (e0) (e0)) != (e2))) ((e1) != (e2)) ((e1) != (e3)) ((e2) != (e3)) ((e0) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ((e0) != (e1)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e0) (e3))) ((e0) != (e2)) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) ### And 293
% 2.77/2.98 295. ((op (e0) (e0)) != (e3)) ((op (e0) (e0)) = (e3)) ### Axiom
% 2.77/2.98 296. (((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) ((op (e0) (e0)) != (e3)) ### And 295
% 2.77/2.98 297. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.98 298. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 2.77/2.98 299. ((op (e1) (e0)) = (e2)) ((e2) != (op (e1) (e0))) ### Sym(=)
% 2.77/2.98 300. ((op (e1) (e0)) != (op (e1) (e1))) ((op (e1) (e1)) = (e2)) ((op (e1) (e0)) = (e2)) ### TransEq-sym 297 298 299
% 2.77/2.98 301. ((op (e2) (e0)) = (e2)) ((e2) != (op (e2) (e0))) ### Sym(=)
% 2.77/2.98 302. ((op (e2) (e0)) = (e2)) ((e2) != (op (e2) (e0))) ### Sym(=)
% 2.77/2.98 303. ((e0) != (e2)) ((op (e2) (e0)) = (e0)) ((op (e2) (e0)) = (e2)) ### TransEq-sym 301 302 43
% 2.77/2.98 304. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 2.77/2.98 305. ((op (op (e1) (e1)) (e1)) != (op (e2) (e1))) ((op (e1) (e1)) = (e2)) ### NotEqual 304 19
% 2.77/2.98 306. ((e0) != (op (op (e1) (e1)) (e1))) ((op (e2) (e1)) = (e0)) ((op (e1) (e1)) = (e2)) ### Trans-sym 305 43
% 2.77/2.98 307. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 2.77/2.98 308. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 2.77/2.98 309. ((op (op (e1) (e1)) (op (e1) (e1))) != (op (e2) (e2))) ((op (e1) (e1)) = (e2)) ### NotEqual 307 308
% 2.77/2.98 310. ((e3) != (op (op (e1) (e1)) (op (e1) (e1)))) ((op (e2) (e2)) = (e3)) ((op (e1) (e1)) = (e2)) ### Trans-sym 309 14
% 2.77/2.98 311. ((op (e1) (e1)) = (e2)) ((e2) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.98 312. (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e2) (e2)) = (e3)) ((op (e1) (e1)) = (e2)) ((op (e2) (e1)) = (e0)) ### DisjTree 306 310 311
% 2.77/2.98 313. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 314. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 315. ((op (e2) (e3)) = (e0)) ((e0) != (op (e2) (e3))) ### Sym(=)
% 2.77/2.98 316. ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) ((op (e2) (e3)) = (e0)) ### TransEq-sym 313 314 315
% 2.77/2.98 317. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e3) (e3)) = (e0)) ((op (e2) (e3)) != (op (e3) (e3))) ((e0) != (e3)) ((op (e1) (e1)) = (e2)) ((op (e2) (e2)) = (e3)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e2) (e0)) = (e2)) ((e0) != (e2)) ### DisjTree 303 312 177 316
% 2.77/2.98 318. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 319. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 320. ((op (e3) (e2)) = (e0)) ((e0) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 321. ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) ((op (e3) (e2)) = (e0)) ### TransEq-sym 318 319 320
% 2.77/2.98 322. ((e1) != (op (op (e2) (e2)) (e2))) ((op (e3) (e2)) = (e1)) ((op (e2) (e2)) = (e3)) ### Trans-sym 119 19
% 2.77/2.98 323. ((e0) != (op (op (e2) (e2)) (op (e2) (e2)))) ((op (e3) (e3)) = (e0)) ((op (e2) (e2)) = (e3)) ### Trans-sym 123 43
% 2.77/2.98 324. ((op (e2) (e2)) = (e3)) ((e3) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.98 325. (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e3)) = (e0)) ((op (e2) (e2)) = (e3)) ((op (e3) (e2)) = (e1)) ### DisjTree 322 323 324
% 2.77/2.98 326. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 2.77/2.98 327. ((op (e3) (e0)) != (op (e3) (e0))) ### Refl(=)
% 2.77/2.98 328. ((op (e3) (e2)) = (e2)) ((e2) != (op (e3) (e2))) ### Sym(=)
% 2.77/2.98 329. ((op (e3) (e0)) != (op (e3) (e2))) ((op (e3) (e0)) = (e2)) ((op (e3) (e2)) = (e2)) ### TransEq 326 327 328
% 2.77/2.98 330. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) = (e2)) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e2) (e2)) = (e3)) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e3)) = (e0)) ((op (e3) (e2)) != (op (e3) (e3))) ### DisjTree 321 325 329 148
% 2.77/2.98 331. (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((e0) != (e2)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e2) (e2)) = (e3)) ((e0) != (e3)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e1) (e1)) = (e2)) ((op (e1) (e0)) != (op (e1) (e1))) ((op (e0) (e0)) = (e1)) ((e1) != (e2)) ### DisjTree 165 300 317 330
% 2.77/2.98 332. (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) ((e1) != (e2)) ((op (e0) (e0)) = (e1)) ((op (e1) (e0)) != (op (e1) (e1))) ((op (e1) (e1)) = (e2)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e3) (e3)) = (e0)) ((op (e2) (e3)) != (op (e3) (e3))) ((e0) != (e3)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((e0) != (e2)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) ### And 331
% 2.77/2.98 333. ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((e0) != (e2)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((e0) != (e3)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) (((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)) ((e1) != (e2)) ((e2) != (e3)) ((op (e1) (e1)) = (e2)) ((op (e0) (e0)) != (e3)) ### DisjTree 296 174 332 23
% 2.77/2.98 334. (((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) ((op (e0) (e0)) != (e3)) ((e2) != (e3)) ((e1) != (e2)) ((op (e0) (e0)) = (e1)) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e3) (e3)) = (e0)) ((op (e2) (e3)) != (op (e3) (e3))) ((e0) != (e3)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((e0) != (e2)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 333
% 2.77/2.98 335. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.98 336. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=)
% 2.77/2.98 337. ((e0) != (e2)) ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) = (e2)) ### TransEq-sym 335 336 43
% 2.77/2.98 338. (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3))) ((op (e3) (e3)) = (e0)) ((e0) != (e2)) ### And 337
% 2.77/2.98 339. ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((e0) != (e2)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((e0) != (e3)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e1) (e0)) != (op (e1) (e1))) ((e2) != (e3)) ((op (e0) (e0)) != (e3)) ((e1) != (e2)) ((op (e0) (e0)) = (e1)) ### DisjTree 166 334 29 338
% 2.77/2.98 340. (((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) ((e1) != (e2)) ((op (e0) (e0)) != (e3)) ((e2) != (e3)) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e3) (e3)) = (e0)) ((op (e2) (e3)) != (op (e3) (e3))) ((e0) != (e3)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((e0) != (e2)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ### And 339
% 2.77/2.98 341. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 2.77/2.98 342. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 2.77/2.98 343. ((op (e0) (e1)) = (e0)) ((e0) != (op (e0) (e1))) ### Sym(=)
% 2.77/2.98 344. ((op (e0) (e1)) != (op (e0) (e2))) ((op (e0) (e2)) = (e0)) ((op (e0) (e1)) = (e0)) ### TransEq-sym 341 342 343
% 2.77/2.98 345. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 346. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 2.77/2.98 347. ((op (e3) (e1)) = (e0)) ((e0) != (op (e3) (e1))) ### Sym(=)
% 2.77/2.98 348. ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) ((op (e3) (e1)) = (e0)) ### TransEq-sym 345 346 347
% 2.77/2.98 349. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 2.77/2.98 350. ((op (e0) (e1)) != (op (e0) (e1))) ### Refl(=)
% 2.77/2.98 351. ((op (e3) (e1)) = (e1)) ((e1) != (op (e3) (e1))) ### Sym(=)
% 2.77/2.98 352. ((op (e0) (e1)) != (op (e3) (e1))) ((op (e0) (e1)) = (e1)) ((op (e3) (e1)) = (e1)) ### TransEq 349 350 351
% 2.77/2.98 353. ((e2) != (op (op (e1) (e1)) (e1))) ((op (e3) (e1)) = (e2)) ((op (e1) (e1)) = (e3)) ### Trans-sym 186 9
% 2.77/2.98 354. ((e0) != (op (op (e1) (e1)) (op (e1) (e1)))) ((op (e3) (e3)) = (e0)) ((op (e1) (e1)) = (e3)) ### Trans-sym 190 43
% 2.77/2.98 355. ((op (e1) (e1)) = (e3)) ((e3) != (op (e1) (e1))) ### Sym(=)
% 2.77/2.98 356. (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e3) (e3)) = (e0)) ((op (e1) (e1)) = (e3)) ((op (e3) (e1)) = (e2)) ### DisjTree 353 354 355
% 2.77/2.98 357. (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e1) (e1)) = (e3)) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e3) (e3)) = (e0)) ((op (e3) (e1)) != (op (e3) (e3))) ### DisjTree 348 352 356 218
% 2.77/2.98 358. (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e2)) = (e0)) ((op (e0) (e1)) != (op (e0) (e2))) ### DisjTree 344 357 92 184
% 2.77/2.98 359. ((op (e2) (e2)) = (e1)) ((op (e2) (e2)) != (e1)) ### Axiom
% 2.77/2.98 360. ((op (op (e2) (e2)) (e2)) != (op (e1) (e2))) ((op (e2) (e2)) = (e1)) ### NotEqual 359 9
% 2.77/2.98 361. ((e0) != (op (op (e2) (e2)) (e2))) ((op (e1) (e2)) = (e0)) ((op (e2) (e2)) = (e1)) ### Trans-sym 360 43
% 2.77/2.98 362. ((op (e2) (e2)) = (e1)) ((op (e2) (e2)) != (e1)) ### Axiom
% 2.77/2.98 363. ((op (e2) (e2)) = (e1)) ((op (e2) (e2)) != (e1)) ### Axiom
% 2.77/2.98 364. ((op (op (e2) (e2)) (op (e2) (e2))) != (op (e1) (e1))) ((op (e2) (e2)) = (e1)) ### NotEqual 362 363
% 2.77/2.98 365. ((e3) != (op (op (e2) (e2)) (op (e2) (e2)))) ((op (e1) (e1)) = (e3)) ((op (e2) (e2)) = (e1)) ### Trans-sym 364 14
% 2.77/2.98 366. ((op (e2) (e2)) = (e1)) ((e1) != (op (e2) (e2))) ### Sym(=)
% 2.77/2.98 367. (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e1) (e1)) = (e3)) ((op (e2) (e2)) = (e1)) ((op (e1) (e2)) = (e0)) ### DisjTree 361 365 366
% 2.77/2.98 368. ((op (e2) (e2)) != (e0)) ((op (e2) (e2)) = (e0)) ### Axiom
% 2.77/2.98 369. (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e2) (e2)) != (e0)) ((op (e2) (e2)) = (e1)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e1)) != (op (e0) (e2))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e1) (e1)) = (e3)) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e3) (e3)) = (e0)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ### DisjTree 358 367 368 321
% 2.77/2.98 370. (((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e0)) = (e2)) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e0) (e2))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e2) (e2)) = (e1)) ((op (e2) (e2)) != (e0)) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ### And 369
% 2.77/2.98 371. ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e1) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e2) (e2)) != (e0)) ((op (e2) (e2)) = (e1)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e1)) != (op (e0) (e2))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e3) (e3)) = (e0)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e0)) = (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((op (e0) (e0)) != (e3)) ### DisjTree 296 370 21 23
% 2.77/2.98 372. (((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) ((op (e0) (e0)) != (e3)) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e0) (e2))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e2) (e2)) = (e1)) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e1) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ### And 371
% 2.77/2.98 373. ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ((e0) != (e2)) ((op (e1) (e1)) != (e2)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e1) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e2) (e2)) = (e1)) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e1)) != (op (e0) (e2))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e3) (e3)) = (e0)) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((op (e0) (e0)) != (e3)) ### DisjTree 372 27 29 338
% 2.77/2.98 374. (((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) ((op (e0) (e0)) != (e3)) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e0) (e2))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e1) != (e3)) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e0) != (e2)) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ### And 373
% 2.77/2.98 375. ((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) ((e0) != (e1)) ((e1) != (e3)) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e1)) != (op (e0) (e2))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e0)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((e0) != (e2)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((e0) != (e3)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e0)) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e1) (e0)) != (op (e1) (e1))) ((e2) != (e3)) ((op (e0) (e0)) != (e3)) ((e1) != (e2)) ### DisjTree 340 6 374 130
% 2.77/2.98 376. (((op (e3) (e3)) = (e0)) /\ ((op (e0) (e0)) != (e3))) ((e1) != (e2)) ((e2) != (e3)) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) ((op (e2) (e3)) != (op (e3) (e3))) ((e0) != (e3)) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((e0) != (e2)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e0)) != (op (e0) (e1))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e0) (e2))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ((e1) != (e3)) ((e0) != (e1)) ((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) ### And 375
% 2.77/2.98 377. ((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e1)) = (e0)) /\ ((op (e0) (e0)) != (e1))) \/ ((((op (e2) (e2)) = (e0)) /\ ((op (e0) (e0)) != (e2))) \/ (((op (e3) (e3)) = (e0)) /\ ((op (e0) (e0)) != (e3)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e1)) != (op (e0) (e2))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (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 (e3) (e0)) != (op (e3) (e1))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e0) (e1)) != (op (e0) (e3))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) ((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) ((e1) != (e2)) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((e0) != (e2)) ((op (e0) (e0)) != (op (e0) (e1))) ((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((e0) != (e1)) ((op (e1) (e1)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) != (op (e3) (e3))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3)))))) ((e1) != (e3)) ((e0) != (e3)) ((e2) != (e3)) ### DisjTree 2 162 294 376
% 2.77/2.98 378. (((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e1)) = (e0)) /\ ((op (e0) (e0)) != (e1))) \/ ((((op (e2) (e2)) = (e0)) /\ ((op (e0) (e0)) != (e2))) \/ (((op (e3) (e3)) = (e0)) /\ ((op (e0) (e0)) != (e3)))))) /\ (((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) /\ (((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) /\ ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3))))))))) ((e2) != (e3)) ((e0) != (e3)) ((e1) != (e3)) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e3) (e0)) != (op (e3) (e2))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e3))) ((op (e0) (e0)) != (op (e3) (e0))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e1) (e1)) != (op (e3) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e2) (e1))) ((e0) != (e1)) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (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)) != (op (e0) (e1))) ((e0) != (e2)) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e0)) != (op (e2) (e2))) ((op (e2) (e0)) != (op (e2) (e1))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((e1) != (e2)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e3) (e1)) != (op (e3) (e3))) ((op (e0) (e2)) != (op (e3) (e2))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e2) (e2)) != (op (e2) (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 (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e0) (e1)) != (op (e0) (e3))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e3) (e0)) != (op (e3) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) ((op (e1) (e0)) != (op (e1) (e1))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e3) (e1))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e0) (e2))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) ### ConjTree 377
% 2.77/2.98 379. (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) ((op (e0) (e1)) != (op (e0) (e2))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e1)) != (op (e3) (e1))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) ((op (e1) (e0)) != (op (e1) (e1))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (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 (e3) (e0)) != (op (e3) (e1))) ((op (e2) (e1)) != (op (e2) (e2))) ((op (e0) (e1)) != (op (e0) (e3))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e1) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e3) (e1)) != (op (e3) (e3))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e1)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) ((op (e2) (e0)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e2) (e2))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) ((op (e0) (e0)) != (op (e0) (e1))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) ((op (e1) (e1)) != (op (e2) (e1))) ((op (e2) (e0)) != (op (e3) (e0))) ((op (e1) (e1)) != (op (e3) (e1))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) ((op (e0) (e0)) != (op (e3) (e0))) ((op (e3) (e0)) != (op (e3) (e3))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) ((op (e3) (e0)) != (op (e3) (e2))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e1)) = (e0)) /\ ((op (e0) (e0)) != (e1))) \/ ((((op (e2) (e2)) = (e0)) /\ ((op (e0) (e0)) != (e2))) \/ (((op (e3) (e3)) = (e0)) /\ ((op (e0) (e0)) != (e3)))))) /\ (((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) /\ (((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) /\ ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3))))))))) ### ConjTree 378
% 2.77/2.98 380. (((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)))))))))))))))))))))))))))))))))))))))))))))))))) (((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e1)) = (e0)) /\ ((op (e0) (e0)) != (e1))) \/ ((((op (e2) (e2)) = (e0)) /\ ((op (e0) (e0)) != (e2))) \/ (((op (e3) (e3)) = (e0)) /\ ((op (e0) (e0)) != (e3)))))) /\ (((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) /\ (((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) /\ ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3))))))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (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 (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) ### ConjTree 379
% 2.77/2.98 381. 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(((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e1) = (op (e2) (e2)))))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (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))))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e1)) = (e0)) /\ ((op (e0) (e0)) != (e1))) \/ ((((op (e2) (e2)) = (e0)) /\ ((op (e0) (e0)) != (e2))) \/ (((op (e3) (e3)) = (e0)) /\ ((op (e0) (e0)) != (e3)))))) /\ (((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) /\ (((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) /\ ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((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 380
% 2.77/2.99 382. ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ ((op (e1) (e0)) = (e3))))) /\ ((((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) /\ ((((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) /\ ((((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) /\ ((((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e2) (e1)) = (e3))))) /\ ((((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) /\ ((((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) /\ (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3)))))))))))))))))))) (((op (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)))))))))))))))))))))))))))))))))))))))))))))))))) (((((op (e0) (e0)) = (e0)) /\ ((op (e0) (e0)) != (e0))) \/ ((((op (e1) (e1)) = (e0)) /\ ((op (e0) (e0)) != (e1))) \/ ((((op (e2) (e2)) = (e0)) /\ ((op (e0) (e0)) != (e2))) \/ (((op (e3) (e3)) = (e0)) /\ ((op (e0) (e0)) != (e3)))))) /\ (((((op (e0) (e0)) = (e1)) /\ ((op (e1) (e1)) != (e0))) \/ ((((op (e1) (e1)) = (e1)) /\ ((op (e1) (e1)) != (e1))) \/ ((((op (e2) (e2)) = (e1)) /\ ((op (e1) (e1)) != (e2))) \/ (((op (e3) (e3)) = (e1)) /\ ((op (e1) (e1)) != (e3)))))) /\ (((((op (e0) (e0)) = (e2)) /\ ((op (e2) (e2)) != (e0))) \/ ((((op (e1) (e1)) = (e2)) /\ ((op (e2) (e2)) != (e1))) \/ ((((op (e2) (e2)) = (e2)) /\ ((op (e2) (e2)) != (e2))) \/ (((op (e3) (e3)) = (e2)) /\ ((op (e2) (e2)) != (e3)))))) /\ ((((op (e0) (e0)) = (e3)) /\ ((op (e3) (e3)) != (e0))) \/ ((((op (e1) (e1)) = (e3)) /\ ((op (e3) (e3)) != (e1))) \/ ((((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) != (e2))) \/ (((op (e3) (e3)) = (e3)) /\ ((op (e3) (e3)) != (e3))))))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e2) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e1) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e1) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e1) = (op (op (e0) (e0)) (e0))) /\ (((e3) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e2) = (op (e0) (e0)))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e2) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e1) = (op (op (e3) (e3)) (e3))) /\ (((e0) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e2) = (op (e3) (e3)))))) (-. (((e2) = (op (op (e0) (e0)) (e0))) /\ (((e1) = (op (op (e0) (e0)) (op (e0) (e0)))) /\ ((e3) = (op (e0) (e0)))))) (-. (((e0) = (op (op (e3) (e3)) (e3))) /\ (((e2) = (op (op (e3) (e3)) (op (e3) (e3)))) /\ ((e1) = (op (e3) (e3)))))) (-. (((e0) = (op (op (e1) (e1)) (e1))) /\ (((e3) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e2) = (op (e1) (e1)))))) (-. (((e1) = (op (op (e2) (e2)) (e2))) /\ (((e0) = (op (op (e2) (e2)) (op (e2) (e2)))) /\ ((e3) = (op (e2) (e2)))))) (-. (((e2) = (op (op (e1) (e1)) (e1))) /\ (((e0) = (op (op (e1) (e1)) (op (e1) (e1)))) /\ ((e3) = (op (e1) (e1)))))) (-. (((e0) = (op (op (e2) (e2)) (e2))) /\ (((e3) = (op (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 381
% 2.77/2.99 % SZS output end Proof
% 2.77/2.99 (* END-PROOF *)
%------------------------------------------------------------------------------