TSTP Solution File: ALG187+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : ALG187+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 : n032.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 18:06:10 EDT 2022
% Result : Theorem 0.52s 0.77s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG187+1 : TPTP v8.1.0. Released v2.7.0.
% 0.00/0.10 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Wed Jun 8 07:22:36 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.52/0.77 % SZS status Theorem
% 0.52/0.77 (* PROOF-FOUND *)
% 0.52/0.77 (* BEGIN-PROOF *)
% 0.52/0.77 % SZS output start Proof
% 0.52/0.77 1. ((op (e4) (e0)) = (e0)) ((e0) != (op (e4) (e0))) ### Sym(=)
% 0.52/0.77 2. ((op (e4) (e0)) = (e0)) ((e0) != (op (e4) (e0))) ### Sym(=)
% 0.52/0.77 3. ((e2) != (e2)) ### NotEqual
% 0.52/0.77 4. ((e0) != (e2)) ((op (e4) (e0)) = (e2)) ((op (e4) (e0)) = (e0)) ### TransEq 1 2 3
% 0.52/0.77 5. ((op (e4) (e1)) = (e1)) ((e1) != (op (e4) (e1))) ### Sym(=)
% 0.52/0.77 6. ((op (e4) (e1)) = (e1)) ((e1) != (op (e4) (e1))) ### Sym(=)
% 0.52/0.77 7. ((e3) != (e3)) ### NotEqual
% 0.52/0.77 8. ((e1) != (e3)) ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) = (e1)) ### TransEq 5 6 7
% 0.52/0.77 9. ((op (e4) (e2)) = (e2)) ((e2) != (op (e4) (e2))) ### Sym(=)
% 0.52/0.77 10. ((op (e4) (e2)) = (e2)) ((e2) != (op (e4) (e2))) ### Sym(=)
% 0.52/0.77 11. ((e1) != (e1)) ### NotEqual
% 0.52/0.77 12. ((e1) != (e2)) ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) = (e2)) ### TransEq-sym 9 10 11
% 0.52/0.77 13. ((op (e4) (e3)) = (e3)) ((e3) != (op (e4) (e3))) ### Sym(=)
% 0.52/0.77 14. ((op (e4) (e3)) = (e3)) ((e3) != (op (e4) (e3))) ### Sym(=)
% 0.52/0.77 15. ((e4) != (e4)) ### NotEqual
% 0.52/0.77 16. ((e3) != (e4)) ((op (e4) (e3)) = (e4)) ((op (e4) (e3)) = (e3)) ### TransEq 13 14 15
% 0.52/0.77 17. ((op (e4) (e4)) = (e4)) ((e4) != (op (e4) (e4))) ### Sym(=)
% 0.52/0.77 18. ((op (e4) (e4)) = (e4)) ((e4) != (op (e4) (e4))) ### Sym(=)
% 0.52/0.77 19. ((e0) != (e0)) ### NotEqual
% 0.52/0.77 20. ((e0) != (e4)) ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) = (e4)) ### TransEq-sym 17 18 19
% 0.52/0.77 21. (-. (((op (e4) (e0)) != (e0)) /\ (((op (e4) (e1)) != (e1)) /\ (((op (e4) (e2)) != (e2)) /\ (((op (e4) (e3)) != (e3)) /\ ((op (e4) (e4)) != (e4))))))) ((op (e4) (e4)) = (e0)) ((e0) != (e4)) ((op (e4) (e3)) = (e4)) ((e3) != (e4)) ((op (e4) (e2)) = (e1)) ((e1) != (e2)) ((op (e4) (e1)) = (e3)) ((e1) != (e3)) ((op (e4) (e0)) = (e2)) ((e0) != (e2)) ### DisjTree 4 8 12 16 20
% 0.52/0.77 22. (-. ((((op (e0) (e0)) != (e0)) /\ (((op (e0) (e1)) != (e1)) /\ (((op (e0) (e2)) != (e2)) /\ (((op (e0) (e3)) != (e3)) /\ ((op (e0) (e4)) != (e4)))))) \/ ((((op (e1) (e0)) != (e0)) /\ (((op (e1) (e1)) != (e1)) /\ (((op (e1) (e2)) != (e2)) /\ (((op (e1) (e3)) != (e3)) /\ ((op (e1) (e4)) != (e4)))))) \/ ((((op (e2) (e0)) != (e0)) /\ (((op (e2) (e1)) != (e1)) /\ (((op (e2) (e2)) != (e2)) /\ (((op (e2) (e3)) != (e3)) /\ ((op (e2) (e4)) != (e4)))))) \/ ((((op (e3) (e0)) != (e0)) /\ (((op (e3) (e1)) != (e1)) /\ (((op (e3) (e2)) != (e2)) /\ (((op (e3) (e3)) != (e3)) /\ ((op (e3) (e4)) != (e4)))))) \/ (((op (e4) (e0)) != (e0)) /\ (((op (e4) (e1)) != (e1)) /\ (((op (e4) (e2)) != (e2)) /\ (((op (e4) (e3)) != (e3)) /\ ((op (e4) (e4)) != (e4))))))))))) ((e0) != (e2)) ((op (e4) (e0)) = (e2)) ((e1) != (e3)) ((op (e4) (e1)) = (e3)) ((e1) != (e2)) ((op (e4) (e2)) = (e1)) ((e3) != (e4)) ((op (e4) (e3)) = (e4)) ((e0) != (e4)) ((op (e4) (e4)) = (e0)) ### ConjTree 21
% 0.52/0.77 23. ((op (e0) (e0)) = (e4)) ((op (e0) (e0)) != (e4)) ### Axiom
% 0.52/0.77 24. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e0)) = (e3)) \/ ((op (e0) (e0)) = (e4))))))) ((op (e0) (e0)) = (e4)) ### ConjTree 23
% 0.52/0.77 25. ((op (e0) (e1)) = (e2)) ((op (e0) (e1)) != (e2)) ### Axiom
% 0.52/0.77 26. (-. (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e1)) = (e3)) \/ ((op (e0) (e1)) = (e4))))))) ((op (e0) (e1)) = (e2)) ### ConjTree 25
% 0.52/0.77 27. ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (e0)) ### Axiom
% 0.52/0.77 28. (-. (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e2)) = (e4))))))) ((op (e0) (e2)) = (e0)) ### ConjTree 27
% 0.52/0.77 29. ((op (e0) (e3)) = (e1)) ((op (e0) (e3)) != (e1)) ### Axiom
% 0.52/0.77 30. (-. (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ (((op (e0) (e3)) = (e3)) \/ ((op (e0) (e3)) = (e4))))))) ((op (e0) (e3)) = (e1)) ### ConjTree 29
% 0.52/0.77 31. ((op (e0) (e4)) = (e3)) ((op (e0) (e4)) != (e3)) ### Axiom
% 0.52/0.77 32. (-. (((op (e0) (e4)) = (e0)) \/ (((op (e0) (e4)) = (e1)) \/ (((op (e0) (e4)) = (e2)) \/ (((op (e0) (e4)) = (e3)) \/ ((op (e0) (e4)) = (e4))))))) ((op (e0) (e4)) = (e3)) ### ConjTree 31
% 0.52/0.77 33. ((op (e1) (e0)) = (e0)) ((op (e1) (e0)) != (e0)) ### Axiom
% 0.52/0.77 34. (-. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e3)) \/ ((op (e1) (e0)) = (e4))))))) ((op (e1) (e0)) = (e0)) ### ConjTree 33
% 0.52/0.77 35. ((op (e1) (e1)) = (e1)) ((op (e1) (e1)) != (e1)) ### Axiom
% 0.52/0.77 36. (-. (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e3)) \/ ((op (e1) (e1)) = (e4))))))) ((op (e1) (e1)) = (e1)) ### ConjTree 35
% 0.52/0.77 37. ((op (e1) (e2)) = (e2)) ((op (e1) (e2)) != (e2)) ### Axiom
% 0.52/0.77 38. (-. (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e2)) = (e4))))))) ((op (e1) (e2)) = (e2)) ### ConjTree 37
% 0.52/0.77 39. ((op (e1) (e3)) = (e3)) ((op (e1) (e3)) != (e3)) ### Axiom
% 0.52/0.77 40. (-. (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e3)) \/ ((op (e1) (e3)) = (e4))))))) ((op (e1) (e3)) = (e3)) ### ConjTree 39
% 0.52/0.77 41. ((op (e1) (e4)) = (e4)) ((op (e1) (e4)) != (e4)) ### Axiom
% 0.52/0.77 42. (-. (((op (e1) (e4)) = (e0)) \/ (((op (e1) (e4)) = (e1)) \/ (((op (e1) (e4)) = (e2)) \/ (((op (e1) (e4)) = (e3)) \/ ((op (e1) (e4)) = (e4))))))) ((op (e1) (e4)) = (e4)) ### ConjTree 41
% 0.52/0.77 43. ((op (e2) (e0)) = (e1)) ((op (e2) (e0)) != (e1)) ### Axiom
% 0.52/0.77 44. (-. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e2) (e0)) = (e4))))))) ((op (e2) (e0)) = (e1)) ### ConjTree 43
% 0.52/0.77 45. ((op (e2) (e1)) = (e4)) ((op (e2) (e1)) != (e4)) ### Axiom
% 0.52/0.77 46. (-. (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e2) (e1)) = (e4))))))) ((op (e2) (e1)) = (e4)) ### ConjTree 45
% 0.52/0.77 47. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 0.52/0.77 48. (-. (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e2)) = (e4))))))) ((op (e2) (e2)) = (e3)) ### ConjTree 47
% 0.52/0.77 49. ((op (e2) (e3)) = (e0)) ((op (e2) (e3)) != (e0)) ### Axiom
% 0.52/0.77 50. (-. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e2) (e3)) = (e4))))))) ((op (e2) (e3)) = (e0)) ### ConjTree 49
% 0.52/0.77 51. ((op (e2) (e4)) = (e2)) ((op (e2) (e4)) != (e2)) ### Axiom
% 0.52/0.77 52. (-. (((op (e2) (e4)) = (e0)) \/ (((op (e2) (e4)) = (e1)) \/ (((op (e2) (e4)) = (e2)) \/ (((op (e2) (e4)) = (e3)) \/ ((op (e2) (e4)) = (e4))))))) ((op (e2) (e4)) = (e2)) ### ConjTree 51
% 0.52/0.77 53. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 0.52/0.77 54. (-. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e4))))))) ((op (e3) (e0)) = (e3)) ### ConjTree 53
% 0.52/0.77 55. ((op (e3) (e1)) = (e0)) ((op (e3) (e1)) != (e0)) ### Axiom
% 0.52/0.77 56. (-. (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e4))))))) ((op (e3) (e1)) = (e0)) ### ConjTree 55
% 0.52/0.77 57. ((op (e3) (e2)) = (e4)) ((op (e3) (e2)) != (e4)) ### Axiom
% 0.52/0.77 58. (-. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e4))))))) ((op (e3) (e2)) = (e4)) ### ConjTree 57
% 0.52/0.77 59. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 0.52/0.77 60. (-. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e4))))))) ((op (e3) (e3)) = (e2)) ### ConjTree 59
% 0.52/0.77 61. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom
% 0.52/0.77 62. (-. (((op (e3) (e4)) = (e0)) \/ (((op (e3) (e4)) = (e1)) \/ (((op (e3) (e4)) = (e2)) \/ (((op (e3) (e4)) = (e3)) \/ ((op (e3) (e4)) = (e4))))))) ((op (e3) (e4)) = (e1)) ### ConjTree 61
% 0.52/0.77 63. ((op (e4) (e0)) = (e2)) ((op (e4) (e0)) != (e2)) ### Axiom
% 0.52/0.77 64. (-. (((op (e4) (e0)) = (e0)) \/ (((op (e4) (e0)) = (e1)) \/ (((op (e4) (e0)) = (e2)) \/ (((op (e4) (e0)) = (e3)) \/ ((op (e4) (e0)) = (e4))))))) ((op (e4) (e0)) = (e2)) ### ConjTree 63
% 0.52/0.77 65. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom
% 0.52/0.77 66. (-. (((op (e4) (e1)) = (e0)) \/ (((op (e4) (e1)) = (e1)) \/ (((op (e4) (e1)) = (e2)) \/ (((op (e4) (e1)) = (e3)) \/ ((op (e4) (e1)) = (e4))))))) ((op (e4) (e1)) = (e3)) ### ConjTree 65
% 0.52/0.77 67. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom
% 0.52/0.77 68. (-. (((op (e4) (e2)) = (e0)) \/ (((op (e4) (e2)) = (e1)) \/ (((op (e4) (e2)) = (e2)) \/ (((op (e4) (e2)) = (e3)) \/ ((op (e4) (e2)) = (e4))))))) ((op (e4) (e2)) = (e1)) ### ConjTree 67
% 0.52/0.77 69. ((op (e4) (e3)) = (e4)) ((op (e4) (e3)) != (e4)) ### Axiom
% 0.52/0.77 70. (-. (((op (e4) (e3)) = (e0)) \/ (((op (e4) (e3)) = (e1)) \/ (((op (e4) (e3)) = (e2)) \/ (((op (e4) (e3)) = (e3)) \/ ((op (e4) (e3)) = (e4))))))) ((op (e4) (e3)) = (e4)) ### ConjTree 69
% 0.52/0.77 71. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom
% 0.52/0.77 72. (-. (((op (e4) (e4)) = (e0)) \/ (((op (e4) (e4)) = (e1)) \/ (((op (e4) (e4)) = (e2)) \/ (((op (e4) (e4)) = (e3)) \/ ((op (e4) (e4)) = (e4))))))) ((op (e4) (e4)) = (e0)) ### ConjTree 71
% 0.52/0.77 73. ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (e0)) ### Axiom
% 0.52/0.77 74. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e3)) = (e0)) \/ ((op (e0) (e4)) = (e0))))))) ((op (e0) (e2)) = (e0)) ### ConjTree 73
% 0.52/0.77 75. ((op (e1) (e0)) = (e0)) ((op (e1) (e0)) != (e0)) ### Axiom
% 0.52/0.77 76. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e0)) \/ ((op (e4) (e0)) = (e0))))))) ((op (e1) (e0)) = (e0)) ### ConjTree 75
% 0.52/0.77 77. ((op (e0) (e3)) = (e1)) ((op (e0) (e3)) != (e1)) ### Axiom
% 0.52/0.77 78. (-. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e3)) = (e1)) \/ ((op (e0) (e4)) = (e1))))))) ((op (e0) (e3)) = (e1)) ### ConjTree 77
% 0.52/0.77 79. ((op (e2) (e0)) = (e1)) ((op (e2) (e0)) != (e1)) ### Axiom
% 0.52/0.77 80. (-. (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e1)) \/ ((op (e4) (e0)) = (e1))))))) ((op (e2) (e0)) = (e1)) ### ConjTree 79
% 0.52/0.77 81. ((op (e0) (e1)) = (e2)) ((op (e0) (e1)) != (e2)) ### Axiom
% 0.52/0.77 82. (-. (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e4)) = (e2))))))) ((op (e0) (e1)) = (e2)) ### ConjTree 81
% 0.52/0.77 83. ((op (e4) (e0)) = (e2)) ((op (e4) (e0)) != (e2)) ### Axiom
% 0.52/0.77 84. (-. (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e4) (e0)) = (e2))))))) ((op (e4) (e0)) = (e2)) ### ConjTree 83
% 0.52/0.77 85. ((op (e0) (e4)) = (e3)) ((op (e0) (e4)) != (e3)) ### Axiom
% 0.52/0.77 86. (-. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ (((op (e0) (e3)) = (e3)) \/ ((op (e0) (e4)) = (e3))))))) ((op (e0) (e4)) = (e3)) ### ConjTree 85
% 0.52/0.77 87. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 0.52/0.77 88. (-. (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ (((op (e3) (e0)) = (e3)) \/ ((op (e4) (e0)) = (e3))))))) ((op (e3) (e0)) = (e3)) ### ConjTree 87
% 0.52/0.77 89. ((op (e0) (e0)) = (e4)) ((op (e0) (e0)) != (e4)) ### Axiom
% 0.52/0.77 90. (-. (((op (e0) (e0)) = (e4)) \/ (((op (e0) (e1)) = (e4)) \/ (((op (e0) (e2)) = (e4)) \/ (((op (e0) (e3)) = (e4)) \/ ((op (e0) (e4)) = (e4))))))) ((op (e0) (e0)) = (e4)) ### ConjTree 89
% 0.52/0.77 91. ((op (e0) (e0)) = (e4)) ((op (e0) (e0)) != (e4)) ### Axiom
% 0.52/0.77 92. (-. (((op (e0) (e0)) = (e4)) \/ (((op (e1) (e0)) = (e4)) \/ (((op (e2) (e0)) = (e4)) \/ (((op (e3) (e0)) = (e4)) \/ ((op (e4) (e0)) = (e4))))))) ((op (e0) (e0)) = (e4)) ### ConjTree 91
% 0.52/0.77 93. ((op (e1) (e0)) = (e0)) ((op (e1) (e0)) != (e0)) ### Axiom
% 0.52/0.77 94. (-. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ ((op (e1) (e4)) = (e0))))))) ((op (e1) (e0)) = (e0)) ### ConjTree 93
% 0.52/0.77 95. ((op (e3) (e1)) = (e0)) ((op (e3) (e1)) != (e0)) ### Axiom
% 0.52/0.77 96. (-. (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ ((op (e4) (e1)) = (e0))))))) ((op (e3) (e1)) = (e0)) ### ConjTree 95
% 0.52/0.77 97. ((op (e1) (e1)) = (e1)) ((op (e1) (e1)) != (e1)) ### Axiom
% 0.52/0.77 98. (-. (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ ((op (e1) (e4)) = (e1))))))) ((op (e1) (e1)) = (e1)) ### ConjTree 97
% 0.52/0.77 99. ((op (e1) (e1)) = (e1)) ((op (e1) (e1)) != (e1)) ### Axiom
% 0.52/0.77 100. (-. (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ ((op (e4) (e1)) = (e1))))))) ((op (e1) (e1)) = (e1)) ### ConjTree 99
% 0.52/0.77 101. ((op (e1) (e2)) = (e2)) ((op (e1) (e2)) != (e2)) ### Axiom
% 0.52/0.77 102. (-. (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e4)) = (e2))))))) ((op (e1) (e2)) = (e2)) ### ConjTree 101
% 0.52/0.77 103. ((op (e0) (e1)) = (e2)) ((op (e0) (e1)) != (e2)) ### Axiom
% 0.52/0.77 104. (-. (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e4) (e1)) = (e2))))))) ((op (e0) (e1)) = (e2)) ### ConjTree 103
% 0.52/0.77 105. ((op (e1) (e3)) = (e3)) ((op (e1) (e3)) != (e3)) ### Axiom
% 0.52/0.77 106. (-. (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ ((op (e1) (e4)) = (e3))))))) ((op (e1) (e3)) = (e3)) ### ConjTree 105
% 0.52/0.77 107. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom
% 0.52/0.77 108. (-. (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ ((op (e4) (e1)) = (e3))))))) ((op (e4) (e1)) = (e3)) ### ConjTree 107
% 0.52/0.77 109. ((op (e1) (e4)) = (e4)) ((op (e1) (e4)) != (e4)) ### Axiom
% 0.52/0.77 110. (-. (((op (e1) (e0)) = (e4)) \/ (((op (e1) (e1)) = (e4)) \/ (((op (e1) (e2)) = (e4)) \/ (((op (e1) (e3)) = (e4)) \/ ((op (e1) (e4)) = (e4))))))) ((op (e1) (e4)) = (e4)) ### ConjTree 109
% 0.52/0.77 111. ((op (e2) (e1)) = (e4)) ((op (e2) (e1)) != (e4)) ### Axiom
% 0.52/0.77 112. (-. (((op (e0) (e1)) = (e4)) \/ (((op (e1) (e1)) = (e4)) \/ (((op (e2) (e1)) = (e4)) \/ (((op (e3) (e1)) = (e4)) \/ ((op (e4) (e1)) = (e4))))))) ((op (e2) (e1)) = (e4)) ### ConjTree 111
% 0.52/0.77 113. ((op (e2) (e3)) = (e0)) ((op (e2) (e3)) != (e0)) ### Axiom
% 0.52/0.77 114. (-. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e2) (e4)) = (e0))))))) ((op (e2) (e3)) = (e0)) ### ConjTree 113
% 0.52/0.77 115. ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (e0)) ### Axiom
% 0.52/0.77 116. (-. (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e4) (e2)) = (e0))))))) ((op (e0) (e2)) = (e0)) ### ConjTree 115
% 0.52/0.77 117. ((op (e2) (e0)) = (e1)) ((op (e2) (e0)) != (e1)) ### Axiom
% 0.52/0.77 118. (-. (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e2) (e4)) = (e1))))))) ((op (e2) (e0)) = (e1)) ### ConjTree 117
% 0.52/0.77 119. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom
% 0.52/0.77 120. (-. (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e4) (e2)) = (e1))))))) ((op (e4) (e2)) = (e1)) ### ConjTree 119
% 0.52/0.77 121. ((op (e2) (e4)) = (e2)) ((op (e2) (e4)) != (e2)) ### Axiom
% 0.52/0.77 122. (-. (((op (e2) (e0)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e4)) = (e2))))))) ((op (e2) (e4)) = (e2)) ### ConjTree 121
% 0.52/0.77 123. ((op (e1) (e2)) = (e2)) ((op (e1) (e2)) != (e2)) ### Axiom
% 0.52/0.77 124. (-. (((op (e0) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e4) (e2)) = (e2))))))) ((op (e1) (e2)) = (e2)) ### ConjTree 123
% 0.52/0.77 125. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 0.52/0.77 126. (-. (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e2) (e4)) = (e3))))))) ((op (e2) (e2)) = (e3)) ### ConjTree 125
% 0.52/0.77 127. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 0.52/0.77 128. (-. (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e4) (e2)) = (e3))))))) ((op (e2) (e2)) = (e3)) ### ConjTree 127
% 0.52/0.77 129. ((op (e2) (e1)) = (e4)) ((op (e2) (e1)) != (e4)) ### Axiom
% 0.52/0.77 130. (-. (((op (e2) (e0)) = (e4)) \/ (((op (e2) (e1)) = (e4)) \/ (((op (e2) (e2)) = (e4)) \/ (((op (e2) (e3)) = (e4)) \/ ((op (e2) (e4)) = (e4))))))) ((op (e2) (e1)) = (e4)) ### ConjTree 129
% 0.52/0.77 131. ((op (e3) (e2)) = (e4)) ((op (e3) (e2)) != (e4)) ### Axiom
% 0.52/0.77 132. (-. (((op (e0) (e2)) = (e4)) \/ (((op (e1) (e2)) = (e4)) \/ (((op (e2) (e2)) = (e4)) \/ (((op (e3) (e2)) = (e4)) \/ ((op (e4) (e2)) = (e4))))))) ((op (e3) (e2)) = (e4)) ### ConjTree 131
% 0.52/0.77 133. ((op (e3) (e1)) = (e0)) ((op (e3) (e1)) != (e0)) ### Axiom
% 0.52/0.77 134. (-. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e3)) = (e0)) \/ ((op (e3) (e4)) = (e0))))))) ((op (e3) (e1)) = (e0)) ### ConjTree 133
% 0.52/0.77 135. ((op (e2) (e3)) = (e0)) ((op (e2) (e3)) != (e0)) ### Axiom
% 0.52/0.77 136. (-. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e0)) \/ ((op (e4) (e3)) = (e0))))))) ((op (e2) (e3)) = (e0)) ### ConjTree 135
% 0.52/0.77 137. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom
% 0.52/0.77 138. (-. (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e3)) = (e1)) \/ ((op (e3) (e4)) = (e1))))))) ((op (e3) (e4)) = (e1)) ### ConjTree 137
% 0.52/0.77 139. ((op (e0) (e3)) = (e1)) ((op (e0) (e3)) != (e1)) ### Axiom
% 0.52/0.77 140. (-. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e1)) \/ ((op (e4) (e3)) = (e1))))))) ((op (e0) (e3)) = (e1)) ### ConjTree 139
% 0.52/0.77 141. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 0.52/0.77 142. (-. (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e4)) = (e2))))))) ((op (e3) (e3)) = (e2)) ### ConjTree 141
% 0.52/0.77 143. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 0.52/0.77 144. (-. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e4) (e3)) = (e2))))))) ((op (e3) (e3)) = (e2)) ### ConjTree 143
% 0.52/0.77 145. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 0.52/0.77 146. (-. (((op (e3) (e0)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e3) (e4)) = (e3))))))) ((op (e3) (e0)) = (e3)) ### ConjTree 145
% 0.52/0.77 147. ((op (e1) (e3)) = (e3)) ((op (e1) (e3)) != (e3)) ### Axiom
% 0.52/0.77 148. (-. (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e4) (e3)) = (e3))))))) ((op (e1) (e3)) = (e3)) ### ConjTree 147
% 0.52/0.77 149. ((op (e3) (e2)) = (e4)) ((op (e3) (e2)) != (e4)) ### Axiom
% 0.52/0.77 150. (-. (((op (e3) (e0)) = (e4)) \/ (((op (e3) (e1)) = (e4)) \/ (((op (e3) (e2)) = (e4)) \/ (((op (e3) (e3)) = (e4)) \/ ((op (e3) (e4)) = (e4))))))) ((op (e3) (e2)) = (e4)) ### ConjTree 149
% 0.52/0.77 151. ((op (e4) (e3)) = (e4)) ((op (e4) (e3)) != (e4)) ### Axiom
% 0.52/0.77 152. (-. (((op (e0) (e3)) = (e4)) \/ (((op (e1) (e3)) = (e4)) \/ (((op (e2) (e3)) = (e4)) \/ (((op (e3) (e3)) = (e4)) \/ ((op (e4) (e3)) = (e4))))))) ((op (e4) (e3)) = (e4)) ### ConjTree 151
% 0.52/0.77 153. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom
% 0.52/0.77 154. (-. (((op (e4) (e0)) = (e0)) \/ (((op (e4) (e1)) = (e0)) \/ (((op (e4) (e2)) = (e0)) \/ (((op (e4) (e3)) = (e0)) \/ ((op (e4) (e4)) = (e0))))))) ((op (e4) (e4)) = (e0)) ### ConjTree 153
% 0.52/0.77 155. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom
% 0.52/0.77 156. (-. (((op (e0) (e4)) = (e0)) \/ (((op (e1) (e4)) = (e0)) \/ (((op (e2) (e4)) = (e0)) \/ (((op (e3) (e4)) = (e0)) \/ ((op (e4) (e4)) = (e0))))))) ((op (e4) (e4)) = (e0)) ### ConjTree 155
% 0.52/0.77 157. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom
% 0.52/0.77 158. (-. (((op (e4) (e0)) = (e1)) \/ (((op (e4) (e1)) = (e1)) \/ (((op (e4) (e2)) = (e1)) \/ (((op (e4) (e3)) = (e1)) \/ ((op (e4) (e4)) = (e1))))))) ((op (e4) (e2)) = (e1)) ### ConjTree 157
% 0.52/0.77 159. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom
% 0.52/0.77 160. (-. (((op (e0) (e4)) = (e1)) \/ (((op (e1) (e4)) = (e1)) \/ (((op (e2) (e4)) = (e1)) \/ (((op (e3) (e4)) = (e1)) \/ ((op (e4) (e4)) = (e1))))))) ((op (e3) (e4)) = (e1)) ### ConjTree 159
% 0.52/0.77 161. ((op (e4) (e0)) = (e2)) ((op (e4) (e0)) != (e2)) ### Axiom
% 0.52/0.77 162. (-. (((op (e4) (e0)) = (e2)) \/ (((op (e4) (e1)) = (e2)) \/ (((op (e4) (e2)) = (e2)) \/ (((op (e4) (e3)) = (e2)) \/ ((op (e4) (e4)) = (e2))))))) ((op (e4) (e0)) = (e2)) ### ConjTree 161
% 0.52/0.77 163. ((op (e2) (e4)) = (e2)) ((op (e2) (e4)) != (e2)) ### Axiom
% 0.52/0.77 164. (-. (((op (e0) (e4)) = (e2)) \/ (((op (e1) (e4)) = (e2)) \/ (((op (e2) (e4)) = (e2)) \/ (((op (e3) (e4)) = (e2)) \/ ((op (e4) (e4)) = (e2))))))) ((op (e2) (e4)) = (e2)) ### ConjTree 163
% 0.52/0.77 165. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom
% 0.52/0.77 166. (-. (((op (e4) (e0)) = (e3)) \/ (((op (e4) (e1)) = (e3)) \/ (((op (e4) (e2)) = (e3)) \/ (((op (e4) (e3)) = (e3)) \/ ((op (e4) (e4)) = (e3))))))) ((op (e4) (e1)) = (e3)) ### ConjTree 165
% 0.52/0.77 167. ((op (e0) (e4)) = (e3)) ((op (e0) (e4)) != (e3)) ### Axiom
% 0.52/0.77 168. (-. (((op (e0) (e4)) = (e3)) \/ (((op (e1) (e4)) = (e3)) \/ (((op (e2) (e4)) = (e3)) \/ (((op (e3) (e4)) = (e3)) \/ ((op (e4) (e4)) = (e3))))))) ((op (e0) (e4)) = (e3)) ### ConjTree 167
% 0.52/0.77 169. ((op (e4) (e3)) = (e4)) ((op (e4) (e3)) != (e4)) ### Axiom
% 0.52/0.77 170. (-. (((op (e4) (e0)) = (e4)) \/ (((op (e4) (e1)) = (e4)) \/ (((op (e4) (e2)) = (e4)) \/ (((op (e4) (e3)) = (e4)) \/ ((op (e4) (e4)) = (e4))))))) ((op (e4) (e3)) = (e4)) ### ConjTree 169
% 0.52/0.77 171. ((op (e1) (e4)) = (e4)) ((op (e1) (e4)) != (e4)) ### Axiom
% 0.52/0.77 172. (-. (((op (e0) (e4)) = (e4)) \/ (((op (e1) (e4)) = (e4)) \/ (((op (e2) (e4)) = (e4)) \/ (((op (e3) (e4)) = (e4)) \/ ((op (e4) (e4)) = (e4))))))) ((op (e1) (e4)) = (e4)) ### ConjTree 171
% 0.52/0.77 173. ((op (e0) (e0)) = (e4)) ((op (e0) (e0)) != (e4)) ### Axiom
% 0.52/0.77 174. ((op (e0) (e0)) = (e4)) ((op (e0) (e0)) != (e4)) ### Axiom
% 0.52/0.77 175. ((op (op (e0) (e0)) (op (e0) (e0))) != (op (e4) (e4))) ((op (e0) (e0)) = (e4)) ### NotEqual 173 174
% 0.52/0.77 176. ((op (op (e0) (e0)) (op (e0) (e0))) != (e0)) ((op (e4) (e4)) = (e0)) ((op (e0) (e0)) = (e4)) ### Trans 175 19
% 0.52/0.77 177. ((op (e1) (e0)) = (e0)) ((op (e1) (e0)) != (e0)) ### Axiom
% 0.52/0.77 178. ((op (e0) (e1)) = (e2)) ((op (e0) (e1)) != (e2)) ### Axiom
% 0.52/0.77 179. ((op (op (e1) (e0)) (op (e0) (e1))) != (op (e0) (e2))) ((op (e0) (e1)) = (e2)) ((op (e1) (e0)) = (e0)) ### NotEqual 177 178
% 0.52/0.77 180. ((op (op (e1) (e0)) (op (e0) (e1))) != (e0)) ((op (e0) (e2)) = (e0)) ((op (e1) (e0)) = (e0)) ((op (e0) (e1)) = (e2)) ### Trans 179 19
% 0.52/0.77 181. ((op (e2) (e0)) = (e1)) ((op (e2) (e0)) != (e1)) ### Axiom
% 0.52/0.77 182. ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (e0)) ### Axiom
% 0.52/0.77 183. ((op (op (e2) (e0)) (op (e0) (e2))) != (op (e1) (e0))) ((op (e0) (e2)) = (e0)) ((op (e2) (e0)) = (e1)) ### NotEqual 181 182
% 0.52/0.77 184. ((op (op (e2) (e0)) (op (e0) (e2))) != (e0)) ((op (e1) (e0)) = (e0)) ((op (e2) (e0)) = (e1)) ((op (e0) (e2)) = (e0)) ### Trans 183 19
% 0.52/0.77 185. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 0.52/0.77 186. ((op (e0) (e3)) = (e1)) ((op (e0) (e3)) != (e1)) ### Axiom
% 0.52/0.77 187. ((op (op (e3) (e0)) (op (e0) (e3))) != (op (e3) (e1))) ((op (e0) (e3)) = (e1)) ((op (e3) (e0)) = (e3)) ### NotEqual 185 186
% 0.52/0.77 188. ((op (op (e3) (e0)) (op (e0) (e3))) != (e0)) ((op (e3) (e1)) = (e0)) ((op (e3) (e0)) = (e3)) ((op (e0) (e3)) = (e1)) ### Trans 187 19
% 0.52/0.77 189. ((op (e4) (e0)) = (e2)) ((op (e4) (e0)) != (e2)) ### Axiom
% 0.52/0.77 190. ((op (e0) (e4)) = (e3)) ((op (e0) (e4)) != (e3)) ### Axiom
% 0.52/0.77 191. ((op (op (e4) (e0)) (op (e0) (e4))) != (op (e2) (e3))) ((op (e0) (e4)) = (e3)) ((op (e4) (e0)) = (e2)) ### NotEqual 189 190
% 0.52/0.77 192. ((op (op (e4) (e0)) (op (e0) (e4))) != (e0)) ((op (e2) (e3)) = (e0)) ((op (e4) (e0)) = (e2)) ((op (e0) (e4)) = (e3)) ### Trans 191 19
% 0.52/0.77 193. ((op (e0) (e1)) = (e2)) ((op (e0) (e1)) != (e2)) ### Axiom
% 0.52/0.77 194. ((op (e1) (e0)) = (e0)) ((op (e1) (e0)) != (e0)) ### Axiom
% 0.52/0.77 195. ((op (op (e0) (e1)) (op (e1) (e0))) != (op (e2) (e0))) ((op (e1) (e0)) = (e0)) ((op (e0) (e1)) = (e2)) ### NotEqual 193 194
% 0.52/0.77 196. ((op (op (e0) (e1)) (op (e1) (e0))) != (e1)) ((op (e2) (e0)) = (e1)) ((op (e0) (e1)) = (e2)) ((op (e1) (e0)) = (e0)) ### Trans 195 11
% 0.52/0.77 197. ((op (e1) (e1)) = (e1)) ((op (e1) (e1)) != (e1)) ### Axiom
% 0.52/0.77 198. ((op (e1) (e1)) = (e1)) ((op (e1) (e1)) != (e1)) ### Axiom
% 0.52/0.77 199. ((op (op (e1) (e1)) (op (e1) (e1))) != (op (e1) (e1))) ((op (e1) (e1)) = (e1)) ### NotEqual 197 198
% 0.60/0.77 200. ((op (op (e1) (e1)) (op (e1) (e1))) != (e1)) ((op (e1) (e1)) = (e1)) ### Trans 199 11
% 0.60/0.77 201. ((op (e2) (e1)) = (e4)) ((op (e2) (e1)) != (e4)) ### Axiom
% 0.60/0.77 202. ((op (e1) (e2)) = (e2)) ((op (e1) (e2)) != (e2)) ### Axiom
% 0.60/0.77 203. ((op (op (e2) (e1)) (op (e1) (e2))) != (op (e4) (e2))) ((op (e1) (e2)) = (e2)) ((op (e2) (e1)) = (e4)) ### NotEqual 201 202
% 0.60/0.77 204. ((op (op (e2) (e1)) (op (e1) (e2))) != (e1)) ((op (e4) (e2)) = (e1)) ((op (e2) (e1)) = (e4)) ((op (e1) (e2)) = (e2)) ### Trans 203 11
% 0.60/0.77 205. ((op (e3) (e1)) = (e0)) ((op (e3) (e1)) != (e0)) ### Axiom
% 0.60/0.77 206. ((op (e1) (e3)) = (e3)) ((op (e1) (e3)) != (e3)) ### Axiom
% 0.60/0.77 207. ((op (op (e3) (e1)) (op (e1) (e3))) != (op (e0) (e3))) ((op (e1) (e3)) = (e3)) ((op (e3) (e1)) = (e0)) ### NotEqual 205 206
% 0.60/0.77 208. ((op (op (e3) (e1)) (op (e1) (e3))) != (e1)) ((op (e0) (e3)) = (e1)) ((op (e3) (e1)) = (e0)) ((op (e1) (e3)) = (e3)) ### Trans 207 11
% 0.60/0.77 209. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom
% 0.60/0.77 210. ((op (e1) (e4)) = (e4)) ((op (e1) (e4)) != (e4)) ### Axiom
% 0.60/0.77 211. ((op (op (e4) (e1)) (op (e1) (e4))) != (op (e3) (e4))) ((op (e1) (e4)) = (e4)) ((op (e4) (e1)) = (e3)) ### NotEqual 209 210
% 0.60/0.77 212. ((op (op (e4) (e1)) (op (e1) (e4))) != (e1)) ((op (e3) (e4)) = (e1)) ((op (e4) (e1)) = (e3)) ((op (e1) (e4)) = (e4)) ### Trans 211 11
% 0.60/0.77 213. ((op (e0) (e2)) = (e0)) ((op (e0) (e2)) != (e0)) ### Axiom
% 0.60/0.77 214. ((op (e2) (e0)) = (e1)) ((op (e2) (e0)) != (e1)) ### Axiom
% 0.60/0.77 215. ((op (op (e0) (e2)) (op (e2) (e0))) != (op (e0) (e1))) ((op (e2) (e0)) = (e1)) ((op (e0) (e2)) = (e0)) ### NotEqual 213 214
% 0.60/0.77 216. ((op (op (e0) (e2)) (op (e2) (e0))) != (e2)) ((op (e0) (e1)) = (e2)) ((op (e0) (e2)) = (e0)) ((op (e2) (e0)) = (e1)) ### Trans 215 3
% 0.60/0.77 217. ((op (e1) (e2)) = (e2)) ((op (e1) (e2)) != (e2)) ### Axiom
% 0.60/0.77 218. ((op (e2) (e1)) = (e4)) ((op (e2) (e1)) != (e4)) ### Axiom
% 0.60/0.77 219. ((op (op (e1) (e2)) (op (e2) (e1))) != (op (e2) (e4))) ((op (e2) (e1)) = (e4)) ((op (e1) (e2)) = (e2)) ### NotEqual 217 218
% 0.60/0.77 220. ((op (op (e1) (e2)) (op (e2) (e1))) != (e2)) ((op (e2) (e4)) = (e2)) ((op (e1) (e2)) = (e2)) ((op (e2) (e1)) = (e4)) ### Trans 219 3
% 0.60/0.77 221. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 0.60/0.77 222. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 0.60/0.77 223. ((op (op (e2) (e2)) (op (e2) (e2))) != (op (e3) (e3))) ((op (e2) (e2)) = (e3)) ### NotEqual 221 222
% 0.60/0.77 224. ((op (op (e2) (e2)) (op (e2) (e2))) != (e2)) ((op (e3) (e3)) = (e2)) ((op (e2) (e2)) = (e3)) ### Trans 223 3
% 0.60/0.77 225. ((op (e3) (e2)) = (e4)) ((op (e3) (e2)) != (e4)) ### Axiom
% 0.60/0.77 226. ((op (e2) (e3)) = (e0)) ((op (e2) (e3)) != (e0)) ### Axiom
% 0.60/0.77 227. ((op (op (e3) (e2)) (op (e2) (e3))) != (op (e4) (e0))) ((op (e2) (e3)) = (e0)) ((op (e3) (e2)) = (e4)) ### NotEqual 225 226
% 0.60/0.77 228. ((op (op (e3) (e2)) (op (e2) (e3))) != (e2)) ((op (e4) (e0)) = (e2)) ((op (e3) (e2)) = (e4)) ((op (e2) (e3)) = (e0)) ### Trans 227 3
% 0.60/0.77 229. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom
% 0.60/0.77 230. ((op (e2) (e4)) = (e2)) ((op (e2) (e4)) != (e2)) ### Axiom
% 0.60/0.77 231. ((op (op (e4) (e2)) (op (e2) (e4))) != (op (e1) (e2))) ((op (e2) (e4)) = (e2)) ((op (e4) (e2)) = (e1)) ### NotEqual 229 230
% 0.60/0.77 232. ((op (op (e4) (e2)) (op (e2) (e4))) != (e2)) ((op (e1) (e2)) = (e2)) ((op (e4) (e2)) = (e1)) ((op (e2) (e4)) = (e2)) ### Trans 231 3
% 0.60/0.77 233. ((op (e0) (e3)) = (e1)) ((op (e0) (e3)) != (e1)) ### Axiom
% 0.60/0.77 234. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 0.60/0.77 235. ((op (op (e0) (e3)) (op (e3) (e0))) != (op (e1) (e3))) ((op (e3) (e0)) = (e3)) ((op (e0) (e3)) = (e1)) ### NotEqual 233 234
% 0.60/0.77 236. ((op (op (e0) (e3)) (op (e3) (e0))) != (e3)) ((op (e1) (e3)) = (e3)) ((op (e0) (e3)) = (e1)) ((op (e3) (e0)) = (e3)) ### Trans 235 7
% 0.60/0.77 237. ((op (e1) (e3)) = (e3)) ((op (e1) (e3)) != (e3)) ### Axiom
% 0.60/0.77 238. ((op (e3) (e1)) = (e0)) ((op (e3) (e1)) != (e0)) ### Axiom
% 0.60/0.77 239. ((op (op (e1) (e3)) (op (e3) (e1))) != (op (e3) (e0))) ((op (e3) (e1)) = (e0)) ((op (e1) (e3)) = (e3)) ### NotEqual 237 238
% 0.60/0.77 240. ((op (op (e1) (e3)) (op (e3) (e1))) != (e3)) ((op (e3) (e0)) = (e3)) ((op (e1) (e3)) = (e3)) ((op (e3) (e1)) = (e0)) ### Trans 239 7
% 0.60/0.77 241. ((op (e2) (e3)) = (e0)) ((op (e2) (e3)) != (e0)) ### Axiom
% 0.60/0.77 242. ((op (e3) (e2)) = (e4)) ((op (e3) (e2)) != (e4)) ### Axiom
% 0.60/0.77 243. ((op (op (e2) (e3)) (op (e3) (e2))) != (op (e0) (e4))) ((op (e3) (e2)) = (e4)) ((op (e2) (e3)) = (e0)) ### NotEqual 241 242
% 0.60/0.77 244. ((op (op (e2) (e3)) (op (e3) (e2))) != (e3)) ((op (e0) (e4)) = (e3)) ((op (e2) (e3)) = (e0)) ((op (e3) (e2)) = (e4)) ### Trans 243 7
% 0.60/0.77 245. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 0.60/0.77 246. ((op (e3) (e3)) = (e2)) ((op (e3) (e3)) != (e2)) ### Axiom
% 0.60/0.77 247. ((op (op (e3) (e3)) (op (e3) (e3))) != (op (e2) (e2))) ((op (e3) (e3)) = (e2)) ### NotEqual 245 246
% 0.60/0.77 248. ((op (op (e3) (e3)) (op (e3) (e3))) != (e3)) ((op (e2) (e2)) = (e3)) ((op (e3) (e3)) = (e2)) ### Trans 247 7
% 0.60/0.77 249. ((op (e4) (e3)) = (e4)) ((op (e4) (e3)) != (e4)) ### Axiom
% 0.60/0.77 250. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom
% 0.60/0.77 251. ((op (op (e4) (e3)) (op (e3) (e4))) != (op (e4) (e1))) ((op (e3) (e4)) = (e1)) ((op (e4) (e3)) = (e4)) ### NotEqual 249 250
% 0.60/0.77 252. ((op (op (e4) (e3)) (op (e3) (e4))) != (e3)) ((op (e4) (e1)) = (e3)) ((op (e4) (e3)) = (e4)) ((op (e3) (e4)) = (e1)) ### Trans 251 7
% 0.60/0.77 253. ((op (e0) (e4)) = (e3)) ((op (e0) (e4)) != (e3)) ### Axiom
% 0.60/0.77 254. ((op (e4) (e0)) = (e2)) ((op (e4) (e0)) != (e2)) ### Axiom
% 0.60/0.77 255. ((op (op (e0) (e4)) (op (e4) (e0))) != (op (e3) (e2))) ((op (e4) (e0)) = (e2)) ((op (e0) (e4)) = (e3)) ### NotEqual 253 254
% 0.60/0.77 256. ((op (op (e0) (e4)) (op (e4) (e0))) != (e4)) ((op (e3) (e2)) = (e4)) ((op (e0) (e4)) = (e3)) ((op (e4) (e0)) = (e2)) ### Trans 255 15
% 0.60/0.77 257. ((op (e1) (e4)) = (e4)) ((op (e1) (e4)) != (e4)) ### Axiom
% 0.60/0.77 258. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom
% 0.60/0.77 259. ((op (op (e1) (e4)) (op (e4) (e1))) != (op (e4) (e3))) ((op (e4) (e1)) = (e3)) ((op (e1) (e4)) = (e4)) ### NotEqual 257 258
% 0.60/0.77 260. ((op (op (e1) (e4)) (op (e4) (e1))) != (e4)) ((op (e4) (e3)) = (e4)) ((op (e1) (e4)) = (e4)) ((op (e4) (e1)) = (e3)) ### Trans 259 15
% 0.60/0.77 261. ((op (e2) (e4)) = (e2)) ((op (e2) (e4)) != (e2)) ### Axiom
% 0.60/0.77 262. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom
% 0.60/0.77 263. ((op (op (e2) (e4)) (op (e4) (e2))) != (op (e2) (e1))) ((op (e4) (e2)) = (e1)) ((op (e2) (e4)) = (e2)) ### NotEqual 261 262
% 0.60/0.77 264. ((op (op (e2) (e4)) (op (e4) (e2))) != (e4)) ((op (e2) (e1)) = (e4)) ((op (e2) (e4)) = (e2)) ((op (e4) (e2)) = (e1)) ### Trans 263 15
% 0.60/0.77 265. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom
% 0.60/0.77 266. ((op (e4) (e3)) = (e4)) ((op (e4) (e3)) != (e4)) ### Axiom
% 0.60/0.77 267. ((op (op (e3) (e4)) (op (e4) (e3))) != (op (e1) (e4))) ((op (e4) (e3)) = (e4)) ((op (e3) (e4)) = (e1)) ### NotEqual 265 266
% 0.60/0.77 268. ((op (op (e3) (e4)) (op (e4) (e3))) != (e4)) ((op (e1) (e4)) = (e4)) ((op (e3) (e4)) = (e1)) ((op (e4) (e3)) = (e4)) ### Trans 267 15
% 0.60/0.77 269. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom
% 0.60/0.77 270. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom
% 0.60/0.77 271. ((op (op (e4) (e4)) (op (e4) (e4))) != (op (e0) (e0))) ((op (e4) (e4)) = (e0)) ### NotEqual 269 270
% 0.60/0.77 272. ((op (op (e4) (e4)) (op (e4) (e4))) != (e4)) ((op (e0) (e0)) = (e4)) ((op (e4) (e4)) = (e0)) ### Trans 271 15
% 0.60/0.77 273. (-. (((((op (e0) (e0)) != (e0)) /\ (((op (e0) (e1)) != (e1)) /\ (((op (e0) (e2)) != (e2)) /\ (((op (e0) (e3)) != (e3)) /\ ((op (e0) (e4)) != (e4)))))) \/ ((((op (e1) (e0)) != (e0)) /\ (((op (e1) (e1)) != (e1)) /\ (((op (e1) (e2)) != (e2)) /\ (((op (e1) (e3)) != (e3)) /\ ((op (e1) (e4)) != (e4)))))) \/ ((((op (e2) (e0)) != (e0)) /\ (((op (e2) (e1)) != (e1)) /\ (((op (e2) (e2)) != (e2)) /\ (((op (e2) (e3)) != (e3)) /\ ((op (e2) (e4)) != (e4)))))) \/ ((((op (e3) (e0)) != (e0)) /\ (((op (e3) (e1)) != (e1)) /\ (((op (e3) (e2)) != (e2)) /\ (((op (e3) (e3)) != (e3)) /\ ((op (e3) (e4)) != (e4)))))) \/ (((op (e4) (e0)) != (e0)) /\ (((op (e4) (e1)) != (e1)) /\ (((op (e4) (e2)) != (e2)) /\ (((op (e4) (e3)) != (e3)) /\ ((op (e4) (e4)) != (e4)))))))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e0)) = (e3)) \/ ((op (e0) (e0)) = (e4)))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e1)) = (e3)) \/ ((op (e0) (e1)) = (e4)))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e2)) = (e4)))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ (((op (e0) (e3)) = (e3)) \/ ((op (e0) (e3)) = (e4)))))) /\ ((((op (e0) (e4)) = (e0)) \/ (((op (e0) (e4)) = (e1)) \/ (((op (e0) (e4)) = (e2)) \/ (((op (e0) (e4)) = (e3)) \/ ((op (e0) (e4)) = (e4)))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e3)) \/ ((op (e1) (e0)) = (e4)))))) /\ ((((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e3)) \/ ((op (e1) (e1)) = (e4)))))) /\ ((((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e2)) = (e4)))))) /\ ((((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e3)) \/ ((op (e1) (e3)) = (e4)))))) /\ ((((op (e1) (e4)) = (e0)) \/ (((op (e1) (e4)) = (e1)) \/ (((op (e1) (e4)) = (e2)) \/ (((op (e1) (e4)) = (e3)) \/ ((op (e1) (e4)) = (e4)))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e2) (e0)) = (e4)))))) /\ ((((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e2) (e1)) = (e4)))))) /\ ((((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e2)) = (e4)))))) /\ ((((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e2) (e3)) = (e4)))))) /\ ((((op (e2) (e4)) = (e0)) \/ (((op (e2) (e4)) = (e1)) \/ (((op (e2) (e4)) = (e2)) \/ (((op (e2) (e4)) = (e3)) \/ ((op (e2) (e4)) = (e4)))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ 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(e2)) \/ (((op (e4) (e2)) = (e3)) \/ ((op (e4) (e2)) = (e4)))))) /\ ((((op (e4) (e3)) = (e0)) \/ (((op (e4) (e3)) = (e1)) \/ (((op (e4) (e3)) = (e2)) \/ (((op (e4) (e3)) = (e3)) \/ ((op (e4) (e3)) = (e4)))))) /\ ((((op (e4) (e4)) = (e0)) \/ (((op (e4) (e4)) = (e1)) \/ (((op (e4) (e4)) = (e2)) \/ (((op (e4) (e4)) = (e3)) \/ ((op (e4) (e4)) = (e4)))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e3)) = (e0)) \/ ((op (e0) (e4)) = (e0)))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e0)) \/ ((op (e4) (e0)) = (e0)))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e3)) = (e1)) \/ ((op (e0) (e4)) = (e1)))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e1)) \/ ((op (e4) (e0)) = (e1)))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) 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(((op (op (e4) (e1)) (op (e1) (e4))) = (e1)) /\ (((op (op (e0) (e2)) (op (e2) (e0))) = (e2)) /\ (((op (op (e1) (e2)) (op (e2) (e1))) = (e2)) /\ (((op (op (e2) (e2)) (op (e2) (e2))) = (e2)) /\ (((op (op (e3) (e2)) (op (e2) (e3))) = (e2)) /\ (((op (op (e4) (e2)) (op (e2) (e4))) = (e2)) /\ (((op (op (e0) (e3)) (op (e3) (e0))) = (e3)) /\ (((op (op (e1) (e3)) (op (e3) (e1))) = (e3)) /\ (((op (op (e2) (e3)) (op (e3) (e2))) = (e3)) /\ (((op (op (e3) (e3)) (op (e3) (e3))) = (e3)) /\ (((op (op (e4) (e3)) (op (e3) (e4))) = (e3)) /\ (((op (op (e0) (e4)) (op (e4) (e0))) = (e4)) /\ (((op (op (e1) (e4)) (op (e4) (e1))) = (e4)) /\ (((op (op (e2) (e4)) (op (e4) (e2))) = (e4)) /\ (((op (op (e3) (e4)) (op (e4) (e3))) = (e4)) /\ ((op (op (e4) (e4)) (op (e4) (e4))) = (e4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ### ConjTree 273
% 0.60/0.78 275. (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e0) != (e4)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ (((e1) != (e4)) /\ (((e2) != (e3)) /\ (((e2) != (e4)) /\ ((e3) != (e4))))))))))) (-. 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(e4)) \/ (((op (e1) (e3)) = (e4)) \/ (((op (e2) (e3)) = (e4)) \/ (((op (e3) (e3)) = (e4)) \/ ((op (e4) (e3)) = (e4)))))) /\ ((((op (e4) (e0)) = (e0)) \/ (((op (e4) (e1)) = (e0)) \/ (((op (e4) (e2)) = (e0)) \/ (((op (e4) (e3)) = (e0)) \/ ((op (e4) (e4)) = (e0)))))) /\ ((((op (e0) (e4)) = (e0)) \/ (((op (e1) (e4)) = (e0)) \/ (((op (e2) (e4)) = (e0)) \/ (((op (e3) (e4)) = (e0)) \/ ((op (e4) (e4)) = (e0)))))) /\ ((((op (e4) (e0)) = (e1)) \/ (((op (e4) (e1)) = (e1)) \/ (((op (e4) (e2)) = (e1)) \/ (((op (e4) (e3)) = (e1)) \/ ((op (e4) (e4)) = (e1)))))) /\ ((((op (e0) (e4)) = (e1)) \/ (((op (e1) (e4)) = (e1)) \/ (((op (e2) (e4)) = (e1)) \/ (((op (e3) (e4)) = (e1)) \/ ((op (e4) (e4)) = (e1)))))) /\ ((((op (e4) (e0)) = (e2)) \/ (((op (e4) (e1)) = (e2)) \/ (((op (e4) (e2)) = (e2)) \/ (((op (e4) (e3)) = (e2)) \/ ((op (e4) (e4)) = (e2)))))) /\ ((((op (e0) (e4)) = (e2)) \/ (((op (e1) (e4)) = (e2)) \/ (((op (e2) (e4)) = (e2)) \/ (((op (e3) (e4)) = (e2)) \/ ((op (e4) (e4)) = (e2)))))) /\ ((((op (e4) (e0)) = (e3)) \/ (((op (e4) (e1)) = (e3)) \/ (((op (e4) (e2)) = (e3)) \/ (((op (e4) (e3)) = (e3)) \/ ((op (e4) (e4)) = (e3)))))) /\ ((((op (e0) (e4)) = (e3)) \/ (((op (e1) (e4)) = (e3)) \/ (((op (e2) (e4)) = (e3)) \/ (((op (e3) (e4)) = (e3)) \/ ((op (e4) (e4)) = (e3)))))) /\ ((((op (e4) (e0)) = (e4)) \/ (((op (e4) (e1)) = (e4)) \/ (((op (e4) (e2)) = (e4)) \/ (((op (e4) (e3)) = (e4)) \/ ((op (e4) (e4)) = (e4)))))) /\ ((((op (e0) (e4)) = (e4)) \/ (((op (e1) (e4)) = (e4)) \/ (((op (e2) (e4)) = (e4)) \/ (((op (e3) (e4)) = (e4)) \/ ((op (e4) (e4)) = (e4)))))) /\ (((op (op (e0) (e0)) (op (e0) (e0))) = (e0)) /\ (((op (op (e1) (e0)) (op (e0) (e1))) = (e0)) /\ (((op (op (e2) (e0)) (op (e0) (e2))) = (e0)) /\ (((op (op (e3) (e0)) (op (e0) (e3))) = (e0)) /\ (((op (op (e4) (e0)) (op (e0) (e4))) = (e0)) /\ (((op (op (e0) (e1)) (op (e1) (e0))) = (e1)) /\ (((op (op (e1) (e1)) (op (e1) (e1))) = (e1)) /\ (((op (op (e2) (e1)) (op (e1) (e2))) = (e1)) /\ (((op (op (e3) (e1)) (op (e1) (e3))) = (e1)) /\ (((op (op (e4) (e1)) (op (e1) (e4))) = (e1)) /\ (((op (op (e0) (e2)) (op (e2) (e0))) = (e2)) /\ (((op (op (e1) (e2)) (op (e2) (e1))) = (e2)) /\ (((op (op (e2) (e2)) (op (e2) (e2))) = (e2)) /\ (((op (op (e3) (e2)) (op (e2) (e3))) = (e2)) /\ (((op (op (e4) (e2)) (op (e2) (e4))) = (e2)) /\ (((op (op (e0) (e3)) (op (e3) (e0))) = (e3)) /\ (((op (op (e1) (e3)) (op (e3) (e1))) = (e3)) /\ (((op (op (e2) (e3)) (op (e3) (e2))) = (e3)) /\ (((op (op (e3) (e3)) (op (e3) (e3))) = (e3)) /\ (((op (op (e4) (e3)) (op (e3) (e4))) = (e3)) /\ (((op (op (e0) (e4)) (op (e4) (e0))) = (e4)) /\ (((op (op (e1) (e4)) (op (e4) (e1))) = (e4)) /\ (((op (op (e2) (e4)) (op (e4) (e2))) = (e4)) /\ (((op (op (e3) (e4)) (op (e4) (e3))) = (e4)) /\ ((op (op (e4) (e4)) (op (e4) (e4))) = (e4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (((op (e0) (e0)) = (e4)) /\ (((op (e0) (e1)) = (e2)) /\ (((op (e0) (e2)) = (e0)) /\ (((op (e0) (e3)) = (e1)) /\ (((op (e0) (e4)) = (e3)) /\ (((op (e1) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e1) (e2)) = (e2)) /\ (((op (e1) (e3)) = (e3)) /\ (((op (e1) (e4)) = (e4)) /\ (((op (e2) (e0)) = (e1)) /\ (((op (e2) (e1)) = (e4)) /\ (((op (e2) (e2)) = (e3)) /\ (((op (e2) (e3)) = (e0)) /\ (((op (e2) (e4)) = (e2)) /\ (((op (e3) (e0)) = (e3)) /\ (((op (e3) (e1)) = (e0)) /\ (((op (e3) (e2)) = (e4)) /\ (((op (e3) (e3)) = (e2)) /\ (((op (e3) (e4)) = (e1)) /\ (((op (e4) (e0)) = (e2)) /\ (((op (e4) (e1)) = (e3)) /\ (((op (e4) (e2)) = (e1)) /\ (((op (e4) (e3)) = (e4)) /\ ((op (e4) (e4)) = (e0)))))))))))))))))))))))))) ### ConjTree 274
% 0.60/0.78 % SZS output end Proof
% 0.60/0.78 (* END-PROOF *)
%------------------------------------------------------------------------------