TSTP Solution File: ALG095+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : ALG095+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 18:05:00 EDT 2022
% Result : Theorem 0.99s 1.22s
% Output : Proof 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG095+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 8 21:04:03 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.99/1.22 % SZS status Theorem
% 0.99/1.22 (* PROOF-FOUND *)
% 0.99/1.22 (* BEGIN-PROOF *)
% 0.99/1.22 % SZS output start Proof
% 0.99/1.22 1. ((op (e3) (e2)) = (op (e2) (e3))) ((op (e3) (e2)) != (op (e2) (e3))) ### Axiom
% 0.99/1.22 2. ((e4) != (e4)) ### NotEqual
% 0.99/1.22 3. ((e4) != (op (e3) (e2))) ((op (e2) (e3)) = (e4)) ((op (e3) (e2)) = (op (e2) (e3))) ### Trans-sym 1 2
% 0.99/1.22 4. ((e0) != (e0)) ### NotEqual
% 0.99/1.22 5. ((e0) != (e4)) ((op (e3) (e2)) = (e0)) ((op (e3) (e2)) = (op (e2) (e3))) ((op (e2) (e3)) = (e4)) ### TransEq-sym 3 4 4
% 0.99/1.22 6. ((op (e2) (e3)) = (e4)) ((op (e2) (e3)) != (e4)) ### Axiom
% 0.99/1.22 7. ((e3) != (e3)) ### NotEqual
% 0.99/1.22 8. ((op (op (e2) (e3)) (e3)) != (op (e4) (e3))) ((op (e2) (e3)) = (e4)) ### NotEqual 6 7
% 0.99/1.22 9. ((e2) != (e2)) ### NotEqual
% 0.99/1.22 10. ((op (op (e2) (e3)) (e3)) != (e2)) ((op (e4) (e3)) = (e2)) ((op (e2) (e3)) = (e4)) ### Trans 8 9
% 0.99/1.22 11. ((op (e2) (e3)) = (e4)) ((e4) != (op (e2) (e3))) ### Sym(=)
% 0.99/1.22 12. ((op (e4) (e2)) != (op (op (e2) (e3)) (e2))) ((op (e2) (e3)) = (e4)) ### NotEqual 11 9
% 0.99/1.22 13. ((e3) != (op (e4) (e2))) ((op (op (e2) (e3)) (e2)) = (e3)) ((op (e2) (e3)) = (e4)) ### Trans-sym 12 7
% 0.99/1.22 14. ((e1) != (e1)) ### NotEqual
% 0.99/1.22 15. ((e1) != (e3)) ((op (e4) (e2)) = (e1)) ((op (e2) (e3)) = (e4)) ((op (op (e2) (e3)) (e2)) = (e3)) ### TransEq-sym 13 14 14
% 0.99/1.22 16. (-. (((op (e3) (e2)) != (op (e2) (e3))) /\ (((op (op (e2) (e3)) (e3)) = (e2)) /\ ((op (op (e2) (e3)) (e2)) != (e3))))) ((op (e4) (e2)) = (e1)) ((e1) != (e3)) ((op (e4) (e3)) = (e2)) ((op (e2) (e3)) = (e4)) ((op (e3) (e2)) = (e0)) ((e0) != (e4)) ### DisjTree 5 10 15
% 0.99/1.22 17. (-. ((((op (e0) (e0)) != (op (e0) (e0))) /\ (((op (op (e0) (e0)) (e0)) = (e0)) /\ ((op (op (e0) (e0)) (e0)) != (e0)))) \/ ((((op (e1) (e0)) != (op (e0) (e1))) /\ (((op (op (e0) (e1)) (e1)) = (e0)) /\ ((op (op (e0) (e1)) (e0)) != (e1)))) \/ ((((op (e2) (e0)) != (op (e0) (e2))) /\ (((op (op (e0) (e2)) (e2)) = (e0)) /\ ((op (op (e0) (e2)) (e0)) != (e2)))) \/ ((((op (e3) (e0)) != (op (e0) (e3))) /\ (((op (op (e0) (e3)) (e3)) = (e0)) /\ ((op (op (e0) (e3)) (e0)) != (e3)))) \/ ((((op (e4) (e0)) != (op (e0) (e4))) /\ (((op (op (e0) (e4)) (e4)) = (e0)) /\ ((op (op (e0) (e4)) (e0)) != (e4)))) \/ ((((op (e0) (e1)) != (op (e1) (e0))) /\ (((op (op (e1) (e0)) (e0)) = (e1)) /\ ((op (op (e1) (e0)) (e1)) != (e0)))) \/ ((((op (e1) (e1)) != (op (e1) (e1))) /\ (((op (op (e1) (e1)) (e1)) = (e1)) /\ ((op (op (e1) (e1)) (e1)) != (e1)))) \/ ((((op (e2) (e1)) != (op (e1) (e2))) /\ (((op (op (e1) (e2)) (e2)) = (e1)) /\ ((op (op (e1) (e2)) (e1)) != (e2)))) \/ ((((op (e3) (e1)) != (op (e1) (e3))) /\ (((op (op (e1) (e3)) (e3)) = (e1)) /\ ((op (op (e1) (e3)) (e1)) != (e3)))) \/ ((((op (e4) (e1)) != (op (e1) (e4))) /\ (((op (op (e1) (e4)) (e4)) = (e1)) /\ ((op (op (e1) (e4)) (e1)) != (e4)))) \/ ((((op (e0) (e2)) != (op (e2) (e0))) /\ (((op (op (e2) (e0)) (e0)) = (e2)) /\ ((op (op (e2) (e0)) (e2)) != (e0)))) \/ ((((op (e1) (e2)) != (op (e2) (e1))) /\ (((op (op (e2) (e1)) (e1)) = (e2)) /\ ((op (op (e2) (e1)) (e2)) != (e1)))) \/ ((((op (e2) (e2)) != (op (e2) (e2))) /\ (((op (op (e2) (e2)) (e2)) = (e2)) /\ ((op (op (e2) (e2)) (e2)) != (e2)))) \/ ((((op (e3) (e2)) != (op (e2) (e3))) /\ (((op (op (e2) (e3)) (e3)) = (e2)) /\ ((op (op (e2) (e3)) (e2)) != (e3)))) \/ ((((op (e4) (e2)) != (op (e2) (e4))) /\ (((op (op (e2) (e4)) (e4)) = (e2)) /\ ((op (op (e2) (e4)) (e2)) != (e4)))) \/ ((((op (e0) (e3)) != (op (e3) (e0))) /\ (((op (op (e3) (e0)) (e0)) = (e3)) /\ ((op (op (e3) (e0)) (e3)) != (e0)))) \/ ((((op (e1) (e3)) != (op (e3) (e1))) /\ (((op (op (e3) (e1)) (e1)) = (e3)) /\ ((op (op (e3) (e1)) (e3)) != (e1)))) \/ ((((op (e2) (e3)) != (op (e3) (e2))) /\ (((op (op (e3) (e2)) (e2)) = (e3)) /\ ((op (op (e3) (e2)) (e3)) != (e2)))) \/ ((((op (e3) (e3)) != (op (e3) (e3))) /\ (((op (op (e3) (e3)) (e3)) = (e3)) /\ ((op (op (e3) (e3)) (e3)) != (e3)))) \/ ((((op (e4) (e3)) != (op (e3) (e4))) /\ (((op (op (e3) (e4)) (e4)) = (e3)) /\ ((op (op (e3) (e4)) (e3)) != (e4)))) \/ ((((op (e0) (e4)) != (op (e4) (e0))) /\ (((op (op (e4) (e0)) (e0)) = (e4)) /\ ((op (op (e4) (e0)) (e4)) != (e0)))) \/ ((((op (e1) (e4)) != (op (e4) (e1))) /\ (((op (op (e4) (e1)) (e1)) = (e4)) /\ ((op (op (e4) (e1)) (e4)) != (e1)))) \/ ((((op (e2) (e4)) != (op (e4) (e2))) /\ (((op (op (e4) (e2)) (e2)) = (e4)) /\ ((op (op (e4) (e2)) (e4)) != (e2)))) \/ ((((op (e3) (e4)) != (op (e4) (e3))) /\ (((op (op (e4) (e3)) (e3)) = (e4)) /\ ((op (op (e4) (e3)) (e4)) != (e3)))) \/ (((op (e4) (e4)) != (op (e4) (e4))) /\ (((op (op (e4) (e4)) (e4)) = (e4)) /\ ((op (op (e4) (e4)) (e4)) != (e4))))))))))))))))))))))))))))) ((e0) != (e4)) ((op (e3) (e2)) = (e0)) ((op (e2) (e3)) = (e4)) ((op (e4) (e3)) = (e2)) ((e1) != (e3)) ((op (e4) (e2)) = (e1)) ### ConjTree 16
% 0.99/1.22 18. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 0.99/1.22 19. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e0)) = (e3)) \/ ((op (e0) (e0)) = (e4))))))) ((op (e0) (e0)) = (e0)) ### ConjTree 18
% 0.99/1.22 20. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom
% 0.99/1.22 21. (-. (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e1)) = (e3)) \/ ((op (e0) (e1)) = (e4))))))) ((op (e0) (e1)) = (e1)) ### ConjTree 20
% 0.99/1.22 22. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom
% 0.99/1.22 23. (-. (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e2)) = (e4))))))) ((op (e0) (e2)) = (e2)) ### ConjTree 22
% 0.99/1.22 24. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom
% 0.99/1.22 25. (-. (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ (((op (e0) (e3)) = (e3)) \/ ((op (e0) (e3)) = (e4))))))) ((op (e0) (e3)) = (e3)) ### ConjTree 24
% 0.99/1.22 26. ((op (e0) (e4)) = (e4)) ((op (e0) (e4)) != (e4)) ### Axiom
% 0.99/1.22 27. (-. (((op (e0) (e4)) = (e0)) \/ (((op (e0) (e4)) = (e1)) \/ (((op (e0) (e4)) = (e2)) \/ (((op (e0) (e4)) = (e3)) \/ ((op (e0) (e4)) = (e4))))))) ((op (e0) (e4)) = (e4)) ### ConjTree 26
% 0.99/1.22 28. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 0.99/1.22 29. (-. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e3)) \/ ((op (e1) (e0)) = (e4))))))) ((op (e1) (e0)) = (e1)) ### ConjTree 28
% 0.99/1.22 30. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 0.99/1.22 31. (-. (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e3)) \/ ((op (e1) (e1)) = (e4))))))) ((op (e1) (e1)) = (e2)) ### ConjTree 30
% 0.99/1.22 32. ((op (e1) (e2)) = (e4)) ((op (e1) (e2)) != (e4)) ### Axiom
% 0.99/1.22 33. (-. (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e2)) = (e4))))))) ((op (e1) (e2)) = (e4)) ### ConjTree 32
% 0.99/1.22 34. ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (e0)) ### Axiom
% 0.99/1.22 35. (-. (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e3)) \/ ((op (e1) (e3)) = (e4))))))) ((op (e1) (e3)) = (e0)) ### ConjTree 34
% 0.99/1.22 36. ((op (e1) (e4)) = (e3)) ((op (e1) (e4)) != (e3)) ### Axiom
% 0.99/1.22 37. (-. (((op (e1) (e4)) = (e0)) \/ (((op (e1) (e4)) = (e1)) \/ (((op (e1) (e4)) = (e2)) \/ (((op (e1) (e4)) = (e3)) \/ ((op (e1) (e4)) = (e4))))))) ((op (e1) (e4)) = (e3)) ### ConjTree 36
% 0.99/1.22 38. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 0.99/1.22 39. (-. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e2) (e0)) = (e4))))))) ((op (e2) (e0)) = (e2)) ### ConjTree 38
% 0.99/1.22 40. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom
% 0.99/1.22 41. (-. (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e2) (e1)) = (e4))))))) ((op (e2) (e1)) = (e0)) ### ConjTree 40
% 0.99/1.22 42. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 0.99/1.22 43. (-. (((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 42
% 0.99/1.22 44. ((op (e2) (e3)) = (e4)) ((op (e2) (e3)) != (e4)) ### Axiom
% 0.99/1.22 45. (-. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e2) (e3)) = (e4))))))) ((op (e2) (e3)) = (e4)) ### ConjTree 44
% 0.99/1.22 46. ((op (e2) (e4)) = (e1)) ((op (e2) (e4)) != (e1)) ### Axiom
% 0.99/1.22 47. (-. (((op (e2) (e4)) = (e0)) \/ (((op (e2) (e4)) = (e1)) \/ (((op (e2) (e4)) = (e2)) \/ (((op (e2) (e4)) = (e3)) \/ ((op (e2) (e4)) = (e4))))))) ((op (e2) (e4)) = (e1)) ### ConjTree 46
% 0.99/1.22 48. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 0.99/1.22 49. (-. (((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 48
% 0.99/1.22 50. ((op (e3) (e1)) = (e4)) ((op (e3) (e1)) != (e4)) ### Axiom
% 0.99/1.22 51. (-. (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e4))))))) ((op (e3) (e1)) = (e4)) ### ConjTree 50
% 0.99/1.22 52. ((op (e3) (e2)) = (e0)) ((op (e3) (e2)) != (e0)) ### Axiom
% 0.99/1.22 53. (-. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e4))))))) ((op (e3) (e2)) = (e0)) ### ConjTree 52
% 0.99/1.22 54. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 0.99/1.22 55. (-. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e4))))))) ((op (e3) (e3)) = (e1)) ### ConjTree 54
% 0.99/1.22 56. ((op (e3) (e4)) = (e2)) ((op (e3) (e4)) != (e2)) ### Axiom
% 0.99/1.22 57. (-. (((op (e3) (e4)) = (e0)) \/ (((op (e3) (e4)) = (e1)) \/ (((op (e3) (e4)) = (e2)) \/ (((op (e3) (e4)) = (e3)) \/ ((op (e3) (e4)) = (e4))))))) ((op (e3) (e4)) = (e2)) ### ConjTree 56
% 0.99/1.22 58. ((op (e4) (e0)) = (e4)) ((op (e4) (e0)) != (e4)) ### Axiom
% 0.99/1.22 59. (-. (((op (e4) (e0)) = (e0)) \/ (((op (e4) (e0)) = (e1)) \/ (((op (e4) (e0)) = (e2)) \/ (((op (e4) (e0)) = (e3)) \/ ((op (e4) (e0)) = (e4))))))) ((op (e4) (e0)) = (e4)) ### ConjTree 58
% 0.99/1.22 60. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom
% 0.99/1.22 61. (-. (((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 60
% 0.99/1.22 62. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom
% 0.99/1.22 63. (-. (((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 62
% 0.99/1.22 64. ((op (e4) (e3)) = (e2)) ((op (e4) (e3)) != (e2)) ### Axiom
% 0.99/1.22 65. (-. (((op (e4) (e3)) = (e0)) \/ (((op (e4) (e3)) = (e1)) \/ (((op (e4) (e3)) = (e2)) \/ (((op (e4) (e3)) = (e3)) \/ ((op (e4) (e3)) = (e4))))))) ((op (e4) (e3)) = (e2)) ### ConjTree 64
% 0.99/1.22 66. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom
% 0.99/1.22 67. (-. (((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 66
% 0.99/1.22 68. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 69. ((op (unit) (e0)) != (op (e0) (e0))) ((unit) = (e0)) ### NotEqual 68 4
% 0.99/1.22 70. ((op (unit) (e0)) != (e0)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ### Trans 69 4
% 0.99/1.22 71. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 72. ((op (e0) (unit)) != (op (e0) (e0))) ((unit) = (e0)) ### NotEqual 4 71
% 0.99/1.22 73. ((op (e0) (unit)) != (e0)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ### Trans 72 4
% 0.99/1.22 74. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 75. ((op (unit) (e1)) != (op (e0) (e1))) ((unit) = (e0)) ### NotEqual 74 14
% 0.99/1.22 76. ((op (unit) (e1)) != (e1)) ((op (e0) (e1)) = (e1)) ((unit) = (e0)) ### Trans 75 14
% 0.99/1.22 77. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 78. ((op (e1) (unit)) != (op (e1) (e0))) ((unit) = (e0)) ### NotEqual 14 77
% 0.99/1.22 79. ((op (e1) (unit)) != (e1)) ((op (e1) (e0)) = (e1)) ((unit) = (e0)) ### Trans 78 14
% 0.99/1.22 80. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 81. ((op (unit) (e2)) != (op (e0) (e2))) ((unit) = (e0)) ### NotEqual 80 9
% 0.99/1.22 82. ((op (unit) (e2)) != (e2)) ((op (e0) (e2)) = (e2)) ((unit) = (e0)) ### Trans 81 9
% 0.99/1.22 83. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 84. ((op (e2) (unit)) != (op (e2) (e0))) ((unit) = (e0)) ### NotEqual 9 83
% 0.99/1.22 85. ((op (e2) (unit)) != (e2)) ((op (e2) (e0)) = (e2)) ((unit) = (e0)) ### Trans 84 9
% 0.99/1.22 86. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 87. ((op (unit) (e3)) != (op (e0) (e3))) ((unit) = (e0)) ### NotEqual 86 7
% 0.99/1.22 88. ((op (unit) (e3)) != (e3)) ((op (e0) (e3)) = (e3)) ((unit) = (e0)) ### Trans 87 7
% 0.99/1.22 89. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 90. ((op (e3) (unit)) != (op (e3) (e0))) ((unit) = (e0)) ### NotEqual 7 89
% 0.99/1.22 91. ((op (e3) (unit)) != (e3)) ((op (e3) (e0)) = (e3)) ((unit) = (e0)) ### Trans 90 7
% 0.99/1.22 92. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 93. ((op (unit) (e4)) != (op (e0) (e4))) ((unit) = (e0)) ### NotEqual 92 2
% 0.99/1.22 94. ((op (unit) (e4)) != (e4)) ((op (e0) (e4)) = (e4)) ((unit) = (e0)) ### Trans 93 2
% 0.99/1.22 95. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 96. ((op (e4) (unit)) != (op (e4) (e0))) ((unit) = (e0)) ### NotEqual 2 95
% 0.99/1.22 97. ((op (e4) (unit)) != (e4)) ((op (e4) (e0)) = (e4)) ((unit) = (e0)) ### Trans 96 2
% 0.99/1.22 98. ((unit) = (e0)) ((unit) != (e0)) ### Axiom
% 0.99/1.22 99. (-. (((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ (((unit) = (e3)) \/ ((unit) = (e4))))))) ((unit) = (e0)) ### ConjTree 98
% 0.99/1.22 100. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 0.99/1.22 101. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e3)) = (e0)) \/ ((op (e0) (e4)) = (e0))))))) ((op (e0) (e0)) = (e0)) ### ConjTree 100
% 0.99/1.22 102. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom
% 0.99/1.22 103. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e0)) \/ ((op (e4) (e0)) = (e0))))))) ((op (e0) (e0)) = (e0)) ### ConjTree 102
% 0.99/1.22 104. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom
% 0.99/1.22 105. (-. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e3)) = (e1)) \/ ((op (e0) (e4)) = (e1))))))) ((op (e0) (e1)) = (e1)) ### ConjTree 104
% 0.99/1.22 106. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 0.99/1.22 107. (-. (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e1)) \/ ((op (e4) (e0)) = (e1))))))) ((op (e1) (e0)) = (e1)) ### ConjTree 106
% 0.99/1.22 108. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom
% 0.99/1.22 109. (-. (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e4)) = (e2))))))) ((op (e0) (e2)) = (e2)) ### ConjTree 108
% 0.99/1.22 110. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 0.99/1.22 111. (-. (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e4) (e0)) = (e2))))))) ((op (e2) (e0)) = (e2)) ### ConjTree 110
% 0.99/1.22 112. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom
% 0.99/1.22 113. (-. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ (((op (e0) (e3)) = (e3)) \/ ((op (e0) (e4)) = (e3))))))) ((op (e0) (e3)) = (e3)) ### ConjTree 112
% 0.99/1.22 114. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 0.99/1.22 115. (-. (((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 114
% 0.99/1.22 116. ((op (e0) (e4)) = (e4)) ((op (e0) (e4)) != (e4)) ### Axiom
% 0.99/1.22 117. (-. (((op (e0) (e0)) = (e4)) \/ (((op (e0) (e1)) = (e4)) \/ (((op (e0) (e2)) = (e4)) \/ (((op (e0) (e3)) = (e4)) \/ ((op (e0) (e4)) = (e4))))))) ((op (e0) (e4)) = (e4)) ### ConjTree 116
% 0.99/1.22 118. ((op (e4) (e0)) = (e4)) ((op (e4) (e0)) != (e4)) ### Axiom
% 0.99/1.22 119. (-. (((op (e0) (e0)) = (e4)) \/ (((op (e1) (e0)) = (e4)) \/ (((op (e2) (e0)) = (e4)) \/ (((op (e3) (e0)) = (e4)) \/ ((op (e4) (e0)) = (e4))))))) ((op (e4) (e0)) = (e4)) ### ConjTree 118
% 0.99/1.22 120. ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (e0)) ### Axiom
% 0.99/1.22 121. (-. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ ((op (e1) (e4)) = (e0))))))) ((op (e1) (e3)) = (e0)) ### ConjTree 120
% 0.99/1.22 122. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom
% 0.99/1.22 123. (-. (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ ((op (e4) (e1)) = (e0))))))) ((op (e2) (e1)) = (e0)) ### ConjTree 122
% 0.99/1.22 124. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom
% 0.99/1.22 125. (-. (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ ((op (e1) (e4)) = (e1))))))) ((op (e1) (e0)) = (e1)) ### ConjTree 124
% 0.99/1.22 126. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom
% 0.99/1.22 127. (-. (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ ((op (e4) (e1)) = (e1))))))) ((op (e0) (e1)) = (e1)) ### ConjTree 126
% 0.99/1.22 128. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 0.99/1.22 129. (-. (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e4)) = (e2))))))) ((op (e1) (e1)) = (e2)) ### ConjTree 128
% 0.99/1.22 130. ((op (e1) (e1)) = (e2)) ((op (e1) (e1)) != (e2)) ### Axiom
% 0.99/1.22 131. (-. (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e4) (e1)) = (e2))))))) ((op (e1) (e1)) = (e2)) ### ConjTree 130
% 0.99/1.22 132. ((op (e1) (e4)) = (e3)) ((op (e1) (e4)) != (e3)) ### Axiom
% 0.99/1.22 133. (-. (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ ((op (e1) (e4)) = (e3))))))) ((op (e1) (e4)) = (e3)) ### ConjTree 132
% 0.99/1.22 134. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom
% 0.99/1.22 135. (-. (((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 134
% 0.99/1.22 136. ((op (e1) (e2)) = (e4)) ((op (e1) (e2)) != (e4)) ### Axiom
% 0.99/1.22 137. (-. (((op (e1) (e0)) = (e4)) \/ (((op (e1) (e1)) = (e4)) \/ (((op (e1) (e2)) = (e4)) \/ (((op (e1) (e3)) = (e4)) \/ ((op (e1) (e4)) = (e4))))))) ((op (e1) (e2)) = (e4)) ### ConjTree 136
% 0.99/1.22 138. ((op (e3) (e1)) = (e4)) ((op (e3) (e1)) != (e4)) ### Axiom
% 0.99/1.22 139. (-. (((op (e0) (e1)) = (e4)) \/ (((op (e1) (e1)) = (e4)) \/ (((op (e2) (e1)) = (e4)) \/ (((op (e3) (e1)) = (e4)) \/ ((op (e4) (e1)) = (e4))))))) ((op (e3) (e1)) = (e4)) ### ConjTree 138
% 0.99/1.22 140. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom
% 0.99/1.22 141. (-. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e2) (e4)) = (e0))))))) ((op (e2) (e1)) = (e0)) ### ConjTree 140
% 0.99/1.22 142. ((op (e3) (e2)) = (e0)) ((op (e3) (e2)) != (e0)) ### Axiom
% 0.99/1.22 143. (-. (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e4) (e2)) = (e0))))))) ((op (e3) (e2)) = (e0)) ### ConjTree 142
% 0.99/1.22 144. ((op (e2) (e4)) = (e1)) ((op (e2) (e4)) != (e1)) ### Axiom
% 0.99/1.22 145. (-. (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e2) (e4)) = (e1))))))) ((op (e2) (e4)) = (e1)) ### ConjTree 144
% 0.99/1.22 146. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom
% 0.99/1.22 147. (-. (((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 146
% 0.99/1.22 148. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom
% 0.99/1.22 149. (-. (((op (e2) (e0)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e4)) = (e2))))))) ((op (e2) (e0)) = (e2)) ### ConjTree 148
% 0.99/1.22 150. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom
% 0.99/1.22 151. (-. (((op (e0) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e4) (e2)) = (e2))))))) ((op (e0) (e2)) = (e2)) ### ConjTree 150
% 0.99/1.22 152. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 0.99/1.22 153. (-. (((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 152
% 0.99/1.22 154. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom
% 0.99/1.22 155. (-. (((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 154
% 0.99/1.22 156. ((op (e2) (e3)) = (e4)) ((op (e2) (e3)) != (e4)) ### Axiom
% 0.99/1.22 157. (-. (((op (e2) (e0)) = (e4)) \/ (((op (e2) (e1)) = (e4)) \/ (((op (e2) (e2)) = (e4)) \/ (((op (e2) (e3)) = (e4)) \/ ((op (e2) (e4)) = (e4))))))) ((op (e2) (e3)) = (e4)) ### ConjTree 156
% 0.99/1.22 158. ((op (e1) (e2)) = (e4)) ((op (e1) (e2)) != (e4)) ### Axiom
% 0.99/1.22 159. (-. (((op (e0) (e2)) = (e4)) \/ (((op (e1) (e2)) = (e4)) \/ (((op (e2) (e2)) = (e4)) \/ (((op (e3) (e2)) = (e4)) \/ ((op (e4) (e2)) = (e4))))))) ((op (e1) (e2)) = (e4)) ### ConjTree 158
% 0.99/1.22 160. ((op (e3) (e2)) = (e0)) ((op (e3) (e2)) != (e0)) ### Axiom
% 0.99/1.22 161. (-. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e3)) = (e0)) \/ ((op (e3) (e4)) = (e0))))))) ((op (e3) (e2)) = (e0)) ### ConjTree 160
% 0.99/1.22 162. ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (e0)) ### Axiom
% 0.99/1.22 163. (-. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e0)) \/ ((op (e4) (e3)) = (e0))))))) ((op (e1) (e3)) = (e0)) ### ConjTree 162
% 0.99/1.22 164. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 0.99/1.22 165. (-. (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e3)) = (e1)) \/ ((op (e3) (e4)) = (e1))))))) ((op (e3) (e3)) = (e1)) ### ConjTree 164
% 0.99/1.22 166. ((op (e3) (e3)) = (e1)) ((op (e3) (e3)) != (e1)) ### Axiom
% 0.99/1.22 167. (-. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e1)) \/ ((op (e4) (e3)) = (e1))))))) ((op (e3) (e3)) = (e1)) ### ConjTree 166
% 0.99/1.22 168. ((op (e3) (e4)) = (e2)) ((op (e3) (e4)) != (e2)) ### Axiom
% 0.99/1.22 169. (-. (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e4)) = (e2))))))) ((op (e3) (e4)) = (e2)) ### ConjTree 168
% 0.99/1.22 170. ((op (e4) (e3)) = (e2)) ((op (e4) (e3)) != (e2)) ### Axiom
% 0.99/1.22 171. (-. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e4) (e3)) = (e2))))))) ((op (e4) (e3)) = (e2)) ### ConjTree 170
% 0.99/1.22 172. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom
% 0.99/1.22 173. (-. (((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 172
% 0.99/1.22 174. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom
% 0.99/1.22 175. (-. (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e4) (e3)) = (e3))))))) ((op (e0) (e3)) = (e3)) ### ConjTree 174
% 0.99/1.22 176. ((op (e3) (e1)) = (e4)) ((op (e3) (e1)) != (e4)) ### Axiom
% 0.99/1.22 177. (-. (((op (e3) (e0)) = (e4)) \/ (((op (e3) (e1)) = (e4)) \/ (((op (e3) (e2)) = (e4)) \/ (((op (e3) (e3)) = (e4)) \/ ((op (e3) (e4)) = (e4))))))) ((op (e3) (e1)) = (e4)) ### ConjTree 176
% 0.99/1.22 178. ((op (e2) (e3)) = (e4)) ((op (e2) (e3)) != (e4)) ### Axiom
% 0.99/1.22 179. (-. (((op (e0) (e3)) = (e4)) \/ (((op (e1) (e3)) = (e4)) \/ (((op (e2) (e3)) = (e4)) \/ (((op (e3) (e3)) = (e4)) \/ ((op (e4) (e3)) = (e4))))))) ((op (e2) (e3)) = (e4)) ### ConjTree 178
% 0.99/1.22 180. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom
% 0.99/1.22 181. (-. (((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 180
% 0.99/1.22 182. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom
% 0.99/1.22 183. (-. (((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 182
% 0.99/1.22 184. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom
% 0.99/1.22 185. (-. (((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 184
% 0.99/1.22 186. ((op (e2) (e4)) = (e1)) ((op (e2) (e4)) != (e1)) ### Axiom
% 0.99/1.22 187. (-. (((op (e0) (e4)) = (e1)) \/ (((op (e1) (e4)) = (e1)) \/ (((op (e2) (e4)) = (e1)) \/ (((op (e3) (e4)) = (e1)) \/ ((op (e4) (e4)) = (e1))))))) ((op (e2) (e4)) = (e1)) ### ConjTree 186
% 0.99/1.22 188. ((op (e4) (e3)) = (e2)) ((op (e4) (e3)) != (e2)) ### Axiom
% 0.99/1.22 189. (-. (((op (e4) (e0)) = (e2)) \/ (((op (e4) (e1)) = (e2)) \/ (((op (e4) (e2)) = (e2)) \/ (((op (e4) (e3)) = (e2)) \/ ((op (e4) (e4)) = (e2))))))) ((op (e4) (e3)) = (e2)) ### ConjTree 188
% 0.99/1.22 190. ((op (e3) (e4)) = (e2)) ((op (e3) (e4)) != (e2)) ### Axiom
% 0.99/1.22 191. (-. (((op (e0) (e4)) = (e2)) \/ (((op (e1) (e4)) = (e2)) \/ (((op (e2) (e4)) = (e2)) \/ (((op (e3) (e4)) = (e2)) \/ ((op (e4) (e4)) = (e2))))))) ((op (e3) (e4)) = (e2)) ### ConjTree 190
% 0.99/1.22 192. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom
% 0.99/1.22 193. (-. (((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 192
% 0.99/1.22 194. ((op (e1) (e4)) = (e3)) ((op (e1) (e4)) != (e3)) ### Axiom
% 0.99/1.22 195. (-. (((op (e0) (e4)) = (e3)) \/ (((op (e1) (e4)) = (e3)) \/ (((op (e2) (e4)) = (e3)) \/ (((op (e3) (e4)) = (e3)) \/ ((op (e4) (e4)) = (e3))))))) ((op (e1) (e4)) = (e3)) ### ConjTree 194
% 0.99/1.22 196. ((op (e4) (e0)) = (e4)) ((op (e4) (e0)) != (e4)) ### Axiom
% 0.99/1.22 197. (-. (((op (e4) (e0)) = (e4)) \/ (((op (e4) (e1)) = (e4)) \/ (((op (e4) (e2)) = (e4)) \/ (((op (e4) (e3)) = (e4)) \/ ((op (e4) (e4)) = (e4))))))) ((op (e4) (e0)) = (e4)) ### ConjTree 196
% 0.99/1.22 198. ((op (e0) (e4)) = (e4)) ((op (e0) (e4)) != (e4)) ### Axiom
% 0.99/1.22 199. (-. (((op (e0) (e4)) = (e4)) \/ (((op (e1) (e4)) = (e4)) \/ (((op (e2) (e4)) = (e4)) \/ (((op (e3) (e4)) = (e4)) \/ ((op (e4) (e4)) = (e4))))))) ((op (e0) (e4)) = (e4)) ### ConjTree 198
% 0.99/1.22 200. (-. (((((op (e0) (e0)) != (op (e0) (e0))) /\ (((op (op (e0) (e0)) (e0)) = (e0)) /\ ((op (op (e0) (e0)) (e0)) != (e0)))) \/ ((((op (e1) (e0)) != (op (e0) (e1))) /\ (((op (op (e0) (e1)) (e1)) = (e0)) /\ ((op (op (e0) (e1)) (e0)) != (e1)))) \/ ((((op (e2) (e0)) != (op (e0) (e2))) /\ (((op (op (e0) (e2)) (e2)) = (e0)) /\ ((op (op (e0) (e2)) (e0)) != (e2)))) \/ ((((op (e3) (e0)) != (op (e0) (e3))) /\ (((op (op (e0) (e3)) (e3)) = (e0)) /\ ((op (op (e0) (e3)) (e0)) != (e3)))) \/ ((((op (e4) (e0)) != (op (e0) (e4))) /\ (((op (op (e0) (e4)) (e4)) = (e0)) /\ ((op (op (e0) (e4)) (e0)) != (e4)))) \/ ((((op (e0) (e1)) != (op (e1) (e0))) /\ (((op (op (e1) (e0)) (e0)) = (e1)) /\ ((op (op (e1) (e0)) (e1)) != (e0)))) \/ ((((op (e1) (e1)) != (op (e1) (e1))) /\ (((op (op (e1) (e1)) (e1)) = (e1)) /\ ((op (op (e1) (e1)) (e1)) != (e1)))) \/ ((((op (e2) (e1)) != (op (e1) (e2))) /\ (((op (op (e1) (e2)) (e2)) = (e1)) /\ ((op (op (e1) (e2)) (e1)) != (e2)))) \/ ((((op (e3) (e1)) != (op (e1) (e3))) /\ (((op (op (e1) (e3)) (e3)) = (e1)) /\ ((op (op (e1) (e3)) (e1)) != (e3)))) \/ ((((op (e4) (e1)) != (op (e1) (e4))) /\ (((op (op (e1) (e4)) (e4)) = (e1)) /\ ((op (op (e1) (e4)) (e1)) != (e4)))) \/ ((((op (e0) (e2)) != (op (e2) (e0))) /\ (((op (op (e2) (e0)) (e0)) = (e2)) /\ ((op (op (e2) (e0)) (e2)) != (e0)))) \/ ((((op (e1) (e2)) != (op (e2) (e1))) /\ (((op (op (e2) (e1)) (e1)) = (e2)) /\ ((op (op (e2) (e1)) (e2)) != (e1)))) \/ ((((op (e2) (e2)) != (op (e2) (e2))) /\ (((op (op (e2) (e2)) (e2)) = (e2)) /\ ((op (op (e2) (e2)) (e2)) != (e2)))) \/ ((((op (e3) (e2)) != (op (e2) (e3))) /\ (((op (op (e2) (e3)) (e3)) = (e2)) /\ ((op (op (e2) (e3)) (e2)) != (e3)))) \/ ((((op (e4) (e2)) != (op (e2) (e4))) /\ (((op (op (e2) (e4)) (e4)) = (e2)) /\ ((op (op (e2) (e4)) (e2)) != (e4)))) \/ ((((op (e0) (e3)) != (op (e3) (e0))) /\ (((op (op (e3) (e0)) (e0)) = (e3)) /\ ((op (op (e3) (e0)) (e3)) != (e0)))) \/ ((((op (e1) (e3)) != (op (e3) (e1))) /\ (((op (op (e3) (e1)) (e1)) = (e3)) /\ ((op (op (e3) (e1)) (e3)) != (e1)))) \/ ((((op (e2) (e3)) != (op (e3) (e2))) /\ (((op (op (e3) (e2)) (e2)) = (e3)) /\ ((op (op (e3) (e2)) (e3)) != (e2)))) \/ ((((op (e3) (e3)) != (op (e3) (e3))) /\ (((op (op (e3) (e3)) (e3)) = (e3)) /\ ((op (op (e3) (e3)) (e3)) != (e3)))) \/ ((((op (e4) (e3)) != (op (e3) (e4))) /\ (((op (op (e3) (e4)) (e4)) = (e3)) /\ ((op (op (e3) (e4)) (e3)) != (e4)))) \/ ((((op (e0) (e4)) != (op (e4) (e0))) /\ (((op (op (e4) (e0)) (e0)) = (e4)) /\ ((op (op (e4) (e0)) (e4)) != (e0)))) \/ ((((op (e1) (e4)) != (op (e4) (e1))) /\ (((op (op (e4) (e1)) (e1)) = (e4)) /\ ((op (op (e4) (e1)) (e4)) != (e1)))) \/ ((((op (e2) (e4)) != (op (e4) (e2))) /\ (((op (op (e4) (e2)) (e2)) = (e4)) /\ ((op (op (e4) (e2)) (e4)) != (e2)))) \/ ((((op (e3) (e4)) != (op (e4) (e3))) /\ (((op (op (e4) (e3)) (e3)) = (e4)) /\ ((op (op (e4) (e3)) (e4)) != (e3)))) \/ (((op (e4) (e4)) != (op (e4) (e4))) /\ (((op (op (e4) (e4)) (e4)) = (e4)) /\ ((op (op (e4) (e4)) (e4)) != (e4)))))))))))))))))))))))))))) /\ ((((op (e0) (e0)) = 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(((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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ((unit) = (e0)) ((op (e4) (e4)) = (e0)) ((op (e4) (e1)) = (e3)) ((op (e4) (e0)) = (e4)) ((op (e3) (e4)) = (e2)) ((op (e3) (e3)) = (e1)) ((op (e3) (e1)) = (e4)) ((op (e3) (e0)) = (e3)) ((op (e2) (e4)) = (e1)) ((op (e2) (e2)) = (e3)) ((op (e2) (e1)) = (e0)) ((op (e2) (e0)) = (e2)) ((op (e1) (e4)) = (e3)) ((op (e1) (e3)) = (e0)) ((op (e1) (e2)) = (e4)) ((op (e1) (e1)) = (e2)) ((op (e1) (e0)) = (e1)) ((op (e0) (e4)) = (e4)) ((op (e0) (e3)) = (e3)) ((op (e0) (e2)) = (e2)) ((op (e0) (e1)) = (e1)) ((op (e0) (e0)) = (e0)) ((op (e4) (e2)) = (e1)) ((e1) != (e3)) ((op (e4) (e3)) = (e2)) ((op (e2) (e3)) = (e4)) ((op (e3) (e2)) = (e0)) ((e0) != (e4)) ### DisjTree 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 70 73 76 79 82 85 88 91 94 97 99 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149 151 153 155 157 159 161 163 165 167 169 171 173 175 177 179 181 183 185 187 189 191 193 195 197 199
% 0.99/1.22 201. (((op (e0) (e0)) = (e0)) /\ (((op (e0) (e1)) = (e1)) /\ (((op (e0) (e2)) = (e2)) /\ (((op (e0) (e3)) = (e3)) /\ (((op (e0) (e4)) = (e4)) /\ (((op (e1) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e1) (e2)) = (e4)) /\ (((op (e1) (e3)) = (e0)) /\ (((op (e1) (e4)) = (e3)) /\ (((op (e2) (e0)) = (e2)) /\ (((op (e2) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e3)) /\ (((op (e2) (e3)) = (e4)) /\ (((op (e2) (e4)) = (e1)) /\ (((op (e3) (e0)) = (e3)) /\ (((op (e3) (e1)) = (e4)) /\ (((op (e3) (e2)) = (e0)) /\ (((op (e3) (e3)) = (e1)) /\ (((op (e3) (e4)) = (e2)) /\ (((op (e4) (e0)) = (e4)) /\ (((op (e4) (e1)) = (e3)) /\ (((op (e4) (e2)) = (e1)) /\ (((op (e4) (e3)) = (e2)) /\ ((op (e4) (e4)) = (e0)))))))))))))))))))))))))) ((e0) != (e4)) ((e1) != (e3)) ((unit) = (e0)) (-. 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(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ### ConjTree 200
% 0.99/1.22 202. (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e0) != (e4)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ (((e1) != (e4)) /\ (((e2) != (e3)) /\ (((e2) != (e4)) /\ ((e3) != (e4))))))))))) (-. 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(e2)) \/ ((op (e3) (e4)) = (e2)))))) /\ ((((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e4) (e3)) = (e2)))))) /\ ((((op (e3) (e0)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e3) (e4)) = (e3)))))) /\ ((((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e4) (e3)) = (e3)))))) /\ ((((op (e3) (e0)) = (e4)) \/ (((op (e3) (e1)) = (e4)) \/ (((op (e3) (e2)) = (e4)) \/ (((op (e3) (e3)) = (e4)) \/ ((op (e3) (e4)) = (e4)))))) /\ ((((op (e0) (e3)) = (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) 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(((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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ((unit) = (e0)) (((op (e0) (e0)) = (e0)) /\ (((op (e0) (e1)) = (e1)) /\ (((op (e0) (e2)) = (e2)) /\ (((op (e0) (e3)) = (e3)) /\ (((op (e0) (e4)) = (e4)) /\ (((op (e1) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e1) (e2)) = (e4)) /\ (((op (e1) (e3)) = (e0)) /\ (((op (e1) (e4)) = (e3)) /\ (((op (e2) (e0)) = (e2)) /\ (((op (e2) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e3)) /\ (((op (e2) (e3)) = (e4)) /\ (((op (e2) (e4)) = (e1)) /\ (((op (e3) (e0)) = (e3)) /\ (((op (e3) (e1)) = (e4)) /\ (((op (e3) (e2)) = (e0)) /\ (((op (e3) (e3)) = (e1)) /\ (((op (e3) (e4)) = (e2)) /\ (((op (e4) (e0)) = (e4)) /\ (((op (e4) (e1)) = (e3)) /\ (((op (e4) (e2)) = (e1)) /\ (((op (e4) (e3)) = (e2)) /\ ((op (e4) (e4)) = (e0)))))))))))))))))))))))))) ### ConjTree 201
% 1.06/1.23 % SZS output end Proof
% 1.06/1.23 (* END-PROOF *)
%------------------------------------------------------------------------------