%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : ALG092+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 : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 14 18:04:59 EDT 2022 % Result : Theorem 1.05s 1.26s % Output : Proof 1.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : ALG092+1 : TPTP v8.1.0. Released v2.7.0. % 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n026.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 : Wed Jun 8 23:17:47 EDT 2022 % 0.12/0.33 % CPUTime : % 1.05/1.26 % SZS status Theorem % 1.05/1.26 (* PROOF-FOUND *) % 1.05/1.26 (* BEGIN-PROOF *) % 1.05/1.26 % SZS output start Proof % 1.05/1.26 1. ((e3) != (e3)) ### NotEqual % 1.05/1.26 2. ((op (e3) (e0)) = (e3)) ((e3) != (op (e3) (e0))) ### Sym(=) % 1.05/1.26 3. ((op (e3) (e3)) != (op (e3) (op (e3) (e0)))) ((op (e3) (e0)) = (e3)) ### NotEqual 1 2 % 1.05/1.26 4. ((e0) != (e0)) ### NotEqual % 1.05/1.26 5. ((e0) != (op (e3) (e3))) ((op (e3) (op (e3) (e0))) = (e0)) ((op (e3) (e0)) = (e3)) ### Trans-sym 3 4 % 1.05/1.26 6. ((e4) != (e4)) ### NotEqual % 1.05/1.26 7. ((e0) != (e4)) ((op (e3) (e3)) = (e4)) ((op (e3) (e0)) = (e3)) ((op (e3) (op (e3) (e0))) = (e0)) ### TransEq 5 6 6 % 1.05/1.26 8. (-. ((op (e3) (op (e3) (e0))) != (e0))) ((op (e3) (e0)) = (e3)) ((op (e3) (e3)) = (e4)) ((e0) != (e4)) ### NotNot 7 % 1.05/1.26 9. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom % 1.05/1.26 10. ((op (e0) (op (e3) (e0))) != (op (e0) (e3))) ((op (e3) (e0)) = (e3)) ### NotEqual 4 9 % 1.05/1.26 11. ((op (e0) (op (e3) (e0))) != (e3)) ((op (e0) (e3)) = (e3)) ((op (e3) (e0)) = (e3)) ### Trans 10 1 % 1.05/1.26 12. (-. (((op (e3) (op (e3) (e0))) != (e0)) /\ ((op (e0) (op (e3) (e0))) = (e3)))) ((op (e0) (e3)) = (e3)) ((e0) != (e4)) ((op (e3) (e3)) = (e4)) ((op (e3) (e0)) = (e3)) ### NotAnd 8 11 % 1.05/1.26 13. (-. ((((op (e0) (op (e0) (e0))) != (e0)) /\ ((op (e0) (op (e0) (e0))) = (e0))) \/ ((((op (e1) (op (e1) (e0))) != (e0)) /\ ((op (e0) (op (e1) (e0))) = (e1))) \/ ((((op (e2) (op (e2) (e0))) != (e0)) /\ ((op (e0) (op (e2) (e0))) = (e2))) \/ ((((op (e3) (op (e3) (e0))) != (e0)) /\ ((op (e0) (op (e3) (e0))) = (e3))) \/ (((op (e4) (op (e4) (e0))) != (e0)) /\ ((op (e0) (op (e4) (e0))) = (e4)))))))) ((op (e3) (e0)) = (e3)) ((op (e3) (e3)) = (e4)) ((e0) != (e4)) ((op (e0) (e3)) = (e3)) ### ConjTree 12 % 1.05/1.26 14. ((op (e3) (e1)) = (e2)) ((e2) != (op (e3) (e1))) ### Sym(=) % 1.05/1.26 15. ((op (e3) (e2)) != (op (e3) (op (e3) (e1)))) ((op (e3) (e1)) = (e2)) ### NotEqual 1 14 % 1.05/1.26 16. ((e1) != (e1)) ### NotEqual % 1.05/1.26 17. ((e1) != (op (e3) (e2))) ((op (e3) (op (e3) (e1))) = (e1)) ((op (e3) (e1)) = (e2)) ### Trans-sym 15 16 % 1.05/1.26 18. ((e0) != (e1)) ((op (e3) (e2)) = (e0)) ((op (e3) (e1)) = (e2)) ((op (e3) (op (e3) (e1))) = (e1)) ### TransEq-sym 17 4 4 % 1.05/1.26 19. (-. ((op (e3) (op (e3) (e1))) != (e1))) ((op (e3) (e1)) = (e2)) ((op (e3) (e2)) = (e0)) ((e0) != (e1)) ### NotNot 18 % 1.05/1.26 20. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom % 1.05/1.26 21. ((op (e1) (op (e3) (e1))) != (op (e1) (e2))) ((op (e3) (e1)) = (e2)) ### NotEqual 16 20 % 1.05/1.26 22. ((op (e1) (op (e3) (e1))) != (e3)) ((op (e1) (e2)) = (e3)) ((op (e3) (e1)) = (e2)) ### Trans 21 1 % 1.05/1.26 23. (-. (((op (e3) (op (e3) (e1))) != (e1)) /\ ((op (e1) (op (e3) (e1))) = (e3)))) ((op (e1) (e2)) = (e3)) ((e0) != (e1)) ((op (e3) (e2)) = (e0)) ((op (e3) (e1)) = (e2)) ### NotAnd 19 22 % 1.05/1.26 24. (-. ((((op (e0) (op (e0) (e1))) != (e1)) /\ ((op (e1) (op (e0) (e1))) = (e0))) \/ ((((op (e1) (op (e1) (e1))) != (e1)) /\ ((op (e1) (op (e1) (e1))) = (e1))) \/ ((((op (e2) (op (e2) (e1))) != (e1)) /\ ((op (e1) (op (e2) (e1))) = (e2))) \/ ((((op (e3) (op (e3) (e1))) != (e1)) /\ ((op (e1) (op (e3) (e1))) = (e3))) \/ (((op (e4) (op (e4) (e1))) != (e1)) /\ ((op (e1) (op (e4) (e1))) = (e4)))))))) ((op (e3) (e1)) = (e2)) ((op (e3) (e2)) = (e0)) ((e0) != (e1)) ((op (e1) (e2)) = (e3)) ### ConjTree 23 % 1.05/1.26 25. ((op (e1) (e2)) = (e3)) ((e3) != (op (e1) (e2))) ### Sym(=) % 1.05/1.26 26. ((op (e1) (e3)) != (op (e1) (op (e1) (e2)))) ((op (e1) (e2)) = (e3)) ### NotEqual 16 25 % 1.05/1.26 27. ((e2) != (e2)) ### NotEqual % 1.05/1.26 28. ((e2) != (op (e1) (e3))) ((op (e1) (op (e1) (e2))) = (e2)) ((op (e1) (e2)) = (e3)) ### Trans-sym 26 27 % 1.05/1.26 29. ((e0) != (e2)) ((op (e1) (e3)) = (e0)) ((op (e1) (e2)) = (e3)) ((op (e1) (op (e1) (e2))) = (e2)) ### TransEq-sym 28 4 4 % 1.05/1.26 30. (-. ((op (e1) (op (e1) (e2))) != (e2))) ((op (e1) (e2)) = (e3)) ((op (e1) (e3)) = (e0)) ((e0) != (e2)) ### NotNot 29 % 1.05/1.26 31. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom % 1.05/1.26 32. ((op (e2) (op (e1) (e2))) != (op (e2) (e3))) ((op (e1) (e2)) = (e3)) ### NotEqual 27 31 % 1.05/1.26 33. ((op (e2) (op (e1) (e2))) != (e1)) ((op (e2) (e3)) = (e1)) ((op (e1) (e2)) = (e3)) ### Trans 32 16 % 1.05/1.26 34. (-. (((op (e1) (op (e1) (e2))) != (e2)) /\ ((op (e2) (op (e1) (e2))) = (e1)))) ((op (e2) (e3)) = (e1)) ((e0) != (e2)) ((op (e1) (e3)) = (e0)) ((op (e1) (e2)) = (e3)) ### NotAnd 30 33 % 1.05/1.26 35. (-. ((((op (e0) (op (e0) (e2))) != (e2)) /\ ((op (e2) (op (e0) (e2))) = (e0))) \/ ((((op (e1) (op (e1) (e2))) != (e2)) /\ ((op (e2) (op (e1) (e2))) = (e1))) \/ ((((op (e2) (op (e2) (e2))) != (e2)) /\ ((op (e2) (op (e2) (e2))) = (e2))) \/ ((((op (e3) (op (e3) (e2))) != (e2)) /\ ((op (e2) (op (e3) (e2))) = (e3))) \/ (((op (e4) (op (e4) (e2))) != (e2)) /\ ((op (e2) (op (e4) (e2))) = (e4)))))))) ((op (e1) (e2)) = (e3)) ((op (e1) (e3)) = (e0)) ((e0) != (e2)) ((op (e2) (e3)) = (e1)) ### ConjTree 34 % 1.05/1.26 36. ((op (e2) (e3)) = (e1)) ((e1) != (op (e2) (e3))) ### Sym(=) % 1.05/1.26 37. ((op (e2) (e1)) != (op (e2) (op (e2) (e3)))) ((op (e2) (e3)) = (e1)) ### NotEqual 27 36 % 1.05/1.26 38. ((e3) != (op (e2) (e1))) ((op (e2) (op (e2) (e3))) = (e3)) ((op (e2) (e3)) = (e1)) ### Trans-sym 37 1 % 1.05/1.26 39. ((e0) != (e3)) ((op (e2) (e1)) = (e0)) ((op (e2) (e3)) = (e1)) ((op (e2) (op (e2) (e3))) = (e3)) ### TransEq-sym 38 4 4 % 1.05/1.26 40. (-. ((op (e2) (op (e2) (e3))) != (e3))) ((op (e2) (e3)) = (e1)) ((op (e2) (e1)) = (e0)) ((e0) != (e3)) ### NotNot 39 % 1.05/1.26 41. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom % 1.05/1.26 42. ((op (e3) (op (e2) (e3))) != (op (e3) (e1))) ((op (e2) (e3)) = (e1)) ### NotEqual 1 41 % 1.05/1.26 43. ((op (e3) (op (e2) (e3))) != (e2)) ((op (e3) (e1)) = (e2)) ((op (e2) (e3)) = (e1)) ### Trans 42 27 % 1.05/1.26 44. (-. (((op (e2) (op (e2) (e3))) != (e3)) /\ ((op (e3) (op (e2) (e3))) = (e2)))) ((op (e3) (e1)) = (e2)) ((e0) != (e3)) ((op (e2) (e1)) = (e0)) ((op (e2) (e3)) = (e1)) ### NotAnd 40 43 % 1.05/1.26 45. (-. ((((op (e0) (op (e0) (e3))) != (e3)) /\ ((op (e3) (op (e0) (e3))) = (e0))) \/ ((((op (e1) (op (e1) (e3))) != (e3)) /\ ((op (e3) (op (e1) (e3))) = (e1))) \/ ((((op (e2) (op (e2) (e3))) != (e3)) /\ ((op (e3) (op (e2) (e3))) = (e2))) \/ ((((op (e3) (op (e3) (e3))) != (e3)) /\ ((op (e3) (op (e3) (e3))) = (e3))) \/ (((op (e4) (op (e4) (e3))) != (e3)) /\ ((op (e3) (op (e4) (e3))) = (e4)))))))) ((op (e2) (e3)) = (e1)) ((op (e2) (e1)) = (e0)) ((e0) != (e3)) ((op (e3) (e1)) = (e2)) ### ConjTree 44 % 1.05/1.26 46. ((op (e3) (e4)) = (e1)) ((e1) != (op (e3) (e4))) ### Sym(=) % 1.05/1.26 47. ((op (e3) (e1)) != (op (e3) (op (e3) (e4)))) ((op (e3) (e4)) = (e1)) ### NotEqual 1 46 % 1.05/1.26 48. ((e4) != (op (e3) (e1))) ((op (e3) (op (e3) (e4))) = (e4)) ((op (e3) (e4)) = (e1)) ### Trans-sym 47 6 % 1.05/1.26 49. ((e2) != (e4)) ((op (e3) (e1)) = (e2)) ((op (e3) (e4)) = (e1)) ((op (e3) (op (e3) (e4))) = (e4)) ### TransEq-sym 48 27 27 % 1.05/1.26 50. (-. ((op (e3) (op (e3) (e4))) != (e4))) ((op (e3) (e4)) = (e1)) ((op (e3) (e1)) = (e2)) ((e2) != (e4)) ### NotNot 49 % 1.05/1.26 51. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom % 1.05/1.26 52. ((op (e4) (op (e3) (e4))) != (op (e4) (e1))) ((op (e3) (e4)) = (e1)) ### NotEqual 6 51 % 1.05/1.26 53. ((op (e4) (op (e3) (e4))) != (e3)) ((op (e4) (e1)) = (e3)) ((op (e3) (e4)) = (e1)) ### Trans 52 1 % 1.05/1.26 54. (-. (((op (e3) (op (e3) (e4))) != (e4)) /\ ((op (e4) (op (e3) (e4))) = (e3)))) ((op (e4) (e1)) = (e3)) ((e2) != (e4)) ((op (e3) (e1)) = (e2)) ((op (e3) (e4)) = (e1)) ### NotAnd 50 53 % 1.05/1.26 55. (-. ((((op (e0) (op (e0) (e4))) != (e4)) /\ ((op (e4) (op (e0) (e4))) = (e0))) \/ ((((op (e1) (op (e1) (e4))) != (e4)) /\ ((op (e4) (op (e1) (e4))) = (e1))) \/ ((((op (e2) (op (e2) (e4))) != (e4)) /\ ((op (e4) (op (e2) (e4))) = (e2))) \/ ((((op (e3) (op (e3) (e4))) != (e4)) /\ ((op (e4) (op (e3) (e4))) = (e3))) \/ (((op (e4) (op (e4) (e4))) != (e4)) /\ ((op (e4) (op (e4) (e4))) = (e4)))))))) ((op (e3) (e4)) = (e1)) ((op (e3) (e1)) = (e2)) ((e2) != (e4)) ((op (e4) (e1)) = (e3)) ### ConjTree 54 % 1.05/1.26 56. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom % 1.05/1.26 57. (-. (((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 56 % 1.05/1.26 58. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom % 1.05/1.26 59. (-. (((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 58 % 1.05/1.26 60. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom % 1.05/1.26 61. (-. (((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 60 % 1.05/1.26 62. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom % 1.05/1.26 63. (-. (((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 62 % 1.05/1.26 64. ((op (e0) (e4)) = (e4)) ((op (e0) (e4)) != (e4)) ### Axiom % 1.05/1.26 65. (-. (((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 64 % 1.05/1.26 66. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom % 1.05/1.26 67. (-. (((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 66 % 1.05/1.26 68. ((op (e1) (e1)) = (e4)) ((op (e1) (e1)) != (e4)) ### Axiom % 1.05/1.26 69. (-. (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e3)) \/ ((op (e1) (e1)) = (e4))))))) ((op (e1) (e1)) = (e4)) ### ConjTree 68 % 1.05/1.26 70. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom % 1.05/1.26 71. (-. (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e2)) = (e4))))))) ((op (e1) (e2)) = (e3)) ### ConjTree 70 % 1.05/1.26 72. ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (e0)) ### Axiom % 1.05/1.26 73. (-. (((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 72 % 1.05/1.26 74. ((op (e1) (e4)) = (e2)) ((op (e1) (e4)) != (e2)) ### Axiom % 1.05/1.26 75. (-. (((op (e1) (e4)) = (e0)) \/ (((op (e1) (e4)) = (e1)) \/ (((op (e1) (e4)) = (e2)) \/ (((op (e1) (e4)) = (e3)) \/ ((op (e1) (e4)) = (e4))))))) ((op (e1) (e4)) = (e2)) ### ConjTree 74 % 1.05/1.26 76. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom % 1.05/1.26 77. (-. (((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 76 % 1.05/1.26 78. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom % 1.05/1.26 79. (-. (((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 78 % 1.05/1.26 80. ((op (e2) (e2)) = (e4)) ((op (e2) (e2)) != (e4)) ### Axiom % 1.05/1.26 81. (-. (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e2)) = (e4))))))) ((op (e2) (e2)) = (e4)) ### ConjTree 80 % 1.05/1.26 82. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom % 1.05/1.26 83. (-. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e2) (e3)) = (e4))))))) ((op (e2) (e3)) = (e1)) ### ConjTree 82 % 1.05/1.26 84. ((op (e2) (e4)) = (e3)) ((op (e2) (e4)) != (e3)) ### Axiom % 1.05/1.26 85. (-. (((op (e2) (e4)) = (e0)) \/ (((op (e2) (e4)) = (e1)) \/ (((op (e2) (e4)) = (e2)) \/ (((op (e2) (e4)) = (e3)) \/ ((op (e2) (e4)) = (e4))))))) ((op (e2) (e4)) = (e3)) ### ConjTree 84 % 1.05/1.26 86. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom % 1.05/1.26 87. (-. (((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 86 % 1.05/1.26 88. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom % 1.05/1.26 89. (-. (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e4))))))) ((op (e3) (e1)) = (e2)) ### ConjTree 88 % 1.05/1.26 90. ((op (e3) (e2)) = (e0)) ((op (e3) (e2)) != (e0)) ### Axiom % 1.05/1.26 91. (-. (((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 90 % 1.05/1.26 92. ((op (e3) (e3)) = (e4)) ((op (e3) (e3)) != (e4)) ### Axiom % 1.05/1.26 93. (-. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e4))))))) ((op (e3) (e3)) = (e4)) ### ConjTree 92 % 1.05/1.26 94. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom % 1.05/1.26 95. (-. (((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 94 % 1.05/1.26 96. ((op (e4) (e0)) = (e4)) ((op (e4) (e0)) != (e4)) ### Axiom % 1.05/1.26 97. (-. (((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 96 % 1.05/1.26 98. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom % 1.05/1.26 99. (-. (((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 98 % 1.05/1.26 100. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom % 1.05/1.26 101. (-. (((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 100 % 1.05/1.26 102. ((op (e4) (e3)) = (e2)) ((op (e4) (e3)) != (e2)) ### Axiom % 1.05/1.26 103. (-. (((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 102 % 1.05/1.26 104. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom % 1.05/1.26 105. (-. (((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 104 % 1.05/1.26 106. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 107. ((op (unit) (e0)) != (op (e0) (e0))) ((unit) = (e0)) ### NotEqual 106 4 % 1.05/1.26 108. ((op (unit) (e0)) != (e0)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ### Trans 107 4 % 1.05/1.26 109. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 110. ((op (e0) (unit)) != (op (e0) (e0))) ((unit) = (e0)) ### NotEqual 4 109 % 1.05/1.26 111. ((op (e0) (unit)) != (e0)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ### Trans 110 4 % 1.05/1.26 112. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 113. ((op (unit) (e1)) != (op (e0) (e1))) ((unit) = (e0)) ### NotEqual 112 16 % 1.05/1.26 114. ((op (unit) (e1)) != (e1)) ((op (e0) (e1)) = (e1)) ((unit) = (e0)) ### Trans 113 16 % 1.05/1.26 115. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 116. ((op (e1) (unit)) != (op (e1) (e0))) ((unit) = (e0)) ### NotEqual 16 115 % 1.05/1.26 117. ((op (e1) (unit)) != (e1)) ((op (e1) (e0)) = (e1)) ((unit) = (e0)) ### Trans 116 16 % 1.05/1.26 118. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 119. ((op (unit) (e2)) != (op (e0) (e2))) ((unit) = (e0)) ### NotEqual 118 27 % 1.05/1.26 120. ((op (unit) (e2)) != (e2)) ((op (e0) (e2)) = (e2)) ((unit) = (e0)) ### Trans 119 27 % 1.05/1.26 121. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 122. ((op (e2) (unit)) != (op (e2) (e0))) ((unit) = (e0)) ### NotEqual 27 121 % 1.05/1.26 123. ((op (e2) (unit)) != (e2)) ((op (e2) (e0)) = (e2)) ((unit) = (e0)) ### Trans 122 27 % 1.05/1.26 124. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 125. ((op (unit) (e3)) != (op (e0) (e3))) ((unit) = (e0)) ### NotEqual 124 1 % 1.05/1.26 126. ((op (unit) (e3)) != (e3)) ((op (e0) (e3)) = (e3)) ((unit) = (e0)) ### Trans 125 1 % 1.05/1.26 127. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 128. ((op (e3) (unit)) != (op (e3) (e0))) ((unit) = (e0)) ### NotEqual 1 127 % 1.05/1.26 129. ((op (e3) (unit)) != (e3)) ((op (e3) (e0)) = (e3)) ((unit) = (e0)) ### Trans 128 1 % 1.05/1.26 130. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 131. ((op (unit) (e4)) != (op (e0) (e4))) ((unit) = (e0)) ### NotEqual 130 6 % 1.05/1.26 132. ((op (unit) (e4)) != (e4)) ((op (e0) (e4)) = (e4)) ((unit) = (e0)) ### Trans 131 6 % 1.05/1.26 133. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 134. ((op (e4) (unit)) != (op (e4) (e0))) ((unit) = (e0)) ### NotEqual 6 133 % 1.05/1.26 135. ((op (e4) (unit)) != (e4)) ((op (e4) (e0)) = (e4)) ((unit) = (e0)) ### Trans 134 6 % 1.05/1.26 136. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 1.05/1.26 137. (-. (((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ (((unit) = (e3)) \/ ((unit) = (e4))))))) ((unit) = (e0)) ### ConjTree 136 % 1.05/1.26 138. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom % 1.05/1.26 139. (-. (((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 138 % 1.05/1.26 140. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom % 1.05/1.26 141. (-. (((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 140 % 1.05/1.26 142. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom % 1.05/1.26 143. (-. (((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 142 % 1.05/1.26 144. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom % 1.05/1.26 145. (-. (((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 144 % 1.05/1.26 146. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom % 1.05/1.26 147. (-. (((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 146 % 1.05/1.26 148. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom % 1.05/1.26 149. (-. (((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 148 % 1.05/1.26 150. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom % 1.05/1.26 151. (-. (((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 150 % 1.05/1.26 152. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom % 1.05/1.26 153. (-. (((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 152 % 1.05/1.26 154. ((op (e0) (e4)) = (e4)) ((op (e0) (e4)) != (e4)) ### Axiom % 1.05/1.26 155. (-. (((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 154 % 1.05/1.26 156. ((op (e4) (e0)) = (e4)) ((op (e4) (e0)) != (e4)) ### Axiom % 1.05/1.26 157. (-. (((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 156 % 1.05/1.26 158. ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (e0)) ### Axiom % 1.05/1.26 159. (-. (((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 158 % 1.05/1.26 160. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom % 1.05/1.26 161. (-. (((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 160 % 1.05/1.26 162. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom % 1.05/1.26 163. (-. (((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 162 % 1.05/1.26 164. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom % 1.05/1.26 165. (-. (((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 164 % 1.05/1.26 166. ((op (e1) (e4)) = (e2)) ((op (e1) (e4)) != (e2)) ### Axiom % 1.05/1.26 167. (-. (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e4)) = (e2))))))) ((op (e1) (e4)) = (e2)) ### ConjTree 166 % 1.05/1.26 168. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom % 1.05/1.26 169. (-. (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e4) (e1)) = (e2))))))) ((op (e3) (e1)) = (e2)) ### ConjTree 168 % 1.05/1.26 170. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom % 1.05/1.26 171. (-. (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ ((op (e1) (e4)) = (e3))))))) ((op (e1) (e2)) = (e3)) ### ConjTree 170 % 1.05/1.26 172. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom % 1.05/1.26 173. (-. (((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 172 % 1.05/1.26 174. ((op (e1) (e1)) = (e4)) ((op (e1) (e1)) != (e4)) ### Axiom % 1.05/1.26 175. (-. (((op (e1) (e0)) = (e4)) \/ (((op (e1) (e1)) = (e4)) \/ (((op (e1) (e2)) = (e4)) \/ (((op (e1) (e3)) = (e4)) \/ ((op (e1) (e4)) = (e4))))))) ((op (e1) (e1)) = (e4)) ### ConjTree 174 % 1.05/1.26 176. ((op (e1) (e1)) = (e4)) ((op (e1) (e1)) != (e4)) ### Axiom % 1.05/1.26 177. (-. (((op (e0) (e1)) = (e4)) \/ (((op (e1) (e1)) = (e4)) \/ (((op (e2) (e1)) = (e4)) \/ (((op (e3) (e1)) = (e4)) \/ ((op (e4) (e1)) = (e4))))))) ((op (e1) (e1)) = (e4)) ### ConjTree 176 % 1.05/1.26 178. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom % 1.05/1.26 179. (-. (((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 178 % 1.05/1.26 180. ((op (e3) (e2)) = (e0)) ((op (e3) (e2)) != (e0)) ### Axiom % 1.05/1.26 181. (-. (((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 180 % 1.05/1.26 182. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom % 1.05/1.26 183. (-. (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e2) (e4)) = (e1))))))) ((op (e2) (e3)) = (e1)) ### ConjTree 182 % 1.05/1.26 184. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom % 1.05/1.26 185. (-. (((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 184 % 1.05/1.26 186. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom % 1.05/1.26 187. (-. (((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 186 % 1.05/1.26 188. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom % 1.05/1.26 189. (-. (((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 188 % 1.05/1.26 190. ((op (e2) (e4)) = (e3)) ((op (e2) (e4)) != (e3)) ### Axiom % 1.05/1.26 191. (-. (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e2) (e4)) = (e3))))))) ((op (e2) (e4)) = (e3)) ### ConjTree 190 % 1.05/1.26 192. ((op (e1) (e2)) = (e3)) ((op (e1) (e2)) != (e3)) ### Axiom % 1.05/1.26 193. (-. (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e4) (e2)) = (e3))))))) ((op (e1) (e2)) = (e3)) ### ConjTree 192 % 1.05/1.26 194. ((op (e2) (e2)) = (e4)) ((op (e2) (e2)) != (e4)) ### Axiom % 1.05/1.26 195. (-. (((op (e2) (e0)) = (e4)) \/ (((op (e2) (e1)) = (e4)) \/ (((op (e2) (e2)) = (e4)) \/ (((op (e2) (e3)) = (e4)) \/ ((op (e2) (e4)) = (e4))))))) ((op (e2) (e2)) = (e4)) ### ConjTree 194 % 1.05/1.26 196. ((op (e2) (e2)) = (e4)) ((op (e2) (e2)) != (e4)) ### Axiom % 1.05/1.26 197. (-. (((op (e0) (e2)) = (e4)) \/ (((op (e1) (e2)) = (e4)) \/ (((op (e2) (e2)) = (e4)) \/ (((op (e3) (e2)) = (e4)) \/ ((op (e4) (e2)) = (e4))))))) ((op (e2) (e2)) = (e4)) ### ConjTree 196 % 1.05/1.26 198. ((op (e3) (e2)) = (e0)) ((op (e3) (e2)) != (e0)) ### Axiom % 1.05/1.26 199. (-. (((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 198 % 1.05/1.26 200. ((op (e1) (e3)) = (e0)) ((op (e1) (e3)) != (e0)) ### Axiom % 1.05/1.26 201. (-. (((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 200 % 1.05/1.26 202. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom % 1.05/1.26 203. (-. (((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 202 % 1.05/1.26 204. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom % 1.05/1.26 205. (-. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e1)) \/ ((op (e4) (e3)) = (e1))))))) ((op (e2) (e3)) = (e1)) ### ConjTree 204 % 1.05/1.26 206. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom % 1.05/1.26 207. (-. (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e4)) = (e2))))))) ((op (e3) (e1)) = (e2)) ### ConjTree 206 % 1.05/1.26 208. ((op (e4) (e3)) = (e2)) ((op (e4) (e3)) != (e2)) ### Axiom % 1.05/1.26 209. (-. (((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 208 % 1.05/1.26 210. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom % 1.05/1.26 211. (-. (((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 210 % 1.05/1.26 212. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom % 1.05/1.26 213. (-. (((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 212 % 1.05/1.26 214. ((op (e3) (e3)) = (e4)) ((op (e3) (e3)) != (e4)) ### Axiom % 1.05/1.26 215. (-. (((op (e3) (e0)) = (e4)) \/ (((op (e3) (e1)) = (e4)) \/ (((op (e3) (e2)) = (e4)) \/ (((op (e3) (e3)) = (e4)) \/ ((op (e3) (e4)) = (e4))))))) ((op (e3) (e3)) = (e4)) ### ConjTree 214 % 1.05/1.26 216. ((op (e3) (e3)) = (e4)) ((op (e3) (e3)) != (e4)) ### Axiom % 1.05/1.26 217. (-. (((op (e0) (e3)) = (e4)) \/ (((op (e1) (e3)) = (e4)) \/ (((op (e2) (e3)) = (e4)) \/ (((op (e3) (e3)) = (e4)) \/ ((op (e4) (e3)) = (e4))))))) ((op (e3) (e3)) = (e4)) ### ConjTree 216 % 1.05/1.26 218. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom % 1.05/1.26 219. (-. (((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 218 % 1.05/1.26 220. ((op (e4) (e4)) = (e0)) ((op (e4) (e4)) != (e0)) ### Axiom % 1.05/1.26 221. (-. (((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 220 % 1.05/1.26 222. ((op (e4) (e2)) = (e1)) ((op (e4) (e2)) != (e1)) ### Axiom % 1.05/1.26 223. (-. (((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 222 % 1.05/1.26 224. ((op (e3) (e4)) = (e1)) ((op (e3) (e4)) != (e1)) ### Axiom % 1.05/1.26 225. (-. (((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 224 % 1.05/1.26 226. ((op (e4) (e3)) = (e2)) ((op (e4) (e3)) != (e2)) ### Axiom % 1.05/1.26 227. (-. (((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 226 % 1.05/1.26 228. ((op (e1) (e4)) = (e2)) ((op (e1) (e4)) != (e2)) ### Axiom % 1.05/1.26 229. (-. (((op (e0) (e4)) = (e2)) \/ (((op (e1) (e4)) = (e2)) \/ (((op (e2) (e4)) = (e2)) \/ (((op (e3) (e4)) = (e2)) \/ ((op (e4) (e4)) = (e2))))))) ((op (e1) (e4)) = (e2)) ### ConjTree 228 % 1.05/1.26 230. ((op (e4) (e1)) = (e3)) ((op (e4) (e1)) != (e3)) ### Axiom % 1.05/1.26 231. (-. (((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 230 % 1.05/1.26 232. ((op (e2) (e4)) = (e3)) ((op (e2) (e4)) != (e3)) ### Axiom % 1.05/1.26 233. (-. (((op (e0) (e4)) = (e3)) \/ (((op (e1) (e4)) = (e3)) \/ (((op (e2) (e4)) = (e3)) \/ (((op (e3) (e4)) = (e3)) \/ ((op (e4) (e4)) = (e3))))))) ((op (e2) (e4)) = (e3)) ### ConjTree 232 % 1.05/1.26 234. ((op (e4) (e0)) = (e4)) ((op (e4) (e0)) != (e4)) ### Axiom % 1.05/1.26 235. (-. (((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 234 % 1.05/1.26 236. ((op (e0) (e4)) = (e4)) ((op (e0) (e4)) != (e4)) ### Axiom % 1.05/1.26 237. (-. (((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 236 % 1.05/1.26 238. (-. (((((op (e0) (op (e0) (e0))) != (e0)) /\ ((op (e0) (op (e0) (e0))) = (e0))) \/ ((((op (e1) (op (e1) (e0))) != (e0)) /\ ((op (e0) (op (e1) (e0))) = (e1))) \/ ((((op (e2) (op (e2) (e0))) != (e0)) /\ ((op (e0) (op (e2) (e0))) = (e2))) \/ ((((op (e3) (op (e3) (e0))) != (e0)) /\ ((op (e0) (op (e3) (e0))) = (e3))) \/ (((op (e4) (op (e4) (e0))) != (e0)) /\ ((op (e0) (op (e4) (e0))) = (e4))))))) /\ (((((op (e0) (op (e0) (e1))) != (e1)) /\ ((op (e1) (op (e0) (e1))) = (e0))) \/ ((((op (e1) (op (e1) (e1))) != (e1)) /\ ((op (e1) (op (e1) (e1))) = (e1))) \/ ((((op (e2) (op (e2) (e1))) != (e1)) /\ ((op (e1) (op (e2) (e1))) = (e2))) \/ ((((op (e3) (op (e3) (e1))) != (e1)) /\ ((op (e1) (op (e3) (e1))) = (e3))) \/ (((op (e4) (op (e4) (e1))) != (e1)) /\ ((op (e1) (op (e4) (e1))) = (e4))))))) /\ (((((op (e0) (op (e0) (e2))) != (e2)) /\ ((op (e2) (op (e0) (e2))) = (e0))) \/ ((((op (e1) (op (e1) (e2))) != (e2)) /\ ((op (e2) (op (e1) (e2))) = (e1))) \/ ((((op (e2) (op (e2) (e2))) != (e2)) /\ ((op (e2) (op (e2) (e2))) = (e2))) \/ ((((op (e3) (op (e3) (e2))) != (e2)) /\ ((op (e2) (op (e3) (e2))) = (e3))) \/ (((op (e4) (op (e4) (e2))) != (e2)) /\ ((op (e2) (op (e4) (e2))) = (e4))))))) /\ (((((op (e0) (op (e0) (e3))) != (e3)) /\ ((op (e3) (op (e0) (e3))) = (e0))) \/ ((((op (e1) (op (e1) (e3))) != (e3)) /\ ((op (e3) (op (e1) (e3))) = (e1))) \/ ((((op (e2) (op (e2) (e3))) != (e3)) /\ ((op (e3) (op (e2) (e3))) = (e2))) \/ ((((op (e3) (op (e3) (e3))) != (e3)) /\ ((op (e3) (op (e3) (e3))) = (e3))) \/ (((op (e4) (op (e4) (e3))) != (e3)) /\ ((op (e3) (op (e4) (e3))) = (e4))))))) /\ (((((op (e0) (op (e0) (e4))) != (e4)) /\ ((op (e4) (op (e0) (e4))) = (e0))) \/ ((((op (e1) (op (e1) (e4))) != (e4)) /\ ((op (e4) (op (e1) (e4))) = (e1))) \/ ((((op (e2) (op (e2) (e4))) != (e4)) /\ ((op (e4) (op (e2) (e4))) = (e2))) \/ ((((op (e3) (op (e3) (e4))) != (e4)) /\ ((op (e4) (op (e3) (e4))) = (e3))) \/ (((op (e4) (op (e4) (e4))) != (e4)) /\ ((op (e4) (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)) \/ (((op (e3) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e4)))))) /\ ((((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e4)))))) /\ ((((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e4)))))) /\ ((((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ (((op (e3) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e4)))))) /\ ((((op (e3) (e4)) = (e0)) \/ (((op (e3) (e4)) = (e1)) \/ (((op (e3) (e4)) = (e2)) \/ (((op (e3) (e4)) = (e3)) \/ ((op (e3) (e4)) = (e4)))))) /\ ((((op (e4) (e0)) = (e0)) \/ (((op (e4) (e0)) = (e1)) \/ (((op (e4) (e0)) = (e2)) \/ (((op (e4) (e0)) = (e3)) \/ ((op (e4) (e0)) = (e4)))))) /\ 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(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 238 % 1.05/1.26 240. (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e0) != (e4)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ (((e1) != (e4)) /\ (((e2) != (e3)) /\ (((e2) != (e4)) /\ ((e3) != (e4))))))))))) (-. 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((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) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ((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)) = (e4)) /\ (((op (e1) (e2)) = (e3)) /\ (((op (e1) (e3)) = (e0)) /\ (((op (e1) (e4)) = (e2)) /\ (((op (e2) (e0)) = (e2)) /\ (((op (e2) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e4)) /\ (((op (e2) (e3)) = (e1)) /\ (((op (e2) (e4)) = (e3)) /\ (((op (e3) (e0)) = (e3)) /\ (((op (e3) (e1)) = (e2)) /\ (((op (e3) (e2)) = (e0)) /\ (((op (e3) (e3)) = (e4)) /\ (((op (e3) (e4)) = (e1)) /\ (((op (e4) (e0)) = (e4)) /\ (((op (e4) (e1)) = (e3)) /\ (((op (e4) (e2)) = (e1)) /\ (((op (e4) (e3)) = (e2)) /\ ((op (e4) (e4)) = (e0)))))))))))))))))))))))))) ### ConjTree 239 % 1.05/1.27 % SZS output end Proof % 1.05/1.27 (* END-PROOF *) %------------------------------------------------------------------------------