%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : ALG044+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 : n021.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 18:04:51 EDT 2022 % Result : Theorem 0.19s 0.49s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG044+1 : TPTP v8.1.0. Released v2.7.0. % 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n021.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 01:01:51 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.49 % SZS status Theorem % 0.19/0.49 (* PROOF-FOUND *) % 0.19/0.49 (* BEGIN-PROOF *) % 0.19/0.49 % SZS output start Proof % 0.19/0.49 1. ((op (e2) (e2)) = (e0)) ((e0) != (op (e2) (e2))) ### Sym(=) % 0.19/0.49 2. ((op (e2) (e2)) = (e0)) ((e0) != (op (e2) (e2))) ### Sym(=) % 0.19/0.49 3. ((e3) != (e3)) ### NotEqual % 0.19/0.49 4. ((e0) != (e3)) ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) = (e0)) ### TransEq 1 2 3 % 0.19/0.49 5. (((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0))))) ((op (e2) (e2)) = (e3)) ((e0) != (e3)) ### ConjTree 4 % 0.19/0.49 6. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=) % 0.19/0.49 7. ((op (e3) (e3)) = (e1)) ((e1) != (op (e3) (e3))) ### Sym(=) % 0.19/0.49 8. ((e0) != (e0)) ### NotEqual % 0.19/0.49 9. ((e0) != (e1)) ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) = (e1)) ### TransEq-sym 6 7 8 % 0.19/0.49 10. (((op (e0) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e1))))) ((op (e3) (e3)) = (e0)) ((e0) != (e1)) ### ConjTree 9 % 0.19/0.49 11. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=) % 0.19/0.49 12. ((op (e3) (e3)) = (e2)) ((e2) != (op (e3) (e3))) ### Sym(=) % 0.19/0.49 13. ((e0) != (e2)) ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) = (e2)) ### TransEq-sym 11 12 8 % 0.19/0.49 14. (((op (e0) (e0)) = (e2)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e2))))) ((op (e3) (e3)) = (e0)) ((e0) != (e2)) ### ConjTree 13 % 0.19/0.49 15. ((op (e3) (e3)) = (e3)) ((e3) != (op (e3) (e3))) ### Sym(=) % 0.19/0.49 16. ((op (e3) (e3)) = (e3)) ((e3) != (op (e3) (e3))) ### Sym(=) % 0.19/0.49 17. ((e0) != (e3)) ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) = (e3)) ### TransEq-sym 15 16 8 % 0.19/0.49 18. (((op (e0) (e0)) = (e3)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) = (e3))))) ((op (e3) (e3)) = (e0)) ((e0) != (e3)) ### ConjTree 17 % 0.19/0.49 19. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom % 0.19/0.49 20. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3)))))) ((op (e0) (e0)) = (e0)) ### ConjTree 19 % 0.19/0.49 21. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom % 0.19/0.49 22. (-. (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3)))))) ((op (e0) (e1)) = (e1)) ### ConjTree 21 % 0.19/0.49 23. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom % 0.19/0.49 24. (-. (((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3)))))) ((op (e0) (e2)) = (e2)) ### ConjTree 23 % 0.19/0.49 25. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom % 0.19/0.49 26. (-. (((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3)))))) ((op (e0) (e3)) = (e3)) ### ConjTree 25 % 0.19/0.49 27. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom % 0.19/0.49 28. (-. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ ((op (e1) (e0)) = (e3)))))) ((op (e1) (e0)) = (e1)) ### ConjTree 27 % 0.19/0.49 29. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom % 0.19/0.49 30. (-. (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3)))))) ((op (e1) (e1)) = (e3)) ### ConjTree 29 % 0.19/0.49 31. ((op (e1) (e2)) = (e0)) ((op (e1) (e2)) != (e0)) ### Axiom % 0.19/0.49 32. (-. (((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3)))))) ((op (e1) (e2)) = (e0)) ### ConjTree 31 % 0.19/0.49 33. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom % 0.19/0.49 34. (-. (((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3)))))) ((op (e1) (e3)) = (e2)) ### ConjTree 33 % 0.19/0.49 35. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom % 0.19/0.49 36. (-. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3)))))) ((op (e2) (e0)) = (e2)) ### ConjTree 35 % 0.19/0.49 37. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom % 0.19/0.49 38. (-. (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e2) (e1)) = (e3)))))) ((op (e2) (e1)) = (e0)) ### ConjTree 37 % 0.19/0.49 39. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom % 0.19/0.49 40. (-. (((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3)))))) ((op (e2) (e2)) = (e3)) ### ConjTree 39 % 0.19/0.49 41. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom % 0.19/0.49 42. (-. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3)))))) ((op (e2) (e3)) = (e1)) ### ConjTree 41 % 0.19/0.49 43. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom % 0.19/0.49 44. (-. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3)))))) ((op (e3) (e0)) = (e3)) ### ConjTree 43 % 0.19/0.49 45. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom % 0.19/0.49 46. (-. (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3)))))) ((op (e3) (e1)) = (e2)) ### ConjTree 45 % 0.19/0.49 47. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom % 0.19/0.49 48. (-. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3)))))) ((op (e3) (e2)) = (e1)) ### ConjTree 47 % 0.19/0.49 49. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom % 0.19/0.49 50. (-. (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3)))))) ((op (e3) (e3)) = (e0)) ### ConjTree 49 % 0.19/0.49 51. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 52. ((op (unit) (e0)) != (op (e0) (e0))) ((unit) = (e0)) ### NotEqual 51 8 % 0.19/0.49 53. ((op (unit) (e0)) != (e0)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ### Trans 52 8 % 0.19/0.49 54. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 55. ((op (e0) (unit)) != (op (e0) (e0))) ((unit) = (e0)) ### NotEqual 8 54 % 0.19/0.49 56. ((op (e0) (unit)) != (e0)) ((op (e0) (e0)) = (e0)) ((unit) = (e0)) ### Trans 55 8 % 0.19/0.49 57. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 58. ((e1) != (e1)) ### NotEqual % 0.19/0.49 59. ((op (unit) (e1)) != (op (e0) (e1))) ((unit) = (e0)) ### NotEqual 57 58 % 0.19/0.49 60. ((op (unit) (e1)) != (e1)) ((op (e0) (e1)) = (e1)) ((unit) = (e0)) ### Trans 59 58 % 0.19/0.49 61. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 62. ((op (e1) (unit)) != (op (e1) (e0))) ((unit) = (e0)) ### NotEqual 58 61 % 0.19/0.49 63. ((op (e1) (unit)) != (e1)) ((op (e1) (e0)) = (e1)) ((unit) = (e0)) ### Trans 62 58 % 0.19/0.49 64. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 65. ((e2) != (e2)) ### NotEqual % 0.19/0.49 66. ((op (unit) (e2)) != (op (e0) (e2))) ((unit) = (e0)) ### NotEqual 64 65 % 0.19/0.49 67. ((op (unit) (e2)) != (e2)) ((op (e0) (e2)) = (e2)) ((unit) = (e0)) ### Trans 66 65 % 0.19/0.49 68. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 69. ((op (e2) (unit)) != (op (e2) (e0))) ((unit) = (e0)) ### NotEqual 65 68 % 0.19/0.49 70. ((op (e2) (unit)) != (e2)) ((op (e2) (e0)) = (e2)) ((unit) = (e0)) ### Trans 69 65 % 0.19/0.49 71. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 72. ((op (unit) (e3)) != (op (e0) (e3))) ((unit) = (e0)) ### NotEqual 71 3 % 0.19/0.49 73. ((op (unit) (e3)) != (e3)) ((op (e0) (e3)) = (e3)) ((unit) = (e0)) ### Trans 72 3 % 0.19/0.49 74. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 75. ((op (e3) (unit)) != (op (e3) (e0))) ((unit) = (e0)) ### NotEqual 3 74 % 0.19/0.49 76. ((op (e3) (unit)) != (e3)) ((op (e3) (e0)) = (e3)) ((unit) = (e0)) ### Trans 75 3 % 0.19/0.49 77. ((unit) = (e0)) ((unit) != (e0)) ### Axiom % 0.19/0.49 78. (-. (((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ ((unit) = (e3)))))) ((unit) = (e0)) ### ConjTree 77 % 0.19/0.49 79. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom % 0.19/0.49 80. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ ((op (e0) (e3)) = (e0)))))) ((op (e0) (e0)) = (e0)) ### ConjTree 79 % 0.19/0.49 81. ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) != (e0)) ### Axiom % 0.19/0.49 82. (-. (((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0)))))) ((op (e0) (e0)) = (e0)) ### ConjTree 81 % 0.19/0.49 83. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom % 0.19/0.49 84. (-. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1)))))) ((op (e0) (e1)) = (e1)) ### ConjTree 83 % 0.19/0.49 85. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom % 0.19/0.49 86. (-. (((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1)))))) ((op (e1) (e0)) = (e1)) ### ConjTree 85 % 0.19/0.49 87. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom % 0.19/0.49 88. (-. (((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2)))))) ((op (e0) (e2)) = (e2)) ### ConjTree 87 % 0.19/0.49 89. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom % 0.19/0.49 90. (-. (((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2)))))) ((op (e2) (e0)) = (e2)) ### ConjTree 89 % 0.19/0.49 91. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom % 0.19/0.49 92. (-. (((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3)))))) ((op (e0) (e3)) = (e3)) ### ConjTree 91 % 0.19/0.49 93. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom % 0.19/0.49 94. (-. (((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3)))))) ((op (e3) (e0)) = (e3)) ### ConjTree 93 % 0.19/0.49 95. ((op (e1) (e2)) = (e0)) ((op (e1) (e2)) != (e0)) ### Axiom % 0.19/0.49 96. (-. (((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0)))))) ((op (e1) (e2)) = (e0)) ### ConjTree 95 % 0.19/0.49 97. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom % 0.19/0.49 98. (-. (((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0)))))) ((op (e2) (e1)) = (e0)) ### ConjTree 97 % 0.19/0.49 99. ((op (e1) (e0)) = (e1)) ((op (e1) (e0)) != (e1)) ### Axiom % 0.19/0.49 100. (-. (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ ((op (e1) (e3)) = (e1)))))) ((op (e1) (e0)) = (e1)) ### ConjTree 99 % 0.19/0.49 101. ((op (e0) (e1)) = (e1)) ((op (e0) (e1)) != (e1)) ### Axiom % 0.19/0.49 102. (-. (((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1)))))) ((op (e0) (e1)) = (e1)) ### ConjTree 101 % 0.19/0.49 103. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom % 0.19/0.49 104. (-. (((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2)))))) ((op (e1) (e3)) = (e2)) ### ConjTree 103 % 0.19/0.49 105. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom % 0.19/0.49 106. (-. (((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2)))))) ((op (e3) (e1)) = (e2)) ### ConjTree 105 % 0.19/0.49 107. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom % 0.19/0.49 108. (-. (((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3)))))) ((op (e1) (e1)) = (e3)) ### ConjTree 107 % 0.19/0.49 109. ((op (e1) (e1)) = (e3)) ((op (e1) (e1)) != (e3)) ### Axiom % 0.19/0.49 110. (-. (((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3)))))) ((op (e1) (e1)) = (e3)) ### ConjTree 109 % 0.19/0.49 111. ((op (e2) (e1)) = (e0)) ((op (e2) (e1)) != (e0)) ### Axiom % 0.19/0.49 112. (-. (((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0)))))) ((op (e2) (e1)) = (e0)) ### ConjTree 111 % 0.19/0.49 113. ((op (e1) (e2)) = (e0)) ((op (e1) (e2)) != (e0)) ### Axiom % 0.19/0.49 114. (-. (((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0)))))) ((op (e1) (e2)) = (e0)) ### ConjTree 113 % 0.19/0.49 115. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom % 0.19/0.49 116. (-. (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1)))))) ((op (e2) (e3)) = (e1)) ### ConjTree 115 % 0.19/0.49 117. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom % 0.19/0.49 118. (-. (((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1)))))) ((op (e3) (e2)) = (e1)) ### ConjTree 117 % 0.19/0.49 119. ((op (e2) (e0)) = (e2)) ((op (e2) (e0)) != (e2)) ### Axiom % 0.19/0.49 120. (-. (((op (e2) (e0)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e3)) = (e2)))))) ((op (e2) (e0)) = (e2)) ### ConjTree 119 % 0.19/0.49 121. ((op (e0) (e2)) = (e2)) ((op (e0) (e2)) != (e2)) ### Axiom % 0.19/0.49 122. (-. (((op (e0) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e2)))))) ((op (e0) (e2)) = (e2)) ### ConjTree 121 % 0.19/0.49 123. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom % 0.19/0.49 124. (-. (((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3)))))) ((op (e2) (e2)) = (e3)) ### ConjTree 123 % 0.19/0.49 125. ((op (e2) (e2)) = (e3)) ((op (e2) (e2)) != (e3)) ### Axiom % 0.19/0.49 126. (-. (((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3)))))) ((op (e2) (e2)) = (e3)) ### ConjTree 125 % 0.19/0.49 127. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom % 0.19/0.49 128. (-. (((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0)))))) ((op (e3) (e3)) = (e0)) ### ConjTree 127 % 0.19/0.49 129. ((op (e3) (e3)) = (e0)) ((op (e3) (e3)) != (e0)) ### Axiom % 0.19/0.49 130. (-. (((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0)))))) ((op (e3) (e3)) = (e0)) ### ConjTree 129 % 0.19/0.49 131. ((op (e3) (e2)) = (e1)) ((op (e3) (e2)) != (e1)) ### Axiom % 0.19/0.49 132. (-. (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1)))))) ((op (e3) (e2)) = (e1)) ### ConjTree 131 % 0.19/0.49 133. ((op (e2) (e3)) = (e1)) ((op (e2) (e3)) != (e1)) ### Axiom % 0.19/0.49 134. (-. (((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1)))))) ((op (e2) (e3)) = (e1)) ### ConjTree 133 % 0.19/0.49 135. ((op (e3) (e1)) = (e2)) ((op (e3) (e1)) != (e2)) ### Axiom % 0.19/0.49 136. (-. (((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2)))))) ((op (e3) (e1)) = (e2)) ### ConjTree 135 % 0.19/0.49 137. ((op (e1) (e3)) = (e2)) ((op (e1) (e3)) != (e2)) ### Axiom % 0.19/0.49 138. (-. (((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2)))))) ((op (e1) (e3)) = (e2)) ### ConjTree 137 % 0.19/0.49 139. ((op (e3) (e0)) = (e3)) ((op (e3) (e0)) != (e3)) ### Axiom % 0.19/0.49 140. (-. (((op (e3) (e0)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e3)) = (e3)))))) ((op (e3) (e0)) = (e3)) ### ConjTree 139 % 0.19/0.49 141. ((op (e0) (e3)) = (e3)) ((op (e0) (e3)) != (e3)) ### Axiom % 0.19/0.49 142. (-. (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3)))))) ((op (e0) (e3)) = (e3)) ### ConjTree 141 % 0.19/0.49 143. (-. ((-. ((((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0))))) \/ ((((op (e0) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e1))))) \/ ((((op (e0) (e0)) = (e2)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e2))))) \/ (((op (e0) (e0)) = (e3)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) = (e3))))))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ ((op (e1) (e0)) = (e3))))) /\ ((((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) /\ ((((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) /\ ((((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) /\ ((((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e2) (e1)) = (e3))))) /\ ((((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) /\ ((((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (unit) (e0)) = (e0)) /\ (((op (e0) (unit)) = (e0)) /\ (((op (unit) (e1)) = (e1)) /\ (((op (e1) (unit)) = (e1)) /\ (((op (unit) (e2)) = (e2)) /\ (((op (e2) (unit)) = (e2)) /\ (((op (unit) (e3)) = (e3)) /\ (((op (e3) (unit)) = (e3)) /\ ((((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ ((unit) = (e3))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ ((op (e0) (e3)) = (e0))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) /\ ((((op (e1) (e0)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ ((op (e1) (e3)) = (e1))))) /\ ((((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) /\ ((((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) /\ ((((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) /\ ((((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) /\ ((((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) /\ ((((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) /\ ((((op (e2) (e0)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e3)) = (e2))))) /\ ((((op (e0) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e2))))) /\ ((((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e3) (e0)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ((unit) = (e0)) ((op (e3) (e2)) = (e1)) ((op (e3) (e1)) = (e2)) ((op (e3) (e0)) = (e3)) ((op (e2) (e3)) = (e1)) ((op (e2) (e1)) = (e0)) ((op (e2) (e0)) = (e2)) ((op (e1) (e3)) = (e2)) ((op (e1) (e2)) = (e0)) ((op (e1) (e1)) = (e3)) ((op (e1) (e0)) = (e1)) ((op (e0) (e3)) = (e3)) ((op (e0) (e2)) = (e2)) ((op (e0) (e1)) = (e1)) ((op (e0) (e0)) = (e0)) ((e0) != (e2)) ((e0) != (e1)) ((op (e3) (e3)) = (e0)) ((e0) != (e3)) ((op (e2) (e2)) = (e3)) ### DisjTree 5 10 14 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 53 56 60 63 67 70 73 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 % 0.19/0.49 144. (((op (e0) (e0)) = (e0)) /\ (((op (e0) (e1)) = (e1)) /\ (((op (e0) (e2)) = (e2)) /\ (((op (e0) (e3)) = (e3)) /\ (((op (e1) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e1) (e2)) = (e0)) /\ (((op (e1) (e3)) = (e2)) /\ (((op (e2) (e0)) = (e2)) /\ (((op (e2) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e3)) /\ (((op (e2) (e3)) = (e1)) /\ (((op (e3) (e0)) = (e3)) /\ (((op (e3) (e1)) = (e2)) /\ (((op (e3) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e0))))))))))))))))) ((e0) != (e3)) ((e0) != (e1)) ((e0) != (e2)) ((unit) = (e0)) (-. ((-. ((((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0))))) \/ ((((op (e0) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e1))))) \/ ((((op (e0) (e0)) = (e2)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e2))))) \/ (((op (e0) (e0)) = (e3)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) = (e3))))))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ ((op (e1) (e0)) = (e3))))) /\ ((((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) /\ ((((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) /\ ((((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) /\ ((((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e2) (e1)) = (e3))))) /\ ((((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) /\ ((((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (unit) (e0)) = (e0)) /\ (((op (e0) (unit)) = (e0)) /\ (((op (unit) (e1)) = (e1)) /\ (((op (e1) (unit)) = (e1)) /\ (((op (unit) (e2)) = (e2)) /\ (((op (e2) (unit)) = (e2)) /\ (((op (unit) (e3)) = (e3)) /\ (((op (e3) (unit)) = (e3)) /\ ((((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ ((unit) = (e3))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ ((op (e0) (e3)) = (e0))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) /\ ((((op (e1) (e0)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ ((op (e1) (e3)) = (e1))))) /\ ((((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) /\ ((((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) /\ ((((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) /\ ((((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) /\ ((((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) /\ ((((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) /\ ((((op (e2) (e0)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e3)) = (e2))))) /\ ((((op (e0) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e2))))) /\ ((((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e3) (e0)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ### ConjTree 143 % 0.19/0.49 145. (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) (-. ((-. ((((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e0)) /\ ((op (e3) (e3)) = (e0))))) \/ ((((op (e0) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e1))))) \/ ((((op (e0) (e0)) = (e2)) /\ (((op (e1) (e1)) = (e2)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e2))))) \/ (((op (e0) (e0)) = (e3)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e2) (e2)) = (e3)) /\ ((op (e3) (e3)) = (e3))))))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ ((op (e1) (e0)) = (e3))))) /\ ((((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) /\ ((((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) /\ ((((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) /\ ((((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e2) (e1)) = (e3))))) /\ ((((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) /\ ((((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (unit) (e0)) = (e0)) /\ (((op (e0) (unit)) = (e0)) /\ (((op (unit) (e1)) = (e1)) /\ (((op (e1) (unit)) = (e1)) /\ (((op (unit) (e2)) = (e2)) /\ (((op (e2) (unit)) = (e2)) /\ (((op (unit) (e3)) = (e3)) /\ (((op (e3) (unit)) = (e3)) /\ ((((unit) = (e0)) \/ (((unit) = (e1)) \/ (((unit) = (e2)) \/ ((unit) = (e3))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ ((op (e0) (e3)) = (e0))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) /\ ((((op (e1) (e0)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ ((op (e1) (e3)) = (e1))))) /\ ((((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) /\ ((((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) /\ ((((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) /\ ((((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) /\ ((((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) /\ ((((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) /\ ((((op (e2) (e0)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e3)) = (e2))))) /\ ((((op (e0) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e2))))) /\ ((((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e3) (e0)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ((unit) = (e0)) (((op (e0) (e0)) = (e0)) /\ (((op (e0) (e1)) = (e1)) /\ (((op (e0) (e2)) = (e2)) /\ (((op (e0) (e3)) = (e3)) /\ (((op (e1) (e0)) = (e1)) /\ (((op (e1) (e1)) = (e3)) /\ (((op (e1) (e2)) = (e0)) /\ (((op (e1) (e3)) = (e2)) /\ (((op (e2) (e0)) = (e2)) /\ (((op (e2) (e1)) = (e0)) /\ (((op (e2) (e2)) = (e3)) /\ (((op (e2) (e3)) = (e1)) /\ (((op (e3) (e0)) = (e3)) /\ (((op (e3) (e1)) = (e2)) /\ (((op (e3) (e2)) = (e1)) /\ ((op (e3) (e3)) = (e0))))))))))))))))) ### ConjTree 144 % 0.19/0.49 % SZS output end Proof % 0.19/0.49 (* END-PROOF *) %------------------------------------------------------------------------------