%------------------------------------------------------------------------------ % 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)) = (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)) = 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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. 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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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ((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 *) %------------------------------------------------------------------------------