%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWV198+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n019.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 : Wed Jul 20 21:50:19 EDT 2022 % Result : Theorem 156.32s 156.57s % Output : Proof 156.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SWV198+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.08/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue Jun 14 15:37:09 EDT 2022 % 0.13/0.35 % CPUTime : % 156.32/156.57 % SZS status Theorem % 156.32/156.57 (* PROOF-FOUND *) % 156.32/156.57 (* BEGIN-PROOF *) % 156.32/156.57 % SZS output start Proof % 156.32/156.57 1. ((u_defuse) != (u_defuse)) ### NotEqual % 156.32/156.57 2. (gt (succ T_0) (n0)) (-. (gt (succ T_0) (n0))) ### Axiom % 156.32/156.57 3. (-. (leq (n0) T_0)) (gt (succ T_0) (n0)) ### Definition-Pseudo(leq) 2 % 156.32/156.57 4. ((succ (succ (succ (n0)))) = (n3)) ((n3) != (succ (succ (succ (n0))))) ### Sym(=) % 156.32/156.57 5. ((succ (n3)) != (succ (succ (succ (succ (n0)))))) ((succ (succ (succ (n0)))) = (n3)) ### NotEqual 4 % 156.32/156.57 6. ((n4) != (n4)) ### NotEqual % 156.32/156.57 7. ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (succ (succ (n0))))) != (n4)) ### Axiom % 156.32/156.57 8. ((n3) != (n3)) ### NotEqual % 156.32/156.57 9. (-. (gt (succ (succ (succ (succ (n0))))) (n3))) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ### Trans 7 8 % 156.32/156.57 10. ((succ (succ (n0))) = (n2)) ((succ (succ (n0))) != (n2)) ### Axiom % 156.32/156.57 11. ((succ (succ (succ (n0)))) != (succ (n2))) ((succ (succ (n0))) = (n2)) ### NotEqual 10 % 156.32/156.57 12. (-. (gt (succ (succ (succ (succ (n0))))) (succ (n2)))) ((succ (succ (succ (n0)))) = (n3)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ### TransEq2 9 9 11 % 156.32/156.57 13. (-. (gt (n4) (succ (n2)))) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (n0)))) = (n3)) ### TransEq2 6 12 12 % 156.32/156.57 14. (-. (gt (succ (n3)) (succ (n2)))) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) ### TransEq 5 13 13 % 156.32/156.57 15. (T_0 != T_0) ### Refl(=) % 156.32/156.57 16. (-. (gt (succ (n3)) T_0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) ### Trans 14 15 % 156.32/156.57 17. (-. (leq T_0 (n3))) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) ### Definition-Pseudo(leq) 16 % 156.32/156.57 18. (T_0 != (n0)) (T_0 = (n0)) ### Axiom % 156.32/156.57 19. (T_0 != (n1)) (T_0 = (n1)) ### Axiom % 156.32/156.57 20. (T_0 != (n2)) (T_0 = (n2)) ### Axiom % 156.32/156.57 21. (T_0 != (n3)) (T_0 = (n3)) ### Axiom % 156.32/156.57 22. (((leq (n0) T_0) /\ (leq T_0 (n3))) => ((T_0 = (n0)) \/ ((T_0 = (n1)) \/ ((T_0 = (n2)) \/ (T_0 = (n3)))))) (T_0 != (n3)) (T_0 != (n2)) (T_0 != (n1)) (T_0 != (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) ### DisjTree 3 17 18 19 20 21 % 156.32/156.57 23. (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n0)) (T_0 != (n1)) (T_0 != (n2)) (T_0 != (n3)) ### All 22 % 156.32/156.57 24. (gt (succ T_1) (n0)) (-. (gt (succ T_1) (n0))) ### Axiom % 156.32/156.57 25. (-. (leq (n0) T_1)) (gt (succ T_1) (n0)) ### Definition-Pseudo(leq) 24 % 156.32/156.57 26. ((succ (succ (succ (n0)))) = (n3)) ((n3) != (succ (succ (succ (n0))))) ### Sym(=) % 156.32/156.57 27. (-. (gt (n4) (succ (succ (succ (n0)))))) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) ### Trans 6 26 % 156.32/156.57 28. (-. (gt (succ (n3)) (succ (succ (succ (n0)))))) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) ### TransEq 5 27 27 % 156.32/156.57 29. ((n2) != (n2)) ### NotEqual % 156.32/156.57 30. ((succ (succ (n0))) = (n2)) ((succ (succ (n0))) != (n2)) ### Axiom % 156.32/156.57 31. ((n1) != (n1)) ### NotEqual % 156.32/156.57 32. (-. (gt (succ (succ (n0))) (n1))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ### Trans 30 31 % 156.32/156.57 33. (gt (succ (pv5)) (n0)) (-. (gt (succ (pv5)) (n0))) ### Axiom % 156.32/156.57 34. (-. (leq (n0) (pv5))) (gt (succ (pv5)) (n0)) ### Definition-Pseudo(leq) 33 % 156.32/156.57 35. ((succ (succ (n0))) = (n2)) ((n2) != (succ (succ (n0)))) ### Sym(=) % 156.32/156.57 36. ((succ (n2)) != (succ (succ (succ (n0))))) ((succ (succ (n0))) = (n2)) ### NotEqual 35 % 156.32/156.57 37. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 156.32/156.57 38. (-. (gt (n3) (succ (n0)))) (gt (n3) (n1)) ((succ (n0)) = (n1)) ### Trans 8 37 % 156.32/156.57 39. (-. (gt (succ (n2)) (succ (n0)))) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) ### TransEq 36 38 38 % 156.32/156.57 40. ((pv5) != (pv5)) ### NotEqual % 156.32/156.57 41. (-. (gt (succ (n2)) (pv5))) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) ### Trans 39 40 % 156.32/156.57 42. (-. (leq (pv5) (n2))) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ### Definition-Pseudo(leq) 41 % 156.32/156.57 43. ((n0) != (pv5)) ((pv5) = (n0)) ### Sym(=) % 156.32/156.57 44. ((pv5) != (n1)) ((pv5) = (n1)) ### Axiom % 156.32/156.57 45. ((pv5) != (n2)) ((pv5) = (n2)) ### Axiom % 156.32/156.57 46. (((leq (n0) (pv5)) /\ (leq (pv5) (n2))) => (((pv5) = (n0)) \/ (((pv5) = (n1)) \/ ((pv5) = (n2))))) ((pv5) != (n2)) ((pv5) != (n1)) ((n0) != (pv5)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) ### DisjTree 34 42 43 44 45 % 156.32/156.57 47. (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((n0) != (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### All 46 % 156.32/156.57 48. ((succ (n0)) != (succ (pv5))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ### NotEqual 47 % 156.32/156.57 49. (-. (gt (succ (succ (n0))) (succ (pv5)))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ((succ (succ (n0))) = (n2)) (gt (n2) (n1)) ### TransEq2 32 32 48 % 156.32/156.57 50. (-. (gt (n2) (succ (pv5)))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ### TransEq2 29 49 49 % 156.32/156.57 51. (-. (gt (n3) (succ (pv5)))) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ((succ (succ (n0))) = (n2)) (gt (n2) (n1)) ### Trans 8 50 % 156.32/156.57 52. (-. (gt (succ (n3)) (succ (pv5)))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ### TransEq 28 51 51 % 156.32/156.57 53. (T_1 != T_1) ### Refl(=) % 156.32/156.57 54. (-. (gt (succ (n3)) T_1)) (gt (succ (pv5)) T_1) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ((succ (succ (n0))) = (n2)) (gt (n2) (n1)) ### Trans 52 53 % 156.32/156.57 55. (-. (leq T_1 (n3))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ (pv5)) T_1) ### Definition-Pseudo(leq) 54 % 156.32/156.57 56. (T_1 != (n0)) (T_1 = (n0)) ### Axiom % 156.32/156.57 57. (T_1 != (n1)) (T_1 = (n1)) ### Axiom % 156.32/156.57 58. (T_1 != (n2)) (T_1 = (n2)) ### Axiom % 156.32/156.57 59. (T_1 != (n3)) (T_1 = (n3)) ### Axiom % 156.32/156.57 60. (((leq (n0) T_1) /\ (leq T_1 (n3))) => ((T_1 = (n0)) \/ ((T_1 = (n1)) \/ ((T_1 = (n2)) \/ (T_1 = (n3)))))) (T_1 != (n3)) (T_1 != (n2)) (T_1 != (n1)) (T_1 != (n0)) (gt (succ (pv5)) T_1) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ((succ (succ (n0))) = (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) ### DisjTree 25 55 56 57 58 59 % 156.32/156.58 61. (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ (pv5)) T_1) (T_1 != (n0)) (T_1 != (n1)) (T_1 != (n2)) (T_1 != (n3)) ### All 60 % 156.32/156.58 62. ((a_select3 (u_defuse) T_0 T_1) != (a_select3 (u_defuse) (n0) (n0))) (T_1 != (n3)) (T_1 != (n2)) (T_1 != (n1)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (T_0 != (n1)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ### NotEqual 1 23 61 % 156.32/156.58 63. ((a_select3 (u_defuse) T_0 T_1) != (a_select3 (u_defuse) (n1) (n0))) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n1)) (T_1 != (n2)) (T_1 != (n3)) ((a_select3 (u_defuse) T_0 T_1) != (a_select3 (u_defuse) (n0) (n0))) ### NotEqual 1 62 61 % 156.32/156.58 64. ((use) != (use)) ### NotEqual % 156.32/156.58 65. ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (a_select3 (u_defuse) (n0) (n0))) (T_1 != (n3)) (T_1 != (n2)) (T_1 != (n1)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ### Trans 63 64 % 156.32/156.58 66. ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n1)) (T_1 != (n2)) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ### Trans 65 64 % 156.32/156.58 67. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.32/156.58 68. (-. (gt (succ (n0)) (n1))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 48 66 % 156.32/156.58 69. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.32/156.58 70. (-. (gt (succ (n0)) (succ (n0)))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((succ (n0)) = (n1)) ### TransEq2 67 68 69 % 156.32/156.58 71. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.32/156.58 72. (-. (gt T_1 (succ (n0)))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ### TransEq2 66 70 71 % 156.32/156.58 73. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.32/156.58 74. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.32/156.58 75. ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (-. (gt (succ (n0)) (n1))) ### Trans 74 68 % 156.32/156.58 76. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.32/156.58 77. (-. (gt (succ (n0)) (succ (n0)))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) ((succ (n0)) = (n1)) ### TransEq2 73 75 76 % 156.62/156.82 78. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.82 79. (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (-. (gt T_1 (succ (n0)))) ### TransEq2 72 77 78 % 156.62/156.82 80. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.82 81. (-. (gt (n1) (n1))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) ### TransEq2 31 75 80 % 156.62/156.82 82. (-. (gt T_1 (n1))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq 79 79 81 % 156.62/156.82 83. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.82 84. (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n2)) ((n0) != (pv5)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ### TransEq2 47 77 83 % 156.62/156.82 85. ((succ (n0)) != (succ (pv5))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### NotEqual 84 % 156.62/156.82 86. (-. (gt T_1 (succ (pv5)))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ### TransEq2 82 82 85 % 156.62/156.82 87. ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt T_1 (succ (pv5)))) ### TransEq2 86 49 49 % 156.62/156.82 88. (T_1 != T_1) ### Refl(=) % 156.62/156.82 89. (-. (gt T_1 T_1)) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) ### Trans 87 88 % 156.62/156.82 90. (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### All 89 % 156.62/156.82 91. ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n1)) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n1)) (T_1 != (n2)) (T_1 != (n3)) ### Trans 62 64 % 156.62/156.82 92. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.82 93. (-. (gt (succ (n0)) (n1))) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (T_0 != (n1)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 48 91 % 156.62/156.84 94. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.84 95. (-. (gt (succ (n0)) (succ (n0)))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n1)) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ((succ (n0)) = (n1)) ### TransEq2 92 93 94 % 156.62/156.84 96. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.84 97. (-. (gt T_1 (succ (n0)))) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (T_0 != (n1)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ### TransEq2 91 95 96 % 156.62/156.84 98. (-. (gt T_1 (n1))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n1)) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ### TransEq 97 97 31 % 156.62/156.84 99. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.84 100. (-. (gt (succ (n0)) (succ (pv5)))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n1)) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ((succ (n0)) = (n1)) ### TransEq2 99 93 48 % 156.62/156.84 101. (-. (gt T_1 (succ (pv5)))) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (T_0 != (n1)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ### TransEq2 98 98 100 % 156.62/156.84 102. (T_1 != T_1) ### Refl(=) % 156.62/156.84 103. (-. (gt T_1 T_1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n1)) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ### Trans 101 102 % 156.62/156.84 104. (All X, (-. (gt X X))) (T_1 != (n3)) (T_1 != (n2)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (T_0 != (n1)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ### All 103 % 156.62/156.84 105. (-. (gt (succ (n0)) (n2))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n1)) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) (All X, (-. (gt X X))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 48 104 % 156.62/156.84 106. (-. (gt (n1) (n2))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (All X, (-. (gt X X))) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (T_0 != (n1)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ### TransEq2 31 105 105 % 156.62/156.84 107. (-. (gt (n1) (n1))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n1)) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) (All X, (-. (gt X X))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 106 31 % 156.62/156.85 108. (-. (gt (pv5) (n1))) (T_0 != (n1)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) ### TransEq 90 90 107 % 156.62/156.85 109. ((a_select3 (u_defuse) T_0 T_1) != (a_select3 (u_defuse) (n2) (n0))) (T_1 != (n2)) (T_1 != (n1)) (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (T_0 != (n1)) (-. (gt (pv5) (n1))) ### NotEqual 1 108 61 % 156.62/156.85 110. ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (n1))) (T_0 != (n1)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) (T_1 != (n1)) (T_1 != (n2)) ### Trans 109 64 % 156.62/156.85 111. ((a_select3 (u_defuse) T_0 T_1) != (a_select3 (u_defuse) (n1) (n0))) (T_1 != (n2)) (T_1 != (n1)) (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### NotEqual 1 110 61 % 156.62/156.85 112. ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) (T_1 != (n1)) (T_1 != (n2)) ### Trans 111 64 % 156.62/156.85 113. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.85 114. (-. (gt (succ (n0)) (n1))) (T_1 != (n2)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 48 112 % 156.62/156.85 115. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 116. (-. (gt (succ (n0)) (succ (n0)))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (T_1 != (n2)) ((succ (n0)) = (n1)) ### TransEq2 113 114 115 % 156.62/156.85 117. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 118. (-. (gt T_1 (succ (n0)))) (T_1 != (n2)) (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### TransEq2 112 116 117 % 156.62/156.85 119. (-. (gt T_1 (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) (T_1 != (n2)) ### TransEq 118 118 31 % 156.62/156.85 120. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.85 121. (-. (gt (succ (n0)) (succ (pv5)))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (T_1 != (n2)) ((succ (n0)) = (n1)) ### TransEq2 120 114 48 % 156.62/156.85 122. (-. (gt T_1 (succ (pv5)))) (T_1 != (n2)) (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### TransEq2 119 119 121 % 156.62/156.85 123. ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) (-. (gt T_1 (succ (pv5)))) ### TransEq2 122 49 49 % 156.62/156.85 124. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.62/156.85 125. (-. (gt (succ (succ (succ (n0)))) (succ (pv5)))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) ### TransEq 124 51 51 % 156.62/156.85 126. (-. (gt T_1 (succ (pv5)))) (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### TransEq2 123 125 125 % 156.62/156.85 127. (T_1 != T_1) ### Refl(=) % 156.62/156.85 128. (-. (gt T_1 T_1)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) ### Trans 126 127 % 156.62/156.85 129. (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### All 128 % 156.62/156.85 130. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 131. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 132. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 133. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 134. (T_1 != T_1) ### Refl(=) % 156.62/156.85 135. (-. (gt T_1 T_1)) (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### Trans 123 134 % 156.62/156.85 136. ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) ### All 135 % 156.62/156.85 137. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 138. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 139. (-. (gt (succ (n0)) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### Trans 138 136 % 156.62/156.85 140. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.85 141. (-. (gt (n1) (n1))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 139 140 % 156.62/156.85 142. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 143. (-. (gt (n1) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### TransEq2 31 141 142 % 156.62/156.85 144. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 156.62/156.85 145. (-. (gt (succ (n0)) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 137 143 144 % 156.62/156.85 146. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 147. (-. (gt (pv5) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### TransEq2 136 145 146 % 156.62/156.85 148. (-. (gt (pv5) (pv5))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 147 40 % 156.62/156.85 149. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### All 148 % 156.62/156.85 150. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.62/156.85 151. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.85 152. (-. (gt (succ (n0)) (n2))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 151 149 % 156.62/156.85 153. (-. (gt (n1) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### TransEq2 31 152 152 % 156.62/156.85 154. (-. (gt (n2) (n2))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 29 153 % 156.62/156.85 155. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.62/156.85 156. (-. (gt (succ (n0)) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### TransEq2 152 152 155 % 156.62/156.87 157. (-. (gt (n1) (succ (succ (n0))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 156 156 % 156.62/156.87 158. (-. (gt (n2) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### Trans 154 157 % 156.62/156.87 159. ((succ (succ (n0))) = (n2)) ((n2) != (succ (succ (n0)))) ### Sym(=) % 156.62/156.87 160. (-. (gt (succ (succ (n0))) (succ (succ (n0))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 150 158 159 % 156.62/156.87 161. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.62/156.87 162. (-. (gt (pv5) (succ (succ (n0))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 149 160 161 % 156.62/156.87 163. (-. (gt (succ (n0)) (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (succ (n0))))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 48 162 % 156.62/156.87 164. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.62/156.87 165. (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (-. (gt (pv5) (succ (succ (n0))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 163 163 164 % 156.62/156.87 166. (-. (gt (succ (n0)) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (succ (n0))))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ### Trans 133 165 % 156.62/156.87 167. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.87 168. (-. (gt (n1) (n1))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (-. (gt (pv5) (succ (succ (n0))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 166 167 % 156.62/156.87 169. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.87 170. (-. (gt (n1) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (succ (n0))))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ### TransEq2 31 168 169 % 156.62/156.87 171. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 156.62/156.87 172. (-. (gt (succ (n0)) (succ (n0)))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (-. (gt (pv5) (succ (succ (n0))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 132 170 171 % 156.62/156.89 173. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.89 174. (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 129 172 173 % 156.62/156.89 175. (-. (gt (succ (n0)) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) ### Trans 131 174 % 156.62/156.89 176. ((succ (succ (succ (n0)))) = (n3)) ((succ (succ (succ (n0)))) != (n3)) ### Axiom % 156.62/156.89 177. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.89 178. (-. (gt (n1) (n1))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n2)) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ### TransEq2 31 68 177 % 156.62/156.89 179. (-. (gt (pv5) (n1))) (T_1 != (n2)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) ### TransEq 90 90 178 % 156.62/156.89 180. (-. (gt T_1 (succ (pv5)))) (All X, (-. (gt X X))) ((pv5) != (n1)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ### TransEq2 179 49 49 % 156.62/156.89 181. (-. (gt (succ (n0)) (succ (pv5)))) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 48 180 % 156.62/156.89 182. (-. (gt (succ (n0)) (n2))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ### Trans 181 179 % 156.62/156.89 183. (-. (gt (n1) (n2))) (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### TransEq2 31 182 182 % 156.62/156.89 184. (-. (gt (n1) (n1))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (pv5) (n1))) ### Trans 183 31 % 156.62/156.90 185. (-. (gt (pv5) (n1))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) ### TransEq 90 90 184 % 156.62/156.90 186. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.90 187. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 188. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 189. (-. (gt (succ (n0)) (succ (n0)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((pv5) != (n1)) (All X, (-. (gt X X))) ### Trans 188 90 % 156.62/156.90 190. (-. (gt (succ (n0)) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt (succ (n0)) (succ (n0)))) ### Trans 187 189 % 156.62/156.90 191. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 192. (-. (gt (succ (n0)) (succ (n0)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ((succ (n0)) = (n1)) ### TransEq2 186 190 191 % 156.62/156.90 193. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 194. (-. (gt (pv5) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ### TransEq2 185 192 193 % 156.62/156.90 195. (-. (gt (pv5) (pv5))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n2)) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 194 40 % 156.62/156.90 196. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (T_0 != (n2)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ### All 195 % 156.62/156.90 197. (-. (gt T_0 (succ (pv5)))) ((pv5) != (n1)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 196 49 49 % 156.62/156.90 198. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 199. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 200. (-. (gt (succ (n0)) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 199 197 % 156.62/156.90 201. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.62/156.90 202. (-. (gt (n1) (n1))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 200 201 % 156.62/156.90 203. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 204. (-. (gt (n1) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 31 202 203 % 156.62/156.90 205. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 156.62/156.90 206. (-. (gt (succ (n0)) (succ (n0)))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 198 204 205 % 156.62/156.90 207. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 208. (-. (gt (pv5) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 197 206 207 % 156.62/156.90 209. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.62/156.90 210. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.62/156.90 211. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 156.62/156.90 212. (-. (gt (n2) (succ (n0)))) (gt (n2) (n1)) ((succ (n0)) = (n1)) ### Trans 29 211 % 156.62/156.90 213. (-. (gt (succ (succ (n0))) (succ (n0)))) ((succ (succ (n0))) = (n2)) ((succ (n0)) = (n1)) (gt (n2) (n1)) ### TransEq 210 212 212 % 156.62/156.90 214. (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (succ (n0)))) ### TransEq2 208 213 213 % 156.62/156.90 215. (-. (gt (pv5) (pv5))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 214 40 % 156.62/156.90 216. (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### All 215 % 156.62/156.90 217. (-. (gt (succ (succ (n0))) (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ### Trans 49 216 % 156.62/156.90 218. (-. (gt (n2) (n3))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ((succ (succ (n0))) = (n2)) (gt (n2) (n1)) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 29 217 217 % 156.62/156.90 219. (-. (gt (n3) (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ### Trans 8 218 % 156.62/156.90 220. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.62/156.90 221. (-. (gt (pv5) (pv5))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 208 40 % 156.62/156.90 222. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### All 221 % 156.62/156.90 223. (-. (gt (succ (n0)) (n2))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 220 222 % 156.62/156.90 224. (-. (gt (n1) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 31 223 223 % 156.62/156.90 225. (-. (gt (succ (n0)) (n3))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (n1) (n2))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 48 224 % 156.62/156.90 226. (-. (gt (n1) (n3))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (-. (gt (n1) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 31 225 225 % 156.62/156.90 227. (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (n1) (n2))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 226 29 % 156.62/156.90 228. (-. (gt (n1) (n1))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 227 31 % 156.62/156.90 229. (-. (gt (succ (n0)) (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### Trans 48 216 % 156.62/156.90 230. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.62/156.90 231. (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 229 229 230 % 156.62/156.90 232. (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### TransEq2 228 228 231 % 156.62/156.90 233. (-. (gt (n3) (succ (succ (succ (n0)))))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ((succ (succ (n0))) = (n2)) (gt (n2) (n1)) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 219 232 % 156.74/156.92 234. ((succ (succ (succ (n0)))) = (n3)) ((n3) != (succ (succ (succ (n0))))) ### Sym(=) % 156.74/156.92 235. (-. (gt (succ (succ (succ (n0)))) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ### TransEq 209 233 234 % 156.74/156.92 236. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.74/156.92 237. (-. (gt T_1 (succ (succ (succ (n0)))))) ((pv5) != (n1)) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (succ (n0)))) ### TransEq2 208 235 236 % 156.74/156.92 238. (-. (gt T_1 (n3))) (-. (gt (pv5) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ((pv5) != (n1)) ### TransEq 237 237 219 % 156.74/156.92 239. (-. (gt T_1 (succ (pv5)))) ((pv5) != (n1)) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (succ (n0)))) ### TransEq2 238 238 125 % 156.74/156.92 240. (T_1 != T_1) ### Refl(=) % 156.74/156.92 241. (-. (gt T_1 T_1)) (-. (gt (pv5) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ((pv5) != (n1)) ### Trans 239 240 % 156.74/156.92 242. ((pv5) != (n1)) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (succ (n0)))) ### All 241 % 156.74/156.92 243. (-. (gt (pv5) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ((pv5) != (n1)) ### TransEq 242 242 228 % 156.74/156.92 244. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.92 245. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.92 246. (-. (gt (succ (n0)) (n1))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 245 243 % 156.74/156.92 247. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.74/156.92 248. (-. (gt (n1) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 31 246 247 % 156.74/156.94 249. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.94 250. (-. (gt (n1) (succ (n0)))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 248 249 % 156.74/156.94 251. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 156.74/156.94 252. (-. (gt (succ (n0)) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq 244 250 251 % 156.74/156.94 253. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.94 254. (-. (gt (pv5) (succ (n0)))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 243 252 253 % 156.74/156.94 255. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (-. (gt (pv5) (succ (n0)))) ### TransEq2 254 213 213 % 156.74/156.94 256. (-. (gt (pv5) (pv5))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 255 40 % 156.74/156.94 257. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### All 256 % 156.74/156.94 258. ((pv5) != (n1)) ((pv5) != (n2)) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 257 125 125 % 156.74/156.94 259. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.94 260. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.94 261. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.94 262. ((pv5) != (n1)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (-. (gt (succ (n0)) (n1))) ### TransEq2 246 125 125 % 156.74/156.94 263. (-. (gt (succ (n0)) (n1))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 261 262 % 156.74/156.94 264. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.74/156.94 265. (-. (gt (n1) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 31 263 264 % 156.74/156.94 266. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.94 267. (-. (gt (n1) (succ (n0)))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 265 266 % 156.74/156.95 268. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 156.74/156.95 269. (-. (gt (succ (n0)) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq 260 267 268 % 156.74/156.95 270. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.95 271. ((succ (n0)) = (n1)) ((succ (n0)) != (n1)) ### Axiom % 156.74/156.95 272. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.95 273. (-. (gt (succ (n0)) (succ (n0)))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ((pv5) != (n1)) ((succ (n0)) = (n1)) ### TransEq2 271 262 272 % 156.74/156.95 274. (-. (gt (succ (n0)) (succ (n2)))) ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 229 229 11 % 156.74/156.95 275. (-. (gt (n1) (succ (n2)))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n1)) ((pv5) != (n2)) ### TransEq2 228 228 274 % 156.74/156.95 276. ((pv5) != (n2)) ((pv5) != (n1)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (-. (gt (n1) (succ (n2)))) ### TransEq2 275 125 125 % 156.74/156.95 277. (-. (gt (succ (n0)) (succ (n2)))) ((succ (n0)) = (n1)) ((pv5) != (n1)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq 270 273 276 % 156.74/156.95 278. (-. (gt (pv5) (pv5))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 254 40 % 156.74/156.95 279. (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### All 278 % 156.74/156.95 280. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/156.95 281. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.95 282. (-. (gt (succ (n0)) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 281 279 % 156.74/156.95 283. (-. (gt (n1) (n2))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 282 282 % 156.74/156.95 284. (-. (gt (n2) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 29 283 % 156.74/156.95 285. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/156.95 286. (-. (gt (succ (n0)) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 282 282 285 % 156.74/156.95 287. (-. (gt (n1) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 31 286 286 % 156.74/156.95 288. (-. (gt (n2) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 284 287 % 156.74/156.95 289. ((succ (succ (n0))) = (n2)) ((n2) != (succ (succ (n0)))) ### Sym(=) % 156.74/156.95 290. (-. (gt (succ (succ (n0))) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq 280 288 289 % 156.74/156.95 291. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/156.95 292. (-. (gt (pv5) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 279 290 291 % 156.74/156.95 293. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.74/156.95 294. ((succ (succ (n0))) = (n2)) ((n2) != (succ (succ (n0)))) ### Sym(=) % 156.74/156.95 295. (-. (gt (n3) (succ (succ (n0))))) (gt (n3) (n2)) ((succ (succ (n0))) = (n2)) ### Trans 8 294 % 156.74/156.95 296. (-. (gt (succ (succ (succ (n0)))) (succ (succ (n0))))) ((succ (succ (succ (n0)))) = (n3)) ((succ (succ (n0))) = (n2)) (gt (n3) (n2)) ### TransEq 293 295 295 % 156.74/156.95 297. (-. (gt T_0 (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (succ (succ (n0))))) ### TransEq2 292 296 296 % 156.74/156.95 298. (-. (gt (succ (n0)) (succ (succ (n0))))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ((pv5) != (n1)) ((succ (n0)) = (n1)) ### Trans 277 297 % 156.74/156.95 299. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.95 300. (-. (gt (pv5) (succ (n0)))) ((succ (n0)) = (n1)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (succ (n0)) (succ (succ (n0))))) ### TransEq2 298 269 299 % 156.74/156.96 301. (-. (gt (n1) (succ (succ (n0))))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (pv5) (succ (n0)))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 265 265 300 % 156.74/156.96 302. (-. (gt (pv5) (pv5))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (n1) (succ (succ (n0))))) ### Trans 301 40 % 156.74/156.96 303. (-. (gt (n1) (succ (succ (n0))))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### All 302 % 156.74/156.96 304. (-. (gt (succ (n0)) (succ (succ (n0))))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 259 269 303 % 156.74/156.96 305. (-. (gt (pv5) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ((pv5) != (n2)) ### TransEq2 258 304 304 % 156.74/156.96 306. (-. (gt (succ (n0)) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (-. (gt (pv5) (succ (succ (n0))))) ### TransEq 304 304 29 % 156.74/156.96 307. (-. (gt (n1) (n2))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 265 265 306 % 156.74/156.96 308. (-. (gt (n2) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (-. (gt (pv5) (succ (succ (n0))))) ### Trans 29 307 % 156.74/156.96 309. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.96 310. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) (-. (gt (succ (n0)) (succ (succ (n0))))) ### Trans 309 304 % 156.74/156.96 311. (-. (gt (succ (n0)) (n2))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 310 310 29 % 156.74/156.96 312. (-. (gt (n1) (n2))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 265 265 311 % 156.74/156.96 313. (-. (gt (n2) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 29 312 % 156.74/156.96 314. (-. (gt (pv5) (n2))) ((pv5) != (n2)) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 305 308 313 % 156.74/156.96 315. (-. (gt (succ (succ (succ (n0)))) (succ (pv5)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((pv5) != (n2)) (-. (gt (pv5) (n2))) ((succ (succ (n0))) = (n2)) ### Trans 11 314 % 156.74/156.96 316. (-. (gt (succ (succ (succ (n0)))) (n3))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (T_0 != (n3)) (-. (gt (pv5) (succ (n0)))) ((succ (succ (n0))) = (n2)) (-. (gt (pv5) (n2))) ((pv5) != (n2)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 315 147 % 156.74/156.96 317. (-. (gt (succ (succ (succ (n0)))) (succ (n2)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((pv5) != (n2)) (-. (gt (pv5) (n2))) ((succ (succ (n0))) = (n2)) (-. (gt (pv5) (succ (n0)))) (T_0 != (n3)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((succ (succ (succ (n0)))) = (n3)) ### TransEq2 176 316 11 % 156.74/156.96 318. (-. (gt (n3) (succ (n2)))) ((succ (succ (succ (n0)))) = (n3)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (T_0 != (n3)) (-. (gt (pv5) (succ (n0)))) ((succ (succ (n0))) = (n2)) (-. (gt (pv5) (n2))) ((pv5) != (n2)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 8 317 317 % 156.74/156.96 319. (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (succ (n0)) (succ (succ (n0))))) ### TransEq 175 175 318 % 156.74/156.96 320. (-. (gt (succ (n0)) (succ (pv5)))) (-. (gt (succ (n0)) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n2))) ### Trans 319 286 % 156.74/156.96 321. (-. (gt T_1 (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (succ (n0))))) ### TransEq2 162 296 296 % 156.74/156.96 322. (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (pv5) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (succ (n0)) (succ (succ (n0))))) ### Trans 320 321 % 156.74/156.96 323. (-. (gt (succ (n0)) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n2))) ### Trans 130 322 % 156.74/156.96 324. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.96 325. (-. (gt (succ (n0)) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (n1) (n1))) ### Trans 324 168 % 156.74/156.96 326. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/156.96 327. (-. (gt (succ (succ (n0))) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (n1) (n1))) (gt (n2) (n1)) ((succ (n0)) = (n1)) ((succ (succ (n0))) = (n2)) ### Trans 213 168 % 156.74/156.96 328. (-. (gt (succ (succ (n0))) (n2))) ((succ (succ (n0))) = (n2)) ((succ (n0)) = (n1)) (gt (n2) (n1)) (-. (gt (n1) (n1))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 326 327 29 % 156.74/156.96 329. ((succ (succ (n0))) = (n2)) ((succ (succ (n0))) != (n2)) ### Axiom % 156.74/156.96 330. (-. (gt (n2) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (n1) (n1))) (gt (n2) (n1)) ((succ (n0)) = (n1)) ((succ (succ (n0))) = (n2)) ### TransEq2 29 328 329 % 156.74/156.96 331. (-. (gt (succ (n0)) (n2))) (-. (gt (n1) (n1))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 325 325 330 % 156.74/156.96 332. (-. (gt (n1) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (n1) (n1))) ### TransEq2 31 331 331 % 156.74/156.96 333. (-. (gt (succ (n0)) (n2))) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 175 175 29 % 156.74/156.96 334. (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (n1) (n2))) ### TransEq2 332 331 333 % 156.74/156.99 335. (-. (gt (n2) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) ### Trans 29 334 % 156.74/156.99 336. (-. (gt (n1) (n1))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 332 31 % 156.74/156.99 337. (-. (gt (succ (n0)) (succ (n0)))) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 175 175 212 % 156.74/156.99 338. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/156.99 339. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) (gt (n2) (n1)) ((succ (succ (n0))) = (n2)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (-. (gt (succ (succ (n0))) (succ (pv5)))) ### TransEq2 49 337 338 % 156.74/156.99 340. (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt (succ (succ (n0))) (succ (pv5)))) (-. (gt (pv5) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) ### TransEq2 31 336 339 % 156.74/156.99 341. (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 149 213 213 % 156.74/156.99 342. (-. (gt (pv5) (pv5))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (T_1 != (n3)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### Trans 341 40 % 156.74/156.99 343. ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) (T_1 != (n3)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### All 342 % 156.74/156.99 344. (-. (gt (succ (succ (n0))) (n3))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (succ (n0)))) (-. (gt (n1) (succ (succ (succ (n0)))))) ### Trans 340 343 % 156.74/156.99 345. (-. (gt (n2) (n3))) (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 335 335 344 % 156.74/157.00 346. (-. (gt (succ (n0)) (n3))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (n1) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n2))) (-. (gt (succ (n0)) (succ (n2)))) ### TransEq 319 319 345 % 156.74/157.00 347. (-. (gt (n1) (n3))) (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (n2))) (-. (gt (pv5) (succ (n0)))) (-. (gt (n1) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ### TransEq2 336 336 346 % 156.74/157.00 348. ((succ (succ (succ (n0)))) = (n3)) ((succ (succ (succ (n0)))) != (n3)) ### Axiom % 156.74/157.00 349. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.74/157.00 350. (-. (gt (succ (succ (succ (n0)))) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((pv5) != (n2)) (-. (gt (pv5) (n2))) ((succ (succ (n0))) = (n2)) (-. (gt (pv5) (succ (n0)))) (T_0 != (n3)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((succ (succ (succ (n0)))) = (n3)) ### TransEq2 348 316 349 % 156.74/157.00 351. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.74/157.00 352. (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n2))) (-. (gt (succ (n0)) (succ (n2)))) ### TransEq2 347 350 351 % 156.74/157.00 353. (-. (gt (n2) (succ (succ (succ (n0)))))) (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (n2))) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) ((succ (succ (n0))) = (n2)) (gt (n3) (n1)) ((succ (n0)) = (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 335 352 % 156.74/157.00 354. (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 323 323 353 % 156.74/157.00 355. (-. (gt (n3) (succ (pv5)))) ((succ (succ (n0))) = (n2)) (-. (gt (pv5) (n2))) ((pv5) != (n2)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 8 315 315 % 156.74/157.00 356. (-. (gt (succ (n0)) (succ (pv5)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n2))) (-. (gt (succ (n0)) (succ (n2)))) ### TransEq 354 355 355 % 156.74/157.00 357. ((succ (succ (succ (n0)))) = (n3)) ((succ (succ (succ (n0)))) != (n3)) ### Axiom % 156.74/157.00 358. (-. (gt (succ (succ (succ (n0)))) (n3))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ((succ (succ (n0))) = (n2)) ### Trans 11 257 % 156.74/157.00 359. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.74/157.00 360. (-. (gt (succ (succ (succ (n0)))) (succ (succ (succ (n0)))))) ((succ (succ (n0))) = (n2)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ((succ (succ (succ (n0)))) = (n3)) ### TransEq2 357 358 359 % 156.74/157.00 361. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.74/157.00 362. (-. (gt T_0 (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 279 360 361 % 156.74/157.00 363. (-. (gt T_0 (succ (succ (succ (n0)))))) (-. (gt (pv5) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (succ (n0)) (succ (pv5)))) ### Trans 356 362 % 156.74/157.00 364. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.74/157.00 365. (-. (gt T_1 (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n2))) ((pv5) != (n2)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### TransEq2 343 350 364 % 156.74/157.00 366. (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n2))) (-. (gt T_0 (succ (succ (succ (n0)))))) ### Trans 363 365 % 156.74/157.00 367. (-. (gt (pv5) (succ (succ (succ (n0)))))) (-. (gt T_0 (succ (succ (succ (n0)))))) (-. (gt (pv5) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 129 366 366 % 156.74/157.00 368. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/157.00 369. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/157.00 370. (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (n2))) ### TransEq 333 333 318 % 156.74/157.00 371. (-. (gt (succ (n0)) (succ (pv5)))) (-. (gt (succ (n0)) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (n2))) ### Trans 370 257 % 156.74/157.00 372. (-. (gt (succ (n0)) (n3))) (-. (gt (pv5) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (n2))) ### Trans 371 343 % 156.74/157.01 373. (-. (gt (succ (n0)) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (succ (n0)) (n3))) ### Trans 369 372 % 156.74/157.01 374. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (n2))) ### Trans 373 29 % 156.74/157.01 375. (-. (gt (n1) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 374 374 % 156.74/157.01 376. (-. (gt (n2) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### Trans 29 375 % 156.74/157.01 377. (-. (gt (n1) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### Trans 375 31 % 156.74/157.01 378. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/157.01 379. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/157.01 380. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.74/157.01 381. (-. (gt (succ (n0)) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 380 314 % 156.74/157.01 382. (-. (gt (n1) (n2))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 381 381 % 156.74/157.01 383. (-. (gt (n2) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 29 382 % 156.74/157.01 384. (-. (gt (n1) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### Trans 382 31 % 156.74/157.01 385. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/157.01 386. (-. (gt (succ (n0)) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 381 381 385 % 156.74/157.01 387. (-. (gt (n1) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 384 384 386 % 156.74/157.01 388. (-. (gt (n2) (succ (succ (n0))))) (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 383 387 % 156.74/157.01 389. ((succ (succ (n0))) = (n2)) ((n2) != (succ (succ (n0)))) ### Sym(=) % 156.74/157.01 390. (-. (gt (succ (succ (n0))) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq 379 388 389 % 156.74/157.01 391. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/157.01 392. (-. (gt T_0 (succ (pv5)))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (succ (succ (n0))))) ### TransEq2 305 390 391 % 156.74/157.01 393. (-. (gt (succ (n0)) (succ (pv5)))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (succ (n0)) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (n2))) ### Trans 370 392 % 156.74/157.01 394. (-. (gt (succ (n0)) (n3))) (-. (gt (pv5) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (n2))) (-. (gt (pv5) (succ (succ (n0))))) ### Trans 393 162 % 156.74/157.01 395. (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (succ (n0)) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (n2))) ### Trans 394 29 % 156.74/157.01 396. (-. (gt (n1) (n2))) (-. (gt (pv5) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (succ (succ (n0))))) ### TransEq2 31 395 395 % 156.74/157.01 397. (-. (gt (n2) (n2))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (n2))) ### Trans 29 396 % 156.74/157.01 398. (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (pv5) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ((succ (succ (n0))) = (n2)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) ### TransEq2 31 336 174 % 156.74/157.01 399. (-. (gt (n2) (succ (succ (succ (n0)))))) (-. (gt (pv5) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (succ (succ (n0))))) ### Trans 397 398 % 156.74/157.01 400. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.74/157.01 401. (-. (gt (succ (n0)) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (n2))) ### Trans 372 29 % 156.74/157.01 402. (-. (gt (n1) (n2))) (-. (gt (pv5) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq2 31 401 401 % 156.74/157.01 403. (-. (gt (n1) (n1))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (n2))) ### Trans 402 31 % 156.74/157.01 404. (-. (gt T_1 (succ (n2)))) (-. (gt (pv5) (n2))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (pv5) (succ (n0)))) ### TransEq2 147 317 317 % 156.74/157.01 405. (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (n2))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) ((pv5) != (n2)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 356 404 % 156.74/157.01 406. (-. (gt (n1) (succ (n2)))) (-. (gt (pv5) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) ((pv5) != (n2)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq2 403 403 405 % 156.74/157.01 407. (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (n1) (succ (n2)))) ### TransEq2 406 213 213 % 156.74/157.01 408. (-. (gt (n2) (succ (n2)))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 376 407 % 156.74/157.01 409. (-. (gt (succ (succ (n0))) (succ (n2)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq 400 408 408 % 156.85/157.03 410. (-. (gt (succ (succ (n0))) (succ (pv5)))) (-. (gt (pv5) (succ (succ (n0))))) (-. (gt T_0 (succ (succ (n0))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 409 297 % 156.85/157.03 411. (-. (gt (succ (succ (n0))) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt T_0 (succ (succ (n0))))) (-. (gt (pv5) (succ (succ (n0))))) ### Trans 410 321 % 156.85/157.03 412. (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (succ (succ (n0))) (succ (succ (n0))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 409 411 % 156.85/157.03 413. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.85/157.03 414. (-. (gt (pv5) (succ (succ (n0))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (n2) (succ (succ (succ (n0)))))) ### TransEq2 399 412 413 % 156.85/157.03 415. (-. (gt (succ (n0)) (succ (succ (n0))))) (-. (gt (n2) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### Trans 378 414 % 156.85/157.03 416. (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (n2) (succ (succ (succ (n0)))))) ### TransEq 415 415 408 % 156.85/157.03 417. (-. (gt (succ (n0)) (succ (pv5)))) (-. (gt (n2) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### Trans 416 255 % 156.85/157.03 418. (-. (gt (succ (n0)) (n3))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (-. (gt (n2) (succ (succ (succ (n0)))))) ### Trans 417 341 % 156.85/157.03 419. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.85/157.03 420. (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (-. (gt (n2) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq2 418 418 419 % 156.85/157.05 421. (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt (n2) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 377 377 420 % 156.85/157.05 422. (-. (gt (n2) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 376 421 % 156.85/157.05 423. (-. (gt (succ (succ (n0))) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq 368 422 422 % 156.85/157.05 424. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt T_0 (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (succ (succ (n0)))))) ### TransEq2 367 423 423 % 156.85/157.05 425. ((succ (succ (succ (n0)))) = (n3)) ((succ (succ (succ (n0)))) != (n3)) ### Axiom % 156.85/157.05 426. (-. (gt (n3) (n3))) ((succ (succ (n0))) = (n2)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (-. (gt T_0 (succ (pv5)))) ### TransEq2 8 358 425 % 156.85/157.05 427. (-. (gt (succ (succ (n0))) (succ (pv5)))) (-. (gt (n3) (n3))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 409 426 % 156.85/157.05 428. (-. (gt (succ (succ (n0))) (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (n3) (n3))) ### Trans 427 341 % 156.85/157.05 429. (-. (gt (n2) (n3))) (-. (gt (n3) (n3))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 376 376 428 % 156.85/157.05 430. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (n3) (n3))) ### Trans 8 429 % 156.85/157.05 431. (-. (gt (pv5) (n3))) (-. (gt T_0 (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 424 424 430 % 156.85/157.05 432. (-. (gt T_0 (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n3))) ### TransEq 431 430 430 % 156.85/157.05 433. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.85/157.05 434. ((succ (succ (succ (n0)))) = (n3)) ((succ (succ (succ (n0)))) != (n3)) ### Axiom % 156.85/157.05 435. (-. (gt (n3) (succ (succ (succ (n0)))))) (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 430 421 % 156.85/157.05 436. (-. (gt (succ (succ (succ (n0)))) (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt (n3) (succ (succ (succ (n0)))))) ((succ (succ (n0))) = (n2)) ### Trans 11 435 % 156.85/157.05 437. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.85/157.05 438. (-. (gt (succ (succ (succ (n0)))) (succ (succ (succ (n0)))))) ((succ (succ (n0))) = (n2)) (-. (gt (n3) (succ (succ (succ (n0)))))) (-. (gt (n1) (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ((succ (succ (succ (n0)))) = (n3)) ### TransEq2 434 436 437 % 156.85/157.05 439. ((succ (succ (succ (n0)))) = (n3)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (n3) (succ (succ (succ (n0)))))) ((succ (succ (n0))) = (n2)) (-. (gt (succ (succ (succ (n0)))) (succ (succ (succ (n0)))))) ### Trans 8 438 % 156.85/157.05 440. ((succ (succ (succ (n0)))) = (n3)) ((n3) != (succ (succ (succ (n0))))) ### Sym(=) % 156.85/157.05 441. (-. (gt (succ (succ (succ (n0)))) (succ (succ (succ (n0)))))) ((succ (succ (n0))) = (n2)) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ((succ (succ (succ (n0)))) = (n3)) ### TransEq 433 439 440 % 156.85/157.05 442. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.85/157.05 443. (-. (gt (pv5) (succ (succ (succ (n0)))))) (-. (gt T_0 (succ (succ (succ (n0)))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 424 441 442 % 156.85/157.05 444. (-. (gt T_0 (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (succ (succ (succ (n0)))))) ### TransEq 443 443 8 % 156.85/157.05 445. (-. (gt T_0 (succ (n2)))) (-. (gt (pv5) (succ (succ (succ (n0)))))) (-. (gt (pv5) (n3))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 432 444 11 % 156.85/157.06 446. (T_0 != T_0) ### Refl(=) % 156.85/157.06 447. (-. (gt T_0 T_0)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n3))) (-. (gt (pv5) (succ (succ (succ (n0)))))) ### Trans 445 446 % 156.85/157.06 448. (-. (gt (pv5) (succ (succ (succ (n0)))))) (-. (gt (pv5) (n3))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### All 447 % 156.85/157.06 449. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.85/157.06 450. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.85/157.06 451. ((succ (n0)) != (succ (n0))) ### Refl(=) % 156.85/157.06 452. (-. (gt (n1) (succ (n0)))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 377 451 % 156.85/157.06 453. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 156.85/157.06 454. (-. (gt (succ (n0)) (succ (n0)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq 450 452 453 % 156.85/157.06 455. ((succ (succ (n0))) != (succ (succ (n0)))) ### Refl(=) % 156.85/157.06 456. (-. (gt (succ (n0)) (succ (succ (n0))))) (-. (gt (succ (n0)) (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq2 373 373 455 % 156.85/157.06 457. (-. (gt (n1) (n3))) (-. (gt (succ (n0)) (succ (succ (n0))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 377 377 456 % 156.85/157.06 458. (-. (gt (n1) (succ (succ (n0))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (succ (n0))))) ### TransEq2 457 457 296 % 156.85/157.06 459. (-. (gt (succ (n0)) (succ (succ (n0))))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 449 454 458 % 156.85/157.06 460. (-. (gt (succ (n0)) (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (T_0 != (n3)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) ### TransEq 459 459 420 % 156.85/157.06 461. (-. (gt (n3) (succ (n2)))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 430 407 % 156.85/157.06 462. (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (T_0 != (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 460 461 461 % 156.85/157.06 463. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.85/157.06 464. (-. (gt T_0 (succ (succ (succ (n0)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (n2)))) ### TransEq2 462 441 463 % 156.85/157.06 465. (-. (gt T_0 (n3))) (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq 464 464 8 % 156.85/157.06 466. (-. (gt T_0 (succ (n2)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (n2)))) ### TransEq2 465 465 11 % 156.85/157.06 467. (T_0 != T_0) ### Refl(=) % 156.85/157.06 468. (-. (gt T_0 T_0)) (-. (gt (succ (n0)) (succ (n2)))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 466 467 % 156.85/157.06 469. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (succ (n0)) (succ (n2)))) ### All 468 % 156.85/157.06 470. (-. (gt (succ (n0)) (n3))) (-. (gt (pv5) (n3))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### Trans 469 432 % 156.85/157.06 471. (-. (gt (succ (n0)) (n2))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n3))) ### Trans 470 29 % 156.85/157.06 472. (-. (gt (n1) (n2))) (-. (gt (pv5) (n3))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 31 471 471 % 156.85/157.06 473. (-. (gt (n1) (n1))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n3))) ### Trans 472 31 % 156.85/157.06 474. (-. (gt (n1) (n3))) (-. (gt (pv5) (n3))) (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 473 473 470 % 156.85/157.06 475. (-. (gt (n3) (n3))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n3))) ### Trans 8 474 % 156.85/157.06 476. (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (-. (gt (pv5) (succ (n0)))) (-. (gt (pv5) (n3))) ### TransEq 448 448 475 % 156.85/157.06 477. ((succ (succ (succ (n0)))) != (succ (succ (succ (n0))))) ### Refl(=) % 156.85/157.06 478. (-. (gt (succ (succ (succ (n0)))) (succ (n0)))) ((succ (succ (succ (n0)))) = (n3)) ((succ (n0)) = (n1)) (gt (n3) (n1)) ### TransEq 477 38 38 % 156.85/157.06 479. (-. (gt (pv5) (succ (n0)))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### TransEq2 476 476 478 % 156.85/157.06 480. (-. (gt (pv5) (pv5))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (succ (pv5)) T_1) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### Trans 479 40 % 156.85/157.06 481. ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ (n2)) T_0) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (gt (succ (pv5)) T_1) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) ### All 480 % 156.85/157.06 482. (leq T_1 (pv5)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) (gt (succ T_1) (n0)) (gt (succ (n2)) T_0) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### Definition-Pseudo(leq) 481 % 156.85/157.06 483. (leq T_0 (n2)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (succ T_1) (n0)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (leq T_1 (pv5)) ### Definition-Pseudo(leq) 482 % 156.85/157.06 484. (leq (n0) T_1) (leq T_1 (pv5)) (All X, (-. (gt X X))) ((a_select3 (u_defuse) T_0 T_1) != (use)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (leq T_0 (n2)) ### Definition-Pseudo(leq) 483 % 156.85/157.06 485. (leq (n0) T_0) (leq T_0 (n2)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) ((a_select3 (u_defuse) T_0 T_1) != (use)) (All X, (-. (gt X X))) (leq T_1 (pv5)) (leq (n0) T_1) ### Definition-Pseudo(leq) 484 % 156.85/157.06 486. (-. (((leq (n0) T_0) /\ ((leq (n0) T_1) /\ ((leq T_0 (n2)) /\ (leq T_1 (pv5))))) => ((a_select3 (u_defuse) T_0 T_1) = (use)))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### ConjTree 485 % 156.85/157.06 487. (-. (All F, (((leq (n0) T_0) /\ ((leq (n0) F) /\ ((leq T_0 (n2)) /\ (leq F (pv5))))) => ((a_select3 (u_defuse) T_0 F) = (use))))) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (n2) (n1)) (gt (succ (n0)) (pv5)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (All X, (-. (gt X X))) ### NotAllEx 486 % 156.85/157.06 488. (-. (All E, (All F, (((leq (n0) E) /\ ((leq (n0) F) /\ ((leq E (n2)) /\ (leq F (pv5))))) => ((a_select3 (u_defuse) E F) = (use)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (succ (pv5)) (n0)) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (succ (n0)) (pv5)) (gt (n2) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ### NotAllEx 487 % 156.85/157.06 489. (leq (pv5) (n0)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) ((a_select3 (u_defuse) (n0) (n0)) = (use)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (n2) (n1)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (gt (succ (pv5)) (n0)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (All X, (-. (gt X X))) (-. (All E, (All F, (((leq (n0) E) /\ ((leq (n0) F) /\ ((leq E (n2)) /\ (leq F (pv5))))) => ((a_select3 (u_defuse) E F) = (use)))))) ### Definition-Pseudo(leq) 488 % 156.85/157.06 490. (leq (n0) (pv5)) (-. (All E, (All F, (((leq (n0) E) /\ ((leq (n0) F) /\ ((leq E (n2)) /\ (leq F (pv5))))) => ((a_select3 (u_defuse) E F) = (use)))))) (All X, (-. (gt X X))) ((a_select3 (u_defuse) (n1) (n0)) = (use)) (gt (n3) (n2)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) ((succ (n0)) = (n1)) (gt (n3) (n1)) (gt (n2) (n1)) ((succ (succ (succ (n0)))) = (n3)) (gt (n4) (n3)) ((succ (succ (succ (succ (n0))))) = (n4)) ((succ (succ (n0))) = (n2)) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((a_select3 (u_defuse) (n0) (n0)) = (use)) ((a_select3 (u_defuse) (n2) (n0)) = (use)) (leq (pv5) (n0)) ### Definition-Pseudo(leq) 489 % 156.85/157.06 491. (-. ((((a_select2 (rho_defuse) (n0)) = (use)) /\ (((a_select2 (rho_defuse) (n1)) = (use)) /\ (((a_select2 (rho_defuse) (n2)) = (use)) /\ (((a_select2 (sigma_defuse) (n0)) = (use)) /\ (((a_select2 (sigma_defuse) (n1)) = (use)) /\ (((a_select2 (sigma_defuse) (n2)) = (use)) /\ (((a_select2 (sigma_defuse) (n3)) = (use)) /\ (((a_select2 (sigma_defuse) (n4)) = (use)) /\ (((a_select2 (sigma_defuse) (n5)) = (use)) /\ (((a_select3 (u_defuse) (n0) (n0)) = (use)) /\ (((a_select3 (u_defuse) (n1) (n0)) = (use)) /\ (((a_select3 (u_defuse) (n2) (n0)) = (use)) /\ (((a_select2 (xinit_defuse) (n3)) = (use)) /\ (((a_select2 (xinit_defuse) (n4)) = (use)) /\ (((a_select2 (xinit_defuse) (n5)) = (use)) /\ (((a_select2 (xinit_mean_defuse) (n0)) = (use)) /\ (((a_select2 (xinit_mean_defuse) (n1)) = (use)) /\ (((a_select2 (xinit_mean_defuse) (n2)) = (use)) /\ (((a_select2 (xinit_mean_defuse) (n3)) = (use)) /\ (((a_select2 (xinit_mean_defuse) (n4)) = (use)) /\ (((a_select2 (xinit_mean_defuse) (n5)) = (use)) /\ (((a_select2 (xinit_noise_defuse) (n0)) = (use)) /\ (((a_select2 (xinit_noise_defuse) (n1)) = (use)) /\ (((a_select2 (xinit_noise_defuse) (n2)) = (use)) /\ (((a_select2 (xinit_noise_defuse) (n3)) = (use)) /\ (((a_select2 (xinit_noise_defuse) (n4)) = (use)) /\ (((a_select2 (xinit_noise_defuse) (n5)) = (use)) /\ ((leq (n0) (pv5)) /\ ((leq (pv5) (n0)) /\ ((leq (pv5) (n998)) /\ ((All A, (All B, (((leq (n0) A) /\ ((leq (n0) B) /\ ((leq A (n2)) /\ (leq B (pred (pv5)))))) => ((a_select3 (u_defuse) A B) = (use))))) /\ (All C, (All D, (((leq (n0) C) /\ ((leq (n0) D) /\ ((leq C (n2)) /\ (leq D (pred (pv5)))))) => ((a_select3 (z_defuse) C D) = (use)))))))))))))))))))))))))))))))))))) => (All E, (All F, (((leq (n0) E) /\ ((leq (n0) F) /\ ((leq E (n2)) /\ (leq F (pv5))))) => ((a_select3 (u_defuse) E F) = (use))))))) (All X, (((leq (n0) X) /\ (leq X (n3))) => ((X = (n0)) \/ ((X = (n1)) \/ ((X = (n2)) \/ (X = (n3))))))) ((succ (succ (n0))) = (n2)) ((succ (succ (succ (succ (n0))))) = (n4)) (gt (n4) (n3)) ((succ (succ (succ (n0)))) = (n3)) (gt (n2) (n1)) (gt (n3) (n1)) ((succ (n0)) = (n1)) (All X, (((leq (n0) X) /\ (leq X (n2))) => ((X = (n0)) \/ ((X = (n1)) \/ (X = (n2)))))) (gt (n3) (n2)) (All X, (-. (gt X X))) ### ConjTree 490 % 156.85/157.06 % SZS output end Proof % 156.85/157.06 (* END-PROOF *) %------------------------------------------------------------------------------