%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV036+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 23:02:45 EDT 2022 % Result : Theorem 67.96s 68.14s % Output : Proof 67.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SWV036+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n024.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.33 % CPULimit : 300 % 0.18/0.33 % WCLimit : 600 % 0.18/0.33 % DateTime : Wed Jun 15 16:26:18 EDT 2022 % 0.18/0.33 % CPUTime : % 67.96/68.14 (* PROOF-FOUND *) % 67.96/68.14 % SZS status Theorem % 67.96/68.14 (* BEGIN-PROOF *) % 67.96/68.14 % SZS output start Proof % 67.96/68.14 Theorem gauss_init_0057 : ((((s_best7_init) = (init))/\(((s_sworst7_init) = (init))/\(((s_worst7_init) = (init))/\((leq (n0) (s_best7))/\((leq (n0) (s_sworst7))/\((leq (n0) (s_worst7))/\((leq (n2) (pv1388))/\((leq (s_best7) (n3))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv1388) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))))))))))))))))))->(((init) = (init))/\(((s_best7_init) = (init))/\(((a_select2 (s_values7_init) (s_best7)) = (init))/\(((a_select2 (s_values7_init) (pv1388)) = (init))/\(((~(gt (a_select2 (s_values7) (pv1388)) (a_select2 (s_values7) (s_best7))))->(((init) = (init))/\(((s_worst7_init) = (init))/\(((a_select2 (s_values7_init) (s_worst7)) = (init))/\(((a_select2 (s_values7_init) (pv1388)) = (init))/\(((~(leq (a_select2 (s_values7) (pv1388)) (a_select2 (s_values7) (s_worst7))))->(((init) = (init))/\(((s_sworst7_init) = (init))/\(((a_select2 (s_values7_init) (s_sworst7)) = (init))/\(((a_select2 (s_values7_init) (pv1388)) = (init))/\(((~(leq (a_select2 (s_values7) (pv1388)) (a_select2 (s_values7) (s_sworst7))))->(((s_best7_init) = (init))/\(((s_sworst7_init) = (init))/\(((s_worst7_init) = (init))/\((leq (n0) (s_best7))/\((leq (n0) (s_sworst7))/\((leq (n0) (s_worst7))/\((leq (s_best7) (n3))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init))))))))))))))))))/\((leq (a_select2 (s_values7) (pv1388)) (a_select2 (s_values7) (s_sworst7)))->(((init) = (init))/\(((s_best7_init) = (init))/\(((s_worst7_init) = (init))/\((leq (n0) (s_best7))/\((leq (n0) (s_worst7))/\((leq (n0) (pv1388))/\((leq (s_best7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv1388) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init))))))))))))))))))))))))/\((leq (a_select2 (s_values7) (pv1388)) (a_select2 (s_values7) (s_worst7)))->(((init) = (init))/\(((s_best7_init) = (init))/\(((s_worst7_init) = (init))/\((leq (n0) (s_best7))/\((leq (n0) (s_worst7))/\((leq (n0) (pv1388))/\((leq (s_best7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv1388) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init))))))))))))))))))))))))/\((gt (a_select2 (s_values7) (pv1388)) (a_select2 (s_values7) (s_best7)))->(((init) = (init))/\(((s_sworst7_init) = (init))/\(((s_worst7_init) = (init))/\((leq (n0) (s_sworst7))/\((leq (n0) (s_worst7))/\((leq (n0) (pv1388))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv1388) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))))))))))))))))))))))). % 67.96/68.14 Proof. % 67.96/68.14 assert (zenon_L1_ : (~((init) = (init))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H55. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 (* end of lemma zenon_L1_ *) % 67.96/68.14 assert (zenon_L2_ : (gt (succ (s_best7)) (n0)) -> (~(leq (n0) (s_best7))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H56 zenon_H57. % 67.96/68.14 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 67.96/68.14 generalize (zenon_H58 (s_best7)). zenon_intro zenon_H59. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H57; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H56 ]. % 67.96/68.14 exact (zenon_H5b zenon_H56). % 67.96/68.14 exact (zenon_H57 zenon_H5a). % 67.96/68.14 (* end of lemma zenon_L2_ *) % 67.96/68.14 assert (zenon_L3_ : (gt (succ (n3)) (s_best7)) -> (~(leq (s_best7) (n3))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H5c zenon_H5d. % 67.96/68.14 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H5e. % 67.96/68.14 generalize (zenon_H5e (n3)). zenon_intro zenon_H5f. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H5f); [ zenon_intro zenon_H5d; zenon_intro zenon_H61 | zenon_intro zenon_H60; zenon_intro zenon_H5c ]. % 67.96/68.14 exact (zenon_H61 zenon_H5c). % 67.96/68.14 exact (zenon_H5d zenon_H60). % 67.96/68.14 (* end of lemma zenon_L3_ *) % 67.96/68.14 assert (zenon_L4_ : (forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init)))) -> (gt (succ (s_best7)) (n0)) -> (gt (succ (n3)) (s_best7)) -> (~((a_select2 (s_values7_init) (s_best7)) = (init))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H62 zenon_H56 zenon_H5c zenon_H63. % 67.96/68.14 generalize (zenon_H62 (s_best7)). zenon_intro zenon_H64. % 67.96/68.14 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H57 | zenon_intro zenon_H5d ]. % 67.96/68.14 apply (zenon_L2_); trivial. % 67.96/68.14 apply (zenon_L3_); trivial. % 67.96/68.14 exact (zenon_H63 zenon_H65). % 67.96/68.14 (* end of lemma zenon_L4_ *) % 67.96/68.14 assert (zenon_L5_ : (~((n0) = (n0))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H67. % 67.96/68.14 apply zenon_H67. apply refl_equal. % 67.96/68.14 (* end of lemma zenon_L5_ *) % 67.96/68.14 assert (zenon_L6_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (pv1388)) (n2)) -> (~(leq (n0) (pv1388))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H68 zenon_H69 zenon_H6a. % 67.96/68.14 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 67.96/68.14 generalize (zenon_H58 (pv1388)). zenon_intro zenon_H6b. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H6b); [ zenon_intro zenon_H6a; zenon_intro zenon_H6e | zenon_intro zenon_H6d; zenon_intro zenon_H6c ]. % 67.96/68.14 elim (classic ((~((succ (pv1388)) = (n2)))/\(~(gt (succ (pv1388)) (n2))))); [ zenon_intro zenon_H6f | zenon_intro zenon_H70 ]. % 67.96/68.14 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71. % 67.96/68.14 exact (zenon_H71 zenon_H69). % 67.96/68.14 cut ((gt (n2) (n0)) = (gt (succ (pv1388)) (n0))). % 67.96/68.14 intro zenon_D_pnotp. % 67.96/68.14 apply zenon_H6e. % 67.96/68.14 rewrite <- zenon_D_pnotp. % 67.96/68.14 exact gt_2_0. % 67.96/68.14 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 67.96/68.14 cut (((n2) = (succ (pv1388)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 67.96/68.14 congruence. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_H70); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 67.96/68.14 apply zenon_H75. zenon_intro zenon_H76. % 67.96/68.14 elim (classic ((succ (pv1388)) = (succ (pv1388)))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 67.96/68.14 cut (((succ (pv1388)) = (succ (pv1388))) = ((n2) = (succ (pv1388)))). % 67.96/68.14 intro zenon_D_pnotp. % 67.96/68.14 apply zenon_H73. % 67.96/68.14 rewrite <- zenon_D_pnotp. % 67.96/68.14 exact zenon_H77. % 67.96/68.14 cut (((succ (pv1388)) = (succ (pv1388)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 67.96/68.14 cut (((succ (pv1388)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 67.96/68.14 congruence. % 67.96/68.14 exact (zenon_H72 zenon_H76). % 67.96/68.14 apply zenon_H78. apply refl_equal. % 67.96/68.14 apply zenon_H78. apply refl_equal. % 67.96/68.14 apply zenon_H74. zenon_intro zenon_H69. % 67.96/68.14 generalize (zenon_H68 (succ (pv1388))). zenon_intro zenon_H79. % 67.96/68.14 generalize (zenon_H79 (n2)). zenon_intro zenon_H7a. % 67.96/68.14 generalize (zenon_H7a (n0)). zenon_intro zenon_H7b. % 67.96/68.14 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H71 | zenon_intro zenon_H7c ]. % 67.96/68.14 exact (zenon_H71 zenon_H69). % 67.96/68.14 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H7d | zenon_intro zenon_H6c ]. % 67.96/68.14 exact (zenon_H7d gt_2_0). % 67.96/68.14 exact (zenon_H6e zenon_H6c). % 67.96/68.14 apply zenon_H67. apply refl_equal. % 67.96/68.14 exact (zenon_H6a zenon_H6d). % 67.96/68.14 (* end of lemma zenon_L6_ *) % 67.96/68.14 assert (zenon_L7_ : (gt (succ (n3)) (pv1388)) -> (~(leq (pv1388) (n3))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H7e zenon_H7f. % 67.96/68.14 generalize (leq_succ_gt_equiv (pv1388)). zenon_intro zenon_H80. % 67.96/68.14 generalize (zenon_H80 (n3)). zenon_intro zenon_H81. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H7f; zenon_intro zenon_H83 | zenon_intro zenon_H82; zenon_intro zenon_H7e ]. % 67.96/68.14 exact (zenon_H83 zenon_H7e). % 67.96/68.14 exact (zenon_H7f zenon_H82). % 67.96/68.14 (* end of lemma zenon_L7_ *) % 67.96/68.14 assert (zenon_L8_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init)))) -> (gt (succ (pv1388)) (n2)) -> (gt (succ (n3)) (pv1388)) -> (~((a_select2 (s_values7_init) (pv1388)) = (init))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H68 zenon_H62 zenon_H69 zenon_H7e zenon_H84. % 67.96/68.14 generalize (zenon_H62 (pv1388)). zenon_intro zenon_H85. % 67.96/68.14 apply (zenon_imply_s _ _ zenon_H85); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ]. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_H87); [ zenon_intro zenon_H6a | zenon_intro zenon_H7f ]. % 67.96/68.14 apply (zenon_L6_); trivial. % 67.96/68.14 apply (zenon_L7_); trivial. % 67.96/68.14 exact (zenon_H84 zenon_H86). % 67.96/68.14 (* end of lemma zenon_L8_ *) % 67.96/68.14 assert (zenon_L9_ : (gt (succ (s_worst7)) (n0)) -> (~(leq (n0) (s_worst7))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H88 zenon_H89. % 67.96/68.14 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 67.96/68.14 generalize (zenon_H58 (s_worst7)). zenon_intro zenon_H8a. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H8a); [ zenon_intro zenon_H89; zenon_intro zenon_H8c | zenon_intro zenon_H8b; zenon_intro zenon_H88 ]. % 67.96/68.14 exact (zenon_H8c zenon_H88). % 67.96/68.14 exact (zenon_H89 zenon_H8b). % 67.96/68.14 (* end of lemma zenon_L9_ *) % 67.96/68.14 assert (zenon_L10_ : (gt (succ (n3)) (s_worst7)) -> (~(leq (s_worst7) (n3))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H8d zenon_H8e. % 67.96/68.14 generalize (leq_succ_gt_equiv (s_worst7)). zenon_intro zenon_H8f. % 67.96/68.14 generalize (zenon_H8f (n3)). zenon_intro zenon_H90. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H90); [ zenon_intro zenon_H8e; zenon_intro zenon_H92 | zenon_intro zenon_H91; zenon_intro zenon_H8d ]. % 67.96/68.14 exact (zenon_H92 zenon_H8d). % 67.96/68.14 exact (zenon_H8e zenon_H91). % 67.96/68.14 (* end of lemma zenon_L10_ *) % 67.96/68.14 assert (zenon_L11_ : (forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init)))) -> (gt (succ (s_worst7)) (n0)) -> (gt (succ (n3)) (s_worst7)) -> (~((a_select2 (s_values7_init) (s_worst7)) = (init))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H62 zenon_H88 zenon_H8d zenon_H93. % 67.96/68.14 generalize (zenon_H62 (s_worst7)). zenon_intro zenon_H94. % 67.96/68.14 apply (zenon_imply_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_H96); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 67.96/68.14 apply (zenon_L9_); trivial. % 67.96/68.14 apply (zenon_L10_); trivial. % 67.96/68.14 exact (zenon_H93 zenon_H95). % 67.96/68.14 (* end of lemma zenon_L11_ *) % 67.96/68.14 assert (zenon_L12_ : (gt (succ (s_sworst7)) (n0)) -> (~(leq (n0) (s_sworst7))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H97 zenon_H98. % 67.96/68.14 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 67.96/68.14 generalize (zenon_H58 (s_sworst7)). zenon_intro zenon_H99. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H99); [ zenon_intro zenon_H98; zenon_intro zenon_H9b | zenon_intro zenon_H9a; zenon_intro zenon_H97 ]. % 67.96/68.14 exact (zenon_H9b zenon_H97). % 67.96/68.14 exact (zenon_H98 zenon_H9a). % 67.96/68.14 (* end of lemma zenon_L12_ *) % 67.96/68.14 assert (zenon_L13_ : (gt (succ (n3)) (s_sworst7)) -> (~(leq (s_sworst7) (n3))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H9c zenon_H9d. % 67.96/68.14 generalize (leq_succ_gt_equiv (s_sworst7)). zenon_intro zenon_H9e. % 67.96/68.14 generalize (zenon_H9e (n3)). zenon_intro zenon_H9f. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H9f); [ zenon_intro zenon_H9d; zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0; zenon_intro zenon_H9c ]. % 67.96/68.14 exact (zenon_Ha1 zenon_H9c). % 67.96/68.14 exact (zenon_H9d zenon_Ha0). % 67.96/68.14 (* end of lemma zenon_L13_ *) % 67.96/68.14 assert (zenon_L14_ : (forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init)))) -> (gt (succ (s_sworst7)) (n0)) -> (gt (succ (n3)) (s_sworst7)) -> (~((a_select2 (s_values7_init) (s_sworst7)) = (init))) -> False). % 67.96/68.14 do 0 intro. intros zenon_H62 zenon_H97 zenon_H9c zenon_Ha2. % 67.96/68.14 generalize (zenon_H62 (s_sworst7)). zenon_intro zenon_Ha3. % 67.96/68.14 apply (zenon_imply_s _ _ zenon_Ha3); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha4 ]. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Ha5); [ zenon_intro zenon_H98 | zenon_intro zenon_H9d ]. % 67.96/68.14 apply (zenon_L12_); trivial. % 67.96/68.14 apply (zenon_L13_); trivial. % 67.96/68.14 exact (zenon_Ha2 zenon_Ha4). % 67.96/68.14 (* end of lemma zenon_L14_ *) % 67.96/68.14 assert (zenon_L15_ : (~((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))))) -> (~(gt (loopcounter) (n1))) -> False). % 67.96/68.14 do 0 intro. intros zenon_Ha6 zenon_Ha7. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Ha6). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 67.96/68.14 exact (zenon_Ha7 zenon_Ha9). % 67.96/68.14 (* end of lemma zenon_L15_ *) % 67.96/68.14 assert (zenon_L16_ : (~(((init) = (init))/\(((s_best7_init) = (init))/\(((s_worst7_init) = (init))/\((leq (n0) (s_best7))/\((leq (n0) (s_worst7))/\((leq (n0) (pv1388))/\((leq (s_best7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv1388) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))))))))))))))))) -> ((s_best7_init) = (init)) -> ((s_worst7_init) = (init)) -> (gt (succ (s_best7)) (n0)) -> (gt (succ (s_worst7)) (n0)) -> (gt (succ (pv1388)) (n2)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (n3)) (s_best7)) -> (gt (succ (n3)) (s_worst7)) -> (gt (succ (n3)) (pv1388)) -> (forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init)))))) -> (forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init)))) -> (forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init)))) -> (~(gt (loopcounter) (n1))) -> False). % 67.96/68.14 do 0 intro. intros zenon_Haa zenon_Hab zenon_Hac zenon_H56 zenon_H88 zenon_H69 zenon_H68 zenon_H5c zenon_H8d zenon_H7e zenon_Had zenon_H62 zenon_Hae zenon_Ha7. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H55 | zenon_intro zenon_Haf ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Haf); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ]. % 67.96/68.14 exact (zenon_Hb1 zenon_Hab). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ]. % 67.96/68.14 exact (zenon_Hb3 zenon_Hac). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_H57 | zenon_intro zenon_Hb4 ]. % 67.96/68.14 apply (zenon_L2_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_H89 | zenon_intro zenon_Hb5 ]. % 67.96/68.14 apply (zenon_L9_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb6 ]. % 67.96/68.14 apply (zenon_L6_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb6); [ zenon_intro zenon_H5d | zenon_intro zenon_Hb7 ]. % 67.96/68.14 apply (zenon_L3_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb7); [ zenon_intro zenon_H8e | zenon_intro zenon_Hb8 ]. % 67.96/68.14 apply (zenon_L10_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hb9 ]. % 67.96/68.14 apply (zenon_L7_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 67.96/68.14 exact (zenon_Hbb zenon_Had). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbc ]. % 67.96/68.14 exact (zenon_Hbd zenon_H62). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Ha6 ]. % 67.96/68.14 exact (zenon_Hbe zenon_Hae). % 67.96/68.14 apply (zenon_L15_); trivial. % 67.96/68.14 (* end of lemma zenon_L16_ *) % 67.96/68.14 assert (zenon_L17_ : (~((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))))) -> (((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))) -> False). % 67.96/68.14 do 0 intro. intros zenon_Ha6 zenon_Hbf. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Ha6). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 67.96/68.14 exact (zenon_Ha8 zenon_Hbf). % 67.96/68.14 (* end of lemma zenon_L17_ *) % 67.96/68.14 assert (zenon_L18_ : (~(((init) = (init))/\(((s_best7_init) = (init))/\(((s_worst7_init) = (init))/\((leq (n0) (s_best7))/\((leq (n0) (s_worst7))/\((leq (n0) (pv1388))/\((leq (s_best7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv1388) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))))))))))))))))) -> ((s_best7_init) = (init)) -> ((s_worst7_init) = (init)) -> (gt (succ (s_best7)) (n0)) -> (gt (succ (s_worst7)) (n0)) -> (gt (succ (pv1388)) (n2)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (n3)) (s_best7)) -> (gt (succ (n3)) (s_worst7)) -> (gt (succ (n3)) (pv1388)) -> (forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init)))))) -> (forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init)))) -> (forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init)))) -> (((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))) -> False). % 67.96/68.14 do 0 intro. intros zenon_Haa zenon_Hab zenon_Hac zenon_H56 zenon_H88 zenon_H69 zenon_H68 zenon_H5c zenon_H8d zenon_H7e zenon_Had zenon_H62 zenon_Hae zenon_Hbf. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H55 | zenon_intro zenon_Haf ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Haf); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ]. % 67.96/68.14 exact (zenon_Hb1 zenon_Hab). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ]. % 67.96/68.14 exact (zenon_Hb3 zenon_Hac). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_H57 | zenon_intro zenon_Hb4 ]. % 67.96/68.14 apply (zenon_L2_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_H89 | zenon_intro zenon_Hb5 ]. % 67.96/68.14 apply (zenon_L9_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb6 ]. % 67.96/68.14 apply (zenon_L6_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb6); [ zenon_intro zenon_H5d | zenon_intro zenon_Hb7 ]. % 67.96/68.14 apply (zenon_L3_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb7); [ zenon_intro zenon_H8e | zenon_intro zenon_Hb8 ]. % 67.96/68.14 apply (zenon_L10_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hb9 ]. % 67.96/68.14 apply (zenon_L7_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 67.96/68.14 exact (zenon_Hbb zenon_Had). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbc ]. % 67.96/68.14 exact (zenon_Hbd zenon_H62). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Ha6 ]. % 67.96/68.14 exact (zenon_Hbe zenon_Hae). % 67.96/68.14 apply (zenon_L17_); trivial. % 67.96/68.14 (* end of lemma zenon_L18_ *) % 67.96/68.14 apply NNPP. intro zenon_G. % 67.96/68.14 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z))))))); [ zenon_intro zenon_H68 | zenon_intro zenon_Hc0 ]. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_Hab. zenon_intro zenon_Hc3. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hac. zenon_intro zenon_Hc6. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H5a. zenon_intro zenon_Hc7. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H9a. zenon_intro zenon_Hc8. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H8b. zenon_intro zenon_Hc9. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hca. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_H60. zenon_intro zenon_Hcc. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_Ha0. zenon_intro zenon_Hcd. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_H91. zenon_intro zenon_Hce. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H82. zenon_intro zenon_Hcf. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Had. zenon_intro zenon_Hd0. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_H62. zenon_intro zenon_Hd1. % 67.96/68.14 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hae. zenon_intro zenon_Hd2. % 67.96/68.14 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 67.96/68.14 generalize (zenon_H58 (s_best7)). zenon_intro zenon_H59. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H57; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H56 ]. % 67.96/68.14 exact (zenon_H57 zenon_H5a). % 67.96/68.14 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 67.96/68.14 generalize (zenon_H58 (s_sworst7)). zenon_intro zenon_H99. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H99); [ zenon_intro zenon_H98; zenon_intro zenon_H9b | zenon_intro zenon_H9a; zenon_intro zenon_H97 ]. % 67.96/68.14 exact (zenon_H98 zenon_H9a). % 67.96/68.14 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 67.96/68.14 generalize (zenon_H58 (s_worst7)). zenon_intro zenon_H8a. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H8a); [ zenon_intro zenon_H89; zenon_intro zenon_H8c | zenon_intro zenon_H8b; zenon_intro zenon_H88 ]. % 67.96/68.14 exact (zenon_H89 zenon_H8b). % 67.96/68.14 generalize (leq_succ_gt_equiv (n2)). zenon_intro zenon_Hd3. % 67.96/68.14 generalize (zenon_Hd3 (pv1388)). zenon_intro zenon_Hd4. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd5; zenon_intro zenon_H71 | zenon_intro zenon_Hcb; zenon_intro zenon_H69 ]. % 67.96/68.14 exact (zenon_Hd5 zenon_Hcb). % 67.96/68.14 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H5e. % 67.96/68.14 generalize (zenon_H5e (n3)). zenon_intro zenon_H5f. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H5f); [ zenon_intro zenon_H5d; zenon_intro zenon_H61 | zenon_intro zenon_H60; zenon_intro zenon_H5c ]. % 67.96/68.14 exact (zenon_H5d zenon_H60). % 67.96/68.14 generalize (leq_succ_gt_equiv (s_sworst7)). zenon_intro zenon_H9e. % 67.96/68.14 generalize (zenon_H9e (n3)). zenon_intro zenon_H9f. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H9f); [ zenon_intro zenon_H9d; zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0; zenon_intro zenon_H9c ]. % 67.96/68.14 exact (zenon_H9d zenon_Ha0). % 67.96/68.14 generalize (leq_succ_gt_equiv (s_worst7)). zenon_intro zenon_H8f. % 67.96/68.14 generalize (zenon_H8f (n3)). zenon_intro zenon_H90. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H90); [ zenon_intro zenon_H8e; zenon_intro zenon_H92 | zenon_intro zenon_H91; zenon_intro zenon_H8d ]. % 67.96/68.14 exact (zenon_H8e zenon_H91). % 67.96/68.14 generalize (leq_succ_gt_equiv (pv1388)). zenon_intro zenon_H80. % 67.96/68.14 generalize (zenon_H80 (n3)). zenon_intro zenon_H81. % 67.96/68.14 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H7f; zenon_intro zenon_H83 | zenon_intro zenon_H82; zenon_intro zenon_H7e ]. % 67.96/68.14 exact (zenon_H7f zenon_H82). % 67.96/68.14 apply (zenon_imply_s _ _ zenon_Hd2); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hbf ]. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hc1); [ zenon_intro zenon_H55 | zenon_intro zenon_Hd6 ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hd7 ]. % 67.96/68.14 exact (zenon_Hb1 zenon_Hab). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hd7); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd8 ]. % 67.96/68.14 apply (zenon_L4_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hd8); [ zenon_intro zenon_H84 | zenon_intro zenon_Hd9 ]. % 67.96/68.14 apply (zenon_L8_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hd9); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hda ]. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Hdb). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hdc); [ zenon_intro zenon_H55 | zenon_intro zenon_Hde ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hde); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hdf ]. % 67.96/68.14 exact (zenon_Hb3 zenon_Hac). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hdf); [ zenon_intro zenon_H93 | zenon_intro zenon_He0 ]. % 67.96/68.14 apply (zenon_L11_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He0); [ zenon_intro zenon_H84 | zenon_intro zenon_He1 ]. % 67.96/68.14 apply (zenon_L8_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He1); [ zenon_intro zenon_He3 | zenon_intro zenon_He2 ]. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_He3). zenon_intro zenon_He5. zenon_intro zenon_He4. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He4); [ zenon_intro zenon_H55 | zenon_intro zenon_He6 ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He6); [ zenon_intro zenon_He8 | zenon_intro zenon_He7 ]. % 67.96/68.14 exact (zenon_He8 zenon_Hc5). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He7); [ zenon_intro zenon_Ha2 | zenon_intro zenon_He9 ]. % 67.96/68.14 apply (zenon_L14_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He9); [ zenon_intro zenon_H84 | zenon_intro zenon_Hea ]. % 67.96/68.14 apply (zenon_L8_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hea); [ zenon_intro zenon_Hec | zenon_intro zenon_Heb ]. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Hec). zenon_intro zenon_Hee. zenon_intro zenon_Hed. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hed); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hef ]. % 67.96/68.14 exact (zenon_Hb1 zenon_Hab). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hef); [ zenon_intro zenon_He8 | zenon_intro zenon_Hf0 ]. % 67.96/68.14 exact (zenon_He8 zenon_Hc5). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf0); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hf1 ]. % 67.96/68.14 exact (zenon_Hb3 zenon_Hac). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H57 | zenon_intro zenon_Hf2 ]. % 67.96/68.14 apply (zenon_L2_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf2); [ zenon_intro zenon_H98 | zenon_intro zenon_Hf3 ]. % 67.96/68.14 apply (zenon_L12_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf3); [ zenon_intro zenon_H89 | zenon_intro zenon_Hf4 ]. % 67.96/68.14 apply (zenon_L9_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf4); [ zenon_intro zenon_H5d | zenon_intro zenon_Hf5 ]. % 67.96/68.14 apply (zenon_L3_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf5); [ zenon_intro zenon_H9d | zenon_intro zenon_Hf6 ]. % 67.96/68.14 apply (zenon_L13_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf6); [ zenon_intro zenon_H8e | zenon_intro zenon_Hb9 ]. % 67.96/68.14 apply (zenon_L10_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 67.96/68.14 exact (zenon_Hbb zenon_Had). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbc ]. % 67.96/68.14 exact (zenon_Hbd zenon_H62). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Ha6 ]. % 67.96/68.14 exact (zenon_Hbe zenon_Hae). % 67.96/68.14 apply (zenon_L15_); trivial. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Heb). zenon_intro zenon_Hf7. zenon_intro zenon_Haa. % 67.96/68.14 apply (zenon_L16_); trivial. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_He2). zenon_intro zenon_Hf8. zenon_intro zenon_Haa. % 67.96/68.14 apply (zenon_L16_); trivial. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Hda). zenon_intro zenon_Hfa. zenon_intro zenon_Hf9. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf9); [ zenon_intro zenon_H55 | zenon_intro zenon_Hfb ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hfb); [ zenon_intro zenon_He8 | zenon_intro zenon_Hfc ]. % 67.96/68.14 exact (zenon_He8 zenon_Hc5). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hfc); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hfd ]. % 67.96/68.14 exact (zenon_Hb3 zenon_Hac). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hfd); [ zenon_intro zenon_H98 | zenon_intro zenon_Hfe ]. % 67.96/68.14 apply (zenon_L12_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hfe); [ zenon_intro zenon_H89 | zenon_intro zenon_Hff ]. % 67.96/68.14 apply (zenon_L9_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hff); [ zenon_intro zenon_H6a | zenon_intro zenon_H100 ]. % 67.96/68.14 apply (zenon_L6_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_H100); [ zenon_intro zenon_H9d | zenon_intro zenon_Hb7 ]. % 67.96/68.14 apply (zenon_L13_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb7); [ zenon_intro zenon_H8e | zenon_intro zenon_Hb8 ]. % 67.96/68.14 apply (zenon_L10_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hb9 ]. % 67.96/68.14 apply (zenon_L7_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 67.96/68.14 exact (zenon_Hbb zenon_Had). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbc ]. % 67.96/68.14 exact (zenon_Hbd zenon_H62). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Ha6 ]. % 67.96/68.14 exact (zenon_Hbe zenon_Hae). % 67.96/68.14 apply (zenon_L15_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hc1); [ zenon_intro zenon_H55 | zenon_intro zenon_Hd6 ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hd7 ]. % 67.96/68.14 exact (zenon_Hb1 zenon_Hab). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hd7); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd8 ]. % 67.96/68.14 apply (zenon_L4_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hd8); [ zenon_intro zenon_H84 | zenon_intro zenon_Hd9 ]. % 67.96/68.14 apply (zenon_L8_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hd9); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hda ]. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Hdb). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hdc); [ zenon_intro zenon_H55 | zenon_intro zenon_Hde ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hde); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hdf ]. % 67.96/68.14 exact (zenon_Hb3 zenon_Hac). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hdf); [ zenon_intro zenon_H93 | zenon_intro zenon_He0 ]. % 67.96/68.14 apply (zenon_L11_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He0); [ zenon_intro zenon_H84 | zenon_intro zenon_He1 ]. % 67.96/68.14 apply (zenon_L8_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He1); [ zenon_intro zenon_He3 | zenon_intro zenon_He2 ]. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_He3). zenon_intro zenon_He5. zenon_intro zenon_He4. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He4); [ zenon_intro zenon_H55 | zenon_intro zenon_He6 ]. % 67.96/68.14 apply zenon_H55. apply refl_equal. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He6); [ zenon_intro zenon_He8 | zenon_intro zenon_He7 ]. % 67.96/68.14 exact (zenon_He8 zenon_Hc5). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He7); [ zenon_intro zenon_Ha2 | zenon_intro zenon_He9 ]. % 67.96/68.14 apply (zenon_L14_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_He9); [ zenon_intro zenon_H84 | zenon_intro zenon_Hea ]. % 67.96/68.14 apply (zenon_L8_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hea); [ zenon_intro zenon_Hec | zenon_intro zenon_Heb ]. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Hec). zenon_intro zenon_Hee. zenon_intro zenon_Hed. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hed); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hef ]. % 67.96/68.14 exact (zenon_Hb1 zenon_Hab). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hef); [ zenon_intro zenon_He8 | zenon_intro zenon_Hf0 ]. % 67.96/68.14 exact (zenon_He8 zenon_Hc5). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf0); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hf1 ]. % 67.96/68.14 exact (zenon_Hb3 zenon_Hac). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H57 | zenon_intro zenon_Hf2 ]. % 67.96/68.14 apply (zenon_L2_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf2); [ zenon_intro zenon_H98 | zenon_intro zenon_Hf3 ]. % 67.96/68.14 apply (zenon_L12_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf3); [ zenon_intro zenon_H89 | zenon_intro zenon_Hf4 ]. % 67.96/68.14 apply (zenon_L9_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf4); [ zenon_intro zenon_H5d | zenon_intro zenon_Hf5 ]. % 67.96/68.14 apply (zenon_L3_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf5); [ zenon_intro zenon_H9d | zenon_intro zenon_Hf6 ]. % 67.96/68.14 apply (zenon_L13_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf6); [ zenon_intro zenon_H8e | zenon_intro zenon_Hb9 ]. % 67.96/68.14 apply (zenon_L10_); trivial. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 67.96/68.14 exact (zenon_Hbb zenon_Had). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbc ]. % 67.96/68.14 exact (zenon_Hbd zenon_H62). % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Ha6 ]. % 67.96/68.14 exact (zenon_Hbe zenon_Hae). % 67.96/68.14 apply (zenon_L17_); trivial. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Heb). zenon_intro zenon_Hf7. zenon_intro zenon_Haa. % 67.96/68.14 apply (zenon_L18_); trivial. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_He2). zenon_intro zenon_Hf8. zenon_intro zenon_Haa. % 67.96/68.14 apply (zenon_L18_); trivial. % 67.96/68.14 apply (zenon_notimply_s _ _ zenon_Hda). zenon_intro zenon_Hfa. zenon_intro zenon_Hf9. % 67.96/68.14 apply (zenon_notand_s _ _ zenon_Hf9); [ zenon_intro zenon_H55 | zenon_intro zenon_Hfb ]. % 67.96/68.15 apply zenon_H55. apply refl_equal. % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hfb); [ zenon_intro zenon_He8 | zenon_intro zenon_Hfc ]. % 67.96/68.15 exact (zenon_He8 zenon_Hc5). % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hfc); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hfd ]. % 67.96/68.15 exact (zenon_Hb3 zenon_Hac). % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hfd); [ zenon_intro zenon_H98 | zenon_intro zenon_Hfe ]. % 67.96/68.15 apply (zenon_L12_); trivial. % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hfe); [ zenon_intro zenon_H89 | zenon_intro zenon_Hff ]. % 67.96/68.15 apply (zenon_L9_); trivial. % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hff); [ zenon_intro zenon_H6a | zenon_intro zenon_H100 ]. % 67.96/68.15 apply (zenon_L6_); trivial. % 67.96/68.15 apply (zenon_notand_s _ _ zenon_H100); [ zenon_intro zenon_H9d | zenon_intro zenon_Hb7 ]. % 67.96/68.15 apply (zenon_L13_); trivial. % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hb7); [ zenon_intro zenon_H8e | zenon_intro zenon_Hb8 ]. % 67.96/68.15 apply (zenon_L10_); trivial. % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hb8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hb9 ]. % 67.96/68.15 apply (zenon_L7_); trivial. % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 67.96/68.15 exact (zenon_Hbb zenon_Had). % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbc ]. % 67.96/68.15 exact (zenon_Hbd zenon_H62). % 67.96/68.15 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Ha6 ]. % 67.96/68.15 exact (zenon_Hbe zenon_Hae). % 67.96/68.15 apply (zenon_L17_); trivial. % 67.96/68.15 apply zenon_Hc0. zenon_intro zenon_Tx_jx. apply NNPP. zenon_intro zenon_H102. % 67.96/68.15 apply zenon_H102. zenon_intro zenon_Ty_jz. apply NNPP. zenon_intro zenon_H104. % 67.96/68.15 apply zenon_H104. zenon_intro zenon_Tz_kb. apply NNPP. zenon_intro zenon_H106. % 67.96/68.15 apply (zenon_notimply_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107. % 67.96/68.15 apply (zenon_notimply_s _ _ zenon_H107). zenon_intro zenon_H10a. zenon_intro zenon_H109. % 67.96/68.15 generalize (transitivity_gt zenon_Tx_jx). zenon_intro zenon_H10b. % 67.96/68.15 generalize (zenon_H10b zenon_Ty_jz). zenon_intro zenon_H10c. % 67.96/68.15 generalize (zenon_H10c zenon_Tz_kb). zenon_intro zenon_H10d. % 67.96/68.15 apply (zenon_imply_s _ _ zenon_H10d); [ zenon_intro zenon_H10f | zenon_intro zenon_H10e ]. % 67.96/68.15 apply (zenon_notand_s _ _ zenon_H10f); [ zenon_intro zenon_H111 | zenon_intro zenon_H110 ]. % 67.96/68.15 exact (zenon_H111 zenon_H108). % 67.96/68.15 exact (zenon_H110 zenon_H10a). % 67.96/68.15 exact (zenon_H109 zenon_H10e). % 67.96/68.15 Qed. % 67.96/68.15 % SZS output end Proof % 67.96/68.15 (* END-PROOF *) % 67.96/68.15 nodes searched: 5574765 % 67.96/68.15 max branch formulas: 18550 % 67.96/68.15 proof nodes created: 11270 % 67.96/68.15 formulas created: 1893474 % 67.96/68.15 %------------------------------------------------------------------------------