%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV026+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 23:02:43 EDT 2022 % Result : Theorem 0.36s 0.57s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SWV026+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.08/0.14 % Command : run_zenon %s %d % 0.14/0.36 % Computer : n013.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Wed Jun 15 06:12:29 EDT 2022 % 0.14/0.36 % CPUTime : % 0.36/0.57 (* PROOF-FOUND *) % 0.36/0.57 % SZS status Theorem % 0.36/0.57 (* BEGIN-PROOF *) % 0.36/0.57 % SZS output start Proof % 0.36/0.57 Theorem gauss_init_0017 : ((((init) = (init))/\(((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 (n0) (pv9))/\((leq (n0) (pv19))/\((leq (n0) (pv20))/\((leq (n0) (pv1376))/\((leq (s_best7) (n3))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv9) (minus (n410) (n1)))/\((leq (pv19) (minus (n410) (n1)))/\((leq (pv20) (minus (n330) (n1)))/\((leq (pv1376) (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))))/\((forall E : zenon_U, (((leq (n0) E)/\(leq E (minus (n3) (n1))))->((a_select2 (s_try7_init) E) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))))))))))))))))))))))))))->(((init) = (init))/\(((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 (n0) (pv19))/\((leq (n0) (pv20))/\((leq (n0) (pv1376))/\((leq (s_best7) (n3))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv19) (minus (n410) (n1)))/\((leq (pv20) (minus (n330) (n1)))/\((leq (pv1376) (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))))/\((forall E : zenon_U, (((leq (n0) E)/\(leq E (minus (n3) (n1))))->((a_select2 (s_try7_init) E) = (init))))/\((gt (loopcounter) (n1))->(((pvar1400_init) = (init))/\(((pvar1401_init) = (init))/\((pvar1402_init) = (init)))))))))))))))))))))))))). % 0.36/0.57 Proof. % 0.36/0.57 assert (zenon_L1_ : (~((init) = (init))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H64. % 0.36/0.57 apply zenon_H64. apply refl_equal. % 0.36/0.57 (* end of lemma zenon_L1_ *) % 0.36/0.57 assert (zenon_L2_ : (gt (succ (s_best7)) (n0)) -> (~(leq (n0) (s_best7))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H65 zenon_H66. % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (s_best7)). zenon_intro zenon_H68. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H66; zenon_intro zenon_H6a | zenon_intro zenon_H69; zenon_intro zenon_H65 ]. % 0.36/0.57 exact (zenon_H6a zenon_H65). % 0.36/0.57 exact (zenon_H66 zenon_H69). % 0.36/0.57 (* end of lemma zenon_L2_ *) % 0.36/0.57 assert (zenon_L3_ : (gt (succ (s_sworst7)) (n0)) -> (~(leq (n0) (s_sworst7))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H6b zenon_H6c. % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (s_sworst7)). zenon_intro zenon_H6d. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H6d); [ zenon_intro zenon_H6c; zenon_intro zenon_H6f | zenon_intro zenon_H6e; zenon_intro zenon_H6b ]. % 0.36/0.57 exact (zenon_H6f zenon_H6b). % 0.36/0.57 exact (zenon_H6c zenon_H6e). % 0.36/0.57 (* end of lemma zenon_L3_ *) % 0.36/0.57 assert (zenon_L4_ : (gt (succ (s_worst7)) (n0)) -> (~(leq (n0) (s_worst7))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H70 zenon_H71. % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (s_worst7)). zenon_intro zenon_H72. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H71; zenon_intro zenon_H74 | zenon_intro zenon_H73; zenon_intro zenon_H70 ]. % 0.36/0.57 exact (zenon_H74 zenon_H70). % 0.36/0.57 exact (zenon_H71 zenon_H73). % 0.36/0.57 (* end of lemma zenon_L4_ *) % 0.36/0.57 assert (zenon_L5_ : (gt (succ (pv19)) (n0)) -> (~(leq (n0) (pv19))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H75 zenon_H76. % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (pv19)). zenon_intro zenon_H77. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H77); [ zenon_intro zenon_H76; zenon_intro zenon_H79 | zenon_intro zenon_H78; zenon_intro zenon_H75 ]. % 0.36/0.57 exact (zenon_H79 zenon_H75). % 0.36/0.57 exact (zenon_H76 zenon_H78). % 0.36/0.57 (* end of lemma zenon_L5_ *) % 0.36/0.57 assert (zenon_L6_ : (gt (succ (pv20)) (n0)) -> (~(leq (n0) (pv20))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H7a zenon_H7b. % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (pv20)). zenon_intro zenon_H7c. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7b; zenon_intro zenon_H7e | zenon_intro zenon_H7d; zenon_intro zenon_H7a ]. % 0.36/0.57 exact (zenon_H7e zenon_H7a). % 0.36/0.57 exact (zenon_H7b zenon_H7d). % 0.36/0.57 (* end of lemma zenon_L6_ *) % 0.36/0.57 assert (zenon_L7_ : (gt (succ (pv1376)) (n0)) -> (~(leq (n0) (pv1376))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H7f zenon_H80. % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (pv1376)). zenon_intro zenon_H81. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H80; zenon_intro zenon_H83 | zenon_intro zenon_H82; zenon_intro zenon_H7f ]. % 0.36/0.57 exact (zenon_H83 zenon_H7f). % 0.36/0.57 exact (zenon_H80 zenon_H82). % 0.36/0.57 (* end of lemma zenon_L7_ *) % 0.36/0.57 assert (zenon_L8_ : (gt (succ (n3)) (s_best7)) -> (~(leq (s_best7) (n3))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H84 zenon_H85. % 0.36/0.57 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H86. % 0.36/0.57 generalize (zenon_H86 (n3)). zenon_intro zenon_H87. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H87); [ zenon_intro zenon_H85; zenon_intro zenon_H89 | zenon_intro zenon_H88; zenon_intro zenon_H84 ]. % 0.36/0.57 exact (zenon_H89 zenon_H84). % 0.36/0.57 exact (zenon_H85 zenon_H88). % 0.36/0.57 (* end of lemma zenon_L8_ *) % 0.36/0.57 assert (zenon_L9_ : (gt (succ (n3)) (s_sworst7)) -> (~(leq (s_sworst7) (n3))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H8a zenon_H8b. % 0.36/0.57 generalize (leq_succ_gt_equiv (s_sworst7)). zenon_intro zenon_H8c. % 0.36/0.57 generalize (zenon_H8c (n3)). zenon_intro zenon_H8d. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H8d); [ zenon_intro zenon_H8b; zenon_intro zenon_H8f | zenon_intro zenon_H8e; zenon_intro zenon_H8a ]. % 0.36/0.57 exact (zenon_H8f zenon_H8a). % 0.36/0.57 exact (zenon_H8b zenon_H8e). % 0.36/0.57 (* end of lemma zenon_L9_ *) % 0.36/0.57 assert (zenon_L10_ : (gt (succ (n3)) (s_worst7)) -> (~(leq (s_worst7) (n3))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H90 zenon_H91. % 0.36/0.57 generalize (leq_succ_gt_equiv (s_worst7)). zenon_intro zenon_H92. % 0.36/0.57 generalize (zenon_H92 (n3)). zenon_intro zenon_H93. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H93); [ zenon_intro zenon_H91; zenon_intro zenon_H95 | zenon_intro zenon_H94; zenon_intro zenon_H90 ]. % 0.36/0.57 exact (zenon_H95 zenon_H90). % 0.36/0.57 exact (zenon_H91 zenon_H94). % 0.36/0.57 (* end of lemma zenon_L10_ *) % 0.36/0.57 assert (zenon_L11_ : (gt (succ (minus (n410) (n1))) (pv19)) -> (~(leq (pv19) (minus (n410) (n1)))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H96 zenon_H97. % 0.36/0.57 generalize (leq_succ_gt_equiv (pv19)). zenon_intro zenon_H98. % 0.36/0.57 generalize (zenon_H98 (minus (n410) (n1))). zenon_intro zenon_H99. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H99); [ zenon_intro zenon_H97; zenon_intro zenon_H9b | zenon_intro zenon_H9a; zenon_intro zenon_H96 ]. % 0.36/0.57 exact (zenon_H9b zenon_H96). % 0.36/0.57 exact (zenon_H97 zenon_H9a). % 0.36/0.57 (* end of lemma zenon_L11_ *) % 0.36/0.57 assert (zenon_L12_ : (gt (succ (minus (n330) (n1))) (pv20)) -> (~(leq (pv20) (minus (n330) (n1)))) -> False). % 0.36/0.57 do 0 intro. intros zenon_H9c zenon_H9d. % 0.36/0.57 generalize (leq_succ_gt_equiv (pv20)). zenon_intro zenon_H9e. % 0.36/0.57 generalize (zenon_H9e (minus (n330) (n1))). zenon_intro zenon_H9f. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H9f); [ zenon_intro zenon_H9d; zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0; zenon_intro zenon_H9c ]. % 0.36/0.57 exact (zenon_Ha1 zenon_H9c). % 0.36/0.57 exact (zenon_H9d zenon_Ha0). % 0.36/0.57 (* end of lemma zenon_L12_ *) % 0.36/0.57 assert (zenon_L13_ : (gt (succ (n3)) (pv1376)) -> (~(leq (pv1376) (n3))) -> False). % 0.36/0.57 do 0 intro. intros zenon_Ha2 zenon_Ha3. % 0.36/0.57 generalize (leq_succ_gt_equiv (pv1376)). zenon_intro zenon_Ha4. % 0.36/0.57 generalize (zenon_Ha4 (n3)). zenon_intro zenon_Ha5. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_Ha5); [ zenon_intro zenon_Ha3; zenon_intro zenon_Ha7 | zenon_intro zenon_Ha6; zenon_intro zenon_Ha2 ]. % 0.36/0.57 exact (zenon_Ha7 zenon_Ha2). % 0.36/0.57 exact (zenon_Ha3 zenon_Ha6). % 0.36/0.57 (* end of lemma zenon_L13_ *) % 0.36/0.57 apply NNPP. intro zenon_G. % 0.36/0.57 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_Hab. zenon_intro zenon_Haa. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Haa). zenon_intro zenon_Had. zenon_intro zenon_Hac. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hac). zenon_intro zenon_Haf. zenon_intro zenon_Hae. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Hb1. zenon_intro zenon_Hb0. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hb0). zenon_intro zenon_H69. zenon_intro zenon_Hb2. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H6e. zenon_intro zenon_Hb3. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H73. zenon_intro zenon_Hb4. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_Hb6. zenon_intro zenon_Hb5. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_H78. zenon_intro zenon_Hb7. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hb7). zenon_intro zenon_H7d. zenon_intro zenon_Hb8. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hb8). zenon_intro zenon_H82. zenon_intro zenon_Hb9. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hb9). zenon_intro zenon_H88. zenon_intro zenon_Hba. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_H8e. zenon_intro zenon_Hbb. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_H94. zenon_intro zenon_Hbc. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_H9a. zenon_intro zenon_Hbf. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hbf). zenon_intro zenon_Ha0. zenon_intro zenon_Hc0. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Ha6. zenon_intro zenon_Hc1. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hc3. zenon_intro zenon_Hc2. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hc7. zenon_intro zenon_Hc6. % 0.36/0.57 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8. % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (s_best7)). zenon_intro zenon_H68. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H66; zenon_intro zenon_H6a | zenon_intro zenon_H69; zenon_intro zenon_H65 ]. % 0.36/0.57 exact (zenon_H66 zenon_H69). % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (s_sworst7)). zenon_intro zenon_H6d. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H6d); [ zenon_intro zenon_H6c; zenon_intro zenon_H6f | zenon_intro zenon_H6e; zenon_intro zenon_H6b ]. % 0.36/0.57 exact (zenon_H6c zenon_H6e). % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (s_worst7)). zenon_intro zenon_H72. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H71; zenon_intro zenon_H74 | zenon_intro zenon_H73; zenon_intro zenon_H70 ]. % 0.36/0.57 exact (zenon_H71 zenon_H73). % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (pv19)). zenon_intro zenon_H77. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H77); [ zenon_intro zenon_H76; zenon_intro zenon_H79 | zenon_intro zenon_H78; zenon_intro zenon_H75 ]. % 0.36/0.57 exact (zenon_H76 zenon_H78). % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (pv20)). zenon_intro zenon_H7c. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7b; zenon_intro zenon_H7e | zenon_intro zenon_H7d; zenon_intro zenon_H7a ]. % 0.36/0.57 exact (zenon_H7b zenon_H7d). % 0.36/0.57 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.36/0.57 generalize (zenon_H67 (pv1376)). zenon_intro zenon_H81. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H80; zenon_intro zenon_H83 | zenon_intro zenon_H82; zenon_intro zenon_H7f ]. % 0.36/0.57 exact (zenon_H80 zenon_H82). % 0.36/0.57 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H86. % 0.36/0.57 generalize (zenon_H86 (n3)). zenon_intro zenon_H87. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H87); [ zenon_intro zenon_H85; zenon_intro zenon_H89 | zenon_intro zenon_H88; zenon_intro zenon_H84 ]. % 0.36/0.57 exact (zenon_H85 zenon_H88). % 0.36/0.57 generalize (leq_succ_gt_equiv (s_sworst7)). zenon_intro zenon_H8c. % 0.36/0.57 generalize (zenon_H8c (n3)). zenon_intro zenon_H8d. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H8d); [ zenon_intro zenon_H8b; zenon_intro zenon_H8f | zenon_intro zenon_H8e; zenon_intro zenon_H8a ]. % 0.36/0.57 exact (zenon_H8b zenon_H8e). % 0.36/0.57 generalize (leq_succ_gt_equiv (s_worst7)). zenon_intro zenon_H92. % 0.36/0.57 generalize (zenon_H92 (n3)). zenon_intro zenon_H93. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H93); [ zenon_intro zenon_H91; zenon_intro zenon_H95 | zenon_intro zenon_H94; zenon_intro zenon_H90 ]. % 0.36/0.57 exact (zenon_H91 zenon_H94). % 0.36/0.57 generalize (leq_succ_gt_equiv (pv19)). zenon_intro zenon_H98. % 0.36/0.57 generalize (zenon_H98 (minus (n410) (n1))). zenon_intro zenon_H99. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H99); [ zenon_intro zenon_H97; zenon_intro zenon_H9b | zenon_intro zenon_H9a; zenon_intro zenon_H96 ]. % 0.36/0.57 exact (zenon_H97 zenon_H9a). % 0.36/0.57 generalize (leq_succ_gt_equiv (pv20)). zenon_intro zenon_H9e. % 0.36/0.57 generalize (zenon_H9e (minus (n330) (n1))). zenon_intro zenon_H9f. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_H9f); [ zenon_intro zenon_H9d; zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0; zenon_intro zenon_H9c ]. % 0.36/0.57 exact (zenon_H9d zenon_Ha0). % 0.36/0.57 generalize (leq_succ_gt_equiv (pv1376)). zenon_intro zenon_Ha4. % 0.36/0.57 generalize (zenon_Ha4 (n3)). zenon_intro zenon_Ha5. % 0.36/0.57 apply (zenon_equiv_s _ _ zenon_Ha5); [ zenon_intro zenon_Ha3; zenon_intro zenon_Ha7 | zenon_intro zenon_Ha6; zenon_intro zenon_Ha2 ]. % 0.36/0.57 exact (zenon_Ha3 zenon_Ha6). % 0.36/0.57 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hca ]. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Ha8); [ zenon_intro zenon_H64 | zenon_intro zenon_Hcc ]. % 0.36/0.57 apply zenon_H64. apply refl_equal. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hcc); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcd ]. % 0.36/0.57 exact (zenon_Hce zenon_Had). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hcd); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcf ]. % 0.36/0.57 exact (zenon_Hd0 zenon_Haf). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd1 ]. % 0.36/0.57 exact (zenon_Hd2 zenon_Hb1). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd1); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd3 ]. % 0.36/0.57 apply (zenon_L2_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd3); [ zenon_intro zenon_H6c | zenon_intro zenon_Hd4 ]. % 0.36/0.57 apply (zenon_L3_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd4); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd5 ]. % 0.36/0.57 apply (zenon_L4_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd5); [ zenon_intro zenon_H76 | zenon_intro zenon_Hd6 ]. % 0.36/0.57 apply (zenon_L5_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_H7b | zenon_intro zenon_Hd7 ]. % 0.36/0.57 apply (zenon_L6_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hd8 ]. % 0.36/0.57 apply (zenon_L7_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd8); [ zenon_intro zenon_H85 | zenon_intro zenon_Hd9 ]. % 0.36/0.57 apply (zenon_L8_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd9); [ zenon_intro zenon_H8b | zenon_intro zenon_Hda ]. % 0.36/0.57 apply (zenon_L9_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hda); [ zenon_intro zenon_H91 | zenon_intro zenon_Hdb ]. % 0.36/0.57 apply (zenon_L10_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hdb); [ zenon_intro zenon_H97 | zenon_intro zenon_Hdc ]. % 0.36/0.57 apply (zenon_L11_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hdc); [ zenon_intro zenon_H9d | zenon_intro zenon_Hdd ]. % 0.36/0.57 apply (zenon_L12_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hdd); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Hde ]. % 0.36/0.57 apply (zenon_L13_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hde); [ zenon_intro zenon_He0 | zenon_intro zenon_Hdf ]. % 0.36/0.57 exact (zenon_He0 zenon_Hc3). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hdf); [ zenon_intro zenon_He2 | zenon_intro zenon_He1 ]. % 0.36/0.57 exact (zenon_He2 zenon_Hc5). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_He1); [ zenon_intro zenon_He4 | zenon_intro zenon_He3 ]. % 0.36/0.57 exact (zenon_He4 zenon_Hc7). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_He3); [ zenon_intro zenon_He6 | zenon_intro zenon_He5 ]. % 0.36/0.57 exact (zenon_He6 zenon_Hc9). % 0.36/0.57 apply (zenon_notimply_s _ _ zenon_He5). zenon_intro zenon_He8. zenon_intro zenon_He7. % 0.36/0.57 exact (zenon_Hcb zenon_He8). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Ha8); [ zenon_intro zenon_H64 | zenon_intro zenon_Hcc ]. % 0.36/0.57 apply zenon_H64. apply refl_equal. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hcc); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcd ]. % 0.36/0.57 exact (zenon_Hce zenon_Had). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hcd); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcf ]. % 0.36/0.57 exact (zenon_Hd0 zenon_Haf). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd1 ]. % 0.36/0.57 exact (zenon_Hd2 zenon_Hb1). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd1); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd3 ]. % 0.36/0.57 apply (zenon_L2_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd3); [ zenon_intro zenon_H6c | zenon_intro zenon_Hd4 ]. % 0.36/0.57 apply (zenon_L3_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd4); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd5 ]. % 0.36/0.57 apply (zenon_L4_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd5); [ zenon_intro zenon_H76 | zenon_intro zenon_Hd6 ]. % 0.36/0.57 apply (zenon_L5_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_H7b | zenon_intro zenon_Hd7 ]. % 0.36/0.57 apply (zenon_L6_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hd8 ]. % 0.36/0.57 apply (zenon_L7_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd8); [ zenon_intro zenon_H85 | zenon_intro zenon_Hd9 ]. % 0.36/0.57 apply (zenon_L8_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hd9); [ zenon_intro zenon_H8b | zenon_intro zenon_Hda ]. % 0.36/0.57 apply (zenon_L9_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hda); [ zenon_intro zenon_H91 | zenon_intro zenon_Hdb ]. % 0.36/0.57 apply (zenon_L10_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hdb); [ zenon_intro zenon_H97 | zenon_intro zenon_Hdc ]. % 0.36/0.57 apply (zenon_L11_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hdc); [ zenon_intro zenon_H9d | zenon_intro zenon_Hdd ]. % 0.36/0.57 apply (zenon_L12_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hdd); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Hde ]. % 0.36/0.57 apply (zenon_L13_); trivial. % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hde); [ zenon_intro zenon_He0 | zenon_intro zenon_Hdf ]. % 0.36/0.57 exact (zenon_He0 zenon_Hc3). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_Hdf); [ zenon_intro zenon_He2 | zenon_intro zenon_He1 ]. % 0.36/0.57 exact (zenon_He2 zenon_Hc5). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_He1); [ zenon_intro zenon_He4 | zenon_intro zenon_He3 ]. % 0.36/0.57 exact (zenon_He4 zenon_Hc7). % 0.36/0.57 apply (zenon_notand_s _ _ zenon_He3); [ zenon_intro zenon_He6 | zenon_intro zenon_He5 ]. % 0.36/0.57 exact (zenon_He6 zenon_Hc9). % 0.36/0.57 apply (zenon_notimply_s _ _ zenon_He5). zenon_intro zenon_He8. zenon_intro zenon_He7. % 0.36/0.57 exact (zenon_He7 zenon_Hca). % 0.36/0.57 Qed. % 0.36/0.57 % SZS output end Proof % 0.36/0.57 (* END-PROOF *) % 0.36/0.57 nodes searched: 112 % 0.36/0.57 max branch formulas: 150 % 0.36/0.57 proof nodes created: 59 % 0.36/0.57 formulas created: 3175 % 0.36/0.57 %------------------------------------------------------------------------------