TSTP Solution File: SWV026+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------