TSTP Solution File: SWV181+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV181+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n021.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 23:03:13 EDT 2022
% Result : Theorem 119.80s 120.08s
% Output : Proof 119.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV181+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Wed Jun 15 07:56:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 119.80/120.08 (* PROOF-FOUND *)
% 119.80/120.08 % SZS status Theorem
% 119.80/120.08 (* BEGIN-PROOF *)
% 119.80/120.08 % SZS output start Proof
% 119.80/120.08 Theorem cl5_nebula_init_0081 : (((leq (tptp_float_0_001) (pv76))/\((leq (n1) (loopcounter))/\((gt (n1) (loopcounter))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n135299)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n4)))->((a_select3 (q_init) A B) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n4)))->((a_select3 (center_init) C (n0)) = (init))))/\(((gt (loopcounter) (n0))->(forall D : zenon_U, (((leq (n0) D)/\(leq D (n4)))->((a_select2 (mu_init) D) = (init)))))/\(((gt (loopcounter) (n0))->(forall E : zenon_U, (((leq (n0) E)/\(leq E (n4)))->((a_select2 (rho_init) E) = (init)))))/\((gt (loopcounter) (n0))->(forall F : zenon_U, (((leq (n0) F)/\(leq F (n4)))->((a_select2 (sigma_init) F) = (init))))))))))))->(forall G : zenon_U, (((leq (n0) G)/\(leq G (n4)))->((a_select2 (muold_init) G) = (init))))).
% 119.80/120.08 Proof.
% 119.80/120.08 assert (zenon_L1_ : forall (zenon_TG_dq : zenon_U), (gt (succ zenon_TG_dq) (n0)) -> (~(leq (n0) zenon_TG_dq)) -> False).
% 119.80/120.08 do 1 intro. intros zenon_H5c zenon_H5d.
% 119.80/120.08 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 119.80/120.08 generalize (zenon_H5f zenon_TG_dq). zenon_intro zenon_H60.
% 119.80/120.08 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H5d; zenon_intro zenon_H62 | zenon_intro zenon_H61; zenon_intro zenon_H5c ].
% 119.80/120.08 exact (zenon_H62 zenon_H5c).
% 119.80/120.08 exact (zenon_H5d zenon_H61).
% 119.80/120.08 (* end of lemma zenon_L1_ *)
% 119.80/120.08 assert (zenon_L2_ : (~((n2) = (n2))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H63.
% 119.80/120.08 apply zenon_H63. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L2_ *)
% 119.80/120.08 assert (zenon_L3_ : (~((n1) = (n1))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H64.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L3_ *)
% 119.80/120.08 assert (zenon_L4_ : (~((n0) = (n0))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H65.
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L4_ *)
% 119.80/120.08 assert (zenon_L5_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (~(leq (n0) (loopcounter))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H67 zenon_H68.
% 119.80/120.08 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 119.80/120.08 generalize (zenon_H5f (loopcounter)). zenon_intro zenon_H69.
% 119.80/120.08 apply (zenon_equiv_s _ _ zenon_H69); [ zenon_intro zenon_H68; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H6a ].
% 119.80/120.08 elim (classic ((~((succ (loopcounter)) = (n1)))/\(~(gt (succ (loopcounter)) (n1))))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 119.80/120.08 exact (zenon_H6f zenon_H67).
% 119.80/120.08 cut ((gt (n1) (n0)) = (gt (succ (loopcounter)) (n0))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H6c.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact gt_1_0.
% 119.80/120.08 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.08 cut (((n1) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H71].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ].
% 119.80/120.08 apply zenon_H73. zenon_intro zenon_H74.
% 119.80/120.08 elim (classic ((succ (loopcounter)) = (succ (loopcounter)))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (loopcounter))) = ((n1) = (succ (loopcounter)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H71.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H75.
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.80/120.08 cut (((succ (loopcounter)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H70].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H70 zenon_H74).
% 119.80/120.08 apply zenon_H76. apply refl_equal.
% 119.80/120.08 apply zenon_H76. apply refl_equal.
% 119.80/120.08 apply zenon_H72. zenon_intro zenon_H67.
% 119.80/120.08 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.80/120.08 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.80/120.08 generalize (zenon_H78 (n0)). zenon_intro zenon_H79.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H6f | zenon_intro zenon_H7a ].
% 119.80/120.08 exact (zenon_H6f zenon_H67).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H7b | zenon_intro zenon_H6a ].
% 119.80/120.08 exact (zenon_H7b gt_1_0).
% 119.80/120.08 exact (zenon_H6c zenon_H6a).
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 exact (zenon_H68 zenon_H6b).
% 119.80/120.08 (* end of lemma zenon_L5_ *)
% 119.80/120.08 assert (zenon_L6_ : (~((loopcounter) = (loopcounter))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H7c.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L6_ *)
% 119.80/120.08 assert (zenon_L7_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (n1) (loopcounter)) -> (~(leq (loopcounter) (n0))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H7d zenon_H7e.
% 119.80/120.08 generalize (leq_succ_gt_equiv (loopcounter)). zenon_intro zenon_H7f.
% 119.80/120.08 generalize (zenon_H7f (n0)). zenon_intro zenon_H80.
% 119.80/120.08 apply (zenon_equiv_s _ _ zenon_H80); [ zenon_intro zenon_H7e; zenon_intro zenon_H83 | zenon_intro zenon_H82; zenon_intro zenon_H81 ].
% 119.80/120.08 elim (classic ((~((succ (n0)) = (n1)))/\(~(gt (succ (n0)) (n1))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_H84). zenon_intro zenon_H87. zenon_intro zenon_H86.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 cut ((gt (n1) (loopcounter)) = (gt (succ (n0)) (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H83.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H7d.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H8a | zenon_intro zenon_H89 ].
% 119.80/120.08 apply zenon_H8a. zenon_intro successor_1.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H88.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H89. zenon_intro zenon_H8d.
% 119.80/120.08 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.80/120.08 generalize (zenon_H8e (n1)). zenon_intro zenon_H8f.
% 119.80/120.08 generalize (zenon_H8f (loopcounter)). zenon_intro zenon_H90.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H86 | zenon_intro zenon_H91 ].
% 119.80/120.08 exact (zenon_H86 zenon_H8d).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H91); [ zenon_intro zenon_H92 | zenon_intro zenon_H81 ].
% 119.80/120.08 exact (zenon_H92 zenon_H7d).
% 119.80/120.08 exact (zenon_H83 zenon_H81).
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 exact (zenon_H7e zenon_H82).
% 119.80/120.08 (* end of lemma zenon_L7_ *)
% 119.80/120.08 assert (zenon_L8_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((n0) = (loopcounter))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H93.
% 119.80/120.08 generalize (finite_domain_0 (loopcounter)). zenon_intro zenon_H94.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ].
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_H96); [ zenon_intro zenon_H68 | zenon_intro zenon_H7e ].
% 119.80/120.08 apply (zenon_L5_); trivial.
% 119.80/120.08 apply (zenon_L7_); trivial.
% 119.80/120.08 apply zenon_H93. apply sym_equal. exact zenon_H95.
% 119.80/120.08 (* end of lemma zenon_L8_ *)
% 119.80/120.08 assert (zenon_L9_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((succ (n0)) = (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H97 zenon_H7d zenon_H67.
% 119.80/120.08 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_L8_); trivial.
% 119.80/120.08 (* end of lemma zenon_L9_ *)
% 119.80/120.08 assert (zenon_L10_ : (~((succ (n3)) = (succ (succ (succ (succ (n0))))))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H98.
% 119.80/120.08 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H99. apply sym_equal. exact successor_3.
% 119.80/120.08 (* end of lemma zenon_L10_ *)
% 119.80/120.08 assert (zenon_L11_ : (~(gt (succ (n3)) (n2))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H9a.
% 119.80/120.08 elim (classic (gt (succ (succ (succ (succ (n0))))) (n2))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ].
% 119.80/120.08 cut ((gt (succ (succ (succ (succ (n0))))) (n2)) = (gt (succ (n3)) (n2))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H9a.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H9b.
% 119.80/120.08 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.80/120.08 cut (((succ (succ (succ (succ (n0))))) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9d].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ].
% 119.80/120.08 cut (((succ (n3)) = (succ (n3))) = ((succ (succ (succ (succ (n0))))) = (succ (n3)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H9d.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H9e.
% 119.80/120.08 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.80/120.08 cut (((succ (n3)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H98].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_L10_); trivial.
% 119.80/120.08 apply zenon_H9f. apply refl_equal.
% 119.80/120.08 apply zenon_H9f. apply refl_equal.
% 119.80/120.08 apply zenon_H63. apply refl_equal.
% 119.80/120.08 cut ((gt (n4) (n2)) = (gt (succ (succ (succ (succ (n0))))) (n2))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H9c.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact gt_4_2.
% 119.80/120.08 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.80/120.08 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ].
% 119.80/120.08 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Ha0.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Ha1.
% 119.80/120.08 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 119.80/120.08 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_Ha3 successor_4).
% 119.80/120.08 apply zenon_Ha2. apply refl_equal.
% 119.80/120.08 apply zenon_Ha2. apply refl_equal.
% 119.80/120.08 apply zenon_H63. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L11_ *)
% 119.80/120.08 assert (zenon_L12_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (n1) (loopcounter)) -> (~(leq (loopcounter) (n3))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H7d zenon_Ha4.
% 119.80/120.08 generalize (leq_succ_gt_equiv (loopcounter)). zenon_intro zenon_H7f.
% 119.80/120.08 generalize (zenon_H7f (n3)). zenon_intro zenon_Ha5.
% 119.80/120.08 apply (zenon_equiv_s _ _ zenon_Ha5); [ zenon_intro zenon_Ha4; zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7; zenon_intro zenon_Ha6 ].
% 119.80/120.08 elim (classic ((~((succ (n3)) = (n1)))/\(~(gt (succ (n3)) (n1))))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_Hac. zenon_intro zenon_Hab.
% 119.80/120.08 elim (classic ((~((succ (n3)) = (n2)))/\(~(gt (succ (n3)) (n2))))); [ zenon_intro zenon_Had | zenon_intro zenon_Hae ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_Haf. zenon_intro zenon_H9a.
% 119.80/120.08 apply (zenon_L11_); trivial.
% 119.80/120.08 cut ((gt (n2) (n1)) = (gt (succ (n3)) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hab.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact gt_2_1.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((n2) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_Hae); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb1 ].
% 119.80/120.08 apply zenon_Hb2. zenon_intro zenon_Hb3.
% 119.80/120.08 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ].
% 119.80/120.08 cut (((succ (n3)) = (succ (n3))) = ((n2) = (succ (n3)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hb0.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H9e.
% 119.80/120.08 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.80/120.08 cut (((succ (n3)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_Haf zenon_Hb3).
% 119.80/120.08 apply zenon_H9f. apply refl_equal.
% 119.80/120.08 apply zenon_H9f. apply refl_equal.
% 119.80/120.08 apply zenon_Hb1. zenon_intro zenon_Hb4.
% 119.80/120.08 generalize (zenon_H66 (succ (n3))). zenon_intro zenon_Hb5.
% 119.80/120.08 generalize (zenon_Hb5 (n2)). zenon_intro zenon_Hb6.
% 119.80/120.08 generalize (zenon_Hb6 (n1)). zenon_intro zenon_Hb7.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_H9a | zenon_intro zenon_Hb8 ].
% 119.80/120.08 exact (zenon_H9a zenon_Hb4).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ].
% 119.80/120.08 exact (zenon_Hba gt_2_1).
% 119.80/120.08 exact (zenon_Hab zenon_Hb9).
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 cut ((gt (n1) (loopcounter)) = (gt (succ (n3)) (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Ha8.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H7d.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((n1) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Hbb].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbc ].
% 119.80/120.08 apply zenon_Hbd. zenon_intro zenon_Hbe.
% 119.80/120.08 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ].
% 119.80/120.08 cut (((succ (n3)) = (succ (n3))) = ((n1) = (succ (n3)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hbb.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H9e.
% 119.80/120.08 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.80/120.08 cut (((succ (n3)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hac].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_Hac zenon_Hbe).
% 119.80/120.08 apply zenon_H9f. apply refl_equal.
% 119.80/120.08 apply zenon_H9f. apply refl_equal.
% 119.80/120.08 apply zenon_Hbc. zenon_intro zenon_Hb9.
% 119.80/120.08 generalize (zenon_H66 (succ (n3))). zenon_intro zenon_Hb5.
% 119.80/120.08 generalize (zenon_Hb5 (n1)). zenon_intro zenon_Hbf.
% 119.80/120.08 generalize (zenon_Hbf (loopcounter)). zenon_intro zenon_Hc0.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc1 ].
% 119.80/120.08 exact (zenon_Hab zenon_Hb9).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_H92 | zenon_intro zenon_Ha6 ].
% 119.80/120.08 exact (zenon_H92 zenon_H7d).
% 119.80/120.08 exact (zenon_Ha8 zenon_Ha6).
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 exact (zenon_Ha4 zenon_Ha7).
% 119.80/120.08 (* end of lemma zenon_L12_ *)
% 119.80/120.08 assert (zenon_L13_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((succ (n0)) = (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n1))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H97 zenon_Hc2 zenon_Hc3 zenon_Hc4 zenon_H7d zenon_H67.
% 119.80/120.08 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.80/120.08 congruence.
% 119.80/120.08 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.80/120.08 apply (zenon_L5_); trivial.
% 119.80/120.08 apply (zenon_L12_); trivial.
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.80/120.08 apply zenon_H93. apply sym_equal. exact zenon_H95.
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.80/120.08 exact (zenon_Hc4 zenon_Hca).
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.80/120.08 exact (zenon_Hc3 zenon_Hcc).
% 119.80/120.08 exact (zenon_Hc2 zenon_Hcb).
% 119.80/120.08 (* end of lemma zenon_L13_ *)
% 119.80/120.08 assert (zenon_L14_ : (gt (n1) (loopcounter)) -> (~((loopcounter) = (n1))) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (n0)))) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H7d zenon_Hc4 zenon_Hc3 zenon_Hc2 zenon_H66 zenon_Hcd zenon_H67.
% 119.80/120.08 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.80/120.08 apply (zenon_L13_); trivial.
% 119.80/120.08 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.08 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (n0)) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hcd.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H67.
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.80/120.08 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((succ (loopcounter)) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hd2.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H97 zenon_Hd5).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_Hd3. zenon_intro zenon_Hd6.
% 119.80/120.08 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.80/120.08 generalize (zenon_H8e (succ (loopcounter))). zenon_intro zenon_Hd7.
% 119.80/120.08 generalize (zenon_Hd7 (n1)). zenon_intro zenon_Hd8.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hd8); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd9 ].
% 119.80/120.08 exact (zenon_Hd0 zenon_Hd6).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hd9); [ zenon_intro zenon_H6f | zenon_intro zenon_H8d ].
% 119.80/120.08 exact (zenon_H6f zenon_H67).
% 119.80/120.08 cut ((gt (succ (n0)) (n1)) = (gt (succ (n0)) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hcd.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8d.
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 apply zenon_H88. apply sym_equal. exact successor_1.
% 119.80/120.08 (* end of lemma zenon_L14_ *)
% 119.80/120.08 assert (zenon_L15_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (n1))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n1))) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H86 zenon_H67 zenon_H7d zenon_Hc4 zenon_Hc3 zenon_Hc2.
% 119.80/120.08 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hcd ].
% 119.80/120.08 cut ((gt (succ (n0)) (succ (n0))) = (gt (succ (n0)) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H86.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hda.
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply (zenon_L14_); trivial.
% 119.80/120.08 (* end of lemma zenon_L15_ *)
% 119.80/120.08 assert (zenon_L16_ : (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n1))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n1) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_Hc2 zenon_Hc3 zenon_Hc4 zenon_H7d zenon_H67 zenon_Hdb zenon_H66.
% 119.80/120.08 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.08 elim (classic (gt (succ (n0)) (succ (loopcounter)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd0 ].
% 119.80/120.08 cut ((gt (succ (n0)) (succ (loopcounter))) = (gt (n1) (succ (loopcounter)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hdb.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hd6.
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.80/120.08 cut (((n1) = (n1)) = ((succ (n0)) = (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H87.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hdc.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply zenon_H76. apply refl_equal.
% 119.80/120.08 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.08 elim (classic (gt (succ (n0)) (n1))); [ zenon_intro zenon_H8d | zenon_intro zenon_H86 ].
% 119.80/120.08 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hcd ].
% 119.80/120.08 cut ((gt (succ (n0)) (succ (n0))) = (gt (succ (n0)) (succ (loopcounter)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hd0.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hda.
% 119.80/120.08 cut (((succ (n0)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply (zenon_L13_); trivial.
% 119.80/120.08 cut ((gt (succ (n0)) (n1)) = (gt (succ (n0)) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hcd.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8d.
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 apply (zenon_L15_); trivial.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H88.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H88.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L16_ *)
% 119.80/120.08 assert (zenon_L17_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> (~(gt (n1) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_Hdd zenon_Hdb zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67.
% 119.80/120.08 elim (classic ((loopcounter) = (n1))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc4 ].
% 119.80/120.08 cut ((gt (n1) (loopcounter)) = (gt (n1) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hdd.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H7d.
% 119.80/120.08 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 exact (zenon_Hc4 zenon_Hca).
% 119.80/120.08 apply (zenon_L16_); trivial.
% 119.80/120.08 (* end of lemma zenon_L17_ *)
% 119.80/120.08 assert (zenon_L18_ : (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H66 zenon_Hdd zenon_H67.
% 119.80/120.08 elim (classic ((~((n1) = (succ (loopcounter))))/\(~(gt (n1) (succ (loopcounter)))))); [ zenon_intro zenon_Hde | zenon_intro zenon_Hdf ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_Hde). zenon_intro zenon_H71. zenon_intro zenon_Hdb.
% 119.80/120.08 apply (zenon_L17_); trivial.
% 119.80/120.08 cut ((gt (succ (loopcounter)) (n1)) = (gt (n1) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hdd.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H67.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((succ (loopcounter)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H70].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_Hdf); [ zenon_intro zenon_He1 | zenon_intro zenon_He0 ].
% 119.80/120.08 apply zenon_He1. zenon_intro zenon_He2.
% 119.80/120.08 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.80/120.08 cut (((n1) = (n1)) = ((succ (loopcounter)) = (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H70.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hdc.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((n1) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H71].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H71 zenon_He2).
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply zenon_He0. zenon_intro zenon_He3.
% 119.80/120.08 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.80/120.08 generalize (zenon_He4 (succ (loopcounter))). zenon_intro zenon_He5.
% 119.80/120.08 generalize (zenon_He5 (n1)). zenon_intro zenon_He6.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_He6); [ zenon_intro zenon_Hdb | zenon_intro zenon_He7 ].
% 119.80/120.08 exact (zenon_Hdb zenon_He3).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_He7); [ zenon_intro zenon_H6f | zenon_intro zenon_He8 ].
% 119.80/120.08 exact (zenon_H6f zenon_H67).
% 119.80/120.08 exact (zenon_Hdd zenon_He8).
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L18_ *)
% 119.80/120.08 assert (zenon_L19_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (n0)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_Hcd zenon_H67 zenon_H7d zenon_Hc3 zenon_Hc2.
% 119.80/120.08 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_He9 | zenon_intro zenon_Hea ].
% 119.80/120.08 cut ((gt (n1) (succ (n0))) = (gt (succ (n0)) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hcd.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_He9.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H88.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.08 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_He8 | zenon_intro zenon_Hdd ].
% 119.80/120.08 cut ((gt (n1) (n1)) = (gt (n1) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hea.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_He8.
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 apply (zenon_L18_); trivial.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H88.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L19_ *)
% 119.80/120.08 assert (zenon_L20_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> (~(gt (n1) (succ (loopcounter)))) -> (~(gt (loopcounter) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc3 zenon_Hc2 zenon_Hdb zenon_Heb zenon_H66.
% 119.80/120.08 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.08 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hcd ].
% 119.80/120.08 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_He9 | zenon_intro zenon_Hea ].
% 119.80/120.08 cut ((gt (n1) (succ (n0))) = (gt (loopcounter) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Heb.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_He9.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.08 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hec.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hed.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_L16_); trivial.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 cut ((gt (succ (n0)) (succ (n0))) = (gt (n1) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hea.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hda.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.80/120.08 cut (((n1) = (n1)) = ((succ (n0)) = (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H87.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hdc.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply (zenon_L19_); trivial.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H88.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L20_ *)
% 119.80/120.08 assert (zenon_L21_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n1))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> (~(gt (n1) (succ (loopcounter)))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_Hee zenon_H67 zenon_H7d zenon_Hc3 zenon_Hc2 zenon_Hdb.
% 119.80/120.08 elim (classic (gt (loopcounter) (succ (n0)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Heb ].
% 119.80/120.08 cut ((gt (loopcounter) (succ (n0))) = (gt (loopcounter) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hee.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hef.
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply (zenon_L20_); trivial.
% 119.80/120.08 (* end of lemma zenon_L21_ *)
% 119.80/120.08 assert (zenon_L22_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> (~(gt (n1) (succ (loopcounter)))) -> (~(gt (loopcounter) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc3 zenon_Hc2 zenon_Hdb zenon_Hf0 zenon_H66.
% 119.80/120.08 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.08 elim (classic (gt (loopcounter) (n1))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hee ].
% 119.80/120.08 elim (classic (gt (loopcounter) (succ (n0)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Heb ].
% 119.80/120.08 cut ((gt (loopcounter) (succ (n0))) = (gt (loopcounter) (succ (loopcounter)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hf0.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hef.
% 119.80/120.08 cut (((succ (n0)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply (zenon_L9_); trivial.
% 119.80/120.08 cut ((gt (loopcounter) (n1)) = (gt (loopcounter) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Heb.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hf1.
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 apply (zenon_L21_); trivial.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H88.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L22_ *)
% 119.80/120.08 assert (zenon_L23_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> (~(gt (n1) (succ (loopcounter)))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_Hc3 zenon_Hc2 zenon_Hdb.
% 119.80/120.08 elim (classic (gt (loopcounter) (succ (loopcounter)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf0 ].
% 119.80/120.08 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.80/120.08 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.80/120.08 generalize (zenon_Hf3 (succ (loopcounter))). zenon_intro zenon_Hf4.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_H92 | zenon_intro zenon_Hf5 ].
% 119.80/120.08 exact (zenon_H92 zenon_H7d).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_He3 ].
% 119.80/120.08 exact (zenon_Hf0 zenon_Hf2).
% 119.80/120.08 exact (zenon_Hdb zenon_He3).
% 119.80/120.08 apply (zenon_L22_); trivial.
% 119.80/120.08 (* end of lemma zenon_L23_ *)
% 119.80/120.08 assert (zenon_L24_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_Hd0 zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67.
% 119.80/120.08 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.80/120.08 apply (zenon_L9_); trivial.
% 119.80/120.08 elim (classic (gt (n1) (succ (loopcounter)))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hdb ].
% 119.80/120.08 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.80/120.08 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.80/120.08 generalize (zenon_H78 (succ (loopcounter))). zenon_intro zenon_Hf6.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hf6); [ zenon_intro zenon_H6f | zenon_intro zenon_Hf7 ].
% 119.80/120.08 exact (zenon_H6f zenon_H67).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hf7); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hf8 ].
% 119.80/120.08 exact (zenon_Hdb zenon_He3).
% 119.80/120.08 cut ((gt (succ (loopcounter)) (succ (loopcounter))) = (gt (succ (n0)) (succ (loopcounter)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hd0.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hf8.
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.80/120.08 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.80/120.08 apply zenon_Hd2. apply sym_equal. exact zenon_Hd5.
% 119.80/120.08 exact (zenon_Hd3 zenon_Hd0).
% 119.80/120.08 apply zenon_H76. apply refl_equal.
% 119.80/120.08 apply (zenon_L23_); trivial.
% 119.80/120.08 (* end of lemma zenon_L24_ *)
% 119.80/120.08 assert (zenon_L25_ : (~(gt (n2) (succ (n0)))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_Hf9.
% 119.80/120.08 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.08 cut ((gt (n2) (n1)) = (gt (n2) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hf9.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact gt_2_1.
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H63. apply refl_equal.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 apply zenon_H88. apply sym_equal. exact successor_1.
% 119.80/120.08 (* end of lemma zenon_L25_ *)
% 119.80/120.08 assert (zenon_L26_ : (~((succ (n1)) = (succ (succ (n0))))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_Hfa.
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H88. apply sym_equal. exact successor_1.
% 119.80/120.08 (* end of lemma zenon_L26_ *)
% 119.80/120.08 assert (zenon_L27_ : (~(gt (succ (n1)) (succ (n0)))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_Hfb.
% 119.80/120.08 elim (classic (gt (n2) (succ (n0)))); [ zenon_intro zenon_Hfc | zenon_intro zenon_Hf9 ].
% 119.80/120.08 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_Hfd | zenon_intro zenon_Hfe ].
% 119.80/120.08 cut ((gt (succ (succ (n0))) (succ (n0))) = (gt (succ (n1)) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hfb.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hfd.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (succ (n0))) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_Hff].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((succ (n1)) = (succ (n1)))); [ zenon_intro zenon_H100 | zenon_intro zenon_H101 ].
% 119.80/120.08 cut (((succ (n1)) = (succ (n1))) = ((succ (succ (n0))) = (succ (n1)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hff.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H100.
% 119.80/120.08 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.80/120.08 cut (((succ (n1)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hfa].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_L26_); trivial.
% 119.80/120.08 apply zenon_H101. apply refl_equal.
% 119.80/120.08 apply zenon_H101. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 cut ((gt (n2) (succ (n0))) = (gt (succ (succ (n0))) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hfe.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hfc.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.80/120.08 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H102.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H103.
% 119.80/120.08 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.80/120.08 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H105 successor_2).
% 119.80/120.08 apply zenon_H104. apply refl_equal.
% 119.80/120.08 apply zenon_H104. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply (zenon_L25_); trivial.
% 119.80/120.08 (* end of lemma zenon_L27_ *)
% 119.80/120.08 assert (zenon_L28_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n1))) -> (~((n0) = (n1))) -> (~((loopcounter) = (n1))) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_Hee zenon_H106 zenon_Hc4 zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67.
% 119.80/120.08 elim (classic (gt (loopcounter) (succ (n0)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Heb ].
% 119.80/120.08 cut ((gt (loopcounter) (succ (n0))) = (gt (loopcounter) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hee.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hef.
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 generalize (finite_domain_0 (n1)). zenon_intro zenon_H107.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H107); [ zenon_intro zenon_H109 | zenon_intro zenon_H108 ].
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_H109); [ zenon_intro zenon_H10b | zenon_intro zenon_H10a ].
% 119.80/120.08 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 119.80/120.08 generalize (zenon_H5f (n1)). zenon_intro zenon_H10c.
% 119.80/120.08 apply (zenon_equiv_s _ _ zenon_H10c); [ zenon_intro zenon_H10b; zenon_intro zenon_H10f | zenon_intro zenon_H10e; zenon_intro zenon_H10d ].
% 119.80/120.08 elim (classic ((~((succ (n1)) = (n1)))/\(~(gt (succ (n1)) (n1))))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_H110). zenon_intro zenon_H113. zenon_intro zenon_H112.
% 119.80/120.08 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.80/120.08 elim (classic (gt (succ (n1)) (succ (n0)))); [ zenon_intro zenon_H118 | zenon_intro zenon_Hfb ].
% 119.80/120.08 elim (classic (gt (succ (n1)) (n1))); [ zenon_intro zenon_H119 | zenon_intro zenon_H112 ].
% 119.80/120.08 elim (classic (gt (n1) (succ (loopcounter)))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hdb ].
% 119.80/120.08 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.80/120.08 generalize (zenon_H11a (n1)). zenon_intro zenon_H11b.
% 119.80/120.08 generalize (zenon_H11b (succ (loopcounter))). zenon_intro zenon_H11c.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ].
% 119.80/120.08 exact (zenon_H112 zenon_H119).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_Hdb | zenon_intro zenon_H11e ].
% 119.80/120.08 exact (zenon_Hdb zenon_He3).
% 119.80/120.08 exact (zenon_H116 zenon_H11e).
% 119.80/120.08 apply (zenon_L20_); trivial.
% 119.80/120.08 cut ((gt (succ (n1)) (succ (n0))) = (gt (succ (n1)) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H112.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H118.
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H101. apply refl_equal.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply (zenon_L27_); trivial.
% 119.80/120.08 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (n1)) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H112.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H67.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.80/120.08 apply zenon_H121. zenon_intro zenon_H122.
% 119.80/120.08 elim (classic ((succ (n1)) = (succ (n1)))); [ zenon_intro zenon_H100 | zenon_intro zenon_H101 ].
% 119.80/120.08 cut (((succ (n1)) = (succ (n1))) = ((succ (loopcounter)) = (succ (n1)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H11f.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H100.
% 119.80/120.08 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.80/120.08 cut (((succ (n1)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H117].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H117 zenon_H122).
% 119.80/120.08 apply zenon_H101. apply refl_equal.
% 119.80/120.08 apply zenon_H101. apply refl_equal.
% 119.80/120.08 apply zenon_H120. zenon_intro zenon_H11e.
% 119.80/120.08 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.80/120.08 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.80/120.08 generalize (zenon_H123 (n1)). zenon_intro zenon_H124.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H124); [ zenon_intro zenon_H116 | zenon_intro zenon_H125 ].
% 119.80/120.08 exact (zenon_H116 zenon_H11e).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H125); [ zenon_intro zenon_H6f | zenon_intro zenon_H119 ].
% 119.80/120.08 exact (zenon_H6f zenon_H67).
% 119.80/120.08 exact (zenon_H112 zenon_H119).
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 cut ((gt (n1) (n0)) = (gt (succ (n1)) (n0))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H10f.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact gt_1_0.
% 119.80/120.08 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.08 cut (((n1) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H126].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_H111); [ zenon_intro zenon_H128 | zenon_intro zenon_H127 ].
% 119.80/120.08 apply zenon_H128. zenon_intro zenon_H129.
% 119.80/120.08 elim (classic ((succ (n1)) = (succ (n1)))); [ zenon_intro zenon_H100 | zenon_intro zenon_H101 ].
% 119.80/120.08 cut (((succ (n1)) = (succ (n1))) = ((n1) = (succ (n1)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H126.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H100.
% 119.80/120.08 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.80/120.08 cut (((succ (n1)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H113 zenon_H129).
% 119.80/120.08 apply zenon_H101. apply refl_equal.
% 119.80/120.08 apply zenon_H101. apply refl_equal.
% 119.80/120.08 apply zenon_H127. zenon_intro zenon_H119.
% 119.80/120.08 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.80/120.08 generalize (zenon_H11a (n1)). zenon_intro zenon_H11b.
% 119.80/120.08 generalize (zenon_H11b (n0)). zenon_intro zenon_H12a.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H12a); [ zenon_intro zenon_H112 | zenon_intro zenon_H12b ].
% 119.80/120.08 exact (zenon_H112 zenon_H119).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H12b); [ zenon_intro zenon_H7b | zenon_intro zenon_H10d ].
% 119.80/120.08 exact (zenon_H7b gt_1_0).
% 119.80/120.08 exact (zenon_H10f zenon_H10d).
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 exact (zenon_H10b zenon_H10e).
% 119.80/120.08 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H12c.
% 119.80/120.08 generalize (zenon_H12c (n0)). zenon_intro zenon_H12d.
% 119.80/120.08 apply (zenon_equiv_s _ _ zenon_H12d); [ zenon_intro zenon_H10a; zenon_intro zenon_H86 | zenon_intro zenon_H12e; zenon_intro zenon_H8d ].
% 119.80/120.08 apply (zenon_L15_); trivial.
% 119.80/120.08 exact (zenon_H10a zenon_H12e).
% 119.80/120.08 apply zenon_H106. apply sym_equal. exact zenon_H108.
% 119.80/120.08 (* end of lemma zenon_L28_ *)
% 119.80/120.08 assert (zenon_L29_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((loopcounter) = (n0)) -> (~((n0) = (n1))) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H12f zenon_H95 zenon_H106 zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67.
% 119.80/120.08 elim (classic (gt (n0) (loopcounter))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ].
% 119.80/120.08 cut ((gt (n0) (loopcounter)) = (gt (n0) (n0))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H12f.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H130.
% 119.80/120.08 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.08 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 exact (zenon_H132 zenon_H95).
% 119.80/120.08 elim (classic ((n0) = (loopcounter))); [ zenon_intro zenon_H133 | zenon_intro zenon_H93 ].
% 119.80/120.08 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.80/120.08 cut ((gt (loopcounter) (loopcounter)) = (gt (n0) (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H131.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H134.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.08 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H132.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H136.
% 119.80/120.08 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.08 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H93 zenon_H133).
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 elim (classic ((~((loopcounter) = (n1)))/\(~(gt (loopcounter) (n1))))); [ zenon_intro zenon_H137 | zenon_intro zenon_H138 ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_H137). zenon_intro zenon_Hc4. zenon_intro zenon_Hee.
% 119.80/120.08 apply (zenon_L28_); trivial.
% 119.80/120.08 cut ((gt (n1) (loopcounter)) = (gt (loopcounter) (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H135.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H7d.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 119.80/120.08 apply zenon_H13a. zenon_intro zenon_Hca.
% 119.80/120.08 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.08 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hec.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hed.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_Hc4 zenon_Hca).
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H139. zenon_intro zenon_Hf1.
% 119.80/120.08 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.80/120.08 generalize (zenon_H13b (n1)). zenon_intro zenon_H13c.
% 119.80/120.08 generalize (zenon_H13c (loopcounter)). zenon_intro zenon_H13d.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H13d); [ zenon_intro zenon_Hee | zenon_intro zenon_H13e ].
% 119.80/120.08 exact (zenon_Hee zenon_Hf1).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H92 | zenon_intro zenon_H134 ].
% 119.80/120.08 exact (zenon_H92 zenon_H7d).
% 119.80/120.08 exact (zenon_H135 zenon_H134).
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.08 cut (((loopcounter) = (loopcounter)) = ((n0) = (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H93.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hed.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H132 zenon_H95).
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 (* end of lemma zenon_L29_ *)
% 119.80/120.08 assert (zenon_L30_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n1)) -> (~(gt (n0) (n1))) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_Hca zenon_H13f zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67.
% 119.80/120.08 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_He8 | zenon_intro zenon_Hdd ].
% 119.80/120.08 elim (classic (gt (loopcounter) (n1))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hee ].
% 119.80/120.08 cut ((gt (loopcounter) (n1)) = (gt (n0) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H13f.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hf1.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.08 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H132.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H136.
% 119.80/120.08 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.08 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_L8_); trivial.
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 cut ((gt (n1) (n1)) = (gt (loopcounter) (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hee.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_He8.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.08 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hec.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hed.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_Hc4 zenon_Hca).
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply (zenon_L18_); trivial.
% 119.80/120.08 (* end of lemma zenon_L30_ *)
% 119.80/120.08 assert (zenon_L31_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((n0) = (n1))) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (~(gt (n0) (n1))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H140 zenon_H106 zenon_Hc2 zenon_Hc3 zenon_H13f.
% 119.80/120.08 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.80/120.08 apply (zenon_L5_); trivial.
% 119.80/120.08 apply (zenon_L12_); trivial.
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.80/120.08 elim (classic ((n0) = (loopcounter))); [ zenon_intro zenon_H133 | zenon_intro zenon_H93 ].
% 119.80/120.08 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.08 elim (classic (gt (n0) (loopcounter))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ].
% 119.80/120.08 elim (classic (gt (loopcounter) (succ (loopcounter)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf0 ].
% 119.80/120.08 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.80/120.08 generalize (zenon_H142 (loopcounter)). zenon_intro zenon_H143.
% 119.80/120.08 generalize (zenon_H143 (succ (loopcounter))). zenon_intro zenon_H144.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H131 | zenon_intro zenon_H145 ].
% 119.80/120.08 exact (zenon_H131 zenon_H130).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H146 ].
% 119.80/120.08 exact (zenon_Hf0 zenon_Hf2).
% 119.80/120.08 exact (zenon_H140 zenon_H146).
% 119.80/120.08 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.08 elim (classic (gt (loopcounter) (n1))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hee ].
% 119.80/120.08 elim (classic (gt (loopcounter) (succ (n0)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Heb ].
% 119.80/120.08 elim (classic (gt (succ (n0)) (succ (loopcounter)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd0 ].
% 119.80/120.08 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.80/120.08 generalize (zenon_H13b (succ (n0))). zenon_intro zenon_H147.
% 119.80/120.08 generalize (zenon_H147 (succ (loopcounter))). zenon_intro zenon_H148.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H148); [ zenon_intro zenon_Heb | zenon_intro zenon_H149 ].
% 119.80/120.08 exact (zenon_Heb zenon_Hef).
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H149); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hf2 ].
% 119.80/120.08 exact (zenon_Hd0 zenon_Hd6).
% 119.80/120.08 exact (zenon_Hf0 zenon_Hf2).
% 119.80/120.08 apply (zenon_L24_); trivial.
% 119.80/120.08 cut ((gt (loopcounter) (n1)) = (gt (loopcounter) (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Heb.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hf1.
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 elim (classic (gt (succ (n0)) (succ (loopcounter)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd0 ].
% 119.80/120.08 elim (classic (gt (n1) (succ (loopcounter)))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hdb ].
% 119.80/120.08 cut ((gt (n1) (succ (loopcounter))) = (gt (loopcounter) (succ (loopcounter)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hf0.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_He3.
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.80/120.08 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.08 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hec.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hed.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_L28_); trivial.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H76. apply refl_equal.
% 119.80/120.08 cut ((gt (succ (n0)) (succ (loopcounter))) = (gt (n1) (succ (loopcounter)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_Hdb.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hd6.
% 119.80/120.08 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.80/120.08 cut (((n1) = (n1)) = ((succ (n0)) = (n1))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H87.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hdc.
% 119.80/120.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.08 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H88 zenon_Hd1).
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply zenon_H64. apply refl_equal.
% 119.80/120.08 apply zenon_H76. apply refl_equal.
% 119.80/120.08 apply (zenon_L24_); trivial.
% 119.80/120.08 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.08 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H88.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H8b.
% 119.80/120.08 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.08 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H87 successor_1).
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 apply zenon_H8c. apply refl_equal.
% 119.80/120.08 cut ((gt (n0) (n0)) = (gt (n0) (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H131.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H141.
% 119.80/120.08 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.80/120.08 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.08 congruence.
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 exact (zenon_H93 zenon_H133).
% 119.80/120.08 apply (zenon_L29_); trivial.
% 119.80/120.08 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.08 cut (((loopcounter) = (loopcounter)) = ((n0) = (loopcounter))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H93.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_Hed.
% 119.80/120.08 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.08 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H132 zenon_H95).
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply zenon_H7c. apply refl_equal.
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.80/120.08 apply (zenon_L30_); trivial.
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.80/120.08 exact (zenon_Hc3 zenon_Hcc).
% 119.80/120.08 exact (zenon_Hc2 zenon_Hcb).
% 119.80/120.08 (* end of lemma zenon_L31_ *)
% 119.80/120.08 assert (zenon_L32_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (n0))) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> (~((n0) = (n1))) -> (~(gt (n0) (n1))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H12f zenon_Hc3 zenon_Hc2 zenon_H106 zenon_H13f.
% 119.80/120.08 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.80/120.08 apply (zenon_L5_); trivial.
% 119.80/120.08 apply (zenon_L12_); trivial.
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.80/120.08 apply (zenon_L29_); trivial.
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.80/120.08 apply (zenon_L30_); trivial.
% 119.80/120.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.80/120.08 exact (zenon_Hc3 zenon_Hcc).
% 119.80/120.08 exact (zenon_Hc2 zenon_Hcb).
% 119.80/120.08 (* end of lemma zenon_L32_ *)
% 119.80/120.08 assert (zenon_L33_ : (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.80/120.08 do 0 intro. intros zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67 zenon_H66 zenon_H12f.
% 119.80/120.08 elim (classic ((~((n0) = (n1)))/\(~(gt (n0) (n1))))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ].
% 119.80/120.08 apply (zenon_and_s _ _ zenon_H14a). zenon_intro zenon_H106. zenon_intro zenon_H13f.
% 119.80/120.08 apply (zenon_L32_); trivial.
% 119.80/120.08 cut ((gt (n1) (n0)) = (gt (n0) (n0))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H12f.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact gt_1_0.
% 119.80/120.08 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.08 cut (((n1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 119.80/120.08 congruence.
% 119.80/120.08 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H14e | zenon_intro zenon_H14d ].
% 119.80/120.08 apply zenon_H14e. zenon_intro zenon_H14f.
% 119.80/120.08 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.08 cut (((n0) = (n0)) = ((n1) = (n0))).
% 119.80/120.08 intro zenon_D_pnotp.
% 119.80/120.08 apply zenon_H14c.
% 119.80/120.08 rewrite <- zenon_D_pnotp.
% 119.80/120.08 exact zenon_H136.
% 119.80/120.08 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.08 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.80/120.08 congruence.
% 119.80/120.08 exact (zenon_H106 zenon_H14f).
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 apply zenon_H65. apply refl_equal.
% 119.80/120.08 apply zenon_H14d. zenon_intro zenon_H150.
% 119.80/120.08 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.80/120.08 generalize (zenon_H142 (n1)). zenon_intro zenon_H151.
% 119.80/120.08 generalize (zenon_H151 (n0)). zenon_intro zenon_H152.
% 119.80/120.08 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H13f | zenon_intro zenon_H153 ].
% 119.80/120.09 exact (zenon_H13f zenon_H150).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H153); [ zenon_intro zenon_H7b | zenon_intro zenon_H141 ].
% 119.80/120.09 exact (zenon_H7b gt_1_0).
% 119.80/120.09 exact (zenon_H12f zenon_H141).
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L33_ *)
% 119.80/120.09 assert (zenon_L34_ : (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67 zenon_H66 zenon_H12f.
% 119.80/120.09 apply (zenon_L33_); trivial.
% 119.80/120.09 (* end of lemma zenon_L34_ *)
% 119.80/120.09 assert (zenon_L35_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H154 zenon_H155 zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.80/120.09 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H154.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H156.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.80/120.09 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.09 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H157.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H141.
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 exact (zenon_H159 zenon_H15c).
% 119.80/120.09 apply (zenon_L34_); trivial.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L35_ *)
% 119.80/120.09 assert (zenon_L36_ : (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n0) (succ (tptp_minus_1)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67 zenon_H15d zenon_H66 zenon_H155.
% 119.80/120.09 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.80/120.09 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.09 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.80/120.09 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))); [ zenon_intro zenon_H15e | zenon_intro zenon_H15f ].
% 119.80/120.09 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.80/120.09 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.80/120.09 generalize (zenon_H160 (succ (tptp_minus_1))). zenon_intro zenon_H161.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H161); [ zenon_intro zenon_H157 | zenon_intro zenon_H162 ].
% 119.80/120.09 exact (zenon_H157 zenon_H156).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H162); [ zenon_intro zenon_H15f | zenon_intro zenon_H163 ].
% 119.80/120.09 exact (zenon_H15f zenon_H15e).
% 119.80/120.09 exact (zenon_H15d zenon_H163).
% 119.80/120.09 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H164 | zenon_intro zenon_H154 ].
% 119.80/120.09 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_H165 | zenon_intro zenon_H166 ].
% 119.80/120.09 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H15f.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H165.
% 119.80/120.09 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H167. apply sym_equal. exact succ_tptp_minus_1.
% 119.80/120.09 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H166.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H164.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply (zenon_L35_); trivial.
% 119.80/120.09 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H157.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H141.
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 exact (zenon_H159 zenon_H15c).
% 119.80/120.09 apply (zenon_L34_); trivial.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L36_ *)
% 119.80/120.09 assert (zenon_L37_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H168 zenon_H155 zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic (gt (n0) (succ (tptp_minus_1)))); [ zenon_intro zenon_H163 | zenon_intro zenon_H15d ].
% 119.80/120.09 cut ((gt (n0) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H168.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H163.
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.09 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H167.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H16a.
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H16b succ_tptp_minus_1).
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 apply (zenon_L36_); trivial.
% 119.80/120.09 (* end of lemma zenon_L37_ *)
% 119.80/120.09 assert (zenon_L38_ : (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H7d zenon_H67 zenon_Hc2 zenon_Hc3 zenon_H140 zenon_H155 zenon_H16c zenon_H66.
% 119.80/120.09 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.09 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16e ].
% 119.80/120.09 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H16f | zenon_intro zenon_H170 ].
% 119.80/120.09 elim (classic (gt (succ (n0)) (succ (loopcounter)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd0 ].
% 119.80/120.09 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.80/120.09 generalize (zenon_H171 (succ (n0))). zenon_intro zenon_H172.
% 119.80/120.09 generalize (zenon_H172 (succ (loopcounter))). zenon_intro zenon_H173.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H173); [ zenon_intro zenon_H170 | zenon_intro zenon_H174 ].
% 119.80/120.09 exact (zenon_H170 zenon_H16f).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H174); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H175 ].
% 119.80/120.09 exact (zenon_Hd0 zenon_Hd6).
% 119.80/120.09 exact (zenon_H16c zenon_H175).
% 119.80/120.09 apply (zenon_L24_); trivial.
% 119.80/120.09 cut ((gt (succ (tptp_minus_1)) (n1)) = (gt (succ (tptp_minus_1)) (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H170.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H16d.
% 119.80/120.09 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 exact (zenon_H88 zenon_Hd1).
% 119.80/120.09 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H176 | zenon_intro zenon_H168 ].
% 119.80/120.09 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_H177 | zenon_intro zenon_H178 ].
% 119.80/120.09 cut ((gt (succ (tptp_minus_1)) (n0)) = (gt (succ (tptp_minus_1)) (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H16e.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H177.
% 119.80/120.09 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 elim (classic (gt (n0) (n1))); [ zenon_intro zenon_H150 | zenon_intro zenon_H13f ].
% 119.80/120.09 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.80/120.09 generalize (zenon_H171 (n0)). zenon_intro zenon_H179.
% 119.80/120.09 generalize (zenon_H179 (n1)). zenon_intro zenon_H17a.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H17a); [ zenon_intro zenon_H178 | zenon_intro zenon_H17b ].
% 119.80/120.09 exact (zenon_H178 zenon_H177).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H17b); [ zenon_intro zenon_H13f | zenon_intro zenon_H16d ].
% 119.80/120.09 exact (zenon_H13f zenon_H150).
% 119.80/120.09 exact (zenon_H16e zenon_H16d).
% 119.80/120.09 apply (zenon_L31_); trivial.
% 119.80/120.09 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H178.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H176.
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 exact (zenon_H16b succ_tptp_minus_1).
% 119.80/120.09 apply (zenon_L37_); trivial.
% 119.80/120.09 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H88.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H8b.
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H87 successor_1).
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L38_ *)
% 119.80/120.09 assert (zenon_L39_ : (~((loopcounter) = (n3))) -> (~((loopcounter) = (n2))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n0) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_Hc2 zenon_Hc3 zenon_H7d zenon_H67 zenon_H140 zenon_H66 zenon_H155.
% 119.80/120.09 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.80/120.09 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.09 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.80/120.09 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (loopcounter)))); [ zenon_intro zenon_H17c | zenon_intro zenon_H17d ].
% 119.80/120.09 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.80/120.09 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.80/120.09 generalize (zenon_H160 (succ (loopcounter))). zenon_intro zenon_H17e.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H17e); [ zenon_intro zenon_H157 | zenon_intro zenon_H17f ].
% 119.80/120.09 exact (zenon_H157 zenon_H156).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H17f); [ zenon_intro zenon_H17d | zenon_intro zenon_H146 ].
% 119.80/120.09 exact (zenon_H17d zenon_H17c).
% 119.80/120.09 exact (zenon_H140 zenon_H146).
% 119.80/120.09 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.80/120.09 elim (classic (gt (succ (tptp_minus_1)) (succ (loopcounter)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H16c ].
% 119.80/120.09 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.80/120.09 cut ((gt (n0) (succ (loopcounter))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (loopcounter)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H17d.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H146.
% 119.80/120.09 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H76. apply refl_equal.
% 119.80/120.09 cut ((gt (succ (tptp_minus_1)) (succ (loopcounter))) = (gt (n0) (succ (loopcounter)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H140.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H175.
% 119.80/120.09 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.09 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H16b.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H136.
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H167 zenon_H180).
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H76. apply refl_equal.
% 119.80/120.09 apply (zenon_L38_); trivial.
% 119.80/120.09 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H167.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H16a.
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H16b succ_tptp_minus_1).
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H157.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H141.
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 exact (zenon_H159 zenon_H15c).
% 119.80/120.09 apply (zenon_L34_); trivial.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L39_ *)
% 119.80/120.09 assert (zenon_L40_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H181 zenon_H155 zenon_H140 zenon_Hc2 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic ((loopcounter) = (n2))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc3 ].
% 119.80/120.09 cut ((gt (n1) (loopcounter)) = (gt (n1) (n2))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H181.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H7d.
% 119.80/120.09 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.80/120.09 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 exact (zenon_Hc3 zenon_Hcc).
% 119.80/120.09 apply (zenon_L39_); trivial.
% 119.80/120.09 (* end of lemma zenon_L40_ *)
% 119.80/120.09 assert (zenon_L41_ : (gt (n1) (loopcounter)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (n0)))) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H7d zenon_H66 zenon_Hcd zenon_H67.
% 119.80/120.09 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.80/120.09 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.80/120.09 apply (zenon_L9_); trivial.
% 119.80/120.09 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.09 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (n0)) (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hcd.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H67.
% 119.80/120.09 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.09 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.80/120.09 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.80/120.09 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0))) = ((succ (loopcounter)) = (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hd2.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H8b.
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 cut (((succ (n0)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H97 zenon_Hd5).
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 apply zenon_Hd3. zenon_intro zenon_Hd6.
% 119.80/120.09 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.80/120.09 generalize (zenon_H8e (succ (loopcounter))). zenon_intro zenon_Hd7.
% 119.80/120.09 generalize (zenon_Hd7 (n1)). zenon_intro zenon_Hd8.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_Hd8); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd9 ].
% 119.80/120.09 exact (zenon_Hd0 zenon_Hd6).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_Hd9); [ zenon_intro zenon_H6f | zenon_intro zenon_H8d ].
% 119.80/120.09 exact (zenon_H6f zenon_H67).
% 119.80/120.09 cut ((gt (succ (n0)) (n1)) = (gt (succ (n0)) (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hcd.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H8d.
% 119.80/120.09 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 exact (zenon_H88 zenon_Hd1).
% 119.80/120.09 exact (zenon_H88 zenon_Hd1).
% 119.80/120.09 apply zenon_H88. apply sym_equal. exact successor_1.
% 119.80/120.09 (* end of lemma zenon_L41_ *)
% 119.80/120.09 assert (zenon_L42_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((loopcounter) = (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (succ (n0)) (n2))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hc2 zenon_H140 zenon_H155 zenon_H182 zenon_H67 zenon_H7d.
% 119.80/120.09 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hcd ].
% 119.80/120.09 elim (classic (gt (succ (n0)) (n1))); [ zenon_intro zenon_H8d | zenon_intro zenon_H86 ].
% 119.80/120.09 elim (classic (gt (n1) (n2))); [ zenon_intro zenon_H183 | zenon_intro zenon_H181 ].
% 119.80/120.09 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.80/120.09 generalize (zenon_H8e (n1)). zenon_intro zenon_H8f.
% 119.80/120.09 generalize (zenon_H8f (n2)). zenon_intro zenon_H184.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H184); [ zenon_intro zenon_H86 | zenon_intro zenon_H185 ].
% 119.80/120.09 exact (zenon_H86 zenon_H8d).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H185); [ zenon_intro zenon_H181 | zenon_intro zenon_H186 ].
% 119.80/120.09 exact (zenon_H181 zenon_H183).
% 119.80/120.09 exact (zenon_H182 zenon_H186).
% 119.80/120.09 apply (zenon_L40_); trivial.
% 119.80/120.09 cut ((gt (succ (n0)) (succ (n0))) = (gt (succ (n0)) (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H86.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hda.
% 119.80/120.09 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 exact (zenon_H87 successor_1).
% 119.80/120.09 apply (zenon_L41_); trivial.
% 119.80/120.09 (* end of lemma zenon_L42_ *)
% 119.80/120.09 assert (zenon_L43_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H155 zenon_H140 zenon_Hc2 zenon_H7d zenon_H67 zenon_H66 zenon_Hdd.
% 119.80/120.09 elim (classic ((~((n1) = (n2)))/\(~(gt (n1) (n2))))); [ zenon_intro zenon_H187 | zenon_intro zenon_H188 ].
% 119.80/120.09 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H189. zenon_intro zenon_H181.
% 119.80/120.09 apply (zenon_L40_); trivial.
% 119.80/120.09 cut ((gt (n2) (n1)) = (gt (n1) (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hdd.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact gt_2_1.
% 119.80/120.09 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.09 cut (((n2) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H18a].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_H188); [ zenon_intro zenon_H18c | zenon_intro zenon_H18b ].
% 119.80/120.09 apply zenon_H18c. zenon_intro zenon_H18d.
% 119.80/120.09 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.80/120.09 cut (((n1) = (n1)) = ((n2) = (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H18a.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hdc.
% 119.80/120.09 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.09 cut (((n1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H189].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H189 zenon_H18d).
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 apply zenon_H18b. zenon_intro zenon_H183.
% 119.80/120.09 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.80/120.09 generalize (zenon_He4 (n2)). zenon_intro zenon_H18e.
% 119.80/120.09 generalize (zenon_H18e (n1)). zenon_intro zenon_H18f.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H18f); [ zenon_intro zenon_H181 | zenon_intro zenon_H190 ].
% 119.80/120.09 exact (zenon_H181 zenon_H183).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H190); [ zenon_intro zenon_Hba | zenon_intro zenon_He8 ].
% 119.80/120.09 exact (zenon_Hba gt_2_1).
% 119.80/120.09 exact (zenon_Hdd zenon_He8).
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L43_ *)
% 119.80/120.09 assert (zenon_L44_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (succ (n0)) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H155 zenon_H140 zenon_Hc2 zenon_H7d zenon_H67 zenon_Hd0 zenon_H66.
% 119.80/120.09 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.09 elim (classic (gt (succ (n0)) (n1))); [ zenon_intro zenon_H8d | zenon_intro zenon_H86 ].
% 119.80/120.09 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hcd ].
% 119.80/120.09 cut ((gt (succ (n0)) (succ (n0))) = (gt (succ (n0)) (succ (loopcounter)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hd0.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hda.
% 119.80/120.09 cut (((succ (n0)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 apply (zenon_L9_); trivial.
% 119.80/120.09 cut ((gt (succ (n0)) (n1)) = (gt (succ (n0)) (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hcd.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H8d.
% 119.80/120.09 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 exact (zenon_H88 zenon_Hd1).
% 119.80/120.09 elim (classic ((~((succ (n0)) = (n2)))/\(~(gt (succ (n0)) (n2))))); [ zenon_intro zenon_H191 | zenon_intro zenon_H192 ].
% 119.80/120.09 apply (zenon_and_s _ _ zenon_H191). zenon_intro zenon_H193. zenon_intro zenon_H182.
% 119.80/120.09 apply (zenon_L42_); trivial.
% 119.80/120.09 cut ((gt (n2) (n1)) = (gt (succ (n0)) (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H86.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact gt_2_1.
% 119.80/120.09 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.09 cut (((n2) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H194].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_H192); [ zenon_intro zenon_H196 | zenon_intro zenon_H195 ].
% 119.80/120.09 apply zenon_H196. zenon_intro zenon_H197.
% 119.80/120.09 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0))) = ((n2) = (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H194.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H8b.
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 cut (((succ (n0)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H193].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H193 zenon_H197).
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 apply zenon_H195. zenon_intro zenon_H186.
% 119.80/120.09 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.80/120.09 generalize (zenon_H8e (n2)). zenon_intro zenon_H198.
% 119.80/120.09 generalize (zenon_H198 (n1)). zenon_intro zenon_H199.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H199); [ zenon_intro zenon_H182 | zenon_intro zenon_H19a ].
% 119.80/120.09 exact (zenon_H182 zenon_H186).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H19a); [ zenon_intro zenon_Hba | zenon_intro zenon_H8d ].
% 119.80/120.09 exact (zenon_Hba gt_2_1).
% 119.80/120.09 exact (zenon_H86 zenon_H8d).
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H88.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H8b.
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H87 successor_1).
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L44_ *)
% 119.80/120.09 assert (zenon_L45_ : (~((loopcounter) = (n1))) -> (~((n0) = (n1))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n1))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_Hc4 zenon_H106 zenon_H66 zenon_Hee zenon_Hc2 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic ((~((loopcounter) = (n2)))/\(~(gt (loopcounter) (n2))))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ].
% 119.80/120.09 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_Hc3. zenon_intro zenon_H19d.
% 119.80/120.09 apply (zenon_L28_); trivial.
% 119.80/120.09 cut ((gt (n2) (n1)) = (gt (loopcounter) (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hee.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact gt_2_1.
% 119.80/120.09 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.09 cut (((n2) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H19e].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_H19c); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H19f ].
% 119.80/120.09 apply zenon_H1a0. zenon_intro zenon_Hcc.
% 119.80/120.09 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.09 cut (((loopcounter) = (loopcounter)) = ((n2) = (loopcounter))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H19e.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hed.
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_Hc3 zenon_Hcc).
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H19f. zenon_intro zenon_H1a1.
% 119.80/120.09 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.80/120.09 generalize (zenon_H13b (n2)). zenon_intro zenon_H1a2.
% 119.80/120.09 generalize (zenon_H1a2 (n1)). zenon_intro zenon_H1a3.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H1a3); [ zenon_intro zenon_H19d | zenon_intro zenon_H1a4 ].
% 119.80/120.09 exact (zenon_H19d zenon_H1a1).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H1a4); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf1 ].
% 119.80/120.09 exact (zenon_Hba gt_2_1).
% 119.80/120.09 exact (zenon_Hee zenon_Hf1).
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L45_ *)
% 119.80/120.09 assert (zenon_L46_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n1))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hee zenon_H155 zenon_H140 zenon_Hc2 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic ((~((loopcounter) = (n2)))/\(~(gt (loopcounter) (n2))))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ].
% 119.80/120.09 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_Hc3. zenon_intro zenon_H19d.
% 119.80/120.09 apply (zenon_L39_); trivial.
% 119.80/120.09 cut ((gt (n2) (n1)) = (gt (loopcounter) (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hee.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact gt_2_1.
% 119.80/120.09 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.09 cut (((n2) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H19e].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_H19c); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H19f ].
% 119.80/120.09 apply zenon_H1a0. zenon_intro zenon_Hcc.
% 119.80/120.09 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.09 cut (((loopcounter) = (loopcounter)) = ((n2) = (loopcounter))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H19e.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hed.
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_Hc3 zenon_Hcc).
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H19f. zenon_intro zenon_H1a1.
% 119.80/120.09 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.80/120.09 generalize (zenon_H13b (n2)). zenon_intro zenon_H1a2.
% 119.80/120.09 generalize (zenon_H1a2 (n1)). zenon_intro zenon_H1a3.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H1a3); [ zenon_intro zenon_H19d | zenon_intro zenon_H1a4 ].
% 119.80/120.09 exact (zenon_H19d zenon_H1a1).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H1a4); [ zenon_intro zenon_Hba | zenon_intro zenon_Hf1 ].
% 119.80/120.09 exact (zenon_Hba gt_2_1).
% 119.80/120.09 exact (zenon_Hee zenon_Hf1).
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L46_ *)
% 119.80/120.09 assert (zenon_L47_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (loopcounter) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H155 zenon_H140 zenon_Hc2 zenon_H7d zenon_H67 zenon_Hf0 zenon_H66.
% 119.80/120.09 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.80/120.09 elim (classic (gt (loopcounter) (n1))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hee ].
% 119.80/120.09 elim (classic (gt (loopcounter) (succ (n0)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Heb ].
% 119.80/120.09 cut ((gt (loopcounter) (succ (n0))) = (gt (loopcounter) (succ (loopcounter)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hf0.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hef.
% 119.80/120.09 cut (((succ (n0)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply (zenon_L9_); trivial.
% 119.80/120.09 cut ((gt (loopcounter) (n1)) = (gt (loopcounter) (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Heb.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hf1.
% 119.80/120.09 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 exact (zenon_H88 zenon_Hd1).
% 119.80/120.09 apply (zenon_L46_); trivial.
% 119.80/120.09 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.80/120.09 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H88.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H8b.
% 119.80/120.09 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.80/120.09 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H87 successor_1).
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 apply zenon_H8c. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L47_ *)
% 119.80/120.09 assert (zenon_L48_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hdb zenon_Hc2 zenon_H7d zenon_H67 zenon_H155 zenon_H140.
% 119.80/120.09 elim (classic (gt (loopcounter) (succ (loopcounter)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf0 ].
% 119.80/120.09 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.80/120.09 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.80/120.09 generalize (zenon_Hf3 (succ (loopcounter))). zenon_intro zenon_Hf4.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_H92 | zenon_intro zenon_Hf5 ].
% 119.80/120.09 exact (zenon_H92 zenon_H7d).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_He3 ].
% 119.80/120.09 exact (zenon_Hf0 zenon_Hf2).
% 119.80/120.09 exact (zenon_Hdb zenon_He3).
% 119.80/120.09 apply (zenon_L47_); trivial.
% 119.80/120.09 (* end of lemma zenon_L48_ *)
% 119.80/120.09 assert (zenon_L49_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((loopcounter) = (n0)) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> (~((n0) = (n1))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H12f zenon_H95 zenon_H67 zenon_H7d zenon_Hc2 zenon_H106.
% 119.80/120.09 elim (classic (gt (n0) (loopcounter))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ].
% 119.80/120.09 cut ((gt (n0) (loopcounter)) = (gt (n0) (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H12f.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H130.
% 119.80/120.09 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 exact (zenon_H132 zenon_H95).
% 119.80/120.09 elim (classic ((n0) = (loopcounter))); [ zenon_intro zenon_H133 | zenon_intro zenon_H93 ].
% 119.80/120.09 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.80/120.09 cut ((gt (loopcounter) (loopcounter)) = (gt (n0) (loopcounter))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H131.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H134.
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.09 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H132.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H136.
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H93 zenon_H133).
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 elim (classic ((~((loopcounter) = (n1)))/\(~(gt (loopcounter) (n1))))); [ zenon_intro zenon_H137 | zenon_intro zenon_H138 ].
% 119.80/120.09 apply (zenon_and_s _ _ zenon_H137). zenon_intro zenon_Hc4. zenon_intro zenon_Hee.
% 119.80/120.09 apply (zenon_L45_); trivial.
% 119.80/120.09 cut ((gt (n1) (loopcounter)) = (gt (loopcounter) (loopcounter))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H135.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H7d.
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 119.80/120.09 apply zenon_H13a. zenon_intro zenon_Hca.
% 119.80/120.09 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.09 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hec.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hed.
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_Hc4 zenon_Hca).
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H139. zenon_intro zenon_Hf1.
% 119.80/120.09 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.80/120.09 generalize (zenon_H13b (n1)). zenon_intro zenon_H13c.
% 119.80/120.09 generalize (zenon_H13c (loopcounter)). zenon_intro zenon_H13d.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H13d); [ zenon_intro zenon_Hee | zenon_intro zenon_H13e ].
% 119.80/120.09 exact (zenon_Hee zenon_Hf1).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H92 | zenon_intro zenon_H134 ].
% 119.80/120.09 exact (zenon_H92 zenon_H7d).
% 119.80/120.09 exact (zenon_H135 zenon_H134).
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.09 cut (((loopcounter) = (loopcounter)) = ((n0) = (loopcounter))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H93.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hed.
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H132 zenon_H95).
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L49_ *)
% 119.80/120.09 assert (zenon_L50_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n1)) -> (~(gt (n0) (n1))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hca zenon_H13f zenon_H155 zenon_H140 zenon_Hc2 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_He8 | zenon_intro zenon_Hdd ].
% 119.80/120.09 elim (classic (gt (loopcounter) (n1))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hee ].
% 119.80/120.09 cut ((gt (loopcounter) (n1)) = (gt (n0) (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H13f.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hf1.
% 119.80/120.09 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.09 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.09 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H132.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H136.
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_L8_); trivial.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 cut ((gt (n1) (n1)) = (gt (loopcounter) (n1))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hee.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_He8.
% 119.80/120.09 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.80/120.09 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.09 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_Hec.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hed.
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_Hc4 zenon_Hca).
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H64. apply refl_equal.
% 119.80/120.09 apply (zenon_L43_); trivial.
% 119.80/120.09 (* end of lemma zenon_L50_ *)
% 119.80/120.09 assert (zenon_L51_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H1a5 zenon_H67 zenon_H7d zenon_Hc2 zenon_H140 zenon_H155.
% 119.80/120.09 elim (classic (gt (n1) (n2))); [ zenon_intro zenon_H183 | zenon_intro zenon_H181 ].
% 119.80/120.09 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.80/120.09 generalize (zenon_H1a6 (n1)). zenon_intro zenon_H1a7.
% 119.80/120.09 generalize (zenon_H1a7 (n2)). zenon_intro zenon_H1a8.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H1a8); [ zenon_intro zenon_Hba | zenon_intro zenon_H1a9 ].
% 119.80/120.09 exact (zenon_Hba gt_2_1).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H1a9); [ zenon_intro zenon_H181 | zenon_intro zenon_H1aa ].
% 119.80/120.09 exact (zenon_H181 zenon_H183).
% 119.80/120.09 exact (zenon_H1a5 zenon_H1aa).
% 119.80/120.09 apply (zenon_L40_); trivial.
% 119.80/120.09 (* end of lemma zenon_L51_ *)
% 119.80/120.09 assert (zenon_L52_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n2)) -> (~(gt (n0) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hcc zenon_H1ab zenon_H155 zenon_H140 zenon_Hc2 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic (gt (n2) (n2))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1a5 ].
% 119.80/120.09 elim (classic (gt (loopcounter) (n2))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H19d ].
% 119.80/120.09 cut ((gt (loopcounter) (n2)) = (gt (n0) (n2))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H1ab.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H1a1.
% 119.80/120.09 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.80/120.09 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.09 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H132.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H136.
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_L8_); trivial.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H63. apply refl_equal.
% 119.80/120.09 cut ((gt (n2) (n2)) = (gt (loopcounter) (n2))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H19d.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H1aa.
% 119.80/120.09 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.80/120.09 cut (((n2) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H19e].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.80/120.09 cut (((loopcounter) = (loopcounter)) = ((n2) = (loopcounter))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H19e.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_Hed.
% 119.80/120.09 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.80/120.09 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_Hc3 zenon_Hcc).
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H7c. apply refl_equal.
% 119.80/120.09 apply zenon_H63. apply refl_equal.
% 119.80/120.09 apply (zenon_L51_); trivial.
% 119.80/120.09 (* end of lemma zenon_L52_ *)
% 119.80/120.09 assert (zenon_L53_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (n0))) -> (~((n0) = (n1))) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (n0) (n1))) -> (~(gt (n0) (n2))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H12f zenon_H106 zenon_Hc2 zenon_H155 zenon_H140 zenon_H13f zenon_H1ab.
% 119.80/120.09 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.80/120.09 apply (zenon_L5_); trivial.
% 119.80/120.09 apply (zenon_L12_); trivial.
% 119.80/120.09 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.80/120.09 apply (zenon_L49_); trivial.
% 119.80/120.09 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.80/120.09 apply (zenon_L50_); trivial.
% 119.80/120.09 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.80/120.09 apply (zenon_L52_); trivial.
% 119.80/120.09 exact (zenon_Hc2 zenon_Hcb).
% 119.80/120.09 (* end of lemma zenon_L53_ *)
% 119.80/120.09 assert (zenon_L54_ : (~(gt (n0) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H1ab zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67 zenon_H66 zenon_H12f.
% 119.80/120.09 elim (classic ((~((n0) = (n1)))/\(~(gt (n0) (n1))))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ].
% 119.80/120.09 apply (zenon_and_s _ _ zenon_H14a). zenon_intro zenon_H106. zenon_intro zenon_H13f.
% 119.80/120.09 apply (zenon_L53_); trivial.
% 119.80/120.09 cut ((gt (n1) (n0)) = (gt (n0) (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H12f.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact gt_1_0.
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 cut (((n1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H14e | zenon_intro zenon_H14d ].
% 119.80/120.09 apply zenon_H14e. zenon_intro zenon_H14f.
% 119.80/120.09 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.09 cut (((n0) = (n0)) = ((n1) = (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H14c.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H136.
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H106 zenon_H14f).
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H14d. zenon_intro zenon_H150.
% 119.80/120.09 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.80/120.09 generalize (zenon_H142 (n1)). zenon_intro zenon_H151.
% 119.80/120.09 generalize (zenon_H151 (n0)). zenon_intro zenon_H152.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H13f | zenon_intro zenon_H153 ].
% 119.80/120.09 exact (zenon_H13f zenon_H150).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H153); [ zenon_intro zenon_H7b | zenon_intro zenon_H141 ].
% 119.80/120.09 exact (zenon_H7b gt_1_0).
% 119.80/120.09 exact (zenon_H12f zenon_H141).
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L54_ *)
% 119.80/120.09 assert (zenon_L55_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (n0) (n2))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H154 zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H140 zenon_H1ab.
% 119.80/120.09 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.80/120.09 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H154.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H156.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.80/120.09 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.09 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H157.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H141.
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 exact (zenon_H159 zenon_H15c).
% 119.80/120.09 apply (zenon_L54_); trivial.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L55_ *)
% 119.80/120.09 assert (zenon_L56_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hdb zenon_Hc2 zenon_H7d zenon_H67 zenon_H155 zenon_H140.
% 119.80/120.09 apply (zenon_L48_); trivial.
% 119.80/120.09 (* end of lemma zenon_L56_ *)
% 119.80/120.09 assert (zenon_L57_ : (~(gt (n0) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H1ab zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67 zenon_H66 zenon_H12f.
% 119.80/120.09 apply (zenon_L54_); trivial.
% 119.80/120.09 (* end of lemma zenon_L57_ *)
% 119.80/120.09 assert (zenon_L58_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> (~(gt (n0) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H154 zenon_H1ab zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.80/120.09 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H154.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H156.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.80/120.09 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.09 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H157.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H141.
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 exact (zenon_H159 zenon_H15c).
% 119.80/120.09 apply (zenon_L57_); trivial.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L58_ *)
% 119.80/120.09 assert (zenon_L59_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (loopcounter)))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hdb zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.80/120.09 apply (zenon_L56_); trivial.
% 119.80/120.09 (* end of lemma zenon_L59_ *)
% 119.80/120.09 assert (zenon_L60_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hdb zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H140.
% 119.80/120.09 apply (zenon_L59_); trivial.
% 119.80/120.09 (* end of lemma zenon_L60_ *)
% 119.80/120.09 assert (zenon_L61_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) -> (~(gt (n0) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H168 zenon_H1ab zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.80/120.09 elim (classic (gt (n0) (succ (tptp_minus_1)))); [ zenon_intro zenon_H163 | zenon_intro zenon_H15d ].
% 119.80/120.09 cut ((gt (n0) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H168.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H163.
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.09 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H167.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H16a.
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H16b succ_tptp_minus_1).
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 apply zenon_H169. apply refl_equal.
% 119.80/120.09 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.80/120.09 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.09 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.80/120.09 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))); [ zenon_intro zenon_H15e | zenon_intro zenon_H15f ].
% 119.80/120.09 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.80/120.09 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.80/120.09 generalize (zenon_H160 (succ (tptp_minus_1))). zenon_intro zenon_H161.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H161); [ zenon_intro zenon_H157 | zenon_intro zenon_H162 ].
% 119.80/120.09 exact (zenon_H157 zenon_H156).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H162); [ zenon_intro zenon_H15f | zenon_intro zenon_H163 ].
% 119.80/120.09 exact (zenon_H15f zenon_H15e).
% 119.80/120.09 exact (zenon_H15d zenon_H163).
% 119.80/120.09 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H164 | zenon_intro zenon_H154 ].
% 119.80/120.09 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_H165 | zenon_intro zenon_H166 ].
% 119.80/120.09 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H15f.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H165.
% 119.80/120.09 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H167. apply sym_equal. exact succ_tptp_minus_1.
% 119.80/120.09 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H166.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H164.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply (zenon_L58_); trivial.
% 119.80/120.09 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H157.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H141.
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 exact (zenon_H159 zenon_H15c).
% 119.80/120.09 apply (zenon_L57_); trivial.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L61_ *)
% 119.80/120.09 assert (zenon_L62_ : (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n1) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H140 zenon_Hc2 zenon_H7d zenon_H67 zenon_Hdb zenon_H66 zenon_H155.
% 119.80/120.09 apply (zenon_L60_); trivial.
% 119.80/120.09 (* end of lemma zenon_L62_ *)
% 119.80/120.09 assert (zenon_L63_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_Hdb zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H140.
% 119.80/120.09 apply (zenon_L62_); trivial.
% 119.80/120.09 (* end of lemma zenon_L63_ *)
% 119.80/120.09 assert (zenon_L64_ : (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67 zenon_H66 zenon_H12f.
% 119.80/120.09 elim (classic ((~((n0) = (n2)))/\(~(gt (n0) (n2))))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H1ad ].
% 119.80/120.09 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_H1ae. zenon_intro zenon_H1ab.
% 119.80/120.09 apply (zenon_L57_); trivial.
% 119.80/120.09 cut ((gt (n2) (n0)) = (gt (n0) (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H12f.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact gt_2_0.
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 cut (((n2) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H1af].
% 119.80/120.09 congruence.
% 119.80/120.09 apply (zenon_notand_s _ _ zenon_H1ad); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ].
% 119.80/120.09 apply zenon_H1b1. zenon_intro zenon_H1b2.
% 119.80/120.09 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.80/120.09 cut (((n0) = (n0)) = ((n2) = (n0))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H1af.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H136.
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 cut (((n0) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ae].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H1ae zenon_H1b2).
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 apply zenon_H1b0. zenon_intro zenon_H1b3.
% 119.80/120.09 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.80/120.09 generalize (zenon_H142 (n2)). zenon_intro zenon_H1b4.
% 119.80/120.09 generalize (zenon_H1b4 (n0)). zenon_intro zenon_H1b5.
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H1b5); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1b6 ].
% 119.80/120.09 exact (zenon_H1ab zenon_H1b3).
% 119.80/120.09 apply (zenon_imply_s _ _ zenon_H1b6); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H141 ].
% 119.80/120.09 exact (zenon_H1b7 gt_2_0).
% 119.80/120.09 exact (zenon_H12f zenon_H141).
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L64_ *)
% 119.80/120.09 assert (zenon_L65_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H154 zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H140.
% 119.80/120.09 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.80/120.09 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H154.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H156.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 congruence.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.80/120.09 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.09 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H157.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H141.
% 119.80/120.09 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.09 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.09 congruence.
% 119.80/120.09 apply zenon_H65. apply refl_equal.
% 119.80/120.09 exact (zenon_H159 zenon_H15c).
% 119.80/120.09 apply (zenon_L64_); trivial.
% 119.80/120.09 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H159.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H15a.
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.09 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.09 congruence.
% 119.80/120.09 exact (zenon_H15b zenon_H155).
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 apply zenon_H158. apply refl_equal.
% 119.80/120.09 (* end of lemma zenon_L65_ *)
% 119.80/120.09 assert (zenon_L66_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.80/120.09 do 0 intro. intros zenon_H66 zenon_H168 zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H140.
% 119.80/120.09 elim (classic (gt (n0) (succ (tptp_minus_1)))); [ zenon_intro zenon_H163 | zenon_intro zenon_H15d ].
% 119.80/120.09 cut ((gt (n0) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))).
% 119.80/120.09 intro zenon_D_pnotp.
% 119.80/120.09 apply zenon_H168.
% 119.80/120.09 rewrite <- zenon_D_pnotp.
% 119.80/120.09 exact zenon_H163.
% 119.80/120.09 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.10 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.80/120.10 congruence.
% 119.80/120.10 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.80/120.10 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.80/120.10 intro zenon_D_pnotp.
% 119.80/120.10 apply zenon_H167.
% 119.80/120.10 rewrite <- zenon_D_pnotp.
% 119.80/120.10 exact zenon_H16a.
% 119.80/120.10 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.80/120.10 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.80/120.10 congruence.
% 119.80/120.10 exact (zenon_H16b succ_tptp_minus_1).
% 119.80/120.10 apply zenon_H169. apply refl_equal.
% 119.80/120.10 apply zenon_H169. apply refl_equal.
% 119.80/120.10 apply zenon_H169. apply refl_equal.
% 119.80/120.10 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.80/120.10 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.80/120.10 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.80/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))); [ zenon_intro zenon_H15e | zenon_intro zenon_H15f ].
% 119.80/120.10 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.80/120.10 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.80/120.10 generalize (zenon_H160 (succ (tptp_minus_1))). zenon_intro zenon_H161.
% 119.80/120.10 apply (zenon_imply_s _ _ zenon_H161); [ zenon_intro zenon_H157 | zenon_intro zenon_H162 ].
% 119.80/120.10 exact (zenon_H157 zenon_H156).
% 119.80/120.10 apply (zenon_imply_s _ _ zenon_H162); [ zenon_intro zenon_H15f | zenon_intro zenon_H163 ].
% 119.80/120.10 exact (zenon_H15f zenon_H15e).
% 119.80/120.10 exact (zenon_H15d zenon_H163).
% 119.80/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H164 | zenon_intro zenon_H154 ].
% 119.80/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_H165 | zenon_intro zenon_H166 ].
% 119.80/120.10 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))).
% 119.80/120.10 intro zenon_D_pnotp.
% 119.80/120.10 apply zenon_H15f.
% 119.80/120.10 rewrite <- zenon_D_pnotp.
% 119.80/120.10 exact zenon_H165.
% 119.80/120.10 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.80/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.10 congruence.
% 119.80/120.10 apply zenon_H158. apply refl_equal.
% 119.80/120.10 apply zenon_H167. apply sym_equal. exact succ_tptp_minus_1.
% 119.80/120.10 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))).
% 119.80/120.10 intro zenon_D_pnotp.
% 119.80/120.10 apply zenon_H166.
% 119.80/120.10 rewrite <- zenon_D_pnotp.
% 119.80/120.10 exact zenon_H164.
% 119.80/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.10 congruence.
% 119.80/120.10 apply zenon_H158. apply refl_equal.
% 119.80/120.10 exact (zenon_H15b zenon_H155).
% 119.80/120.10 apply (zenon_L65_); trivial.
% 119.80/120.10 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.10 intro zenon_D_pnotp.
% 119.80/120.10 apply zenon_H157.
% 119.80/120.10 rewrite <- zenon_D_pnotp.
% 119.80/120.10 exact zenon_H141.
% 119.80/120.10 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.80/120.10 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.80/120.10 congruence.
% 119.80/120.10 apply zenon_H65. apply refl_equal.
% 119.80/120.10 exact (zenon_H159 zenon_H15c).
% 119.80/120.10 apply (zenon_L64_); trivial.
% 119.80/120.10 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.80/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.80/120.10 intro zenon_D_pnotp.
% 119.80/120.10 apply zenon_H159.
% 119.80/120.10 rewrite <- zenon_D_pnotp.
% 119.80/120.10 exact zenon_H15a.
% 119.80/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.80/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.80/120.10 congruence.
% 119.80/120.10 exact (zenon_H15b zenon_H155).
% 119.80/120.10 apply zenon_H158. apply refl_equal.
% 119.80/120.10 apply zenon_H158. apply refl_equal.
% 119.80/120.10 (* end of lemma zenon_L66_ *)
% 119.85/120.10 assert (zenon_L67_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n1) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc2 zenon_H140 zenon_H155 zenon_Hdb zenon_H66.
% 119.85/120.10 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.85/120.10 elim (classic (gt (succ (n0)) (succ (loopcounter)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd0 ].
% 119.85/120.10 cut ((gt (succ (n0)) (succ (loopcounter))) = (gt (n1) (succ (loopcounter)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_Hdb.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hd6.
% 119.85/120.10 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.10 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.10 congruence.
% 119.85/120.10 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.85/120.10 cut (((n1) = (n1)) = ((succ (n0)) = (n1))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H87.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hdc.
% 119.85/120.10 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.10 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H88 zenon_Hd1).
% 119.85/120.10 apply zenon_H64. apply refl_equal.
% 119.85/120.10 apply zenon_H64. apply refl_equal.
% 119.85/120.10 apply zenon_H76. apply refl_equal.
% 119.85/120.10 apply (zenon_L44_); trivial.
% 119.85/120.10 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.85/120.10 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H88.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H8b.
% 119.85/120.10 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.10 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H87 successor_1).
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L67_ *)
% 119.85/120.10 assert (zenon_L68_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (succ (n0)) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc2 zenon_H140 zenon_H155 zenon_H1b8 zenon_H66.
% 119.85/120.10 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.85/120.10 elim (classic (gt (succ (n0)) (n2))); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 119.85/120.10 cut ((gt (succ (n0)) (n2)) = (gt (succ (n0)) (succ (succ (n0))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1b8.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H186.
% 119.85/120.10 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.10 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 exact (zenon_H102 zenon_H1b9).
% 119.85/120.10 apply (zenon_L42_); trivial.
% 119.85/120.10 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.85/120.10 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H102.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H103.
% 119.85/120.10 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.10 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H105 successor_2).
% 119.85/120.10 apply zenon_H104. apply refl_equal.
% 119.85/120.10 apply zenon_H104. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L68_ *)
% 119.85/120.10 assert (zenon_L69_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (~((n0) = (n1))) -> (~(gt (n0) (n1))) -> (~(gt (n0) (n2))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H140 zenon_H155 zenon_Hc2 zenon_H106 zenon_H13f zenon_H1ab.
% 119.85/120.10 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.85/120.10 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.85/120.10 apply (zenon_L5_); trivial.
% 119.85/120.10 apply (zenon_L12_); trivial.
% 119.85/120.10 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.85/120.10 elim (classic ((n0) = (loopcounter))); [ zenon_intro zenon_H133 | zenon_intro zenon_H93 ].
% 119.85/120.10 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.10 elim (classic (gt (n0) (loopcounter))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ].
% 119.85/120.10 elim (classic (gt (loopcounter) (succ (loopcounter)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf0 ].
% 119.85/120.10 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.10 generalize (zenon_H142 (loopcounter)). zenon_intro zenon_H143.
% 119.85/120.10 generalize (zenon_H143 (succ (loopcounter))). zenon_intro zenon_H144.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H131 | zenon_intro zenon_H145 ].
% 119.85/120.10 exact (zenon_H131 zenon_H130).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H146 ].
% 119.85/120.10 exact (zenon_Hf0 zenon_Hf2).
% 119.85/120.10 exact (zenon_H140 zenon_H146).
% 119.85/120.10 apply (zenon_L47_); trivial.
% 119.85/120.10 cut ((gt (n0) (n0)) = (gt (n0) (loopcounter))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H131.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H141.
% 119.85/120.10 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.85/120.10 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H65. apply refl_equal.
% 119.85/120.10 exact (zenon_H93 zenon_H133).
% 119.85/120.10 apply (zenon_L49_); trivial.
% 119.85/120.10 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.10 cut (((loopcounter) = (loopcounter)) = ((n0) = (loopcounter))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H93.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hed.
% 119.85/120.10 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.10 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H132 zenon_H95).
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.85/120.10 apply (zenon_L50_); trivial.
% 119.85/120.10 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.85/120.10 apply (zenon_L52_); trivial.
% 119.85/120.10 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.10 (* end of lemma zenon_L69_ *)
% 119.85/120.10 assert (zenon_L70_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n1))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (n0) (n2))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H1ba zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H140 zenon_H1ab.
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H164 | zenon_intro zenon_H154 ].
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_H165 | zenon_intro zenon_H166 ].
% 119.85/120.10 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1ba.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H165.
% 119.85/120.10 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 elim (classic (gt (n0) (n1))); [ zenon_intro zenon_H150 | zenon_intro zenon_H13f ].
% 119.85/120.10 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.10 generalize (zenon_H1bb (n0)). zenon_intro zenon_H1bc.
% 119.85/120.10 generalize (zenon_H1bc (n1)). zenon_intro zenon_H1bd.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1bd); [ zenon_intro zenon_H166 | zenon_intro zenon_H1be ].
% 119.85/120.10 exact (zenon_H166 zenon_H165).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1be); [ zenon_intro zenon_H13f | zenon_intro zenon_H1bf ].
% 119.85/120.10 exact (zenon_H13f zenon_H150).
% 119.85/120.10 exact (zenon_H1ba zenon_H1bf).
% 119.85/120.10 apply (zenon_L69_); trivial.
% 119.85/120.10 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H166.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H164.
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 exact (zenon_H15b zenon_H155).
% 119.85/120.10 apply (zenon_L58_); trivial.
% 119.85/120.10 (* end of lemma zenon_L70_ *)
% 119.85/120.10 assert (zenon_L71_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n0) (n2))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H155 zenon_H140 zenon_Hc2 zenon_H7d zenon_H67 zenon_H1ab zenon_H1c0 zenon_H66.
% 119.85/120.10 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1ba ].
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ].
% 119.85/120.10 elim (classic (gt (succ (n0)) (succ (succ (n0))))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1b8 ].
% 119.85/120.10 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.10 generalize (zenon_H1bb (succ (n0))). zenon_intro zenon_H1c4.
% 119.85/120.10 generalize (zenon_H1c4 (succ (succ (n0)))). zenon_intro zenon_H1c5.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1c5); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H1c6 ].
% 119.85/120.10 exact (zenon_H1c2 zenon_H1c1).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H1c7 ].
% 119.85/120.10 exact (zenon_H1b8 zenon_H1c3).
% 119.85/120.10 exact (zenon_H1c0 zenon_H1c7).
% 119.85/120.10 apply (zenon_L68_); trivial.
% 119.85/120.10 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n1)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1c2.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H1bf.
% 119.85/120.10 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 exact (zenon_H88 zenon_Hd1).
% 119.85/120.10 apply (zenon_L70_); trivial.
% 119.85/120.10 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.85/120.10 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H88.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H8b.
% 119.85/120.10 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.10 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H87 successor_1).
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L71_ *)
% 119.85/120.10 assert (zenon_L72_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n2))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (n0) (n2))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H1c8 zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H140 zenon_H1ab.
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0))))); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H1c0 ].
% 119.85/120.10 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0)))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n2))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1c8.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H1c7.
% 119.85/120.10 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 exact (zenon_H105 successor_2).
% 119.85/120.10 apply (zenon_L71_); trivial.
% 119.85/120.10 (* end of lemma zenon_L72_ *)
% 119.85/120.10 assert (zenon_L73_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H1c8 zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H164 | zenon_intro zenon_H154 ].
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_H165 | zenon_intro zenon_H166 ].
% 119.85/120.10 elim (classic (gt (n0) (n2))); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1ab ].
% 119.85/120.10 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.10 generalize (zenon_H1bb (n0)). zenon_intro zenon_H1bc.
% 119.85/120.10 generalize (zenon_H1bc (n2)). zenon_intro zenon_H1c9.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1c9); [ zenon_intro zenon_H166 | zenon_intro zenon_H1ca ].
% 119.85/120.10 exact (zenon_H166 zenon_H165).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1cb ].
% 119.85/120.10 exact (zenon_H1ab zenon_H1b3).
% 119.85/120.10 exact (zenon_H1c8 zenon_H1cb).
% 119.85/120.10 apply (zenon_L72_); trivial.
% 119.85/120.10 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H166.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H164.
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 exact (zenon_H15b zenon_H155).
% 119.85/120.10 apply (zenon_L65_); trivial.
% 119.85/120.10 (* end of lemma zenon_L73_ *)
% 119.85/120.10 assert (zenon_L74_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (n0) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc2 zenon_H140 zenon_H1cc zenon_H66 zenon_H155.
% 119.85/120.10 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.10 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.10 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0))))); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H1c0 ].
% 119.85/120.10 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.10 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.85/120.10 generalize (zenon_H160 (succ (succ (n0)))). zenon_intro zenon_H1cd.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1cd); [ zenon_intro zenon_H157 | zenon_intro zenon_H1ce ].
% 119.85/120.10 exact (zenon_H157 zenon_H156).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1ce); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H1cf ].
% 119.85/120.10 exact (zenon_H1c0 zenon_H1c7).
% 119.85/120.10 exact (zenon_H1cc zenon_H1cf).
% 119.85/120.10 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1ba ].
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ].
% 119.85/120.10 elim (classic (gt (succ (n0)) (succ (succ (n0))))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1b8 ].
% 119.85/120.10 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.10 generalize (zenon_H1bb (succ (n0))). zenon_intro zenon_H1c4.
% 119.85/120.10 generalize (zenon_H1c4 (succ (succ (n0)))). zenon_intro zenon_H1c5.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1c5); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H1c6 ].
% 119.85/120.10 exact (zenon_H1c2 zenon_H1c1).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H1c7 ].
% 119.85/120.10 exact (zenon_H1b8 zenon_H1c3).
% 119.85/120.10 exact (zenon_H1c0 zenon_H1c7).
% 119.85/120.10 apply (zenon_L68_); trivial.
% 119.85/120.10 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n1)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1c2.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H1bf.
% 119.85/120.10 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 exact (zenon_H88 zenon_Hd1).
% 119.85/120.10 elim (classic ((~((sum (n0) (tptp_minus_1) zenon_E) = (n2)))/\(~(gt (sum (n0) (tptp_minus_1) zenon_E) (n2))))); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1d1 ].
% 119.85/120.10 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_H1d2. zenon_intro zenon_H1c8.
% 119.85/120.10 apply (zenon_L73_); trivial.
% 119.85/120.10 cut ((gt (n2) (n1)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1ba.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact gt_2_1.
% 119.85/120.10 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.10 cut (((n2) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1d3].
% 119.85/120.10 congruence.
% 119.85/120.10 apply (zenon_notand_s _ _ zenon_H1d1); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1d4 ].
% 119.85/120.10 apply zenon_H1d5. zenon_intro zenon_H1d6.
% 119.85/120.10 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n2) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1d3.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H15a.
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1d2].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H1d2 zenon_H1d6).
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 apply zenon_H1d4. zenon_intro zenon_H1cb.
% 119.85/120.10 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.10 generalize (zenon_H1bb (n2)). zenon_intro zenon_H1d7.
% 119.85/120.10 generalize (zenon_H1d7 (n1)). zenon_intro zenon_H1d8.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1d8); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H1d9 ].
% 119.85/120.10 exact (zenon_H1c8 zenon_H1cb).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1d9); [ zenon_intro zenon_Hba | zenon_intro zenon_H1bf ].
% 119.85/120.10 exact (zenon_Hba gt_2_1).
% 119.85/120.10 exact (zenon_H1ba zenon_H1bf).
% 119.85/120.10 apply zenon_H64. apply refl_equal.
% 119.85/120.10 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.85/120.10 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H88.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H8b.
% 119.85/120.10 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.10 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H87 successor_1).
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H157.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H141.
% 119.85/120.10 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.10 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H65. apply refl_equal.
% 119.85/120.10 exact (zenon_H159 zenon_H15c).
% 119.85/120.10 apply (zenon_L64_); trivial.
% 119.85/120.10 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H159.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H15a.
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H15b zenon_H155).
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L74_ *)
% 119.85/120.10 assert (zenon_L75_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (n0))))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H1da zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H176 | zenon_intro zenon_H168 ].
% 119.85/120.10 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_H177 | zenon_intro zenon_H178 ].
% 119.85/120.10 elim (classic (gt (n0) (succ (succ (n0))))); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1cc ].
% 119.85/120.10 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.10 generalize (zenon_H171 (n0)). zenon_intro zenon_H179.
% 119.85/120.10 generalize (zenon_H179 (succ (succ (n0)))). zenon_intro zenon_H1db.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1db); [ zenon_intro zenon_H178 | zenon_intro zenon_H1dc ].
% 119.85/120.10 exact (zenon_H178 zenon_H177).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1dc); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1dd ].
% 119.85/120.10 exact (zenon_H1cc zenon_H1cf).
% 119.85/120.10 exact (zenon_H1da zenon_H1dd).
% 119.85/120.10 apply (zenon_L74_); trivial.
% 119.85/120.10 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H178.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H176.
% 119.85/120.10 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.10 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H169. apply refl_equal.
% 119.85/120.10 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.10 apply (zenon_L66_); trivial.
% 119.85/120.10 (* end of lemma zenon_L75_ *)
% 119.85/120.10 assert (zenon_L76_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H170 zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1da ].
% 119.85/120.10 elim (classic (gt (succ (tptp_minus_1)) (n2))); [ zenon_intro zenon_H1de | zenon_intro zenon_H1df ].
% 119.85/120.10 elim (classic (gt (n2) (succ (n0)))); [ zenon_intro zenon_Hfc | zenon_intro zenon_Hf9 ].
% 119.85/120.10 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.10 generalize (zenon_H171 (n2)). zenon_intro zenon_H1e0.
% 119.85/120.10 generalize (zenon_H1e0 (succ (n0))). zenon_intro zenon_H1e1.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1e1); [ zenon_intro zenon_H1df | zenon_intro zenon_H1e2 ].
% 119.85/120.10 exact (zenon_H1df zenon_H1de).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1e2); [ zenon_intro zenon_Hf9 | zenon_intro zenon_H16f ].
% 119.85/120.10 exact (zenon_Hf9 zenon_Hfc).
% 119.85/120.10 exact (zenon_H170 zenon_H16f).
% 119.85/120.10 apply (zenon_L25_); trivial.
% 119.85/120.10 cut ((gt (succ (tptp_minus_1)) (succ (succ (n0)))) = (gt (succ (tptp_minus_1)) (n2))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1df.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H1dd.
% 119.85/120.10 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.10 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H169. apply refl_equal.
% 119.85/120.10 exact (zenon_H105 successor_2).
% 119.85/120.10 apply (zenon_L75_); trivial.
% 119.85/120.10 (* end of lemma zenon_L76_ *)
% 119.85/120.10 assert (zenon_L77_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H16c zenon_H140 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H16f | zenon_intro zenon_H170 ].
% 119.85/120.10 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16e ].
% 119.85/120.10 elim (classic (gt (n1) (succ (loopcounter)))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hdb ].
% 119.85/120.10 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.10 generalize (zenon_H171 (n1)). zenon_intro zenon_H1e3.
% 119.85/120.10 generalize (zenon_H1e3 (succ (loopcounter))). zenon_intro zenon_H1e4.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1e4); [ zenon_intro zenon_H16e | zenon_intro zenon_H1e5 ].
% 119.85/120.10 exact (zenon_H16e zenon_H16d).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1e5); [ zenon_intro zenon_Hdb | zenon_intro zenon_H175 ].
% 119.85/120.10 exact (zenon_Hdb zenon_He3).
% 119.85/120.10 exact (zenon_H16c zenon_H175).
% 119.85/120.10 apply (zenon_L67_); trivial.
% 119.85/120.10 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (succ (tptp_minus_1)) (n1))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H16e.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H16f.
% 119.85/120.10 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.10 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H169. apply refl_equal.
% 119.85/120.10 exact (zenon_H87 successor_1).
% 119.85/120.10 apply (zenon_L76_); trivial.
% 119.85/120.10 (* end of lemma zenon_L77_ *)
% 119.85/120.10 assert (zenon_L78_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc2 zenon_H140 zenon_H66 zenon_H155.
% 119.85/120.10 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.10 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.10 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.10 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (loopcounter)))); [ zenon_intro zenon_H17c | zenon_intro zenon_H17d ].
% 119.85/120.10 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.10 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.85/120.10 generalize (zenon_H160 (succ (loopcounter))). zenon_intro zenon_H17e.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H17e); [ zenon_intro zenon_H157 | zenon_intro zenon_H17f ].
% 119.85/120.10 exact (zenon_H157 zenon_H156).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H17f); [ zenon_intro zenon_H17d | zenon_intro zenon_H146 ].
% 119.85/120.10 exact (zenon_H17d zenon_H17c).
% 119.85/120.10 exact (zenon_H140 zenon_H146).
% 119.85/120.10 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.85/120.10 elim (classic (gt (succ (tptp_minus_1)) (succ (loopcounter)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H16c ].
% 119.85/120.10 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.10 cut ((gt (n0) (succ (loopcounter))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (loopcounter)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H17d.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H146.
% 119.85/120.10 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.10 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.10 congruence.
% 119.85/120.10 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H159.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H15a.
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H15b zenon_H155).
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 apply zenon_H76. apply refl_equal.
% 119.85/120.10 cut ((gt (succ (tptp_minus_1)) (succ (loopcounter))) = (gt (n0) (succ (loopcounter)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H140.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H175.
% 119.85/120.10 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.10 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.10 congruence.
% 119.85/120.10 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.10 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H16b.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H136.
% 119.85/120.10 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.10 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H167 zenon_H180).
% 119.85/120.10 apply zenon_H65. apply refl_equal.
% 119.85/120.10 apply zenon_H65. apply refl_equal.
% 119.85/120.10 apply zenon_H76. apply refl_equal.
% 119.85/120.10 apply (zenon_L77_); trivial.
% 119.85/120.10 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.10 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H167.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H16a.
% 119.85/120.10 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.10 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.10 apply zenon_H169. apply refl_equal.
% 119.85/120.10 apply zenon_H169. apply refl_equal.
% 119.85/120.10 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H157.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H141.
% 119.85/120.10 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.10 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H65. apply refl_equal.
% 119.85/120.10 exact (zenon_H159 zenon_H15c).
% 119.85/120.10 apply (zenon_L64_); trivial.
% 119.85/120.10 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H159.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H15a.
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.10 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H15b zenon_H155).
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 apply zenon_H158. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L78_ *)
% 119.85/120.10 assert (zenon_L79_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n3))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H1e6 zenon_H67 zenon_H7d zenon_H155 zenon_H140.
% 119.85/120.10 elim (classic ((loopcounter) = (n3))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hc2 ].
% 119.85/120.10 cut ((gt (n1) (loopcounter)) = (gt (n1) (n3))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1e6.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H7d.
% 119.85/120.10 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.85/120.10 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H64. apply refl_equal.
% 119.85/120.10 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.10 apply (zenon_L78_); trivial.
% 119.85/120.10 (* end of lemma zenon_L79_ *)
% 119.85/120.10 assert (zenon_L80_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H67 zenon_H7d zenon_H155 zenon_H140 zenon_H66 zenon_Hdd.
% 119.85/120.10 elim (classic ((~((n1) = (n3)))/\(~(gt (n1) (n3))))); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1e8 ].
% 119.85/120.10 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e9. zenon_intro zenon_H1e6.
% 119.85/120.10 apply (zenon_L79_); trivial.
% 119.85/120.10 cut ((gt (n3) (n1)) = (gt (n1) (n1))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_Hdd.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact gt_3_1.
% 119.85/120.10 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.10 cut (((n3) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H1ea].
% 119.85/120.10 congruence.
% 119.85/120.10 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ec | zenon_intro zenon_H1eb ].
% 119.85/120.10 apply zenon_H1ec. zenon_intro zenon_H1ed.
% 119.85/120.10 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.85/120.10 cut (((n1) = (n1)) = ((n3) = (n1))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1ea.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hdc.
% 119.85/120.10 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.10 cut (((n1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H1e9].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H1e9 zenon_H1ed).
% 119.85/120.10 apply zenon_H64. apply refl_equal.
% 119.85/120.10 apply zenon_H64. apply refl_equal.
% 119.85/120.10 apply zenon_H1eb. zenon_intro zenon_H1ee.
% 119.85/120.10 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.10 generalize (zenon_He4 (n3)). zenon_intro zenon_H1ef.
% 119.85/120.10 generalize (zenon_H1ef (n1)). zenon_intro zenon_H1f0.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1f0); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H1f1 ].
% 119.85/120.10 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1f1); [ zenon_intro zenon_H1f2 | zenon_intro zenon_He8 ].
% 119.85/120.10 exact (zenon_H1f2 gt_3_1).
% 119.85/120.10 exact (zenon_Hdd zenon_He8).
% 119.85/120.10 apply zenon_H64. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L80_ *)
% 119.85/120.10 assert (zenon_L81_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n1))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_Hee zenon_H67 zenon_H7d zenon_H155 zenon_H140.
% 119.85/120.10 elim (classic ((~((loopcounter) = (n3)))/\(~(gt (loopcounter) (n3))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ].
% 119.85/120.10 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hc2. zenon_intro zenon_H1f5.
% 119.85/120.10 apply (zenon_L46_); trivial.
% 119.85/120.10 cut ((gt (n3) (n1)) = (gt (loopcounter) (n1))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_Hee.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact gt_3_1.
% 119.85/120.10 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.10 cut (((n3) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 119.85/120.10 congruence.
% 119.85/120.10 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f7 ].
% 119.85/120.10 apply zenon_H1f8. zenon_intro zenon_Hcb.
% 119.85/120.10 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.10 cut (((loopcounter) = (loopcounter)) = ((n3) = (loopcounter))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1f6.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hed.
% 119.85/120.10 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.10 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply zenon_H1f7. zenon_intro zenon_H1f9.
% 119.85/120.10 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.10 generalize (zenon_H13b (n3)). zenon_intro zenon_H1fa.
% 119.85/120.10 generalize (zenon_H1fa (n1)). zenon_intro zenon_H1fb.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1fb); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1fc ].
% 119.85/120.10 exact (zenon_H1f5 zenon_H1f9).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1fc); [ zenon_intro zenon_H1f2 | zenon_intro zenon_Hf1 ].
% 119.85/120.10 exact (zenon_H1f2 gt_3_1).
% 119.85/120.10 exact (zenon_Hee zenon_Hf1).
% 119.85/120.10 apply zenon_H64. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L81_ *)
% 119.85/120.10 assert (zenon_L82_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (loopcounter) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H67 zenon_H7d zenon_H140 zenon_H155 zenon_Hf0 zenon_H66.
% 119.85/120.10 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.85/120.10 elim (classic (gt (loopcounter) (n1))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hee ].
% 119.85/120.10 elim (classic (gt (loopcounter) (succ (n0)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Heb ].
% 119.85/120.10 cut ((gt (loopcounter) (succ (n0))) = (gt (loopcounter) (succ (loopcounter)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_Hf0.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hef.
% 119.85/120.10 cut (((succ (n0)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 119.85/120.10 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply (zenon_L9_); trivial.
% 119.85/120.10 cut ((gt (loopcounter) (n1)) = (gt (loopcounter) (succ (n0)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_Heb.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hf1.
% 119.85/120.10 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.85/120.10 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 exact (zenon_H88 zenon_Hd1).
% 119.85/120.10 apply (zenon_L81_); trivial.
% 119.85/120.10 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.85/120.10 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H88.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H8b.
% 119.85/120.10 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.10 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H87 successor_1).
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L82_ *)
% 119.85/120.10 assert (zenon_L83_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_Hdb zenon_H67 zenon_H7d zenon_H140 zenon_H155.
% 119.85/120.10 elim (classic (gt (loopcounter) (succ (loopcounter)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf0 ].
% 119.85/120.10 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.10 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.85/120.10 generalize (zenon_Hf3 (succ (loopcounter))). zenon_intro zenon_Hf4.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_H92 | zenon_intro zenon_Hf5 ].
% 119.85/120.10 exact (zenon_H92 zenon_H7d).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_He3 ].
% 119.85/120.10 exact (zenon_Hf0 zenon_Hf2).
% 119.85/120.10 exact (zenon_Hdb zenon_He3).
% 119.85/120.10 apply (zenon_L82_); trivial.
% 119.85/120.10 (* end of lemma zenon_L83_ *)
% 119.85/120.10 assert (zenon_L84_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (succ (loopcounter)))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H1fd zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic (gt (n1) (succ (loopcounter)))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hdb ].
% 119.85/120.10 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.85/120.10 generalize (zenon_H1a6 (n1)). zenon_intro zenon_H1a7.
% 119.85/120.10 generalize (zenon_H1a7 (succ (loopcounter))). zenon_intro zenon_H1fe.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1fe); [ zenon_intro zenon_Hba | zenon_intro zenon_H1ff ].
% 119.85/120.10 exact (zenon_Hba gt_2_1).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H1ff); [ zenon_intro zenon_Hdb | zenon_intro zenon_H200 ].
% 119.85/120.10 exact (zenon_Hdb zenon_He3).
% 119.85/120.10 exact (zenon_H1fd zenon_H200).
% 119.85/120.10 apply (zenon_L83_); trivial.
% 119.85/120.10 (* end of lemma zenon_L84_ *)
% 119.85/120.10 assert (zenon_L85_ : (~((n3) = (n3))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H201.
% 119.85/120.10 apply zenon_H201. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L85_ *)
% 119.85/120.10 assert (zenon_L86_ : (~(gt (n3) (succ (succ (n0))))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H202.
% 119.85/120.10 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.85/120.10 cut ((gt (n3) (n2)) = (gt (n3) (succ (succ (n0))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H202.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact gt_3_2.
% 119.85/120.10 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.10 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H201. apply refl_equal.
% 119.85/120.10 exact (zenon_H102 zenon_H1b9).
% 119.85/120.10 apply zenon_H102. apply sym_equal. exact successor_2.
% 119.85/120.10 (* end of lemma zenon_L86_ *)
% 119.85/120.10 assert (zenon_L87_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (loopcounter)))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_Hd0 zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.85/120.10 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.85/120.10 apply (zenon_L9_); trivial.
% 119.85/120.10 elim (classic (gt (n1) (succ (loopcounter)))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hdb ].
% 119.85/120.10 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.10 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.10 generalize (zenon_H78 (succ (loopcounter))). zenon_intro zenon_Hf6.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_Hf6); [ zenon_intro zenon_H6f | zenon_intro zenon_Hf7 ].
% 119.85/120.10 exact (zenon_H6f zenon_H67).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_Hf7); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hf8 ].
% 119.85/120.10 exact (zenon_Hdb zenon_He3).
% 119.85/120.10 cut ((gt (succ (loopcounter)) (succ (loopcounter))) = (gt (succ (n0)) (succ (loopcounter)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_Hd0.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hf8.
% 119.85/120.10 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.10 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.85/120.10 congruence.
% 119.85/120.10 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.85/120.10 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.85/120.10 apply zenon_Hd2. apply sym_equal. exact zenon_Hd5.
% 119.85/120.10 exact (zenon_Hd3 zenon_Hd0).
% 119.85/120.10 apply zenon_H76. apply refl_equal.
% 119.85/120.10 apply (zenon_L83_); trivial.
% 119.85/120.10 (* end of lemma zenon_L87_ *)
% 119.85/120.10 assert (zenon_L88_ : (~(gt (succ (succ (n0))) (succ (n0)))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_Hfe.
% 119.85/120.10 elim (classic (gt (n2) (succ (n0)))); [ zenon_intro zenon_Hfc | zenon_intro zenon_Hf9 ].
% 119.85/120.10 cut ((gt (n2) (succ (n0))) = (gt (succ (succ (n0))) (succ (n0)))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_Hfe.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hfc.
% 119.85/120.10 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.10 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.10 congruence.
% 119.85/120.10 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.85/120.10 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H102.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H103.
% 119.85/120.10 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.10 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H105 successor_2).
% 119.85/120.10 apply zenon_H104. apply refl_equal.
% 119.85/120.10 apply zenon_H104. apply refl_equal.
% 119.85/120.10 apply zenon_H8c. apply refl_equal.
% 119.85/120.10 apply (zenon_L25_); trivial.
% 119.85/120.10 (* end of lemma zenon_L88_ *)
% 119.85/120.10 assert (zenon_L89_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (succ (loopcounter)))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H203 zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_Hfd | zenon_intro zenon_Hfe ].
% 119.85/120.10 elim (classic (gt (succ (succ (n0))) (n1))); [ zenon_intro zenon_H204 | zenon_intro zenon_H205 ].
% 119.85/120.10 elim (classic (gt (n1) (succ (loopcounter)))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hdb ].
% 119.85/120.10 generalize (zenon_H66 (succ (succ (n0)))). zenon_intro zenon_H206.
% 119.85/120.10 generalize (zenon_H206 (n1)). zenon_intro zenon_H207.
% 119.85/120.10 generalize (zenon_H207 (succ (loopcounter))). zenon_intro zenon_H208.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H208); [ zenon_intro zenon_H205 | zenon_intro zenon_H209 ].
% 119.85/120.10 exact (zenon_H205 zenon_H204).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H209); [ zenon_intro zenon_Hdb | zenon_intro zenon_H20a ].
% 119.85/120.10 exact (zenon_Hdb zenon_He3).
% 119.85/120.10 exact (zenon_H203 zenon_H20a).
% 119.85/120.10 apply (zenon_L83_); trivial.
% 119.85/120.10 cut ((gt (succ (succ (n0))) (succ (n0))) = (gt (succ (succ (n0))) (n1))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H205.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hfd.
% 119.85/120.10 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.10 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H104. apply refl_equal.
% 119.85/120.10 exact (zenon_H87 successor_1).
% 119.85/120.10 apply (zenon_L88_); trivial.
% 119.85/120.10 (* end of lemma zenon_L89_ *)
% 119.85/120.10 assert (zenon_L90_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H20b zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic ((~((succ (succ (n0))) = (succ (loopcounter))))/\(~(gt (succ (succ (n0))) (succ (loopcounter)))))); [ zenon_intro zenon_H20c | zenon_intro zenon_H20d ].
% 119.85/120.10 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_H20e. zenon_intro zenon_H203.
% 119.85/120.10 apply (zenon_L89_); trivial.
% 119.85/120.10 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1e6 ].
% 119.85/120.10 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.10 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.10 generalize (zenon_H78 (n3)). zenon_intro zenon_H20f.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H20f); [ zenon_intro zenon_H6f | zenon_intro zenon_H210 ].
% 119.85/120.10 exact (zenon_H6f zenon_H67).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H210); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H211 ].
% 119.85/120.10 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.10 cut ((gt (succ (loopcounter)) (n3)) = (gt (succ (succ (n0))) (n3))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H20b.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H211.
% 119.85/120.10 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.85/120.10 cut (((succ (loopcounter)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H212].
% 119.85/120.10 congruence.
% 119.85/120.10 apply (zenon_notand_s _ _ zenon_H20d); [ zenon_intro zenon_H214 | zenon_intro zenon_H213 ].
% 119.85/120.10 apply zenon_H214. zenon_intro zenon_H215.
% 119.85/120.10 apply zenon_H212. apply sym_equal. exact zenon_H215.
% 119.85/120.10 apply zenon_H213. zenon_intro zenon_H20a.
% 119.85/120.10 generalize (zenon_H66 (succ (succ (n0)))). zenon_intro zenon_H206.
% 119.85/120.10 generalize (zenon_H206 (succ (loopcounter))). zenon_intro zenon_H216.
% 119.85/120.10 generalize (zenon_H216 (n3)). zenon_intro zenon_H217.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H217); [ zenon_intro zenon_H203 | zenon_intro zenon_H218 ].
% 119.85/120.10 exact (zenon_H203 zenon_H20a).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H218); [ zenon_intro zenon_H21a | zenon_intro zenon_H219 ].
% 119.85/120.10 exact (zenon_H21a zenon_H211).
% 119.85/120.10 exact (zenon_H20b zenon_H219).
% 119.85/120.10 apply zenon_H201. apply refl_equal.
% 119.85/120.10 apply (zenon_L79_); trivial.
% 119.85/120.10 (* end of lemma zenon_L90_ *)
% 119.85/120.10 assert (zenon_L91_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (succ (succ (n0))) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H67 zenon_H7d zenon_H155 zenon_H140 zenon_H21b zenon_H66.
% 119.85/120.10 elim (classic ((n3) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H21c | zenon_intro zenon_H99 ].
% 119.85/120.10 elim (classic (gt (succ (succ (n0))) (n3))); [ zenon_intro zenon_H219 | zenon_intro zenon_H20b ].
% 119.85/120.10 cut ((gt (succ (succ (n0))) (n3)) = (gt (succ (succ (n0))) (succ (succ (succ (n0)))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H21b.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H219.
% 119.85/120.10 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 119.85/120.10 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H104. apply refl_equal.
% 119.85/120.10 exact (zenon_H99 zenon_H21c).
% 119.85/120.10 apply (zenon_L90_); trivial.
% 119.85/120.10 elim (classic ((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ].
% 119.85/120.10 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0))))) = ((n3) = (succ (succ (succ (n0)))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H99.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H21d.
% 119.85/120.10 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.10 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H21f successor_3).
% 119.85/120.10 apply zenon_H21e. apply refl_equal.
% 119.85/120.10 apply zenon_H21e. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L91_ *)
% 119.85/120.10 assert (zenon_L92_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H220 zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1e6 ].
% 119.85/120.10 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.85/120.10 generalize (zenon_H1a6 (n1)). zenon_intro zenon_H1a7.
% 119.85/120.10 generalize (zenon_H1a7 (n3)). zenon_intro zenon_H221.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H221); [ zenon_intro zenon_Hba | zenon_intro zenon_H222 ].
% 119.85/120.10 exact (zenon_Hba gt_2_1).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H222); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H223 ].
% 119.85/120.10 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.10 exact (zenon_H220 zenon_H223).
% 119.85/120.10 apply (zenon_L79_); trivial.
% 119.85/120.10 (* end of lemma zenon_L92_ *)
% 119.85/120.10 assert (zenon_L93_ : (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H140 zenon_H155 zenon_H7d zenon_H67 zenon_H66 zenon_H1a5.
% 119.85/120.10 elim (classic ((~((n2) = (n3)))/\(~(gt (n2) (n3))))); [ zenon_intro zenon_H224 | zenon_intro zenon_H225 ].
% 119.85/120.10 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H226. zenon_intro zenon_H220.
% 119.85/120.10 apply (zenon_L92_); trivial.
% 119.85/120.10 cut ((gt (n3) (n2)) = (gt (n2) (n2))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1a5.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact gt_3_2.
% 119.85/120.10 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.10 cut (((n3) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H227].
% 119.85/120.10 congruence.
% 119.85/120.10 apply (zenon_notand_s _ _ zenon_H225); [ zenon_intro zenon_H229 | zenon_intro zenon_H228 ].
% 119.85/120.10 apply zenon_H229. zenon_intro zenon_H22a.
% 119.85/120.10 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H22b | zenon_intro zenon_H63 ].
% 119.85/120.10 cut (((n2) = (n2)) = ((n3) = (n2))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H227.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H22b.
% 119.85/120.10 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.10 cut (((n2) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H226].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H226 zenon_H22a).
% 119.85/120.10 apply zenon_H63. apply refl_equal.
% 119.85/120.10 apply zenon_H63. apply refl_equal.
% 119.85/120.10 apply zenon_H228. zenon_intro zenon_H223.
% 119.85/120.10 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.85/120.10 generalize (zenon_H1a6 (n3)). zenon_intro zenon_H22c.
% 119.85/120.10 generalize (zenon_H22c (n2)). zenon_intro zenon_H22d.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H22d); [ zenon_intro zenon_H220 | zenon_intro zenon_H22e ].
% 119.85/120.10 exact (zenon_H220 zenon_H223).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H22e); [ zenon_intro zenon_H22f | zenon_intro zenon_H1aa ].
% 119.85/120.10 exact (zenon_H22f gt_3_2).
% 119.85/120.10 exact (zenon_H1a5 zenon_H1aa).
% 119.85/120.10 apply zenon_H63. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L93_ *)
% 119.85/120.10 assert (zenon_L94_ : (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (~(gt (loopcounter) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H140 zenon_H155 zenon_H7d zenon_H67 zenon_H16c zenon_H230 zenon_H66.
% 119.85/120.10 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.85/120.10 elim (classic (gt (loopcounter) (n2))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H19d ].
% 119.85/120.10 elim (classic (gt (loopcounter) (succ (succ (n0))))); [ zenon_intro zenon_H231 | zenon_intro zenon_H232 ].
% 119.85/120.10 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H233 | zenon_intro zenon_H21b ].
% 119.85/120.10 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.10 generalize (zenon_H13b (succ (succ (n0)))). zenon_intro zenon_H234.
% 119.85/120.10 generalize (zenon_H234 (succ (succ (succ (n0))))). zenon_intro zenon_H235.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H235); [ zenon_intro zenon_H232 | zenon_intro zenon_H236 ].
% 119.85/120.10 exact (zenon_H232 zenon_H231).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H236); [ zenon_intro zenon_H21b | zenon_intro zenon_H237 ].
% 119.85/120.10 exact (zenon_H21b zenon_H233).
% 119.85/120.10 exact (zenon_H230 zenon_H237).
% 119.85/120.10 apply (zenon_L91_); trivial.
% 119.85/120.10 cut ((gt (loopcounter) (n2)) = (gt (loopcounter) (succ (succ (n0))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H232.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H1a1.
% 119.85/120.10 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.10 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.10 congruence.
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 exact (zenon_H102 zenon_H1b9).
% 119.85/120.10 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H233 | zenon_intro zenon_H21b ].
% 119.85/120.10 elim (classic (gt (n2) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H238 | zenon_intro zenon_H239 ].
% 119.85/120.10 cut ((gt (n2) (succ (succ (succ (n0))))) = (gt (loopcounter) (succ (succ (succ (n0)))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H230.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H238.
% 119.85/120.10 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.10 cut (((n2) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H19e].
% 119.85/120.10 congruence.
% 119.85/120.10 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.10 cut (((loopcounter) = (loopcounter)) = ((n2) = (loopcounter))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H19e.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hed.
% 119.85/120.10 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.10 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.85/120.10 congruence.
% 119.85/120.10 elim (classic ((~((loopcounter) = (n3)))/\(~(gt (loopcounter) (n3))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ].
% 119.85/120.10 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hc2. zenon_intro zenon_H1f5.
% 119.85/120.10 apply (zenon_L38_); trivial.
% 119.85/120.10 cut ((gt (n3) (n2)) = (gt (loopcounter) (n2))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H19d.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact gt_3_2.
% 119.85/120.10 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.10 cut (((n3) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 119.85/120.10 congruence.
% 119.85/120.10 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f7 ].
% 119.85/120.10 apply zenon_H1f8. zenon_intro zenon_Hcb.
% 119.85/120.10 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.10 cut (((loopcounter) = (loopcounter)) = ((n3) = (loopcounter))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H1f6.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_Hed.
% 119.85/120.10 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.10 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply zenon_H1f7. zenon_intro zenon_H1f9.
% 119.85/120.10 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.10 generalize (zenon_H13b (n3)). zenon_intro zenon_H1fa.
% 119.85/120.10 generalize (zenon_H1fa (n2)). zenon_intro zenon_H23a.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H23a); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23b ].
% 119.85/120.10 exact (zenon_H1f5 zenon_H1f9).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H22f | zenon_intro zenon_H1a1 ].
% 119.85/120.10 exact (zenon_H22f gt_3_2).
% 119.85/120.10 exact (zenon_H19d zenon_H1a1).
% 119.85/120.10 apply zenon_H63. apply refl_equal.
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply zenon_H7c. apply refl_equal.
% 119.85/120.10 apply zenon_H21e. apply refl_equal.
% 119.85/120.10 cut ((gt (succ (succ (n0))) (succ (succ (succ (n0))))) = (gt (n2) (succ (succ (succ (n0)))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H239.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H233.
% 119.85/120.10 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.10 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.10 congruence.
% 119.85/120.10 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H22b | zenon_intro zenon_H63 ].
% 119.85/120.10 cut (((n2) = (n2)) = ((succ (succ (n0))) = (n2))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H105.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H22b.
% 119.85/120.10 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.10 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H102 zenon_H1b9).
% 119.85/120.10 apply zenon_H63. apply refl_equal.
% 119.85/120.10 apply zenon_H63. apply refl_equal.
% 119.85/120.10 apply zenon_H21e. apply refl_equal.
% 119.85/120.10 apply (zenon_L91_); trivial.
% 119.85/120.10 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.85/120.10 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H102.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H103.
% 119.85/120.10 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.10 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.10 congruence.
% 119.85/120.10 exact (zenon_H105 successor_2).
% 119.85/120.10 apply zenon_H104. apply refl_equal.
% 119.85/120.10 apply zenon_H104. apply refl_equal.
% 119.85/120.10 (* end of lemma zenon_L94_ *)
% 119.85/120.10 assert (zenon_L95_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (succ (succ (n0)))))) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H23c zenon_H16c zenon_H67 zenon_H7d zenon_H155 zenon_H140.
% 119.85/120.10 elim (classic (gt (loopcounter) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H237 | zenon_intro zenon_H230 ].
% 119.85/120.10 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.10 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.85/120.10 generalize (zenon_Hf3 (succ (succ (succ (n0))))). zenon_intro zenon_H23d.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H23d); [ zenon_intro zenon_H92 | zenon_intro zenon_H23e ].
% 119.85/120.10 exact (zenon_H92 zenon_H7d).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H230 | zenon_intro zenon_H23f ].
% 119.85/120.10 exact (zenon_H230 zenon_H237).
% 119.85/120.10 exact (zenon_H23c zenon_H23f).
% 119.85/120.10 apply (zenon_L94_); trivial.
% 119.85/120.10 (* end of lemma zenon_L95_ *)
% 119.85/120.10 assert (zenon_L96_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (succ (succ (n0)))))) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.10 do 0 intro. intros zenon_H66 zenon_H240 zenon_H16c zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.10 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.85/120.10 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.85/120.10 apply (zenon_L87_); trivial.
% 119.85/120.10 elim (classic (gt (n1) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H23f | zenon_intro zenon_H23c ].
% 119.85/120.10 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.10 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.10 generalize (zenon_H78 (succ (succ (succ (n0))))). zenon_intro zenon_H241.
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H241); [ zenon_intro zenon_H6f | zenon_intro zenon_H242 ].
% 119.85/120.10 exact (zenon_H6f zenon_H67).
% 119.85/120.10 apply (zenon_imply_s _ _ zenon_H242); [ zenon_intro zenon_H23c | zenon_intro zenon_H243 ].
% 119.85/120.10 exact (zenon_H23c zenon_H23f).
% 119.85/120.10 cut ((gt (succ (loopcounter)) (succ (succ (succ (n0))))) = (gt (succ (n0)) (succ (succ (succ (n0)))))).
% 119.85/120.10 intro zenon_D_pnotp.
% 119.85/120.10 apply zenon_H240.
% 119.85/120.10 rewrite <- zenon_D_pnotp.
% 119.85/120.10 exact zenon_H243.
% 119.85/120.10 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.10 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.85/120.11 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.85/120.11 apply zenon_Hd2. apply sym_equal. exact zenon_Hd5.
% 119.85/120.11 apply zenon_Hd3. zenon_intro zenon_Hd6.
% 119.85/120.11 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.85/120.11 generalize (zenon_H8e (succ (loopcounter))). zenon_intro zenon_Hd7.
% 119.85/120.11 generalize (zenon_Hd7 (succ (succ (succ (n0))))). zenon_intro zenon_H244.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H245 ].
% 119.85/120.11 exact (zenon_Hd0 zenon_Hd6).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H245); [ zenon_intro zenon_H247 | zenon_intro zenon_H246 ].
% 119.85/120.11 exact (zenon_H247 zenon_H243).
% 119.85/120.11 exact (zenon_H240 zenon_H246).
% 119.85/120.11 apply zenon_H21e. apply refl_equal.
% 119.85/120.11 apply (zenon_L95_); trivial.
% 119.85/120.11 (* end of lemma zenon_L96_ *)
% 119.85/120.11 assert (zenon_L97_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (succ (n0))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H1b8 zenon_H155 zenon_H140 zenon_H67 zenon_H7d zenon_H16c.
% 119.85/120.11 elim (classic (gt (succ (n0)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H246 | zenon_intro zenon_H240 ].
% 119.85/120.11 elim (classic (gt (succ (n0)) (n3))); [ zenon_intro zenon_H248 | zenon_intro zenon_H249 ].
% 119.85/120.11 elim (classic (gt (n3) (succ (succ (n0))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H202 ].
% 119.85/120.11 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.85/120.11 generalize (zenon_H8e (n3)). zenon_intro zenon_H24b.
% 119.85/120.11 generalize (zenon_H24b (succ (succ (n0)))). zenon_intro zenon_H24c.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H24c); [ zenon_intro zenon_H249 | zenon_intro zenon_H24d ].
% 119.85/120.11 exact (zenon_H249 zenon_H248).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H24d); [ zenon_intro zenon_H202 | zenon_intro zenon_H1c3 ].
% 119.85/120.11 exact (zenon_H202 zenon_H24a).
% 119.85/120.11 exact (zenon_H1b8 zenon_H1c3).
% 119.85/120.11 apply (zenon_L86_); trivial.
% 119.85/120.11 cut ((gt (succ (n0)) (succ (succ (succ (n0))))) = (gt (succ (n0)) (n3))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H249.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H246.
% 119.85/120.11 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.85/120.11 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H8c. apply refl_equal.
% 119.85/120.11 exact (zenon_H21f successor_3).
% 119.85/120.11 apply (zenon_L96_); trivial.
% 119.85/120.11 (* end of lemma zenon_L97_ *)
% 119.85/120.11 assert (zenon_L98_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n3) (n3))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H24e zenon_H67 zenon_H7d zenon_H155 zenon_H140.
% 119.85/120.11 elim (classic (gt (n2) (n3))); [ zenon_intro zenon_H223 | zenon_intro zenon_H220 ].
% 119.85/120.11 generalize (zenon_H66 (n3)). zenon_intro zenon_H24f.
% 119.85/120.11 generalize (zenon_H24f (n2)). zenon_intro zenon_H250.
% 119.85/120.11 generalize (zenon_H250 (n3)). zenon_intro zenon_H251.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H251); [ zenon_intro zenon_H22f | zenon_intro zenon_H252 ].
% 119.85/120.11 exact (zenon_H22f gt_3_2).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H252); [ zenon_intro zenon_H220 | zenon_intro zenon_H253 ].
% 119.85/120.11 exact (zenon_H220 zenon_H223).
% 119.85/120.11 exact (zenon_H24e zenon_H253).
% 119.85/120.11 apply (zenon_L92_); trivial.
% 119.85/120.11 (* end of lemma zenon_L98_ *)
% 119.85/120.11 assert (zenon_L99_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((loopcounter) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H12f zenon_H95 zenon_H155 zenon_H140 zenon_H7d zenon_H67.
% 119.85/120.11 elim (classic (gt (n0) (loopcounter))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ].
% 119.85/120.11 cut ((gt (n0) (loopcounter)) = (gt (n0) (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H12f.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H130.
% 119.85/120.11 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 exact (zenon_H132 zenon_H95).
% 119.85/120.11 elim (classic ((n0) = (loopcounter))); [ zenon_intro zenon_H133 | zenon_intro zenon_H93 ].
% 119.85/120.11 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.85/120.11 cut ((gt (loopcounter) (loopcounter)) = (gt (n0) (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H131.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H134.
% 119.85/120.11 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.11 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H132.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H93 zenon_H133).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 elim (classic ((~((loopcounter) = (n1)))/\(~(gt (loopcounter) (n1))))); [ zenon_intro zenon_H137 | zenon_intro zenon_H138 ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H137). zenon_intro zenon_Hc4. zenon_intro zenon_Hee.
% 119.85/120.11 apply (zenon_L81_); trivial.
% 119.85/120.11 cut ((gt (n1) (loopcounter)) = (gt (loopcounter) (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H135.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H7d.
% 119.85/120.11 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.11 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 119.85/120.11 apply zenon_H13a. zenon_intro zenon_Hca.
% 119.85/120.11 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.11 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_Hec.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_Hed.
% 119.85/120.11 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.11 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_Hc4 zenon_Hca).
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H139. zenon_intro zenon_Hf1.
% 119.85/120.11 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.11 generalize (zenon_H13b (n1)). zenon_intro zenon_H13c.
% 119.85/120.11 generalize (zenon_H13c (loopcounter)). zenon_intro zenon_H13d.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H13d); [ zenon_intro zenon_Hee | zenon_intro zenon_H13e ].
% 119.85/120.11 exact (zenon_Hee zenon_Hf1).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H92 | zenon_intro zenon_H134 ].
% 119.85/120.11 exact (zenon_H92 zenon_H7d).
% 119.85/120.11 exact (zenon_H135 zenon_H134).
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.11 cut (((loopcounter) = (loopcounter)) = ((n0) = (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H93.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_Hed.
% 119.85/120.11 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.11 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H132 zenon_H95).
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L99_ *)
% 119.85/120.11 assert (zenon_L100_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n0)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H155 zenon_H140 zenon_H7d zenon_H67 zenon_H66 zenon_H95.
% 119.85/120.11 elim (classic ((n0) = (loopcounter))); [ zenon_intro zenon_H133 | zenon_intro zenon_H93 ].
% 119.85/120.11 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.11 elim (classic (gt (n0) (loopcounter))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ].
% 119.85/120.11 elim (classic (gt (loopcounter) (succ (loopcounter)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf0 ].
% 119.85/120.11 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.11 generalize (zenon_H142 (loopcounter)). zenon_intro zenon_H143.
% 119.85/120.11 generalize (zenon_H143 (succ (loopcounter))). zenon_intro zenon_H144.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H131 | zenon_intro zenon_H145 ].
% 119.85/120.11 exact (zenon_H131 zenon_H130).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H146 ].
% 119.85/120.11 exact (zenon_Hf0 zenon_Hf2).
% 119.85/120.11 exact (zenon_H140 zenon_H146).
% 119.85/120.11 apply (zenon_L82_); trivial.
% 119.85/120.11 cut ((gt (n0) (n0)) = (gt (n0) (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H131.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H141.
% 119.85/120.11 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 exact (zenon_H93 zenon_H133).
% 119.85/120.11 apply (zenon_L99_); trivial.
% 119.85/120.11 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.11 cut (((loopcounter) = (loopcounter)) = ((n0) = (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H93.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_Hed.
% 119.85/120.11 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.11 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H132 zenon_H95).
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L100_ *)
% 119.85/120.11 assert (zenon_L101_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n1)) -> (~(gt (n0) (n1))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_Hca zenon_H13f zenon_H67 zenon_H7d zenon_H155 zenon_H140.
% 119.85/120.11 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_He8 | zenon_intro zenon_Hdd ].
% 119.85/120.11 elim (classic (gt (loopcounter) (n1))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hee ].
% 119.85/120.11 cut ((gt (loopcounter) (n1)) = (gt (n0) (n1))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H13f.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_Hf1.
% 119.85/120.11 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.11 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H132.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_L8_); trivial.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H64. apply refl_equal.
% 119.85/120.11 cut ((gt (n1) (n1)) = (gt (loopcounter) (n1))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_Hee.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_He8.
% 119.85/120.11 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.11 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.11 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_Hec.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_Hed.
% 119.85/120.11 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.11 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_Hc4 zenon_Hca).
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H64. apply refl_equal.
% 119.85/120.11 apply (zenon_L80_); trivial.
% 119.85/120.11 (* end of lemma zenon_L101_ *)
% 119.85/120.11 assert (zenon_L102_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n2)) -> (~(gt (n0) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_Hcc zenon_H1ab zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.11 elim (classic (gt (n2) (n2))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1a5 ].
% 119.85/120.11 elim (classic (gt (loopcounter) (n2))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H19d ].
% 119.85/120.11 cut ((gt (loopcounter) (n2)) = (gt (n0) (n2))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1ab.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H1a1.
% 119.85/120.11 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.11 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H132.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_L8_); trivial.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H63. apply refl_equal.
% 119.85/120.11 cut ((gt (n2) (n2)) = (gt (loopcounter) (n2))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H19d.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H1aa.
% 119.85/120.11 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.11 cut (((n2) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H19e].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.11 cut (((loopcounter) = (loopcounter)) = ((n2) = (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H19e.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_Hed.
% 119.85/120.11 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.11 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_Hc3 zenon_Hcc).
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H63. apply refl_equal.
% 119.85/120.11 apply (zenon_L93_); trivial.
% 119.85/120.11 (* end of lemma zenon_L102_ *)
% 119.85/120.11 assert (zenon_L103_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n3)) -> (~(gt (n0) (n3))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_Hcb zenon_H254 zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.11 elim (classic (gt (n3) (n3))); [ zenon_intro zenon_H253 | zenon_intro zenon_H24e ].
% 119.85/120.11 elim (classic (gt (loopcounter) (n3))); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H1f5 ].
% 119.85/120.11 cut ((gt (loopcounter) (n3)) = (gt (n0) (n3))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H254.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H1f9.
% 119.85/120.11 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.85/120.11 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((loopcounter) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H132.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_L8_); trivial.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H201. apply refl_equal.
% 119.85/120.11 cut ((gt (n3) (n3)) = (gt (loopcounter) (n3))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1f5.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H253.
% 119.85/120.11 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.85/120.11 cut (((n3) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.11 cut (((loopcounter) = (loopcounter)) = ((n3) = (loopcounter))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1f6.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_Hed.
% 119.85/120.11 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.11 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H7c. apply refl_equal.
% 119.85/120.11 apply zenon_H201. apply refl_equal.
% 119.85/120.11 apply (zenon_L98_); trivial.
% 119.85/120.11 (* end of lemma zenon_L103_ *)
% 119.85/120.11 assert (zenon_L104_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (n0) (n1))) -> (~(gt (n0) (n2))) -> (~(gt (n0) (n3))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H140 zenon_H13f zenon_H1ab zenon_H254.
% 119.85/120.11 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.85/120.11 apply (zenon_L5_); trivial.
% 119.85/120.11 apply (zenon_L12_); trivial.
% 119.85/120.11 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.85/120.11 apply (zenon_L100_); trivial.
% 119.85/120.11 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.85/120.11 apply (zenon_L101_); trivial.
% 119.85/120.11 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.85/120.11 apply (zenon_L102_); trivial.
% 119.85/120.11 apply (zenon_L103_); trivial.
% 119.85/120.11 (* end of lemma zenon_L104_ *)
% 119.85/120.11 assert (zenon_L105_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (n0))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (n1))) -> (~(gt (n0) (n2))) -> (~(gt (n0) (n3))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H12f zenon_H140 zenon_H155 zenon_H13f zenon_H1ab zenon_H254.
% 119.85/120.11 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.85/120.11 apply (zenon_L5_); trivial.
% 119.85/120.11 apply (zenon_L12_); trivial.
% 119.85/120.11 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.85/120.11 apply (zenon_L99_); trivial.
% 119.85/120.11 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.85/120.11 apply (zenon_L101_); trivial.
% 119.85/120.11 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.85/120.11 apply (zenon_L102_); trivial.
% 119.85/120.11 apply (zenon_L103_); trivial.
% 119.85/120.11 (* end of lemma zenon_L105_ *)
% 119.85/120.11 assert (zenon_L106_ : (~(gt (n0) (n3))) -> (~(gt (n0) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H254 zenon_H1ab zenon_H155 zenon_H140 zenon_H7d zenon_H67 zenon_H66 zenon_H12f.
% 119.85/120.11 elim (classic ((~((n0) = (n1)))/\(~(gt (n0) (n1))))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H14a). zenon_intro zenon_H106. zenon_intro zenon_H13f.
% 119.85/120.11 apply (zenon_L105_); trivial.
% 119.85/120.11 cut ((gt (n1) (n0)) = (gt (n0) (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H12f.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact gt_1_0.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H14e | zenon_intro zenon_H14d ].
% 119.85/120.11 apply zenon_H14e. zenon_intro zenon_H14f.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((n1) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H14c.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H106 zenon_H14f).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H14d. zenon_intro zenon_H150.
% 119.85/120.11 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.11 generalize (zenon_H142 (n1)). zenon_intro zenon_H151.
% 119.85/120.11 generalize (zenon_H151 (n0)). zenon_intro zenon_H152.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H13f | zenon_intro zenon_H153 ].
% 119.85/120.11 exact (zenon_H13f zenon_H150).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H153); [ zenon_intro zenon_H7b | zenon_intro zenon_H141 ].
% 119.85/120.11 exact (zenon_H7b gt_1_0).
% 119.85/120.11 exact (zenon_H12f zenon_H141).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L106_ *)
% 119.85/120.11 assert (zenon_L107_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (n2))) -> (~(gt (n0) (n3))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H154 zenon_H67 zenon_H7d zenon_H140 zenon_H155 zenon_H1ab zenon_H254.
% 119.85/120.11 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.11 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H154.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H156.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H159.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.11 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.11 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H157.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H141.
% 119.85/120.11 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 exact (zenon_H159 zenon_H15c).
% 119.85/120.11 apply (zenon_L106_); trivial.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H159.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L107_ *)
% 119.85/120.11 assert (zenon_L108_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (n2))) -> (~(gt (n0) (n3))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H168 zenon_H67 zenon_H7d zenon_H140 zenon_H155 zenon_H1ab zenon_H254.
% 119.85/120.11 elim (classic (gt (n0) (succ (tptp_minus_1)))); [ zenon_intro zenon_H163 | zenon_intro zenon_H15d ].
% 119.85/120.11 cut ((gt (n0) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H168.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H163.
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.11 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H167.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H16a.
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.11 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.11 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))); [ zenon_intro zenon_H15e | zenon_intro zenon_H15f ].
% 119.85/120.11 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.11 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.85/120.11 generalize (zenon_H160 (succ (tptp_minus_1))). zenon_intro zenon_H161.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H161); [ zenon_intro zenon_H157 | zenon_intro zenon_H162 ].
% 119.85/120.11 exact (zenon_H157 zenon_H156).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H162); [ zenon_intro zenon_H15f | zenon_intro zenon_H163 ].
% 119.85/120.11 exact (zenon_H15f zenon_H15e).
% 119.85/120.11 exact (zenon_H15d zenon_H163).
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H164 | zenon_intro zenon_H154 ].
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_H165 | zenon_intro zenon_H166 ].
% 119.85/120.11 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H15f.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H165.
% 119.85/120.11 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H167. apply sym_equal. exact succ_tptp_minus_1.
% 119.85/120.11 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H166.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H164.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply (zenon_L107_); trivial.
% 119.85/120.11 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H157.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H141.
% 119.85/120.11 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 exact (zenon_H159 zenon_H15c).
% 119.85/120.11 apply (zenon_L106_); trivial.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H159.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L108_ *)
% 119.85/120.11 assert (zenon_L109_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (~(gt (n0) (n2))) -> (~(gt (n0) (n3))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H155 zenon_H140 zenon_H67 zenon_H7d zenon_H16c zenon_H1ab zenon_H254 zenon_H255 zenon_H66.
% 119.85/120.11 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.85/120.11 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16e ].
% 119.85/120.11 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H16f | zenon_intro zenon_H170 ].
% 119.85/120.11 elim (classic (gt (succ (n0)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H246 | zenon_intro zenon_H240 ].
% 119.85/120.11 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.11 generalize (zenon_H171 (succ (n0))). zenon_intro zenon_H172.
% 119.85/120.11 generalize (zenon_H172 (succ (succ (succ (n0))))). zenon_intro zenon_H256.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H256); [ zenon_intro zenon_H170 | zenon_intro zenon_H257 ].
% 119.85/120.11 exact (zenon_H170 zenon_H16f).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H257); [ zenon_intro zenon_H240 | zenon_intro zenon_H258 ].
% 119.85/120.11 exact (zenon_H240 zenon_H246).
% 119.85/120.11 exact (zenon_H255 zenon_H258).
% 119.85/120.11 apply (zenon_L96_); trivial.
% 119.85/120.11 cut ((gt (succ (tptp_minus_1)) (n1)) = (gt (succ (tptp_minus_1)) (succ (n0)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H170.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H16d.
% 119.85/120.11 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 exact (zenon_H88 zenon_Hd1).
% 119.85/120.11 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H176 | zenon_intro zenon_H168 ].
% 119.85/120.11 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_H177 | zenon_intro zenon_H178 ].
% 119.85/120.11 elim (classic (gt (n0) (n1))); [ zenon_intro zenon_H150 | zenon_intro zenon_H13f ].
% 119.85/120.11 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.11 generalize (zenon_H171 (n0)). zenon_intro zenon_H179.
% 119.85/120.11 generalize (zenon_H179 (n1)). zenon_intro zenon_H17a.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H17a); [ zenon_intro zenon_H178 | zenon_intro zenon_H17b ].
% 119.85/120.11 exact (zenon_H178 zenon_H177).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H17b); [ zenon_intro zenon_H13f | zenon_intro zenon_H16d ].
% 119.85/120.11 exact (zenon_H13f zenon_H150).
% 119.85/120.11 exact (zenon_H16e zenon_H16d).
% 119.85/120.11 apply (zenon_L104_); trivial.
% 119.85/120.11 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H178.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H176.
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.11 apply (zenon_L108_); trivial.
% 119.85/120.11 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.85/120.11 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H88.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H8b.
% 119.85/120.11 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.11 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H87 successor_1).
% 119.85/120.11 apply zenon_H8c. apply refl_equal.
% 119.85/120.11 apply zenon_H8c. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L109_ *)
% 119.85/120.11 assert (zenon_L110_ : (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> (~(gt (n0) (n3))) -> (~(gt (n0) (n2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H255 zenon_H254 zenon_H1ab zenon_H66 zenon_H1df zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.11 elim (classic ((~((succ (tptp_minus_1)) = (n3)))/\(~(gt (succ (tptp_minus_1)) (n3))))); [ zenon_intro zenon_H259 | zenon_intro zenon_H25a ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H259). zenon_intro zenon_H25c. zenon_intro zenon_H25b.
% 119.85/120.11 elim (classic ((~((succ (tptp_minus_1)) = (succ (loopcounter))))/\(~(gt (succ (tptp_minus_1)) (succ (loopcounter)))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H25f. zenon_intro zenon_H16c.
% 119.85/120.11 apply (zenon_L109_); trivial.
% 119.85/120.11 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1e6 ].
% 119.85/120.11 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.11 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.11 generalize (zenon_H78 (n3)). zenon_intro zenon_H20f.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H20f); [ zenon_intro zenon_H6f | zenon_intro zenon_H210 ].
% 119.85/120.11 exact (zenon_H6f zenon_H67).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H210); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H211 ].
% 119.85/120.11 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.11 cut ((gt (succ (loopcounter)) (n3)) = (gt (succ (tptp_minus_1)) (n3))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H25b.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H211.
% 119.85/120.11 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.85/120.11 cut (((succ (loopcounter)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H260].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H25e); [ zenon_intro zenon_H262 | zenon_intro zenon_H261 ].
% 119.85/120.11 apply zenon_H262. zenon_intro zenon_H263.
% 119.85/120.11 apply zenon_H260. apply sym_equal. exact zenon_H263.
% 119.85/120.11 apply zenon_H261. zenon_intro zenon_H175.
% 119.85/120.11 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.11 generalize (zenon_H171 (succ (loopcounter))). zenon_intro zenon_H264.
% 119.85/120.11 generalize (zenon_H264 (n3)). zenon_intro zenon_H265.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H265); [ zenon_intro zenon_H16c | zenon_intro zenon_H266 ].
% 119.85/120.11 exact (zenon_H16c zenon_H175).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H266); [ zenon_intro zenon_H21a | zenon_intro zenon_H267 ].
% 119.85/120.11 exact (zenon_H21a zenon_H211).
% 119.85/120.11 exact (zenon_H25b zenon_H267).
% 119.85/120.11 apply zenon_H201. apply refl_equal.
% 119.85/120.11 apply (zenon_L79_); trivial.
% 119.85/120.11 cut ((gt (n3) (n2)) = (gt (succ (tptp_minus_1)) (n2))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1df.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact gt_3_2.
% 119.85/120.11 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.11 cut (((n3) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H268].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H25a); [ zenon_intro zenon_H26a | zenon_intro zenon_H269 ].
% 119.85/120.11 apply zenon_H26a. zenon_intro zenon_H26b.
% 119.85/120.11 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n3) = (succ (tptp_minus_1)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H268.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H16a.
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H25c].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H25c zenon_H26b).
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 apply zenon_H269. zenon_intro zenon_H267.
% 119.85/120.11 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.11 generalize (zenon_H171 (n3)). zenon_intro zenon_H26c.
% 119.85/120.11 generalize (zenon_H26c (n2)). zenon_intro zenon_H26d.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H26d); [ zenon_intro zenon_H25b | zenon_intro zenon_H26e ].
% 119.85/120.11 exact (zenon_H25b zenon_H267).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H26e); [ zenon_intro zenon_H22f | zenon_intro zenon_H1de ].
% 119.85/120.11 exact (zenon_H22f gt_3_2).
% 119.85/120.11 exact (zenon_H1df zenon_H1de).
% 119.85/120.11 apply zenon_H63. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L110_ *)
% 119.85/120.11 assert (zenon_L111_ : (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> (~(gt (n0) (n3))) -> (~(gt (n0) (n2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H140 zenon_H155 zenon_H7d zenon_H67 zenon_H255 zenon_H254 zenon_H1ab zenon_H66.
% 119.85/120.11 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.85/120.11 elim (classic (gt (succ (tptp_minus_1)) (n2))); [ zenon_intro zenon_H1de | zenon_intro zenon_H1df ].
% 119.85/120.11 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1da ].
% 119.85/120.11 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H233 | zenon_intro zenon_H21b ].
% 119.85/120.11 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.11 generalize (zenon_H171 (succ (succ (n0)))). zenon_intro zenon_H26f.
% 119.85/120.11 generalize (zenon_H26f (succ (succ (succ (n0))))). zenon_intro zenon_H270.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H270); [ zenon_intro zenon_H1da | zenon_intro zenon_H271 ].
% 119.85/120.11 exact (zenon_H1da zenon_H1dd).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H271); [ zenon_intro zenon_H21b | zenon_intro zenon_H258 ].
% 119.85/120.11 exact (zenon_H21b zenon_H233).
% 119.85/120.11 exact (zenon_H255 zenon_H258).
% 119.85/120.11 apply (zenon_L91_); trivial.
% 119.85/120.11 cut ((gt (succ (tptp_minus_1)) (n2)) = (gt (succ (tptp_minus_1)) (succ (succ (n0))))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1da.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H1de.
% 119.85/120.11 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 exact (zenon_H102 zenon_H1b9).
% 119.85/120.11 apply (zenon_L110_); trivial.
% 119.85/120.11 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.85/120.11 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H102.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H103.
% 119.85/120.11 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.11 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H105 successor_2).
% 119.85/120.11 apply zenon_H104. apply refl_equal.
% 119.85/120.11 apply zenon_H104. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L111_ *)
% 119.85/120.11 assert (zenon_L112_ : (~(gt (n0) (n3))) -> (~(gt (n0) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H254 zenon_H1ab zenon_H155 zenon_H140 zenon_H7d zenon_H67 zenon_H272 zenon_H66.
% 119.85/120.11 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.85/120.11 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H258 | zenon_intro zenon_H255 ].
% 119.85/120.11 elim (classic (gt (n0) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H273 | zenon_intro zenon_H274 ].
% 119.85/120.11 cut ((gt (n0) (succ (succ (succ (n0))))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H272.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H273.
% 119.85/120.11 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.11 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H159.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H21e. apply refl_equal.
% 119.85/120.11 cut ((gt (succ (tptp_minus_1)) (succ (succ (succ (n0))))) = (gt (n0) (succ (succ (succ (n0)))))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H274.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H258.
% 119.85/120.11 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H16b.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H167 zenon_H180).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H21e. apply refl_equal.
% 119.85/120.11 apply (zenon_L111_); trivial.
% 119.85/120.11 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H167.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H16a.
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.11 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 apply zenon_H169. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L112_ *)
% 119.85/120.11 assert (zenon_L113_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n3))) -> (~(gt (n0) (n3))) -> (~(gt (n0) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H275 zenon_H254 zenon_H1ab zenon_H140 zenon_H7d zenon_H67 zenon_H155.
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H276 | zenon_intro zenon_H272 ].
% 119.85/120.11 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0))))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n3))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H275.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H276.
% 119.85/120.11 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 exact (zenon_H21f successor_3).
% 119.85/120.11 apply (zenon_L112_); trivial.
% 119.85/120.11 (* end of lemma zenon_L113_ *)
% 119.85/120.11 assert (zenon_L114_ : (~(gt (n0) (n3))) -> (~(gt (n0) (n2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H254 zenon_H1ab zenon_H66 zenon_H1c8 zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.11 elim (classic ((~((sum (n0) (tptp_minus_1) zenon_E) = (n3)))/\(~(gt (sum (n0) (tptp_minus_1) zenon_E) (n3))))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H277). zenon_intro zenon_H279. zenon_intro zenon_H275.
% 119.85/120.11 apply (zenon_L113_); trivial.
% 119.85/120.11 cut ((gt (n3) (n2)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n2))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1c8.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact gt_3_2.
% 119.85/120.11 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.11 cut (((n3) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H27a].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H278); [ zenon_intro zenon_H27c | zenon_intro zenon_H27b ].
% 119.85/120.11 apply zenon_H27c. zenon_intro zenon_H27d.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n3) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H27a.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H279].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H279 zenon_H27d).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H27b. zenon_intro zenon_H27e.
% 119.85/120.11 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.11 generalize (zenon_H1bb (n3)). zenon_intro zenon_H27f.
% 119.85/120.11 generalize (zenon_H27f (n2)). zenon_intro zenon_H280.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H280); [ zenon_intro zenon_H275 | zenon_intro zenon_H281 ].
% 119.85/120.11 exact (zenon_H275 zenon_H27e).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H281); [ zenon_intro zenon_H22f | zenon_intro zenon_H1cb ].
% 119.85/120.11 exact (zenon_H22f gt_3_2).
% 119.85/120.11 exact (zenon_H1c8 zenon_H1cb).
% 119.85/120.11 apply zenon_H63. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L114_ *)
% 119.85/120.11 assert (zenon_L115_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (n0) (n2))) -> (~(gt (n0) (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H67 zenon_H7d zenon_H140 zenon_H1ab zenon_H254 zenon_H66 zenon_H155.
% 119.85/120.11 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.11 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.11 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n2))); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1c8 ].
% 119.85/120.11 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.11 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.85/120.11 generalize (zenon_H160 (n2)). zenon_intro zenon_H282.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H282); [ zenon_intro zenon_H157 | zenon_intro zenon_H283 ].
% 119.85/120.11 exact (zenon_H157 zenon_H156).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H283); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H1b3 ].
% 119.85/120.11 exact (zenon_H1c8 zenon_H1cb).
% 119.85/120.11 exact (zenon_H1ab zenon_H1b3).
% 119.85/120.11 apply (zenon_L114_); trivial.
% 119.85/120.11 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H157.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H141.
% 119.85/120.11 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 exact (zenon_H159 zenon_H15c).
% 119.85/120.11 apply (zenon_L106_); trivial.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H159.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L115_ *)
% 119.85/120.11 assert (zenon_L116_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n2))) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H1ab zenon_H140 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.11 elim (classic ((~((n0) = (n3)))/\(~(gt (n0) (n3))))); [ zenon_intro zenon_H284 | zenon_intro zenon_H285 ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H284). zenon_intro zenon_H286. zenon_intro zenon_H254.
% 119.85/120.11 apply (zenon_L115_); trivial.
% 119.85/120.11 cut ((gt (n3) (n2)) = (gt (n0) (n2))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1ab.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact gt_3_2.
% 119.85/120.11 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.11 cut (((n3) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H287].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H285); [ zenon_intro zenon_H289 | zenon_intro zenon_H288 ].
% 119.85/120.11 apply zenon_H289. zenon_intro zenon_H28a.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((n3) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H287.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H286].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H286 zenon_H28a).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H288. zenon_intro zenon_H28b.
% 119.85/120.11 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.11 generalize (zenon_H142 (n3)). zenon_intro zenon_H28c.
% 119.85/120.11 generalize (zenon_H28c (n2)). zenon_intro zenon_H28d.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H28d); [ zenon_intro zenon_H254 | zenon_intro zenon_H28e ].
% 119.85/120.11 exact (zenon_H254 zenon_H28b).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H22f | zenon_intro zenon_H1b3 ].
% 119.85/120.11 exact (zenon_H22f gt_3_2).
% 119.85/120.11 exact (zenon_H1ab zenon_H1b3).
% 119.85/120.11 apply zenon_H63. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L116_ *)
% 119.85/120.11 assert (zenon_L117_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H67 zenon_H7d zenon_H140 zenon_H155 zenon_H254 zenon_H66 zenon_H12f.
% 119.85/120.11 elim (classic ((~((n0) = (n2)))/\(~(gt (n0) (n2))))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H1ad ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_H1ae. zenon_intro zenon_H1ab.
% 119.85/120.11 apply (zenon_L106_); trivial.
% 119.85/120.11 cut ((gt (n2) (n0)) = (gt (n0) (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H12f.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact gt_2_0.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n2) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H1af].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H1ad); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ].
% 119.85/120.11 apply zenon_H1b1. zenon_intro zenon_H1b2.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((n2) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1af.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ae].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H1ae zenon_H1b2).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H1b0. zenon_intro zenon_H1b3.
% 119.85/120.11 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.11 generalize (zenon_H142 (n2)). zenon_intro zenon_H1b4.
% 119.85/120.11 generalize (zenon_H1b4 (n0)). zenon_intro zenon_H1b5.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H1b5); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1b6 ].
% 119.85/120.11 exact (zenon_H1ab zenon_H1b3).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H1b6); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H141 ].
% 119.85/120.11 exact (zenon_H1b7 gt_2_0).
% 119.85/120.11 exact (zenon_H12f zenon_H141).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L117_ *)
% 119.85/120.11 assert (zenon_L118_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H155 zenon_H140 zenon_H7d zenon_H67 zenon_H66 zenon_H12f.
% 119.85/120.11 elim (classic ((~((n0) = (n3)))/\(~(gt (n0) (n3))))); [ zenon_intro zenon_H284 | zenon_intro zenon_H285 ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H284). zenon_intro zenon_H286. zenon_intro zenon_H254.
% 119.85/120.11 apply (zenon_L117_); trivial.
% 119.85/120.11 cut ((gt (n3) (n0)) = (gt (n0) (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H12f.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact gt_3_0.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n3) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H287].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H285); [ zenon_intro zenon_H289 | zenon_intro zenon_H288 ].
% 119.85/120.11 apply zenon_H289. zenon_intro zenon_H28a.
% 119.85/120.11 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.11 cut (((n0) = (n0)) = ((n3) = (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H287.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H136.
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 cut (((n0) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H286].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H286 zenon_H28a).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 apply zenon_H288. zenon_intro zenon_H28b.
% 119.85/120.11 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.11 generalize (zenon_H142 (n3)). zenon_intro zenon_H28c.
% 119.85/120.11 generalize (zenon_H28c (n0)). zenon_intro zenon_H28f.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H254 | zenon_intro zenon_H290 ].
% 119.85/120.11 exact (zenon_H254 zenon_H28b).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H290); [ zenon_intro zenon_H291 | zenon_intro zenon_H141 ].
% 119.85/120.11 exact (zenon_H291 gt_3_0).
% 119.85/120.11 exact (zenon_H12f zenon_H141).
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L118_ *)
% 119.85/120.11 assert (zenon_L119_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H154 zenon_H67 zenon_H7d zenon_H140 zenon_H155.
% 119.85/120.11 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.11 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H154.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H156.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.11 congruence.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H159.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.11 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.11 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H157.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H141.
% 119.85/120.11 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.11 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H65. apply refl_equal.
% 119.85/120.11 exact (zenon_H159 zenon_H15c).
% 119.85/120.11 apply (zenon_L118_); trivial.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H159.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L119_ *)
% 119.85/120.11 assert (zenon_L120_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H66 zenon_H1c8 zenon_H155 zenon_H140 zenon_H7d zenon_H67.
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H164 | zenon_intro zenon_H154 ].
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_H165 | zenon_intro zenon_H166 ].
% 119.85/120.11 elim (classic (gt (n0) (n2))); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1ab ].
% 119.85/120.11 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.11 generalize (zenon_H1bb (n0)). zenon_intro zenon_H1bc.
% 119.85/120.11 generalize (zenon_H1bc (n2)). zenon_intro zenon_H1c9.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H1c9); [ zenon_intro zenon_H166 | zenon_intro zenon_H1ca ].
% 119.85/120.11 exact (zenon_H166 zenon_H165).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1cb ].
% 119.85/120.11 exact (zenon_H1ab zenon_H1b3).
% 119.85/120.11 exact (zenon_H1c8 zenon_H1cb).
% 119.85/120.11 apply (zenon_L116_); trivial.
% 119.85/120.11 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H166.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H164.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 exact (zenon_H15b zenon_H155).
% 119.85/120.11 apply (zenon_L119_); trivial.
% 119.85/120.11 (* end of lemma zenon_L120_ *)
% 119.85/120.11 assert (zenon_L121_ : (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.11 do 0 intro. intros zenon_H16c zenon_H7d zenon_H67 zenon_H140 zenon_H155 zenon_H1c0 zenon_H66.
% 119.85/120.11 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1ba ].
% 119.85/120.11 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ].
% 119.85/120.11 elim (classic (gt (succ (n0)) (succ (succ (n0))))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1b8 ].
% 119.85/120.11 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.11 generalize (zenon_H1bb (succ (n0))). zenon_intro zenon_H1c4.
% 119.85/120.11 generalize (zenon_H1c4 (succ (succ (n0)))). zenon_intro zenon_H1c5.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H1c5); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H1c6 ].
% 119.85/120.11 exact (zenon_H1c2 zenon_H1c1).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H1c7 ].
% 119.85/120.11 exact (zenon_H1b8 zenon_H1c3).
% 119.85/120.11 exact (zenon_H1c0 zenon_H1c7).
% 119.85/120.11 apply (zenon_L97_); trivial.
% 119.85/120.11 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n1)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1c2.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H1bf.
% 119.85/120.11 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 congruence.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 exact (zenon_H88 zenon_Hd1).
% 119.85/120.11 elim (classic ((~((sum (n0) (tptp_minus_1) zenon_E) = (n2)))/\(~(gt (sum (n0) (tptp_minus_1) zenon_E) (n2))))); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1d1 ].
% 119.85/120.11 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_H1d2. zenon_intro zenon_H1c8.
% 119.85/120.11 apply (zenon_L120_); trivial.
% 119.85/120.11 cut ((gt (n2) (n1)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1ba.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact gt_2_1.
% 119.85/120.11 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.11 cut (((n2) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1d3].
% 119.85/120.11 congruence.
% 119.85/120.11 apply (zenon_notand_s _ _ zenon_H1d1); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1d4 ].
% 119.85/120.11 apply zenon_H1d5. zenon_intro zenon_H1d6.
% 119.85/120.11 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n2) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H1d3.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H15a.
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.11 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1d2].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H1d2 zenon_H1d6).
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H158. apply refl_equal.
% 119.85/120.11 apply zenon_H1d4. zenon_intro zenon_H1cb.
% 119.85/120.11 generalize (zenon_H66 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1bb.
% 119.85/120.11 generalize (zenon_H1bb (n2)). zenon_intro zenon_H1d7.
% 119.85/120.11 generalize (zenon_H1d7 (n1)). zenon_intro zenon_H1d8.
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H1d8); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H1d9 ].
% 119.85/120.11 exact (zenon_H1c8 zenon_H1cb).
% 119.85/120.11 apply (zenon_imply_s _ _ zenon_H1d9); [ zenon_intro zenon_Hba | zenon_intro zenon_H1bf ].
% 119.85/120.11 exact (zenon_Hba gt_2_1).
% 119.85/120.11 exact (zenon_H1ba zenon_H1bf).
% 119.85/120.11 apply zenon_H64. apply refl_equal.
% 119.85/120.11 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.85/120.11 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.85/120.11 intro zenon_D_pnotp.
% 119.85/120.11 apply zenon_H88.
% 119.85/120.11 rewrite <- zenon_D_pnotp.
% 119.85/120.11 exact zenon_H8b.
% 119.85/120.11 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.11 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.11 congruence.
% 119.85/120.11 exact (zenon_H87 successor_1).
% 119.85/120.11 apply zenon_H8c. apply refl_equal.
% 119.85/120.11 apply zenon_H8c. apply refl_equal.
% 119.85/120.11 (* end of lemma zenon_L121_ *)
% 119.85/120.11 assert (zenon_L122_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> (~(gt (n0) (succ (succ (n0))))) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H67 zenon_H7d zenon_H140 zenon_H1cc zenon_H16c zenon_H66 zenon_H155.
% 119.85/120.12 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.12 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.12 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.12 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0))))); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H1c0 ].
% 119.85/120.12 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.12 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.85/120.12 generalize (zenon_H160 (succ (succ (n0)))). zenon_intro zenon_H1cd.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H1cd); [ zenon_intro zenon_H157 | zenon_intro zenon_H1ce ].
% 119.85/120.12 exact (zenon_H157 zenon_H156).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H1ce); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H1cf ].
% 119.85/120.12 exact (zenon_H1c0 zenon_H1c7).
% 119.85/120.12 exact (zenon_H1cc zenon_H1cf).
% 119.85/120.12 apply (zenon_L121_); trivial.
% 119.85/120.12 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H157.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H141.
% 119.85/120.12 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 exact (zenon_H159 zenon_H15c).
% 119.85/120.12 apply (zenon_L118_); trivial.
% 119.85/120.12 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H159.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H15a.
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H15b zenon_H155).
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L122_ *)
% 119.85/120.12 assert (zenon_L123_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H168 zenon_H67 zenon_H7d zenon_H140 zenon_H155.
% 119.85/120.12 elim (classic (gt (n0) (succ (tptp_minus_1)))); [ zenon_intro zenon_H163 | zenon_intro zenon_H15d ].
% 119.85/120.12 cut ((gt (n0) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H168.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H163.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.12 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.12 congruence.
% 119.85/120.12 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H167.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H16a.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.12 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.12 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.12 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))); [ zenon_intro zenon_H15e | zenon_intro zenon_H15f ].
% 119.85/120.12 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.12 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.85/120.12 generalize (zenon_H160 (succ (tptp_minus_1))). zenon_intro zenon_H161.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H161); [ zenon_intro zenon_H157 | zenon_intro zenon_H162 ].
% 119.85/120.12 exact (zenon_H157 zenon_H156).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H162); [ zenon_intro zenon_H15f | zenon_intro zenon_H163 ].
% 119.85/120.12 exact (zenon_H15f zenon_H15e).
% 119.85/120.12 exact (zenon_H15d zenon_H163).
% 119.85/120.12 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H164 | zenon_intro zenon_H154 ].
% 119.85/120.12 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_H165 | zenon_intro zenon_H166 ].
% 119.85/120.12 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H15f.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H165.
% 119.85/120.12 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 apply zenon_H167. apply sym_equal. exact succ_tptp_minus_1.
% 119.85/120.12 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H166.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H164.
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 exact (zenon_H15b zenon_H155).
% 119.85/120.12 apply (zenon_L119_); trivial.
% 119.85/120.12 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H157.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H141.
% 119.85/120.12 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 exact (zenon_H159 zenon_H15c).
% 119.85/120.12 apply (zenon_L118_); trivial.
% 119.85/120.12 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H159.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H15a.
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H15b zenon_H155).
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L123_ *)
% 119.85/120.12 assert (zenon_L124_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (n0))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H16c zenon_H1da zenon_H155 zenon_H140 zenon_H7d zenon_H67.
% 119.85/120.12 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H176 | zenon_intro zenon_H168 ].
% 119.85/120.12 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_H177 | zenon_intro zenon_H178 ].
% 119.85/120.12 elim (classic (gt (n0) (succ (succ (n0))))); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1cc ].
% 119.85/120.12 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.12 generalize (zenon_H171 (n0)). zenon_intro zenon_H179.
% 119.85/120.12 generalize (zenon_H179 (succ (succ (n0)))). zenon_intro zenon_H1db.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H1db); [ zenon_intro zenon_H178 | zenon_intro zenon_H1dc ].
% 119.85/120.12 exact (zenon_H178 zenon_H177).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H1dc); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1dd ].
% 119.85/120.12 exact (zenon_H1cc zenon_H1cf).
% 119.85/120.12 exact (zenon_H1da zenon_H1dd).
% 119.85/120.12 apply (zenon_L122_); trivial.
% 119.85/120.12 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H178.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H176.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.12 apply (zenon_L123_); trivial.
% 119.85/120.12 (* end of lemma zenon_L124_ *)
% 119.85/120.12 assert (zenon_L125_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ (loopcounter)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H16c zenon_H67 zenon_H7d zenon_H155 zenon_H140.
% 119.85/120.12 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1da ].
% 119.85/120.12 elim (classic (gt (succ (tptp_minus_1)) (n2))); [ zenon_intro zenon_H1de | zenon_intro zenon_H1df ].
% 119.85/120.12 elim (classic (gt (n2) (succ (loopcounter)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H1fd ].
% 119.85/120.12 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.12 generalize (zenon_H171 (n2)). zenon_intro zenon_H1e0.
% 119.85/120.12 generalize (zenon_H1e0 (succ (loopcounter))). zenon_intro zenon_H292.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H292); [ zenon_intro zenon_H1df | zenon_intro zenon_H293 ].
% 119.85/120.12 exact (zenon_H1df zenon_H1de).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H293); [ zenon_intro zenon_H1fd | zenon_intro zenon_H175 ].
% 119.85/120.12 exact (zenon_H1fd zenon_H200).
% 119.85/120.12 exact (zenon_H16c zenon_H175).
% 119.85/120.12 apply (zenon_L84_); trivial.
% 119.85/120.12 cut ((gt (succ (tptp_minus_1)) (succ (succ (n0)))) = (gt (succ (tptp_minus_1)) (n2))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H1df.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H1dd.
% 119.85/120.12 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 exact (zenon_H105 successor_2).
% 119.85/120.12 apply (zenon_L124_); trivial.
% 119.85/120.12 (* end of lemma zenon_L125_ *)
% 119.85/120.12 assert (zenon_L126_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H67 zenon_H7d zenon_H140 zenon_H155 zenon_H17d zenon_H66.
% 119.85/120.12 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.85/120.12 elim (classic (gt (succ (tptp_minus_1)) (succ (loopcounter)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H16c ].
% 119.85/120.12 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.12 cut ((gt (n0) (succ (loopcounter))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (loopcounter)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H17d.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H146.
% 119.85/120.12 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.12 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.12 congruence.
% 119.85/120.12 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H159.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H15a.
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H15b zenon_H155).
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 apply zenon_H76. apply refl_equal.
% 119.85/120.12 cut ((gt (succ (tptp_minus_1)) (succ (loopcounter))) = (gt (n0) (succ (loopcounter)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H140.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H175.
% 119.85/120.12 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.12 congruence.
% 119.85/120.12 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.12 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H16b.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H136.
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H167 zenon_H180).
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 apply zenon_H76. apply refl_equal.
% 119.85/120.12 apply (zenon_L125_); trivial.
% 119.85/120.12 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H167.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H16a.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L126_ *)
% 119.85/120.12 assert (zenon_L127_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (n0) (succ (loopcounter)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H67 zenon_H7d zenon_H140 zenon_H66 zenon_H155.
% 119.85/120.12 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.85/120.12 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.85/120.12 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.85/120.12 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (loopcounter)))); [ zenon_intro zenon_H17c | zenon_intro zenon_H17d ].
% 119.85/120.12 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.12 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.85/120.12 generalize (zenon_H160 (succ (loopcounter))). zenon_intro zenon_H17e.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H17e); [ zenon_intro zenon_H157 | zenon_intro zenon_H17f ].
% 119.85/120.12 exact (zenon_H157 zenon_H156).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H17f); [ zenon_intro zenon_H17d | zenon_intro zenon_H146 ].
% 119.85/120.12 exact (zenon_H17d zenon_H17c).
% 119.85/120.12 exact (zenon_H140 zenon_H146).
% 119.85/120.12 apply (zenon_L126_); trivial.
% 119.85/120.12 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H157.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H141.
% 119.85/120.12 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 exact (zenon_H159 zenon_H15c).
% 119.85/120.12 apply (zenon_L118_); trivial.
% 119.85/120.12 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H159.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H15a.
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.85/120.12 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H15b zenon_H155).
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 apply zenon_H158. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L127_ *)
% 119.85/120.12 assert (zenon_L128_ : (~((n4) = (n4))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H294.
% 119.85/120.12 apply zenon_H294. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L128_ *)
% 119.85/120.12 assert (zenon_L129_ : (~(gt (n1) (succ (tptp_minus_1)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H295.
% 119.85/120.12 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.85/120.12 cut ((gt (n1) (n0)) = (gt (n1) (succ (tptp_minus_1)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H295.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact gt_1_0.
% 119.85/120.12 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.12 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H64. apply refl_equal.
% 119.85/120.12 exact (zenon_H167 zenon_H180).
% 119.85/120.12 apply zenon_H167. apply sym_equal. exact succ_tptp_minus_1.
% 119.85/120.12 (* end of lemma zenon_L129_ *)
% 119.85/120.12 assert (zenon_L130_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (succ (tptp_minus_1)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H296.
% 119.85/120.12 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H297 | zenon_intro zenon_H295 ].
% 119.85/120.12 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.85/120.12 generalize (zenon_H1a6 (n1)). zenon_intro zenon_H1a7.
% 119.85/120.12 generalize (zenon_H1a7 (succ (tptp_minus_1))). zenon_intro zenon_H298.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H298); [ zenon_intro zenon_Hba | zenon_intro zenon_H299 ].
% 119.85/120.12 exact (zenon_Hba gt_2_1).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H299); [ zenon_intro zenon_H295 | zenon_intro zenon_H29a ].
% 119.85/120.12 exact (zenon_H295 zenon_H297).
% 119.85/120.12 exact (zenon_H296 zenon_H29a).
% 119.85/120.12 apply (zenon_L129_); trivial.
% 119.85/120.12 (* end of lemma zenon_L130_ *)
% 119.85/120.12 assert (zenon_L131_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n3) (succ (tptp_minus_1)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H29b.
% 119.85/120.12 elim (classic (gt (n2) (succ (tptp_minus_1)))); [ zenon_intro zenon_H29a | zenon_intro zenon_H296 ].
% 119.85/120.12 generalize (zenon_H66 (n3)). zenon_intro zenon_H24f.
% 119.85/120.12 generalize (zenon_H24f (n2)). zenon_intro zenon_H250.
% 119.85/120.12 generalize (zenon_H250 (succ (tptp_minus_1))). zenon_intro zenon_H29c.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H29c); [ zenon_intro zenon_H22f | zenon_intro zenon_H29d ].
% 119.85/120.12 exact (zenon_H22f gt_3_2).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H29d); [ zenon_intro zenon_H296 | zenon_intro zenon_H29e ].
% 119.85/120.12 exact (zenon_H296 zenon_H29a).
% 119.85/120.12 exact (zenon_H29b zenon_H29e).
% 119.85/120.12 apply (zenon_L130_); trivial.
% 119.85/120.12 (* end of lemma zenon_L131_ *)
% 119.85/120.12 assert (zenon_L132_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n4) (succ (tptp_minus_1)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H29f.
% 119.85/120.12 elim (classic (gt (n3) (succ (tptp_minus_1)))); [ zenon_intro zenon_H29e | zenon_intro zenon_H29b ].
% 119.85/120.12 generalize (zenon_H66 (n4)). zenon_intro zenon_H2a0.
% 119.85/120.12 generalize (zenon_H2a0 (n3)). zenon_intro zenon_H2a1.
% 119.85/120.12 generalize (zenon_H2a1 (succ (tptp_minus_1))). zenon_intro zenon_H2a2.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2a2); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2a3 ].
% 119.85/120.12 exact (zenon_H2a4 gt_4_3).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2a3); [ zenon_intro zenon_H29b | zenon_intro zenon_H2a5 ].
% 119.85/120.12 exact (zenon_H29b zenon_H29e).
% 119.85/120.12 exact (zenon_H29f zenon_H2a5).
% 119.85/120.12 apply (zenon_L131_); trivial.
% 119.85/120.12 (* end of lemma zenon_L132_ *)
% 119.85/120.12 assert (zenon_L133_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n3)) (succ (tptp_minus_1)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H2a6.
% 119.85/120.12 elim (classic (gt (n4) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2a5 | zenon_intro zenon_H29f ].
% 119.85/120.12 elim (classic (gt (succ (succ (succ (succ (n0))))) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a8 ].
% 119.85/120.12 cut ((gt (succ (succ (succ (succ (n0))))) (succ (tptp_minus_1))) = (gt (succ (n3)) (succ (tptp_minus_1)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H2a6.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H2a7.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.12 cut (((succ (succ (succ (succ (n0))))) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9d].
% 119.85/120.12 congruence.
% 119.85/120.12 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ].
% 119.85/120.12 cut (((succ (n3)) = (succ (n3))) = ((succ (succ (succ (succ (n0))))) = (succ (n3)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H9d.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H9e.
% 119.85/120.12 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.85/120.12 cut (((succ (n3)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H98].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_L10_); trivial.
% 119.85/120.12 apply zenon_H9f. apply refl_equal.
% 119.85/120.12 apply zenon_H9f. apply refl_equal.
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 cut ((gt (n4) (succ (tptp_minus_1))) = (gt (succ (succ (succ (succ (n0))))) (succ (tptp_minus_1)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H2a8.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H2a5.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.12 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 119.85/120.12 congruence.
% 119.85/120.12 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ].
% 119.85/120.12 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_Ha0.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_Ha1.
% 119.85/120.12 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 119.85/120.12 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_Ha3 successor_4).
% 119.85/120.12 apply zenon_Ha2. apply refl_equal.
% 119.85/120.12 apply zenon_Ha2. apply refl_equal.
% 119.85/120.12 apply zenon_H169. apply refl_equal.
% 119.85/120.12 apply (zenon_L132_); trivial.
% 119.85/120.12 (* end of lemma zenon_L133_ *)
% 119.85/120.12 assert (zenon_L134_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (succ (n3)) (succ (loopcounter)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H2a9.
% 119.85/120.12 elim (classic (gt (succ (n3)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2aa | zenon_intro zenon_H2a6 ].
% 119.85/120.12 elim (classic (gt (succ (n3)) (n0))); [ zenon_intro zenon_H2ab | zenon_intro zenon_H2ac ].
% 119.85/120.12 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.12 generalize (zenon_H66 (succ (n3))). zenon_intro zenon_Hb5.
% 119.85/120.12 generalize (zenon_Hb5 (n0)). zenon_intro zenon_H2ad.
% 119.85/120.12 generalize (zenon_H2ad (succ (loopcounter))). zenon_intro zenon_H2ae.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2ae); [ zenon_intro zenon_H2ac | zenon_intro zenon_H2af ].
% 119.85/120.12 exact (zenon_H2ac zenon_H2ab).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2af); [ zenon_intro zenon_H140 | zenon_intro zenon_H2b0 ].
% 119.85/120.12 exact (zenon_H140 zenon_H146).
% 119.85/120.12 exact (zenon_H2a9 zenon_H2b0).
% 119.85/120.12 apply (zenon_L127_); trivial.
% 119.85/120.12 cut ((gt (succ (n3)) (succ (tptp_minus_1))) = (gt (succ (n3)) (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H2ac.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H2aa.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.12 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H9f. apply refl_equal.
% 119.85/120.12 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.12 apply (zenon_L133_); trivial.
% 119.85/120.12 (* end of lemma zenon_L134_ *)
% 119.85/120.12 assert (zenon_L135_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (succ (tptp_minus_1)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H2b1.
% 119.85/120.12 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_Hfd | zenon_intro zenon_Hfe ].
% 119.85/120.12 elim (classic (gt (succ (succ (n0))) (n1))); [ zenon_intro zenon_H204 | zenon_intro zenon_H205 ].
% 119.85/120.12 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H297 | zenon_intro zenon_H295 ].
% 119.85/120.12 generalize (zenon_H66 (succ (succ (n0)))). zenon_intro zenon_H206.
% 119.85/120.12 generalize (zenon_H206 (n1)). zenon_intro zenon_H207.
% 119.85/120.12 generalize (zenon_H207 (succ (tptp_minus_1))). zenon_intro zenon_H2b2.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2b2); [ zenon_intro zenon_H205 | zenon_intro zenon_H2b3 ].
% 119.85/120.12 exact (zenon_H205 zenon_H204).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2b3); [ zenon_intro zenon_H295 | zenon_intro zenon_H2b4 ].
% 119.85/120.12 exact (zenon_H295 zenon_H297).
% 119.85/120.12 exact (zenon_H2b1 zenon_H2b4).
% 119.85/120.12 apply (zenon_L129_); trivial.
% 119.85/120.12 cut ((gt (succ (succ (n0))) (succ (n0))) = (gt (succ (succ (n0))) (n1))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H205.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_Hfd.
% 119.85/120.12 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.12 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H104. apply refl_equal.
% 119.85/120.12 exact (zenon_H87 successor_1).
% 119.85/120.12 apply (zenon_L88_); trivial.
% 119.85/120.12 (* end of lemma zenon_L135_ *)
% 119.85/120.12 assert (zenon_L136_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (succ (succ (n0))) (succ (loopcounter)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H203.
% 119.85/120.12 elim (classic (gt (succ (succ (n0))) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2b4 | zenon_intro zenon_H2b1 ].
% 119.85/120.12 elim (classic (gt (succ (succ (n0))) (n0))); [ zenon_intro zenon_H2b5 | zenon_intro zenon_H2b6 ].
% 119.85/120.12 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.12 generalize (zenon_H66 (succ (succ (n0)))). zenon_intro zenon_H206.
% 119.85/120.12 generalize (zenon_H206 (n0)). zenon_intro zenon_H2b7.
% 119.85/120.12 generalize (zenon_H2b7 (succ (loopcounter))). zenon_intro zenon_H2b8.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2b8); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b9 ].
% 119.85/120.12 exact (zenon_H2b6 zenon_H2b5).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2b9); [ zenon_intro zenon_H140 | zenon_intro zenon_H20a ].
% 119.85/120.12 exact (zenon_H140 zenon_H146).
% 119.85/120.12 exact (zenon_H203 zenon_H20a).
% 119.85/120.12 apply (zenon_L89_); trivial.
% 119.85/120.12 cut ((gt (succ (succ (n0))) (succ (tptp_minus_1))) = (gt (succ (succ (n0))) (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H2b6.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H2b4.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.12 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H104. apply refl_equal.
% 119.85/120.12 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.12 apply (zenon_L135_); trivial.
% 119.85/120.12 (* end of lemma zenon_L136_ *)
% 119.85/120.12 assert (zenon_L137_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n1)) (succ (tptp_minus_1)))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H2ba.
% 119.85/120.12 elim (classic (gt (succ (n1)) (succ (n0)))); [ zenon_intro zenon_H118 | zenon_intro zenon_Hfb ].
% 119.85/120.12 elim (classic (gt (succ (n1)) (n1))); [ zenon_intro zenon_H119 | zenon_intro zenon_H112 ].
% 119.85/120.12 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H297 | zenon_intro zenon_H295 ].
% 119.85/120.12 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.85/120.12 generalize (zenon_H11a (n1)). zenon_intro zenon_H11b.
% 119.85/120.12 generalize (zenon_H11b (succ (tptp_minus_1))). zenon_intro zenon_H2bb.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2bb); [ zenon_intro zenon_H112 | zenon_intro zenon_H2bc ].
% 119.85/120.12 exact (zenon_H112 zenon_H119).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2bc); [ zenon_intro zenon_H295 | zenon_intro zenon_H2bd ].
% 119.85/120.12 exact (zenon_H295 zenon_H297).
% 119.85/120.12 exact (zenon_H2ba zenon_H2bd).
% 119.85/120.12 apply (zenon_L129_); trivial.
% 119.85/120.12 cut ((gt (succ (n1)) (succ (n0))) = (gt (succ (n1)) (n1))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H112.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H118.
% 119.85/120.12 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.12 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H101. apply refl_equal.
% 119.85/120.12 exact (zenon_H87 successor_1).
% 119.85/120.12 apply (zenon_L27_); trivial.
% 119.85/120.12 (* end of lemma zenon_L137_ *)
% 119.85/120.12 assert (zenon_L138_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n1)) (succ (loopcounter)))) -> ((loopcounter) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H116 zenon_H95 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.12 elim (classic (gt (succ (n1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2bd | zenon_intro zenon_H2ba ].
% 119.85/120.12 elim (classic (gt (succ (n1)) (n0))); [ zenon_intro zenon_H10d | zenon_intro zenon_H10f ].
% 119.85/120.12 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.12 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.85/120.12 generalize (zenon_H11a (n0)). zenon_intro zenon_H2be.
% 119.85/120.12 generalize (zenon_H2be (succ (loopcounter))). zenon_intro zenon_H2bf.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2bf); [ zenon_intro zenon_H10f | zenon_intro zenon_H2c0 ].
% 119.85/120.12 exact (zenon_H10f zenon_H10d).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2c0); [ zenon_intro zenon_H140 | zenon_intro zenon_H11e ].
% 119.85/120.12 exact (zenon_H140 zenon_H146).
% 119.85/120.12 exact (zenon_H116 zenon_H11e).
% 119.85/120.12 apply (zenon_L100_); trivial.
% 119.85/120.12 cut ((gt (succ (n1)) (succ (tptp_minus_1))) = (gt (succ (n1)) (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H10f.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H2bd.
% 119.85/120.12 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.12 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H101. apply refl_equal.
% 119.85/120.12 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.12 apply (zenon_L137_); trivial.
% 119.85/120.12 (* end of lemma zenon_L138_ *)
% 119.85/120.12 assert (zenon_L139_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n0)) -> (~(gt (loopcounter) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H95 zenon_Hf0 zenon_H67 zenon_H7d zenon_H155.
% 119.85/120.12 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.12 cut ((gt (n0) (succ (loopcounter))) = (gt (loopcounter) (succ (loopcounter)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_Hf0.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H146.
% 119.85/120.12 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.12 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.85/120.12 congruence.
% 119.85/120.12 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.12 cut (((loopcounter) = (loopcounter)) = ((n0) = (loopcounter))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H93.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_Hed.
% 119.85/120.12 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.12 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H132 zenon_H95).
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply zenon_H76. apply refl_equal.
% 119.85/120.12 apply (zenon_L82_); trivial.
% 119.85/120.12 (* end of lemma zenon_L139_ *)
% 119.85/120.12 assert (zenon_L140_ : ((loopcounter) = (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (loopcounter))) -> (gt (n1) (loopcounter)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_Hca zenon_H66 zenon_H135 zenon_H7d.
% 119.85/120.12 elim (classic ((~((loopcounter) = (n1)))/\(~(gt (loopcounter) (n1))))); [ zenon_intro zenon_H137 | zenon_intro zenon_H138 ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H137). zenon_intro zenon_Hc4. zenon_intro zenon_Hee.
% 119.85/120.12 exact (zenon_Hc4 zenon_Hca).
% 119.85/120.12 cut ((gt (n1) (loopcounter)) = (gt (loopcounter) (loopcounter))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H135.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H7d.
% 119.85/120.12 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.12 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 119.85/120.12 apply zenon_H13a. zenon_intro zenon_Hca.
% 119.85/120.12 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.12 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_Hec.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_Hed.
% 119.85/120.12 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.12 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_Hc4 zenon_Hca).
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply zenon_H139. zenon_intro zenon_Hf1.
% 119.85/120.12 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.12 generalize (zenon_H13b (n1)). zenon_intro zenon_H13c.
% 119.85/120.12 generalize (zenon_H13c (loopcounter)). zenon_intro zenon_H13d.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H13d); [ zenon_intro zenon_Hee | zenon_intro zenon_H13e ].
% 119.85/120.12 exact (zenon_Hee zenon_Hf1).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H92 | zenon_intro zenon_H134 ].
% 119.85/120.12 exact (zenon_H92 zenon_H7d).
% 119.85/120.12 exact (zenon_H135 zenon_H134).
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L140_ *)
% 119.85/120.12 assert (zenon_L141_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n1)) -> (gt (n1) (loopcounter)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_Hca zenon_H7d.
% 119.85/120.12 generalize (irreflexivity_gt (loopcounter)). zenon_intro zenon_H135.
% 119.85/120.12 apply (zenon_L140_); trivial.
% 119.85/120.12 (* end of lemma zenon_L141_ *)
% 119.85/120.12 assert (zenon_L142_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n2))) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_Hc3 zenon_Hc2 zenon_H155.
% 119.85/120.12 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.85/120.12 apply (zenon_L5_); trivial.
% 119.85/120.12 apply (zenon_L12_); trivial.
% 119.85/120.12 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.85/120.12 generalize (irreflexivity_gt (loopcounter)). zenon_intro zenon_H135.
% 119.85/120.12 elim (classic ((~((loopcounter) = (n1)))/\(~(gt (loopcounter) (n1))))); [ zenon_intro zenon_H137 | zenon_intro zenon_H138 ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H137). zenon_intro zenon_Hc4. zenon_intro zenon_Hee.
% 119.85/120.12 elim (classic ((~((loopcounter) = (succ (loopcounter))))/\(~(gt (loopcounter) (succ (loopcounter)))))); [ zenon_intro zenon_H2c1 | zenon_intro zenon_H2c2 ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H2c1). zenon_intro zenon_H2c3. zenon_intro zenon_Hf0.
% 119.85/120.12 apply (zenon_L139_); trivial.
% 119.85/120.12 cut ((gt (succ (loopcounter)) (n1)) = (gt (loopcounter) (n1))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_Hee.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H67.
% 119.85/120.12 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.12 cut (((succ (loopcounter)) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H2c4].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H2c2); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2c5 ].
% 119.85/120.12 apply zenon_H2c6. zenon_intro zenon_H2c7.
% 119.85/120.12 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.12 cut (((loopcounter) = (loopcounter)) = ((succ (loopcounter)) = (loopcounter))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H2c4.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_Hed.
% 119.85/120.12 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.12 cut (((loopcounter) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H2c3].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H2c3 zenon_H2c7).
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply zenon_H2c5. zenon_intro zenon_Hf2.
% 119.85/120.12 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.12 generalize (zenon_H13b (succ (loopcounter))). zenon_intro zenon_H2c8.
% 119.85/120.12 generalize (zenon_H2c8 (n1)). zenon_intro zenon_H2c9.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2c9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H2ca ].
% 119.85/120.12 exact (zenon_Hf0 zenon_Hf2).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2ca); [ zenon_intro zenon_H6f | zenon_intro zenon_Hf1 ].
% 119.85/120.12 exact (zenon_H6f zenon_H67).
% 119.85/120.12 exact (zenon_Hee zenon_Hf1).
% 119.85/120.12 apply zenon_H64. apply refl_equal.
% 119.85/120.12 cut ((gt (n1) (loopcounter)) = (gt (loopcounter) (loopcounter))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H135.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H7d.
% 119.85/120.12 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.12 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 119.85/120.12 apply zenon_H13a. zenon_intro zenon_Hca.
% 119.85/120.12 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.12 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_Hec.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_Hed.
% 119.85/120.12 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.12 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_Hc4 zenon_Hca).
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply zenon_H139. zenon_intro zenon_Hf1.
% 119.85/120.12 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.12 generalize (zenon_H13b (n1)). zenon_intro zenon_H13c.
% 119.85/120.12 generalize (zenon_H13c (loopcounter)). zenon_intro zenon_H13d.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H13d); [ zenon_intro zenon_Hee | zenon_intro zenon_H13e ].
% 119.85/120.12 exact (zenon_Hee zenon_Hf1).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H92 | zenon_intro zenon_H134 ].
% 119.85/120.12 exact (zenon_H92 zenon_H7d).
% 119.85/120.12 exact (zenon_H135 zenon_H134).
% 119.85/120.12 apply zenon_H7c. apply refl_equal.
% 119.85/120.12 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.85/120.12 apply (zenon_L141_); trivial.
% 119.85/120.12 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.85/120.12 exact (zenon_Hc3 zenon_Hcc).
% 119.85/120.12 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.12 (* end of lemma zenon_L142_ *)
% 119.85/120.12 assert (zenon_L143_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n2))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H181 zenon_H67 zenon_H7d zenon_Hc2 zenon_H155.
% 119.85/120.12 elim (classic ((loopcounter) = (n2))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc3 ].
% 119.85/120.12 cut ((gt (n1) (loopcounter)) = (gt (n1) (n2))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H181.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H7d.
% 119.85/120.12 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.85/120.12 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H64. apply refl_equal.
% 119.85/120.12 exact (zenon_Hc3 zenon_Hcc).
% 119.85/120.12 apply (zenon_L142_); trivial.
% 119.85/120.12 (* end of lemma zenon_L143_ *)
% 119.85/120.12 assert (zenon_L144_ : (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (n2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n1))) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H7d zenon_H155 zenon_H1ab zenon_H66 zenon_H13f zenon_H67.
% 119.85/120.12 elim (classic ((~((n0) = (succ (loopcounter))))/\(~(gt (n0) (succ (loopcounter)))))); [ zenon_intro zenon_H2cb | zenon_intro zenon_H2cc ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H2cb). zenon_intro zenon_H2cd. zenon_intro zenon_H140.
% 119.85/120.12 apply (zenon_L116_); trivial.
% 119.85/120.12 cut ((gt (succ (loopcounter)) (n1)) = (gt (n0) (n1))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H13f.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H67.
% 119.85/120.12 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.12 cut (((succ (loopcounter)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H2ce].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H2cc); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2cf ].
% 119.85/120.12 apply zenon_H2d0. zenon_intro zenon_H2d1.
% 119.85/120.12 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.12 cut (((n0) = (n0)) = ((succ (loopcounter)) = (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H2ce.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H136.
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 cut (((n0) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H2cd].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H2cd zenon_H2d1).
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 apply zenon_H2cf. zenon_intro zenon_H146.
% 119.85/120.12 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.12 generalize (zenon_H142 (succ (loopcounter))). zenon_intro zenon_H2d2.
% 119.85/120.12 generalize (zenon_H2d2 (n1)). zenon_intro zenon_H2d3.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2d3); [ zenon_intro zenon_H140 | zenon_intro zenon_H2d4 ].
% 119.85/120.12 exact (zenon_H140 zenon_H146).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2d4); [ zenon_intro zenon_H6f | zenon_intro zenon_H150 ].
% 119.85/120.12 exact (zenon_H6f zenon_H67).
% 119.85/120.12 exact (zenon_H13f zenon_H150).
% 119.85/120.12 apply zenon_H64. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L144_ *)
% 119.85/120.12 assert (zenon_L145_ : (~(gt (n0) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H1ab zenon_H155 zenon_H7d zenon_H67 zenon_H66 zenon_H12f.
% 119.85/120.12 elim (classic ((~((n0) = (n1)))/\(~(gt (n0) (n1))))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H14a). zenon_intro zenon_H106. zenon_intro zenon_H13f.
% 119.85/120.12 apply (zenon_L144_); trivial.
% 119.85/120.12 cut ((gt (n1) (n0)) = (gt (n0) (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H12f.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact gt_1_0.
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 cut (((n1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H14e | zenon_intro zenon_H14d ].
% 119.85/120.12 apply zenon_H14e. zenon_intro zenon_H14f.
% 119.85/120.12 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.12 cut (((n0) = (n0)) = ((n1) = (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H14c.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H136.
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H106 zenon_H14f).
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 apply zenon_H14d. zenon_intro zenon_H150.
% 119.85/120.12 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.12 generalize (zenon_H142 (n1)). zenon_intro zenon_H151.
% 119.85/120.12 generalize (zenon_H151 (n0)). zenon_intro zenon_H152.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H13f | zenon_intro zenon_H153 ].
% 119.85/120.12 exact (zenon_H13f zenon_H150).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H153); [ zenon_intro zenon_H7b | zenon_intro zenon_H141 ].
% 119.85/120.12 exact (zenon_H7b gt_1_0).
% 119.85/120.12 exact (zenon_H12f zenon_H141).
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L145_ *)
% 119.85/120.12 assert (zenon_L146_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H67 zenon_H7d zenon_H155 zenon_H66 zenon_H12f.
% 119.85/120.12 elim (classic ((~((n0) = (n2)))/\(~(gt (n0) (n2))))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H1ad ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_H1ae. zenon_intro zenon_H1ab.
% 119.85/120.12 apply (zenon_L145_); trivial.
% 119.85/120.12 cut ((gt (n2) (n0)) = (gt (n0) (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H12f.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact gt_2_0.
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 cut (((n2) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H1af].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H1ad); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ].
% 119.85/120.12 apply zenon_H1b1. zenon_intro zenon_H1b2.
% 119.85/120.12 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.85/120.12 cut (((n0) = (n0)) = ((n2) = (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H1af.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H136.
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 cut (((n0) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ae].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H1ae zenon_H1b2).
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 apply zenon_H1b0. zenon_intro zenon_H1b3.
% 119.85/120.12 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.85/120.12 generalize (zenon_H142 (n2)). zenon_intro zenon_H1b4.
% 119.85/120.12 generalize (zenon_H1b4 (n0)). zenon_intro zenon_H1b5.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H1b5); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1b6 ].
% 119.85/120.12 exact (zenon_H1ab zenon_H1b3).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H1b6); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H141 ].
% 119.85/120.12 exact (zenon_H1b7 gt_2_0).
% 119.85/120.12 exact (zenon_H12f zenon_H141).
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L146_ *)
% 119.85/120.12 assert (zenon_L147_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((loopcounter) = (n3))) -> ((loopcounter) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(leq (n0) (n1))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_Hc2 zenon_H95 zenon_H155 zenon_H7d zenon_H67 zenon_H10b.
% 119.85/120.12 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 119.85/120.12 generalize (zenon_H5f (n1)). zenon_intro zenon_H10c.
% 119.85/120.12 apply (zenon_equiv_s _ _ zenon_H10c); [ zenon_intro zenon_H10b; zenon_intro zenon_H10f | zenon_intro zenon_H10e; zenon_intro zenon_H10d ].
% 119.85/120.12 elim (classic ((~((succ (n1)) = (n2)))/\(~(gt (succ (n1)) (n2))))); [ zenon_intro zenon_H2d5 | zenon_intro zenon_H2d6 ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H2d5). zenon_intro zenon_H2d8. zenon_intro zenon_H2d7.
% 119.85/120.12 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.85/120.12 apply (zenon_L138_); trivial.
% 119.85/120.12 elim (classic (gt (n1) (n2))); [ zenon_intro zenon_H183 | zenon_intro zenon_H181 ].
% 119.85/120.12 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.12 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.12 generalize (zenon_H78 (n2)). zenon_intro zenon_H2d9.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2d9); [ zenon_intro zenon_H6f | zenon_intro zenon_H2da ].
% 119.85/120.12 exact (zenon_H6f zenon_H67).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2da); [ zenon_intro zenon_H181 | zenon_intro zenon_H2db ].
% 119.85/120.12 exact (zenon_H181 zenon_H183).
% 119.85/120.12 cut ((gt (succ (loopcounter)) (n2)) = (gt (succ (n1)) (n2))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H2d7.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H2db.
% 119.85/120.12 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.12 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.85/120.12 apply zenon_H121. zenon_intro zenon_H122.
% 119.85/120.12 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.85/120.12 apply zenon_H120. zenon_intro zenon_H11e.
% 119.85/120.12 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.85/120.12 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.85/120.12 generalize (zenon_H123 (n2)). zenon_intro zenon_H2dc.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2dc); [ zenon_intro zenon_H116 | zenon_intro zenon_H2dd ].
% 119.85/120.12 exact (zenon_H116 zenon_H11e).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2dd); [ zenon_intro zenon_H2df | zenon_intro zenon_H2de ].
% 119.85/120.12 exact (zenon_H2df zenon_H2db).
% 119.85/120.12 exact (zenon_H2d7 zenon_H2de).
% 119.85/120.12 apply zenon_H63. apply refl_equal.
% 119.85/120.12 apply (zenon_L143_); trivial.
% 119.85/120.12 cut ((gt (n2) (n0)) = (gt (succ (n1)) (n0))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H10f.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact gt_2_0.
% 119.85/120.12 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.12 cut (((n2) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H2e0].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H2d6); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H2e1 ].
% 119.85/120.12 apply zenon_H2e2. zenon_intro zenon_H2e3.
% 119.85/120.12 elim (classic ((succ (n1)) = (succ (n1)))); [ zenon_intro zenon_H100 | zenon_intro zenon_H101 ].
% 119.85/120.12 cut (((succ (n1)) = (succ (n1))) = ((n2) = (succ (n1)))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H2e0.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H100.
% 119.85/120.12 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.85/120.12 cut (((succ (n1)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H2d8].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H2d8 zenon_H2e3).
% 119.85/120.12 apply zenon_H101. apply refl_equal.
% 119.85/120.12 apply zenon_H101. apply refl_equal.
% 119.85/120.12 apply zenon_H2e1. zenon_intro zenon_H2de.
% 119.85/120.12 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.85/120.12 generalize (zenon_H11a (n2)). zenon_intro zenon_H2e4.
% 119.85/120.12 generalize (zenon_H2e4 (n0)). zenon_intro zenon_H2e5.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2e5); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2e6 ].
% 119.85/120.12 exact (zenon_H2d7 zenon_H2de).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2e6); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H10d ].
% 119.85/120.12 exact (zenon_H1b7 gt_2_0).
% 119.85/120.12 exact (zenon_H10f zenon_H10d).
% 119.85/120.12 apply zenon_H65. apply refl_equal.
% 119.85/120.12 exact (zenon_H10b zenon_H10e).
% 119.85/120.12 (* end of lemma zenon_L147_ *)
% 119.85/120.12 assert (zenon_L148_ : (~((succ (loopcounter)) = (succ (n0)))) -> ((loopcounter) = (n0)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_Hd2 zenon_H95.
% 119.85/120.12 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H132 zenon_H95).
% 119.85/120.12 (* end of lemma zenon_L148_ *)
% 119.85/120.12 assert (zenon_L149_ : ((loopcounter) = (n0)) -> (gt (succ (loopcounter)) (n1)) -> (~(leq (n1) (n0))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H95 zenon_H67 zenon_H10a.
% 119.85/120.12 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H12c.
% 119.85/120.12 generalize (zenon_H12c (n0)). zenon_intro zenon_H12d.
% 119.85/120.12 apply (zenon_equiv_s _ _ zenon_H12d); [ zenon_intro zenon_H10a; zenon_intro zenon_H86 | zenon_intro zenon_H12e; zenon_intro zenon_H8d ].
% 119.85/120.12 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (n0)) (n1))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H86.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H67.
% 119.85/120.12 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.12 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_L148_); trivial.
% 119.85/120.12 apply zenon_H64. apply refl_equal.
% 119.85/120.12 exact (zenon_H10a zenon_H12e).
% 119.85/120.12 (* end of lemma zenon_L149_ *)
% 119.85/120.12 assert (zenon_L150_ : (~((succ (succ (n1))) = (succ (succ (succ (n0)))))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H2e7.
% 119.85/120.12 cut (((succ (n1)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hfa].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_L26_); trivial.
% 119.85/120.12 (* end of lemma zenon_L150_ *)
% 119.85/120.12 assert (zenon_L151_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H66 zenon_Hdd.
% 119.85/120.12 elim (classic ((~((n1) = (n2)))/\(~(gt (n1) (n2))))); [ zenon_intro zenon_H187 | zenon_intro zenon_H188 ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H189. zenon_intro zenon_H181.
% 119.85/120.12 apply (zenon_L143_); trivial.
% 119.85/120.12 cut ((gt (n2) (n1)) = (gt (n1) (n1))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_Hdd.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact gt_2_1.
% 119.85/120.12 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.12 cut (((n2) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H18a].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_H188); [ zenon_intro zenon_H18c | zenon_intro zenon_H18b ].
% 119.85/120.12 apply zenon_H18c. zenon_intro zenon_H18d.
% 119.85/120.12 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.85/120.12 cut (((n1) = (n1)) = ((n2) = (n1))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H18a.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_Hdc.
% 119.85/120.12 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.12 cut (((n1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H189].
% 119.85/120.12 congruence.
% 119.85/120.12 exact (zenon_H189 zenon_H18d).
% 119.85/120.12 apply zenon_H64. apply refl_equal.
% 119.85/120.12 apply zenon_H64. apply refl_equal.
% 119.85/120.12 apply zenon_H18b. zenon_intro zenon_H183.
% 119.85/120.12 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.12 generalize (zenon_He4 (n2)). zenon_intro zenon_H18e.
% 119.85/120.12 generalize (zenon_H18e (n1)). zenon_intro zenon_H18f.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H18f); [ zenon_intro zenon_H181 | zenon_intro zenon_H190 ].
% 119.85/120.12 exact (zenon_H181 zenon_H183).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H190); [ zenon_intro zenon_Hba | zenon_intro zenon_He8 ].
% 119.85/120.12 exact (zenon_Hba gt_2_1).
% 119.85/120.12 exact (zenon_Hdd zenon_He8).
% 119.85/120.12 apply zenon_H64. apply refl_equal.
% 119.85/120.12 (* end of lemma zenon_L151_ *)
% 119.85/120.12 assert (zenon_L152_ : (~((plus (n2) (n0)) = (plus (n2) (n1)))) -> ((n1) = (n0)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H2e8 zenon_H108.
% 119.85/120.12 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.85/120.12 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.12 congruence.
% 119.85/120.12 apply zenon_H63. apply refl_equal.
% 119.85/120.12 apply zenon_H106. apply sym_equal. exact zenon_H108.
% 119.85/120.12 (* end of lemma zenon_L152_ *)
% 119.85/120.12 assert (zenon_L153_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.12 do 0 intro. intros zenon_H66 zenon_H182 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.12 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.85/120.12 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.85/120.12 apply (zenon_L9_); trivial.
% 119.85/120.12 elim (classic (gt (n1) (n2))); [ zenon_intro zenon_H183 | zenon_intro zenon_H181 ].
% 119.85/120.12 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.12 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.12 generalize (zenon_H78 (n2)). zenon_intro zenon_H2d9.
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2d9); [ zenon_intro zenon_H6f | zenon_intro zenon_H2da ].
% 119.85/120.12 exact (zenon_H6f zenon_H67).
% 119.85/120.12 apply (zenon_imply_s _ _ zenon_H2da); [ zenon_intro zenon_H181 | zenon_intro zenon_H2db ].
% 119.85/120.12 exact (zenon_H181 zenon_H183).
% 119.85/120.12 cut ((gt (succ (loopcounter)) (n2)) = (gt (succ (n0)) (n2))).
% 119.85/120.12 intro zenon_D_pnotp.
% 119.85/120.12 apply zenon_H182.
% 119.85/120.12 rewrite <- zenon_D_pnotp.
% 119.85/120.12 exact zenon_H2db.
% 119.85/120.12 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.12 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.85/120.12 congruence.
% 119.85/120.12 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.85/120.12 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.85/120.12 apply zenon_Hd2. apply sym_equal. exact zenon_Hd5.
% 119.85/120.12 apply zenon_Hd3. zenon_intro zenon_Hd6.
% 119.85/120.12 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.85/120.12 generalize (zenon_H8e (succ (loopcounter))). zenon_intro zenon_Hd7.
% 119.85/120.13 generalize (zenon_Hd7 (n2)). zenon_intro zenon_H2e9.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2e9); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H2ea ].
% 119.85/120.13 exact (zenon_Hd0 zenon_Hd6).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2ea); [ zenon_intro zenon_H2df | zenon_intro zenon_H186 ].
% 119.85/120.13 exact (zenon_H2df zenon_H2db).
% 119.85/120.13 exact (zenon_H182 zenon_H186).
% 119.85/120.13 apply zenon_H63. apply refl_equal.
% 119.85/120.13 apply (zenon_L143_); trivial.
% 119.85/120.13 (* end of lemma zenon_L153_ *)
% 119.85/120.13 assert (zenon_L154_ : (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (~(gt (succ (n0)) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H7d zenon_H67 zenon_H155 zenon_Hc2 zenon_H1b8 zenon_H66.
% 119.85/120.13 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.85/120.13 elim (classic (gt (succ (n0)) (n2))); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 119.85/120.13 cut ((gt (succ (n0)) (n2)) = (gt (succ (n0)) (succ (succ (n0))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H1b8.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H186.
% 119.85/120.13 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.13 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H8c. apply refl_equal.
% 119.85/120.13 exact (zenon_H102 zenon_H1b9).
% 119.85/120.13 apply (zenon_L153_); trivial.
% 119.85/120.13 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.85/120.13 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H102.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H103.
% 119.85/120.13 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.13 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H105 successor_2).
% 119.85/120.13 apply zenon_H104. apply refl_equal.
% 119.85/120.13 apply zenon_H104. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L154_ *)
% 119.85/120.13 assert (zenon_L155_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H16c zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.13 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H176 | zenon_intro zenon_H168 ].
% 119.85/120.13 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_H177 | zenon_intro zenon_H178 ].
% 119.85/120.13 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.13 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.13 generalize (zenon_H171 (n0)). zenon_intro zenon_H179.
% 119.85/120.13 generalize (zenon_H179 (succ (loopcounter))). zenon_intro zenon_H2eb.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2eb); [ zenon_intro zenon_H178 | zenon_intro zenon_H2ec ].
% 119.85/120.13 exact (zenon_H178 zenon_H177).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2ec); [ zenon_intro zenon_H140 | zenon_intro zenon_H175 ].
% 119.85/120.13 exact (zenon_H140 zenon_H146).
% 119.85/120.13 exact (zenon_H16c zenon_H175).
% 119.85/120.13 apply (zenon_L125_); trivial.
% 119.85/120.13 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H178.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H176.
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.13 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.13 cut ((gt (n0) (succ (loopcounter))) = (gt (succ (tptp_minus_1)) (succ (loopcounter)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H16c.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H146.
% 119.85/120.13 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.13 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.13 congruence.
% 119.85/120.13 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H167.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H16a.
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 apply zenon_H76. apply refl_equal.
% 119.85/120.13 apply (zenon_L66_); trivial.
% 119.85/120.13 (* end of lemma zenon_L155_ *)
% 119.85/120.13 assert (zenon_L156_ : (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (succ (tptp_minus_1)) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_Hc2 zenon_H155 zenon_H67 zenon_H7d zenon_H1da zenon_H66.
% 119.85/120.13 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.85/120.13 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16e ].
% 119.85/120.13 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H16f | zenon_intro zenon_H170 ].
% 119.85/120.13 elim (classic (gt (succ (n0)) (succ (succ (n0))))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1b8 ].
% 119.85/120.13 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.13 generalize (zenon_H171 (succ (n0))). zenon_intro zenon_H172.
% 119.85/120.13 generalize (zenon_H172 (succ (succ (n0)))). zenon_intro zenon_H2ed.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2ed); [ zenon_intro zenon_H170 | zenon_intro zenon_H2ee ].
% 119.85/120.13 exact (zenon_H170 zenon_H16f).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2ee); [ zenon_intro zenon_H1b8 | zenon_intro zenon_H1dd ].
% 119.85/120.13 exact (zenon_H1b8 zenon_H1c3).
% 119.85/120.13 exact (zenon_H1da zenon_H1dd).
% 119.85/120.13 apply (zenon_L154_); trivial.
% 119.85/120.13 cut ((gt (succ (tptp_minus_1)) (n1)) = (gt (succ (tptp_minus_1)) (succ (n0)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H170.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H16d.
% 119.85/120.13 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 exact (zenon_H88 zenon_Hd1).
% 119.85/120.13 elim (classic ((~((succ (tptp_minus_1)) = (n2)))/\(~(gt (succ (tptp_minus_1)) (n2))))); [ zenon_intro zenon_H2ef | zenon_intro zenon_H2f0 ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H2f1. zenon_intro zenon_H1df.
% 119.85/120.13 elim (classic ((~((succ (tptp_minus_1)) = (succ (loopcounter))))/\(~(gt (succ (tptp_minus_1)) (succ (loopcounter)))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H25f. zenon_intro zenon_H16c.
% 119.85/120.13 apply (zenon_L155_); trivial.
% 119.85/120.13 elim (classic (gt (n1) (n2))); [ zenon_intro zenon_H183 | zenon_intro zenon_H181 ].
% 119.85/120.13 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.13 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.13 generalize (zenon_H78 (n2)). zenon_intro zenon_H2d9.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2d9); [ zenon_intro zenon_H6f | zenon_intro zenon_H2da ].
% 119.85/120.13 exact (zenon_H6f zenon_H67).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2da); [ zenon_intro zenon_H181 | zenon_intro zenon_H2db ].
% 119.85/120.13 exact (zenon_H181 zenon_H183).
% 119.85/120.13 cut ((gt (succ (loopcounter)) (n2)) = (gt (succ (tptp_minus_1)) (n2))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H1df.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H2db.
% 119.85/120.13 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.13 cut (((succ (loopcounter)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H260].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H25e); [ zenon_intro zenon_H262 | zenon_intro zenon_H261 ].
% 119.85/120.13 apply zenon_H262. zenon_intro zenon_H263.
% 119.85/120.13 apply zenon_H260. apply sym_equal. exact zenon_H263.
% 119.85/120.13 apply zenon_H261. zenon_intro zenon_H175.
% 119.85/120.13 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.13 generalize (zenon_H171 (succ (loopcounter))). zenon_intro zenon_H264.
% 119.85/120.13 generalize (zenon_H264 (n2)). zenon_intro zenon_H2f2.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2f2); [ zenon_intro zenon_H16c | zenon_intro zenon_H2f3 ].
% 119.85/120.13 exact (zenon_H16c zenon_H175).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2f3); [ zenon_intro zenon_H2df | zenon_intro zenon_H1de ].
% 119.85/120.13 exact (zenon_H2df zenon_H2db).
% 119.85/120.13 exact (zenon_H1df zenon_H1de).
% 119.85/120.13 apply zenon_H63. apply refl_equal.
% 119.85/120.13 apply (zenon_L143_); trivial.
% 119.85/120.13 cut ((gt (n2) (n1)) = (gt (succ (tptp_minus_1)) (n1))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H16e.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact gt_2_1.
% 119.85/120.13 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.13 cut (((n2) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H2f4].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H2f0); [ zenon_intro zenon_H2f6 | zenon_intro zenon_H2f5 ].
% 119.85/120.13 apply zenon_H2f6. zenon_intro zenon_H2f7.
% 119.85/120.13 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n2) = (succ (tptp_minus_1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H2f4.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H16a.
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H2f1].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H2f1 zenon_H2f7).
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 apply zenon_H2f5. zenon_intro zenon_H1de.
% 119.85/120.13 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.13 generalize (zenon_H171 (n2)). zenon_intro zenon_H1e0.
% 119.85/120.13 generalize (zenon_H1e0 (n1)). zenon_intro zenon_H2f8.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2f8); [ zenon_intro zenon_H1df | zenon_intro zenon_H2f9 ].
% 119.85/120.13 exact (zenon_H1df zenon_H1de).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2f9); [ zenon_intro zenon_Hba | zenon_intro zenon_H16d ].
% 119.85/120.13 exact (zenon_Hba gt_2_1).
% 119.85/120.13 exact (zenon_H16e zenon_H16d).
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.85/120.13 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H88.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H8b.
% 119.85/120.13 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.13 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H87 successor_1).
% 119.85/120.13 apply zenon_H8c. apply refl_equal.
% 119.85/120.13 apply zenon_H8c. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L156_ *)
% 119.85/120.13 assert (zenon_L157_ : (~((loopcounter) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n0))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_Hc2 zenon_H66 zenon_H2fa zenon_H67 zenon_H7d zenon_H155.
% 119.85/120.13 elim (classic ((~((loopcounter) = (n2)))/\(~(gt (loopcounter) (n2))))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H19b). zenon_intro zenon_Hc3. zenon_intro zenon_H19d.
% 119.85/120.13 apply (zenon_L142_); trivial.
% 119.85/120.13 cut ((gt (n2) (n0)) = (gt (loopcounter) (n0))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H2fa.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact gt_2_0.
% 119.85/120.13 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.13 cut (((n2) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H19e].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H19c); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H19f ].
% 119.85/120.13 apply zenon_H1a0. zenon_intro zenon_Hcc.
% 119.85/120.13 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.13 cut (((loopcounter) = (loopcounter)) = ((n2) = (loopcounter))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H19e.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_Hed.
% 119.85/120.13 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.13 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_Hc3 zenon_Hcc).
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 apply zenon_H19f. zenon_intro zenon_H1a1.
% 119.85/120.13 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.13 generalize (zenon_H13b (n2)). zenon_intro zenon_H1a2.
% 119.85/120.13 generalize (zenon_H1a2 (n0)). zenon_intro zenon_H2fb.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2fb); [ zenon_intro zenon_H19d | zenon_intro zenon_H2fc ].
% 119.85/120.13 exact (zenon_H19d zenon_H1a1).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H2fc); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H2fd ].
% 119.85/120.13 exact (zenon_H1b7 gt_2_0).
% 119.85/120.13 exact (zenon_H2fa zenon_H2fd).
% 119.85/120.13 apply zenon_H65. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L157_ *)
% 119.85/120.13 assert (zenon_L158_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (loopcounter) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H232 zenon_H66.
% 119.85/120.13 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.85/120.13 elim (classic (gt (loopcounter) (n0))); [ zenon_intro zenon_H2fd | zenon_intro zenon_H2fa ].
% 119.85/120.13 elim (classic (gt (loopcounter) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2fe | zenon_intro zenon_H2ff ].
% 119.85/120.13 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1da ].
% 119.85/120.13 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.13 generalize (zenon_H13b (succ (tptp_minus_1))). zenon_intro zenon_H300.
% 119.85/120.13 generalize (zenon_H300 (succ (succ (n0)))). zenon_intro zenon_H301.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H301); [ zenon_intro zenon_H2ff | zenon_intro zenon_H302 ].
% 119.85/120.13 exact (zenon_H2ff zenon_H2fe).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H302); [ zenon_intro zenon_H1da | zenon_intro zenon_H231 ].
% 119.85/120.13 exact (zenon_H1da zenon_H1dd).
% 119.85/120.13 exact (zenon_H232 zenon_H231).
% 119.85/120.13 apply (zenon_L156_); trivial.
% 119.85/120.13 cut ((gt (loopcounter) (n0)) = (gt (loopcounter) (succ (tptp_minus_1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H2ff.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H2fd.
% 119.85/120.13 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.13 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 exact (zenon_H167 zenon_H180).
% 119.85/120.13 apply (zenon_L157_); trivial.
% 119.85/120.13 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H167.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H16a.
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L158_ *)
% 119.85/120.13 assert (zenon_L159_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (plus (n2) (n1)))) -> ((plus (n2) (n0)) = (succ (succ (n0)))) -> ((n1) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H303 zenon_H304 zenon_H108 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.13 elim (classic (gt (loopcounter) (plus (n2) (n1)))); [ zenon_intro zenon_H305 | zenon_intro zenon_H306 ].
% 119.85/120.13 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.13 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.85/120.13 generalize (zenon_Hf3 (plus (n2) (n1))). zenon_intro zenon_H307.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H307); [ zenon_intro zenon_H92 | zenon_intro zenon_H308 ].
% 119.85/120.13 exact (zenon_H92 zenon_H7d).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H308); [ zenon_intro zenon_H306 | zenon_intro zenon_H309 ].
% 119.85/120.13 exact (zenon_H306 zenon_H305).
% 119.85/120.13 exact (zenon_H303 zenon_H309).
% 119.85/120.13 elim (classic ((succ (succ (n0))) = (plus (n2) (n0)))); [ zenon_intro zenon_H30a | zenon_intro zenon_H30b ].
% 119.85/120.13 elim (classic (gt (loopcounter) (succ (succ (n0))))); [ zenon_intro zenon_H231 | zenon_intro zenon_H232 ].
% 119.85/120.13 elim (classic (gt (loopcounter) (plus (n2) (n0)))); [ zenon_intro zenon_H30c | zenon_intro zenon_H30d ].
% 119.85/120.13 cut ((gt (loopcounter) (plus (n2) (n0))) = (gt (loopcounter) (plus (n2) (n1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H306.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H30c.
% 119.85/120.13 cut (((plus (n2) (n0)) = (plus (n2) (n1)))); [idtac | apply NNPP; zenon_intro zenon_H2e8].
% 119.85/120.13 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 apply (zenon_L152_); trivial.
% 119.85/120.13 cut ((gt (loopcounter) (succ (succ (n0)))) = (gt (loopcounter) (plus (n2) (n0)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H30d.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H231.
% 119.85/120.13 cut (((succ (succ (n0))) = (plus (n2) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H30b].
% 119.85/120.13 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 exact (zenon_H30b zenon_H30a).
% 119.85/120.13 apply (zenon_L158_); trivial.
% 119.85/120.13 elim (classic ((plus (n2) (n0)) = (plus (n2) (n0)))); [ zenon_intro zenon_H30e | zenon_intro zenon_H30f ].
% 119.85/120.13 cut (((plus (n2) (n0)) = (plus (n2) (n0))) = ((succ (succ (n0))) = (plus (n2) (n0)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H30b.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H30e.
% 119.85/120.13 cut (((plus (n2) (n0)) = (plus (n2) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H30f].
% 119.85/120.13 cut (((plus (n2) (n0)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H310].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H310 zenon_H304).
% 119.85/120.13 apply zenon_H30f. apply refl_equal.
% 119.85/120.13 apply zenon_H30f. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L159_ *)
% 119.85/120.13 assert (zenon_L160_ : (~((succ (succ (n0))) = (succ (succ (n1))))) -> ((n1) = (n0)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H311 zenon_H108.
% 119.85/120.13 cut (((succ (n0)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H312].
% 119.85/120.13 congruence.
% 119.85/120.13 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H106. apply sym_equal. exact zenon_H108.
% 119.85/120.13 (* end of lemma zenon_L160_ *)
% 119.85/120.13 assert (zenon_L161_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H1a5 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.13 elim (classic (gt (n1) (n2))); [ zenon_intro zenon_H183 | zenon_intro zenon_H181 ].
% 119.85/120.13 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.85/120.13 generalize (zenon_H1a6 (n1)). zenon_intro zenon_H1a7.
% 119.85/120.13 generalize (zenon_H1a7 (n2)). zenon_intro zenon_H1a8.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H1a8); [ zenon_intro zenon_Hba | zenon_intro zenon_H1a9 ].
% 119.85/120.13 exact (zenon_Hba gt_2_1).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H1a9); [ zenon_intro zenon_H181 | zenon_intro zenon_H1aa ].
% 119.85/120.13 exact (zenon_H181 zenon_H183).
% 119.85/120.13 exact (zenon_H1a5 zenon_H1aa).
% 119.85/120.13 apply (zenon_L143_); trivial.
% 119.85/120.13 (* end of lemma zenon_L161_ *)
% 119.85/120.13 assert (zenon_L162_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n2) (succ (succ (n1))))) -> ((n1) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H155 zenon_Hc2 zenon_H7d zenon_H67 zenon_H313 zenon_H108 zenon_H66.
% 119.85/120.13 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.85/120.13 elim (classic (gt (n2) (n2))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1a5 ].
% 119.85/120.13 elim (classic (gt (n2) (succ (succ (n0))))); [ zenon_intro zenon_H314 | zenon_intro zenon_H315 ].
% 119.85/120.13 cut ((gt (n2) (succ (succ (n0)))) = (gt (n2) (succ (succ (n1))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H313.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H314.
% 119.85/120.13 cut (((succ (succ (n0))) = (succ (succ (n1))))); [idtac | apply NNPP; zenon_intro zenon_H311].
% 119.85/120.13 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H63. apply refl_equal.
% 119.85/120.13 apply (zenon_L160_); trivial.
% 119.85/120.13 cut ((gt (n2) (n2)) = (gt (n2) (succ (succ (n0))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H315.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H1aa.
% 119.85/120.13 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.13 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H63. apply refl_equal.
% 119.85/120.13 exact (zenon_H102 zenon_H1b9).
% 119.85/120.13 apply (zenon_L161_); trivial.
% 119.85/120.13 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.85/120.13 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H102.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H103.
% 119.85/120.13 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.13 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H105 successor_2).
% 119.85/120.13 apply zenon_H104. apply refl_equal.
% 119.85/120.13 apply zenon_H104. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L162_ *)
% 119.85/120.13 assert (zenon_L163_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> ((n1) = (n0)) -> (~(gt (n2) (plus (n2) (n1)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((plus (n2) (n1)) = (succ (succ (n1)))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H108 zenon_H316 zenon_H66 zenon_H317.
% 119.85/120.13 elim (classic ((succ (succ (n1))) = (plus (n2) (n1)))); [ zenon_intro zenon_H318 | zenon_intro zenon_H319 ].
% 119.85/120.13 elim (classic (gt (n2) (succ (succ (n1))))); [ zenon_intro zenon_H31a | zenon_intro zenon_H313 ].
% 119.85/120.13 cut ((gt (n2) (succ (succ (n1)))) = (gt (n2) (plus (n2) (n1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H316.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H31a.
% 119.85/120.13 cut (((succ (succ (n1))) = (plus (n2) (n1)))); [idtac | apply NNPP; zenon_intro zenon_H319].
% 119.85/120.13 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H63. apply refl_equal.
% 119.85/120.13 exact (zenon_H319 zenon_H318).
% 119.85/120.13 apply (zenon_L162_); trivial.
% 119.85/120.13 elim (classic ((plus (n2) (n1)) = (plus (n2) (n1)))); [ zenon_intro zenon_H31b | zenon_intro zenon_H31c ].
% 119.85/120.13 cut (((plus (n2) (n1)) = (plus (n2) (n1))) = ((succ (succ (n1))) = (plus (n2) (n1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H319.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H31b.
% 119.85/120.13 cut (((plus (n2) (n1)) = (plus (n2) (n1)))); [idtac | apply NNPP; zenon_intro zenon_H31c].
% 119.85/120.13 cut (((plus (n2) (n1)) = (succ (succ (n1))))); [idtac | apply NNPP; zenon_intro zenon_H31d].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H31d zenon_H317).
% 119.85/120.13 apply zenon_H31c. apply refl_equal.
% 119.85/120.13 apply zenon_H31c. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L163_ *)
% 119.85/120.13 assert (zenon_L164_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (plus (n2) (n1)))) -> ((loopcounter) = (n2)) -> ((n1) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((plus (n2) (n1)) = (succ (succ (n1)))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H303 zenon_Hcc zenon_H108 zenon_H155 zenon_Hc2 zenon_H7d zenon_H67 zenon_H317.
% 119.85/120.13 elim (classic (gt (loopcounter) (plus (n2) (n1)))); [ zenon_intro zenon_H305 | zenon_intro zenon_H306 ].
% 119.85/120.13 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.13 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.85/120.13 generalize (zenon_Hf3 (plus (n2) (n1))). zenon_intro zenon_H307.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H307); [ zenon_intro zenon_H92 | zenon_intro zenon_H308 ].
% 119.85/120.13 exact (zenon_H92 zenon_H7d).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H308); [ zenon_intro zenon_H306 | zenon_intro zenon_H309 ].
% 119.85/120.13 exact (zenon_H306 zenon_H305).
% 119.85/120.13 exact (zenon_H303 zenon_H309).
% 119.85/120.13 elim (classic (gt (n2) (plus (n2) (n1)))); [ zenon_intro zenon_H31e | zenon_intro zenon_H316 ].
% 119.85/120.13 cut ((gt (n2) (plus (n2) (n1))) = (gt (loopcounter) (plus (n2) (n1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H306.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H31e.
% 119.85/120.13 cut (((plus (n2) (n1)) = (plus (n2) (n1)))); [idtac | apply NNPP; zenon_intro zenon_H31c].
% 119.85/120.13 cut (((n2) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H19e].
% 119.85/120.13 congruence.
% 119.85/120.13 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.13 cut (((loopcounter) = (loopcounter)) = ((n2) = (loopcounter))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H19e.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_Hed.
% 119.85/120.13 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.13 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_Hc3 zenon_Hcc).
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 apply zenon_H31c. apply refl_equal.
% 119.85/120.13 apply (zenon_L163_); trivial.
% 119.85/120.13 (* end of lemma zenon_L164_ *)
% 119.85/120.13 assert (zenon_L165_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n1) (succ (succ (succ (n0)))))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_Hc2 zenon_H155 zenon_H23c.
% 119.85/120.13 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.85/120.13 apply (zenon_L5_); trivial.
% 119.85/120.13 apply (zenon_L12_); trivial.
% 119.85/120.13 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.85/120.13 generalize (finite_domain_0 (n1)). zenon_intro zenon_H107.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H107); [ zenon_intro zenon_H109 | zenon_intro zenon_H108 ].
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H109); [ zenon_intro zenon_H10b | zenon_intro zenon_H10a ].
% 119.85/120.13 apply (zenon_L147_); trivial.
% 119.85/120.13 apply (zenon_L149_); trivial.
% 119.85/120.13 generalize (succ_plus_2_l (n0)). zenon_intro zenon_H304.
% 119.85/120.13 generalize (succ_plus_2_l (n1)). zenon_intro zenon_H317.
% 119.85/120.13 elim (classic (gt (n1) (plus (n2) (n1)))); [ zenon_intro zenon_H309 | zenon_intro zenon_H303 ].
% 119.85/120.13 elim (classic (gt (n1) (succ (succ (n1))))); [ zenon_intro zenon_H31f | zenon_intro zenon_H320 ].
% 119.85/120.13 cut ((gt (n1) (succ (succ (n1)))) = (gt (n1) (succ (succ (succ (n0)))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H23c.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H31f.
% 119.85/120.13 cut (((succ (succ (n1))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H2e7].
% 119.85/120.13 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 apply (zenon_L150_); trivial.
% 119.85/120.13 cut ((gt (n1) (plus (n2) (n1))) = (gt (n1) (succ (succ (n1))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H320.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H309.
% 119.85/120.13 cut (((plus (n2) (n1)) = (succ (succ (n1))))); [idtac | apply NNPP; zenon_intro zenon_H31d].
% 119.85/120.13 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 exact (zenon_H31d zenon_H317).
% 119.85/120.13 apply (zenon_L159_); trivial.
% 119.85/120.13 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.85/120.13 apply (zenon_L141_); trivial.
% 119.85/120.13 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.85/120.13 generalize (finite_domain_0 (loopcounter)). zenon_intro zenon_H94.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ].
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H96); [ zenon_intro zenon_H68 | zenon_intro zenon_H7e ].
% 119.85/120.13 apply (zenon_L5_); trivial.
% 119.85/120.13 apply (zenon_L7_); trivial.
% 119.85/120.13 generalize (finite_domain_0 (n1)). zenon_intro zenon_H107.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H107); [ zenon_intro zenon_H109 | zenon_intro zenon_H108 ].
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H109); [ zenon_intro zenon_H10b | zenon_intro zenon_H10a ].
% 119.85/120.13 apply (zenon_L147_); trivial.
% 119.85/120.13 apply (zenon_L149_); trivial.
% 119.85/120.13 generalize (succ_plus_2_l (n1)). zenon_intro zenon_H317.
% 119.85/120.13 elim (classic (gt (n1) (plus (n2) (n1)))); [ zenon_intro zenon_H309 | zenon_intro zenon_H303 ].
% 119.85/120.13 elim (classic (gt (n1) (succ (succ (n1))))); [ zenon_intro zenon_H31f | zenon_intro zenon_H320 ].
% 119.85/120.13 cut ((gt (n1) (succ (succ (n1)))) = (gt (n1) (succ (succ (succ (n0)))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H23c.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H31f.
% 119.85/120.13 cut (((succ (succ (n1))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H2e7].
% 119.85/120.13 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 apply (zenon_L150_); trivial.
% 119.85/120.13 cut ((gt (n1) (plus (n2) (n1))) = (gt (n1) (succ (succ (n1))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H320.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H309.
% 119.85/120.13 cut (((plus (n2) (n1)) = (succ (succ (n1))))); [idtac | apply NNPP; zenon_intro zenon_H31d].
% 119.85/120.13 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 exact (zenon_H31d zenon_H317).
% 119.85/120.13 apply (zenon_L164_); trivial.
% 119.85/120.13 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.13 (* end of lemma zenon_L165_ *)
% 119.85/120.13 assert (zenon_L166_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (succ (succ (succ (n0)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H21b zenon_H67 zenon_H7d zenon_Hc2 zenon_H155.
% 119.85/120.13 elim (classic ((~((succ (succ (n0))) = (succ (loopcounter))))/\(~(gt (succ (succ (n0))) (succ (loopcounter)))))); [ zenon_intro zenon_H20c | zenon_intro zenon_H20d ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_H20e. zenon_intro zenon_H203.
% 119.85/120.13 apply (zenon_L136_); trivial.
% 119.85/120.13 elim (classic (gt (n1) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H23f | zenon_intro zenon_H23c ].
% 119.85/120.13 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.13 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.13 generalize (zenon_H78 (succ (succ (succ (n0))))). zenon_intro zenon_H241.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H241); [ zenon_intro zenon_H6f | zenon_intro zenon_H242 ].
% 119.85/120.13 exact (zenon_H6f zenon_H67).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H242); [ zenon_intro zenon_H23c | zenon_intro zenon_H243 ].
% 119.85/120.13 exact (zenon_H23c zenon_H23f).
% 119.85/120.13 cut ((gt (succ (loopcounter)) (succ (succ (succ (n0))))) = (gt (succ (succ (n0))) (succ (succ (succ (n0)))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H21b.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H243.
% 119.85/120.13 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.13 cut (((succ (loopcounter)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H212].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H20d); [ zenon_intro zenon_H214 | zenon_intro zenon_H213 ].
% 119.85/120.13 apply zenon_H214. zenon_intro zenon_H215.
% 119.85/120.13 apply zenon_H212. apply sym_equal. exact zenon_H215.
% 119.85/120.13 apply zenon_H213. zenon_intro zenon_H20a.
% 119.85/120.13 generalize (zenon_H66 (succ (succ (n0)))). zenon_intro zenon_H206.
% 119.85/120.13 generalize (zenon_H206 (succ (loopcounter))). zenon_intro zenon_H216.
% 119.85/120.13 generalize (zenon_H216 (succ (succ (succ (n0))))). zenon_intro zenon_H321.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H321); [ zenon_intro zenon_H203 | zenon_intro zenon_H322 ].
% 119.85/120.13 exact (zenon_H203 zenon_H20a).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H322); [ zenon_intro zenon_H247 | zenon_intro zenon_H233 ].
% 119.85/120.13 exact (zenon_H247 zenon_H243).
% 119.85/120.13 exact (zenon_H21b zenon_H233).
% 119.85/120.13 apply zenon_H21e. apply refl_equal.
% 119.85/120.13 apply (zenon_L165_); trivial.
% 119.85/120.13 (* end of lemma zenon_L166_ *)
% 119.85/120.13 assert (zenon_L167_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n3) (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((loopcounter) = (n3))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H24e zenon_H155 zenon_Hc2 zenon_H7d zenon_H67.
% 119.85/120.13 elim (classic (gt (n2) (n3))); [ zenon_intro zenon_H223 | zenon_intro zenon_H220 ].
% 119.85/120.13 generalize (zenon_H66 (n3)). zenon_intro zenon_H24f.
% 119.85/120.13 generalize (zenon_H24f (n2)). zenon_intro zenon_H250.
% 119.85/120.13 generalize (zenon_H250 (n3)). zenon_intro zenon_H251.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H251); [ zenon_intro zenon_H22f | zenon_intro zenon_H252 ].
% 119.85/120.13 exact (zenon_H22f gt_3_2).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H252); [ zenon_intro zenon_H220 | zenon_intro zenon_H253 ].
% 119.85/120.13 exact (zenon_H220 zenon_H223).
% 119.85/120.13 exact (zenon_H24e zenon_H253).
% 119.85/120.13 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.85/120.13 elim (classic (gt (n2) (n2))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1a5 ].
% 119.85/120.13 elim (classic (gt (n2) (succ (succ (n0))))); [ zenon_intro zenon_H314 | zenon_intro zenon_H315 ].
% 119.85/120.13 elim (classic (gt (succ (succ (n0))) (n3))); [ zenon_intro zenon_H219 | zenon_intro zenon_H20b ].
% 119.85/120.13 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.85/120.13 generalize (zenon_H1a6 (succ (succ (n0)))). zenon_intro zenon_H323.
% 119.85/120.13 generalize (zenon_H323 (n3)). zenon_intro zenon_H324.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H324); [ zenon_intro zenon_H315 | zenon_intro zenon_H325 ].
% 119.85/120.13 exact (zenon_H315 zenon_H314).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H325); [ zenon_intro zenon_H20b | zenon_intro zenon_H223 ].
% 119.85/120.13 exact (zenon_H20b zenon_H219).
% 119.85/120.13 exact (zenon_H220 zenon_H223).
% 119.85/120.13 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H233 | zenon_intro zenon_H21b ].
% 119.85/120.13 cut ((gt (succ (succ (n0))) (succ (succ (succ (n0))))) = (gt (succ (succ (n0))) (n3))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H20b.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H233.
% 119.85/120.13 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.85/120.13 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H104. apply refl_equal.
% 119.85/120.13 exact (zenon_H21f successor_3).
% 119.85/120.13 apply (zenon_L166_); trivial.
% 119.85/120.13 cut ((gt (n2) (n2)) = (gt (n2) (succ (succ (n0))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H315.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H1aa.
% 119.85/120.13 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.13 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H63. apply refl_equal.
% 119.85/120.13 exact (zenon_H102 zenon_H1b9).
% 119.85/120.13 apply (zenon_L161_); trivial.
% 119.85/120.13 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.85/120.13 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H102.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H103.
% 119.85/120.13 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.13 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H105 successor_2).
% 119.85/120.13 apply zenon_H104. apply refl_equal.
% 119.85/120.13 apply zenon_H104. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L167_ *)
% 119.85/120.13 assert (zenon_L168_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H255 zenon_H67 zenon_H7d zenon_Hc2 zenon_H155.
% 119.85/120.13 elim (classic ((~((succ (tptp_minus_1)) = (succ (loopcounter))))/\(~(gt (succ (tptp_minus_1)) (succ (loopcounter)))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H25f. zenon_intro zenon_H16c.
% 119.85/120.13 apply (zenon_L155_); trivial.
% 119.85/120.13 elim (classic (gt (n1) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H23f | zenon_intro zenon_H23c ].
% 119.85/120.13 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.13 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.13 generalize (zenon_H78 (succ (succ (succ (n0))))). zenon_intro zenon_H241.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H241); [ zenon_intro zenon_H6f | zenon_intro zenon_H242 ].
% 119.85/120.13 exact (zenon_H6f zenon_H67).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H242); [ zenon_intro zenon_H23c | zenon_intro zenon_H243 ].
% 119.85/120.13 exact (zenon_H23c zenon_H23f).
% 119.85/120.13 cut ((gt (succ (loopcounter)) (succ (succ (succ (n0))))) = (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H255.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H243.
% 119.85/120.13 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.13 cut (((succ (loopcounter)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H260].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H25e); [ zenon_intro zenon_H262 | zenon_intro zenon_H261 ].
% 119.85/120.13 apply zenon_H262. zenon_intro zenon_H263.
% 119.85/120.13 apply zenon_H260. apply sym_equal. exact zenon_H263.
% 119.85/120.13 apply zenon_H261. zenon_intro zenon_H175.
% 119.85/120.13 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.85/120.13 generalize (zenon_H171 (succ (loopcounter))). zenon_intro zenon_H264.
% 119.85/120.13 generalize (zenon_H264 (succ (succ (succ (n0))))). zenon_intro zenon_H326.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H326); [ zenon_intro zenon_H16c | zenon_intro zenon_H327 ].
% 119.85/120.13 exact (zenon_H16c zenon_H175).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H327); [ zenon_intro zenon_H247 | zenon_intro zenon_H258 ].
% 119.85/120.13 exact (zenon_H247 zenon_H243).
% 119.85/120.13 exact (zenon_H255 zenon_H258).
% 119.85/120.13 apply zenon_H21e. apply refl_equal.
% 119.85/120.13 apply (zenon_L165_); trivial.
% 119.85/120.13 (* end of lemma zenon_L168_ *)
% 119.85/120.13 assert (zenon_L169_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n0))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H2fa zenon_H67 zenon_H7d zenon_H155.
% 119.85/120.13 elim (classic ((~((loopcounter) = (n3)))/\(~(gt (loopcounter) (n3))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hc2. zenon_intro zenon_H1f5.
% 119.85/120.13 apply (zenon_L157_); trivial.
% 119.85/120.13 cut ((gt (n3) (n0)) = (gt (loopcounter) (n0))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H2fa.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact gt_3_0.
% 119.85/120.13 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.13 cut (((n3) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f7 ].
% 119.85/120.13 apply zenon_H1f8. zenon_intro zenon_Hcb.
% 119.85/120.13 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.85/120.13 cut (((loopcounter) = (loopcounter)) = ((n3) = (loopcounter))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H1f6.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_Hed.
% 119.85/120.13 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.13 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 apply zenon_H1f7. zenon_intro zenon_H1f9.
% 119.85/120.13 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.13 generalize (zenon_H13b (n3)). zenon_intro zenon_H1fa.
% 119.85/120.13 generalize (zenon_H1fa (n0)). zenon_intro zenon_H328.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H328); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H329 ].
% 119.85/120.13 exact (zenon_H1f5 zenon_H1f9).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H329); [ zenon_intro zenon_H291 | zenon_intro zenon_H2fd ].
% 119.85/120.13 exact (zenon_H291 gt_3_0).
% 119.85/120.13 exact (zenon_H2fa zenon_H2fd).
% 119.85/120.13 apply zenon_H65. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L169_ *)
% 119.85/120.13 assert (zenon_L170_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n3))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~((loopcounter) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H1f5 zenon_H67 zenon_H7d zenon_Hc2 zenon_H155.
% 119.85/120.13 elim (classic (gt (loopcounter) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H237 | zenon_intro zenon_H230 ].
% 119.85/120.13 cut ((gt (loopcounter) (succ (succ (succ (n0))))) = (gt (loopcounter) (n3))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H1f5.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H237.
% 119.85/120.13 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.85/120.13 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 exact (zenon_H21f successor_3).
% 119.85/120.13 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.85/120.13 elim (classic (gt (loopcounter) (n0))); [ zenon_intro zenon_H2fd | zenon_intro zenon_H2fa ].
% 119.85/120.13 elim (classic (gt (loopcounter) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2fe | zenon_intro zenon_H2ff ].
% 119.85/120.13 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H258 | zenon_intro zenon_H255 ].
% 119.85/120.13 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.85/120.13 generalize (zenon_H13b (succ (tptp_minus_1))). zenon_intro zenon_H300.
% 119.85/120.13 generalize (zenon_H300 (succ (succ (succ (n0))))). zenon_intro zenon_H32a.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H32a); [ zenon_intro zenon_H2ff | zenon_intro zenon_H32b ].
% 119.85/120.13 exact (zenon_H2ff zenon_H2fe).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H32b); [ zenon_intro zenon_H255 | zenon_intro zenon_H237 ].
% 119.85/120.13 exact (zenon_H255 zenon_H258).
% 119.85/120.13 exact (zenon_H230 zenon_H237).
% 119.85/120.13 apply (zenon_L168_); trivial.
% 119.85/120.13 cut ((gt (loopcounter) (n0)) = (gt (loopcounter) (succ (tptp_minus_1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H2ff.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H2fd.
% 119.85/120.13 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.85/120.13 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H7c. apply refl_equal.
% 119.85/120.13 exact (zenon_H167 zenon_H180).
% 119.85/120.13 apply (zenon_L169_); trivial.
% 119.85/120.13 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H167.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H16a.
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.85/120.13 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H16b succ_tptp_minus_1).
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 apply zenon_H169. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L170_ *)
% 119.85/120.13 assert (zenon_L171_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n3))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H1e6 zenon_H67 zenon_H7d zenon_H155.
% 119.85/120.13 elim (classic ((loopcounter) = (n3))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hc2 ].
% 119.85/120.13 cut ((gt (n1) (loopcounter)) = (gt (n1) (n3))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H1e6.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H7d.
% 119.85/120.13 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.85/120.13 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 exact (zenon_Hc2 zenon_Hcb).
% 119.85/120.13 elim (classic (gt (loopcounter) (n3))); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H1f5 ].
% 119.85/120.13 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.13 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.85/120.13 generalize (zenon_Hf3 (n3)). zenon_intro zenon_H32c.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H32c); [ zenon_intro zenon_H92 | zenon_intro zenon_H32d ].
% 119.85/120.13 exact (zenon_H92 zenon_H7d).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H32d); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1ee ].
% 119.85/120.13 exact (zenon_H1f5 zenon_H1f9).
% 119.85/120.13 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.13 apply (zenon_L170_); trivial.
% 119.85/120.13 (* end of lemma zenon_L171_ *)
% 119.85/120.13 assert (zenon_L172_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H67 zenon_H7d zenon_H155 zenon_H66 zenon_Hdd.
% 119.85/120.13 elim (classic ((~((n1) = (n3)))/\(~(gt (n1) (n3))))); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1e8 ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e9. zenon_intro zenon_H1e6.
% 119.85/120.13 apply (zenon_L171_); trivial.
% 119.85/120.13 cut ((gt (n3) (n1)) = (gt (n1) (n1))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_Hdd.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact gt_3_1.
% 119.85/120.13 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.13 cut (((n3) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H1ea].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ec | zenon_intro zenon_H1eb ].
% 119.85/120.13 apply zenon_H1ec. zenon_intro zenon_H1ed.
% 119.85/120.13 elim (classic ((n1) = (n1))); [ zenon_intro zenon_Hdc | zenon_intro zenon_H64 ].
% 119.85/120.13 cut (((n1) = (n1)) = ((n3) = (n1))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H1ea.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_Hdc.
% 119.85/120.13 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.13 cut (((n1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H1e9].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H1e9 zenon_H1ed).
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 apply zenon_H1eb. zenon_intro zenon_H1ee.
% 119.85/120.13 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.13 generalize (zenon_He4 (n3)). zenon_intro zenon_H1ef.
% 119.85/120.13 generalize (zenon_H1ef (n1)). zenon_intro zenon_H1f0.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H1f0); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H1f1 ].
% 119.85/120.13 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H1f1); [ zenon_intro zenon_H1f2 | zenon_intro zenon_He8 ].
% 119.85/120.13 exact (zenon_H1f2 gt_3_1).
% 119.85/120.13 exact (zenon_Hdd zenon_He8).
% 119.85/120.13 apply zenon_H64. apply refl_equal.
% 119.85/120.13 (* end of lemma zenon_L172_ *)
% 119.85/120.13 assert (zenon_L173_ : forall (zenon_TG_dq : zenon_U), (gt (succ (n4)) zenon_TG_dq) -> (~(leq zenon_TG_dq (n4))) -> False).
% 119.85/120.13 do 1 intro. intros zenon_H32e zenon_H32f.
% 119.85/120.13 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.85/120.13 generalize (zenon_H330 (n4)). zenon_intro zenon_H331.
% 119.85/120.13 apply (zenon_equiv_s _ _ zenon_H331); [ zenon_intro zenon_H32f; zenon_intro zenon_H333 | zenon_intro zenon_H332; zenon_intro zenon_H32e ].
% 119.85/120.13 exact (zenon_H333 zenon_H32e).
% 119.85/120.13 exact (zenon_H32f zenon_H332).
% 119.85/120.13 (* end of lemma zenon_L173_ *)
% 119.85/120.13 assert (zenon_L174_ : forall (zenon_TG_dq : zenon_U), (gt (succ zenon_TG_dq) (n0)) -> (gt (succ (n4)) zenon_TG_dq) -> (~((n0) = zenon_TG_dq)) -> (~((n1) = zenon_TG_dq)) -> (~((n2) = zenon_TG_dq)) -> (~((n3) = zenon_TG_dq)) -> (~((n4) = zenon_TG_dq)) -> False).
% 119.85/120.13 do 1 intro. intros zenon_H5c zenon_H32e zenon_H334 zenon_H335 zenon_H336 zenon_H337 zenon_H338.
% 119.85/120.13 generalize (finite_domain_4 zenon_TG_dq). zenon_intro zenon_H339.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H339); [ zenon_intro zenon_H33b | zenon_intro zenon_H33a ].
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H33b); [ zenon_intro zenon_H5d | zenon_intro zenon_H32f ].
% 119.85/120.13 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.85/120.13 apply (zenon_L173_ zenon_TG_dq); trivial.
% 119.85/120.13 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H33d | zenon_intro zenon_H33c ].
% 119.85/120.13 apply zenon_H334. apply sym_equal. exact zenon_H33d.
% 119.85/120.13 apply (zenon_or_s _ _ zenon_H33c); [ zenon_intro zenon_H33f | zenon_intro zenon_H33e ].
% 119.85/120.13 apply zenon_H335. apply sym_equal. exact zenon_H33f.
% 119.85/120.13 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H341 | zenon_intro zenon_H340 ].
% 119.85/120.13 apply zenon_H336. apply sym_equal. exact zenon_H341.
% 119.85/120.13 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H343 | zenon_intro zenon_H342 ].
% 119.85/120.13 apply zenon_H337. apply sym_equal. exact zenon_H343.
% 119.85/120.13 apply zenon_H338. apply sym_equal. exact zenon_H342.
% 119.85/120.13 (* end of lemma zenon_L174_ *)
% 119.85/120.13 assert (zenon_L175_ : forall (zenon_TG_dq : zenon_U), (~(gt (n4) zenon_TG_dq)) -> (gt (succ zenon_TG_dq) (n0)) -> (gt (succ (n4)) zenon_TG_dq) -> (~((n0) = zenon_TG_dq)) -> (~((n1) = zenon_TG_dq)) -> (~((n2) = zenon_TG_dq)) -> (~((n4) = zenon_TG_dq)) -> False).
% 119.85/120.13 do 1 intro. intros zenon_H344 zenon_H5c zenon_H32e zenon_H334 zenon_H335 zenon_H336 zenon_H338.
% 119.85/120.13 elim (classic ((n3) = zenon_TG_dq)); [ zenon_intro zenon_H345 | zenon_intro zenon_H337 ].
% 119.85/120.13 cut ((gt (n4) (n3)) = (gt (n4) zenon_TG_dq)).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H344.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact gt_4_3.
% 119.85/120.13 cut (((n3) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H337].
% 119.85/120.13 cut (((n4) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H294].
% 119.85/120.13 congruence.
% 119.85/120.13 apply zenon_H294. apply refl_equal.
% 119.85/120.13 exact (zenon_H337 zenon_H345).
% 119.85/120.13 apply (zenon_L174_ zenon_TG_dq); trivial.
% 119.85/120.13 (* end of lemma zenon_L175_ *)
% 119.85/120.13 assert (zenon_L176_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(leq (n0) (n1))) -> False).
% 119.85/120.13 do 0 intro. intros zenon_H66 zenon_H95 zenon_H155 zenon_H7d zenon_H67 zenon_H10b.
% 119.85/120.13 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 119.85/120.13 generalize (zenon_H5f (n1)). zenon_intro zenon_H10c.
% 119.85/120.13 apply (zenon_equiv_s _ _ zenon_H10c); [ zenon_intro zenon_H10b; zenon_intro zenon_H10f | zenon_intro zenon_H10e; zenon_intro zenon_H10d ].
% 119.85/120.13 elim (classic ((~((succ (n1)) = (n3)))/\(~(gt (succ (n1)) (n3))))); [ zenon_intro zenon_H346 | zenon_intro zenon_H347 ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H346). zenon_intro zenon_H349. zenon_intro zenon_H348.
% 119.85/120.13 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.85/120.13 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.85/120.13 apply (zenon_L138_); trivial.
% 119.85/120.13 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1e6 ].
% 119.85/120.13 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.13 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.13 generalize (zenon_H78 (n3)). zenon_intro zenon_H20f.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H20f); [ zenon_intro zenon_H6f | zenon_intro zenon_H210 ].
% 119.85/120.13 exact (zenon_H6f zenon_H67).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H210); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H211 ].
% 119.85/120.13 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.13 cut ((gt (succ (loopcounter)) (n3)) = (gt (succ (n1)) (n3))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H348.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H211.
% 119.85/120.13 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.85/120.13 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.85/120.13 apply zenon_H121. zenon_intro zenon_H122.
% 119.85/120.13 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.85/120.13 apply zenon_H120. zenon_intro zenon_H11e.
% 119.85/120.13 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.85/120.13 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.85/120.13 generalize (zenon_H123 (n3)). zenon_intro zenon_H34a.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H34a); [ zenon_intro zenon_H116 | zenon_intro zenon_H34b ].
% 119.85/120.13 exact (zenon_H116 zenon_H11e).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H34b); [ zenon_intro zenon_H21a | zenon_intro zenon_H34c ].
% 119.85/120.13 exact (zenon_H21a zenon_H211).
% 119.85/120.13 exact (zenon_H348 zenon_H34c).
% 119.85/120.13 apply zenon_H201. apply refl_equal.
% 119.85/120.13 apply (zenon_L171_); trivial.
% 119.85/120.13 cut ((gt (n3) (n0)) = (gt (succ (n1)) (n0))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H10f.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact gt_3_0.
% 119.85/120.13 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.85/120.13 cut (((n3) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H34d].
% 119.85/120.13 congruence.
% 119.85/120.13 apply (zenon_notand_s _ _ zenon_H347); [ zenon_intro zenon_H34f | zenon_intro zenon_H34e ].
% 119.85/120.13 apply zenon_H34f. zenon_intro zenon_H350.
% 119.85/120.13 elim (classic ((succ (n1)) = (succ (n1)))); [ zenon_intro zenon_H100 | zenon_intro zenon_H101 ].
% 119.85/120.13 cut (((succ (n1)) = (succ (n1))) = ((n3) = (succ (n1)))).
% 119.85/120.13 intro zenon_D_pnotp.
% 119.85/120.13 apply zenon_H34d.
% 119.85/120.13 rewrite <- zenon_D_pnotp.
% 119.85/120.13 exact zenon_H100.
% 119.85/120.13 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.85/120.13 cut (((succ (n1)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H349].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H349 zenon_H350).
% 119.85/120.13 apply zenon_H101. apply refl_equal.
% 119.85/120.13 apply zenon_H101. apply refl_equal.
% 119.85/120.13 apply zenon_H34e. zenon_intro zenon_H34c.
% 119.85/120.13 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.85/120.13 generalize (zenon_H11a (n3)). zenon_intro zenon_H351.
% 119.85/120.13 generalize (zenon_H351 (n0)). zenon_intro zenon_H352.
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H352); [ zenon_intro zenon_H348 | zenon_intro zenon_H353 ].
% 119.85/120.13 exact (zenon_H348 zenon_H34c).
% 119.85/120.13 apply (zenon_imply_s _ _ zenon_H353); [ zenon_intro zenon_H291 | zenon_intro zenon_H10d ].
% 119.85/120.13 exact (zenon_H291 gt_3_0).
% 119.85/120.13 exact (zenon_H10f zenon_H10d).
% 119.85/120.13 apply zenon_H65. apply refl_equal.
% 119.85/120.13 exact (zenon_H10b zenon_H10e).
% 119.85/120.13 (* end of lemma zenon_L176_ *)
% 119.85/120.13 assert (zenon_L177_ : forall (zenon_TG_dq : zenon_U), (~((succ zenon_TG_dq) = (succ (n4)))) -> (zenon_TG_dq = (n4)) -> False).
% 119.85/120.13 do 1 intro. intros zenon_H354 zenon_H342.
% 119.85/120.13 cut ((zenon_TG_dq = (n4))); [idtac | apply NNPP; zenon_intro zenon_H355].
% 119.85/120.13 congruence.
% 119.85/120.13 exact (zenon_H355 zenon_H342).
% 119.85/120.13 (* end of lemma zenon_L177_ *)
% 119.85/120.13 assert (zenon_L178_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ zenon_TG_dq) (n4))) -> (gt (succ (n4)) zenon_TG_dq) -> (zenon_TG_dq = (n4)) -> False).
% 119.85/120.14 do 1 intro. intros zenon_H66 zenon_H356 zenon_H32e zenon_H342.
% 119.85/120.14 elim (classic ((~((succ zenon_TG_dq) = (succ (n4))))/\(~(gt (succ zenon_TG_dq) (succ (n4)))))); [ zenon_intro zenon_H357 | zenon_intro zenon_H358 ].
% 119.85/120.14 apply (zenon_and_s _ _ zenon_H357). zenon_intro zenon_H354. zenon_intro zenon_H359.
% 119.85/120.14 apply (zenon_L177_ zenon_TG_dq); trivial.
% 119.85/120.14 cut ((gt (succ (n4)) zenon_TG_dq) = (gt (succ zenon_TG_dq) (n4))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H356.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H32e.
% 119.85/120.14 cut ((zenon_TG_dq = (n4))); [idtac | apply NNPP; zenon_intro zenon_H355].
% 119.85/120.14 cut (((succ (n4)) = (succ zenon_TG_dq))); [idtac | apply NNPP; zenon_intro zenon_H35a].
% 119.85/120.14 congruence.
% 119.85/120.14 apply (zenon_notand_s _ _ zenon_H358); [ zenon_intro zenon_H35c | zenon_intro zenon_H35b ].
% 119.85/120.14 apply zenon_H35c. zenon_intro zenon_H35d.
% 119.85/120.14 elim (classic ((succ zenon_TG_dq) = (succ zenon_TG_dq))); [ zenon_intro zenon_H35e | zenon_intro zenon_H35f ].
% 119.85/120.14 cut (((succ zenon_TG_dq) = (succ zenon_TG_dq)) = ((succ (n4)) = (succ zenon_TG_dq))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H35a.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H35e.
% 119.85/120.14 cut (((succ zenon_TG_dq) = (succ zenon_TG_dq))); [idtac | apply NNPP; zenon_intro zenon_H35f].
% 119.85/120.14 cut (((succ zenon_TG_dq) = (succ (n4)))); [idtac | apply NNPP; zenon_intro zenon_H354].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_H354 zenon_H35d).
% 119.85/120.14 apply zenon_H35f. apply refl_equal.
% 119.85/120.14 apply zenon_H35f. apply refl_equal.
% 119.85/120.14 apply zenon_H35b. zenon_intro zenon_H360.
% 119.85/120.14 generalize (zenon_H66 (succ zenon_TG_dq)). zenon_intro zenon_H361.
% 119.85/120.14 generalize (zenon_H361 (succ (n4))). zenon_intro zenon_H362.
% 119.85/120.14 generalize (zenon_H362 zenon_TG_dq). zenon_intro zenon_H363.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H363); [ zenon_intro zenon_H359 | zenon_intro zenon_H364 ].
% 119.85/120.14 exact (zenon_H359 zenon_H360).
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H364); [ zenon_intro zenon_H333 | zenon_intro zenon_H365 ].
% 119.85/120.14 exact (zenon_H333 zenon_H32e).
% 119.85/120.14 cut ((gt (succ zenon_TG_dq) zenon_TG_dq) = (gt (succ zenon_TG_dq) (n4))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H356.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H365.
% 119.85/120.14 cut ((zenon_TG_dq = (n4))); [idtac | apply NNPP; zenon_intro zenon_H355].
% 119.85/120.14 cut (((succ zenon_TG_dq) = (succ zenon_TG_dq))); [idtac | apply NNPP; zenon_intro zenon_H35f].
% 119.85/120.14 congruence.
% 119.85/120.14 apply zenon_H35f. apply refl_equal.
% 119.85/120.14 exact (zenon_H355 zenon_H342).
% 119.85/120.14 exact (zenon_H355 zenon_H342).
% 119.85/120.14 (* end of lemma zenon_L178_ *)
% 119.85/120.14 assert (zenon_L179_ : forall (zenon_TG_dq : zenon_U), (zenon_TG_dq = (n4)) -> (gt (succ (n4)) zenon_TG_dq) -> (~(gt (succ zenon_TG_dq) (succ (succ (succ (succ (n0))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.14 do 1 intro. intros zenon_H342 zenon_H32e zenon_H366 zenon_H66.
% 119.85/120.14 elim (classic ((n4) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_H367 | zenon_intro zenon_Ha0 ].
% 119.85/120.14 elim (classic (gt (succ zenon_TG_dq) (n4))); [ zenon_intro zenon_H368 | zenon_intro zenon_H356 ].
% 119.85/120.14 cut ((gt (succ zenon_TG_dq) (n4)) = (gt (succ zenon_TG_dq) (succ (succ (succ (succ (n0))))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H366.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H368.
% 119.85/120.14 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 119.85/120.14 cut (((succ zenon_TG_dq) = (succ zenon_TG_dq))); [idtac | apply NNPP; zenon_intro zenon_H35f].
% 119.85/120.14 congruence.
% 119.85/120.14 apply zenon_H35f. apply refl_equal.
% 119.85/120.14 exact (zenon_Ha0 zenon_H367).
% 119.85/120.14 apply (zenon_L178_ zenon_TG_dq); trivial.
% 119.85/120.14 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_Ha0.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_Ha1.
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_Ha3 successor_4).
% 119.85/120.14 apply zenon_Ha2. apply refl_equal.
% 119.85/120.14 apply zenon_Ha2. apply refl_equal.
% 119.85/120.14 (* end of lemma zenon_L179_ *)
% 119.85/120.14 assert (zenon_L180_ : forall (zenon_TG_dq : zenon_U), (gt (succ (n4)) zenon_TG_dq) -> (zenon_TG_dq = (n4)) -> (~(gt (succ zenon_TG_dq) (plus (n4) (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((plus (n4) (n0)) = (succ (succ (succ (succ (n0)))))) -> False).
% 119.85/120.14 do 1 intro. intros zenon_H32e zenon_H342 zenon_H369 zenon_H66 zenon_H36a.
% 119.85/120.14 elim (classic ((succ (succ (succ (succ (n0))))) = (plus (n4) (n0)))); [ zenon_intro zenon_H36b | zenon_intro zenon_H36c ].
% 119.85/120.14 elim (classic (gt (succ zenon_TG_dq) (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_H36d | zenon_intro zenon_H366 ].
% 119.85/120.14 cut ((gt (succ zenon_TG_dq) (succ (succ (succ (succ (n0)))))) = (gt (succ zenon_TG_dq) (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H369.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H36d.
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36c].
% 119.85/120.14 cut (((succ zenon_TG_dq) = (succ zenon_TG_dq))); [idtac | apply NNPP; zenon_intro zenon_H35f].
% 119.85/120.14 congruence.
% 119.85/120.14 apply zenon_H35f. apply refl_equal.
% 119.85/120.14 exact (zenon_H36c zenon_H36b).
% 119.85/120.14 apply (zenon_L179_ zenon_TG_dq); trivial.
% 119.85/120.14 elim (classic ((plus (n4) (n0)) = (plus (n4) (n0)))); [ zenon_intro zenon_H36e | zenon_intro zenon_H36f ].
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0))) = ((succ (succ (succ (succ (n0))))) = (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H36c.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H36e.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((plus (n4) (n0)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H370].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_H370 zenon_H36a).
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 (* end of lemma zenon_L180_ *)
% 119.85/120.14 assert (zenon_L181_ : forall (zenon_TG_dq : zenon_U), ((plus zenon_TG_dq (n1)) = (succ zenon_TG_dq)) -> (gt (succ (n4)) zenon_TG_dq) -> ((plus (n4) (n0)) = (succ (succ (succ (succ (n0)))))) -> (zenon_TG_dq = (n4)) -> ((n1) = (n0)) -> (~(gt (n4) (plus (n4) (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.14 do 1 intro. intros zenon_H371 zenon_H32e zenon_H36a zenon_H342 zenon_H108 zenon_H372 zenon_H66.
% 119.85/120.14 elim (classic ((n4) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_H367 | zenon_intro zenon_Ha0 ].
% 119.85/120.14 elim (classic (gt (succ (succ (succ (succ (n0))))) (plus (n4) (n0)))); [ zenon_intro zenon_H373 | zenon_intro zenon_H374 ].
% 119.85/120.14 cut ((gt (succ (succ (succ (succ (n0))))) (plus (n4) (n0))) = (gt (n4) (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H372.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H373.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 119.85/120.14 congruence.
% 119.85/120.14 elim (classic ((n4) = (n4))); [ zenon_intro zenon_H375 | zenon_intro zenon_H294 ].
% 119.85/120.14 cut (((n4) = (n4)) = ((succ (succ (succ (succ (n0))))) = (n4))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_Ha3.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H375.
% 119.85/120.14 cut (((n4) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H294].
% 119.85/120.14 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_Ha0 zenon_H367).
% 119.85/120.14 apply zenon_H294. apply refl_equal.
% 119.85/120.14 apply zenon_H294. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 elim (classic ((succ (succ (succ (succ (n0))))) = (plus (n4) (n0)))); [ zenon_intro zenon_H36b | zenon_intro zenon_H36c ].
% 119.85/120.14 elim (classic (gt (plus (n4) (n0)) (plus (n4) (n0)))); [ zenon_intro zenon_H376 | zenon_intro zenon_H377 ].
% 119.85/120.14 cut ((gt (plus (n4) (n0)) (plus (n4) (n0))) = (gt (succ (succ (succ (succ (n0))))) (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H374.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H376.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((plus (n4) (n0)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H370].
% 119.85/120.14 congruence.
% 119.85/120.14 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((plus (n4) (n0)) = (succ (succ (succ (succ (n0))))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H370.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_Ha1.
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36c].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_H36c zenon_H36b).
% 119.85/120.14 apply zenon_Ha2. apply refl_equal.
% 119.85/120.14 apply zenon_Ha2. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 elim (classic (gt (succ zenon_TG_dq) (plus (n4) (n0)))); [ zenon_intro zenon_H378 | zenon_intro zenon_H369 ].
% 119.85/120.14 elim (classic (gt (plus zenon_TG_dq (n1)) (plus (n4) (n0)))); [ zenon_intro zenon_H379 | zenon_intro zenon_H37a ].
% 119.85/120.14 cut ((gt (plus zenon_TG_dq (n1)) (plus (n4) (n0))) = (gt (plus (n4) (n0)) (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H377.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H379.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((plus zenon_TG_dq (n1)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H37b].
% 119.85/120.14 congruence.
% 119.85/120.14 elim (classic ((plus (n4) (n0)) = (plus (n4) (n0)))); [ zenon_intro zenon_H36e | zenon_intro zenon_H36f ].
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0))) = ((plus zenon_TG_dq (n1)) = (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H37b.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H36e.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus zenon_TG_dq (n1)))); [idtac | apply NNPP; zenon_intro zenon_H37c].
% 119.85/120.14 congruence.
% 119.85/120.14 cut (((n0) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 119.85/120.14 cut (((n4) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H338].
% 119.85/120.14 congruence.
% 119.85/120.14 apply zenon_H338. apply sym_equal. exact zenon_H342.
% 119.85/120.14 apply zenon_H106. apply sym_equal. exact zenon_H108.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 cut ((gt (succ zenon_TG_dq) (plus (n4) (n0))) = (gt (plus zenon_TG_dq (n1)) (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H37a.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H378.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((succ zenon_TG_dq) = (plus zenon_TG_dq (n1)))); [idtac | apply NNPP; zenon_intro zenon_H37d].
% 119.85/120.14 congruence.
% 119.85/120.14 elim (classic ((plus zenon_TG_dq (n1)) = (plus zenon_TG_dq (n1)))); [ zenon_intro zenon_H37e | zenon_intro zenon_H37f ].
% 119.85/120.14 cut (((plus zenon_TG_dq (n1)) = (plus zenon_TG_dq (n1))) = ((succ zenon_TG_dq) = (plus zenon_TG_dq (n1)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H37d.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H37e.
% 119.85/120.14 cut (((plus zenon_TG_dq (n1)) = (plus zenon_TG_dq (n1)))); [idtac | apply NNPP; zenon_intro zenon_H37f].
% 119.85/120.14 cut (((plus zenon_TG_dq (n1)) = (succ zenon_TG_dq))); [idtac | apply NNPP; zenon_intro zenon_H380].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_H380 zenon_H371).
% 119.85/120.14 apply zenon_H37f. apply refl_equal.
% 119.85/120.14 apply zenon_H37f. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 apply (zenon_L180_ zenon_TG_dq); trivial.
% 119.85/120.14 elim (classic ((plus (n4) (n0)) = (plus (n4) (n0)))); [ zenon_intro zenon_H36e | zenon_intro zenon_H36f ].
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0))) = ((succ (succ (succ (succ (n0))))) = (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H36c.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H36e.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((plus (n4) (n0)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H370].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_H370 zenon_H36a).
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_Ha0.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_Ha1.
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_Ha3 successor_4).
% 119.85/120.14 apply zenon_Ha2. apply refl_equal.
% 119.85/120.14 apply zenon_Ha2. apply refl_equal.
% 119.85/120.14 (* end of lemma zenon_L181_ *)
% 119.85/120.14 assert (zenon_L182_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n3)) (plus (n4) (n0)))) -> ((plus zenon_TG_dq (n1)) = (succ zenon_TG_dq)) -> (gt (succ (n4)) zenon_TG_dq) -> ((plus (n4) (n0)) = (succ (succ (succ (succ (n0)))))) -> (zenon_TG_dq = (n4)) -> ((n1) = (n0)) -> False).
% 119.85/120.14 do 1 intro. intros zenon_H66 zenon_H381 zenon_H371 zenon_H32e zenon_H36a zenon_H342 zenon_H108.
% 119.85/120.14 elim (classic (gt (n4) (plus (n4) (n0)))); [ zenon_intro zenon_H382 | zenon_intro zenon_H372 ].
% 119.85/120.14 elim (classic (gt (succ (succ (succ (succ (n0))))) (plus (n4) (n0)))); [ zenon_intro zenon_H373 | zenon_intro zenon_H374 ].
% 119.85/120.14 cut ((gt (succ (succ (succ (succ (n0))))) (plus (n4) (n0))) = (gt (succ (n3)) (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H381.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H373.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9d].
% 119.85/120.14 congruence.
% 119.85/120.14 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ].
% 119.85/120.14 cut (((succ (n3)) = (succ (n3))) = ((succ (succ (succ (succ (n0))))) = (succ (n3)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H9d.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H9e.
% 119.85/120.14 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.85/120.14 cut (((succ (n3)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H98].
% 119.85/120.14 congruence.
% 119.85/120.14 apply (zenon_L10_); trivial.
% 119.85/120.14 apply zenon_H9f. apply refl_equal.
% 119.85/120.14 apply zenon_H9f. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 cut ((gt (n4) (plus (n4) (n0))) = (gt (succ (succ (succ (succ (n0))))) (plus (n4) (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H374.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H382.
% 119.85/120.14 cut (((plus (n4) (n0)) = (plus (n4) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H36f].
% 119.85/120.14 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 119.85/120.14 congruence.
% 119.85/120.14 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_Ha0.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_Ha1.
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 119.85/120.14 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_Ha3 successor_4).
% 119.85/120.14 apply zenon_Ha2. apply refl_equal.
% 119.85/120.14 apply zenon_Ha2. apply refl_equal.
% 119.85/120.14 apply zenon_H36f. apply refl_equal.
% 119.85/120.14 apply (zenon_L181_ zenon_TG_dq); trivial.
% 119.85/120.14 (* end of lemma zenon_L182_ *)
% 119.85/120.14 assert (zenon_L183_ : forall (zenon_TG_dq : zenon_U), (((leq (n0) (n1))/\(leq (n1) (n0)))->((n1) = (n0))) -> (gt (succ (loopcounter)) (n1)) -> ((loopcounter) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n3)) (succ (succ (succ (succ (n0))))))) -> (gt (succ (n4)) zenon_TG_dq) -> (zenon_TG_dq = (n4)) -> False).
% 119.85/120.14 do 1 intro. intros zenon_H107 zenon_H67 zenon_H95 zenon_H155 zenon_H7d zenon_H66 zenon_H383 zenon_H32e zenon_H342.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H107); [ zenon_intro zenon_H109 | zenon_intro zenon_H108 ].
% 119.85/120.14 apply (zenon_notand_s _ _ zenon_H109); [ zenon_intro zenon_H10b | zenon_intro zenon_H10a ].
% 119.85/120.14 apply (zenon_L176_); trivial.
% 119.85/120.14 apply (zenon_L149_); trivial.
% 119.85/120.14 generalize (succ_plus_1_r zenon_TG_dq). zenon_intro zenon_H371.
% 119.85/120.14 generalize (succ_plus_4_l (n0)). zenon_intro zenon_H36a.
% 119.85/120.14 elim (classic (gt (succ (n3)) (plus (n4) (n0)))); [ zenon_intro zenon_H384 | zenon_intro zenon_H381 ].
% 119.85/120.14 cut ((gt (succ (n3)) (plus (n4) (n0))) = (gt (succ (n3)) (succ (succ (succ (succ (n0))))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H383.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H384.
% 119.85/120.14 cut (((plus (n4) (n0)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H370].
% 119.85/120.14 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.85/120.14 congruence.
% 119.85/120.14 apply zenon_H9f. apply refl_equal.
% 119.85/120.14 exact (zenon_H370 zenon_H36a).
% 119.85/120.14 apply (zenon_L182_ zenon_TG_dq); trivial.
% 119.85/120.14 (* end of lemma zenon_L183_ *)
% 119.85/120.14 assert (zenon_L184_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.14 do 0 intro. intros zenon_H66 zenon_Hdb zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.14 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.85/120.14 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.85/120.14 generalize (zenon_He4 (n0)). zenon_intro zenon_H385.
% 119.85/120.14 generalize (zenon_H385 (succ (loopcounter))). zenon_intro zenon_H386.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H386); [ zenon_intro zenon_H7b | zenon_intro zenon_H387 ].
% 119.85/120.14 exact (zenon_H7b gt_1_0).
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H387); [ zenon_intro zenon_H140 | zenon_intro zenon_He3 ].
% 119.85/120.14 exact (zenon_H140 zenon_H146).
% 119.85/120.14 exact (zenon_Hdb zenon_He3).
% 119.85/120.14 apply (zenon_L83_); trivial.
% 119.85/120.14 (* end of lemma zenon_L184_ *)
% 119.85/120.14 assert (zenon_L185_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.85/120.14 do 0 intro. intros zenon_H66 zenon_Hd0 zenon_H67 zenon_H7d zenon_H155.
% 119.85/120.14 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.85/120.14 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.85/120.14 apply (zenon_L9_); trivial.
% 119.85/120.14 elim (classic (gt (n1) (succ (loopcounter)))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hdb ].
% 119.85/120.14 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.14 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.14 generalize (zenon_H78 (succ (loopcounter))). zenon_intro zenon_Hf6.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_Hf6); [ zenon_intro zenon_H6f | zenon_intro zenon_Hf7 ].
% 119.85/120.14 exact (zenon_H6f zenon_H67).
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_Hf7); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hf8 ].
% 119.85/120.14 exact (zenon_Hdb zenon_He3).
% 119.85/120.14 cut ((gt (succ (loopcounter)) (succ (loopcounter))) = (gt (succ (n0)) (succ (loopcounter)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_Hd0.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_Hf8.
% 119.85/120.14 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.85/120.14 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.85/120.14 congruence.
% 119.85/120.14 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.85/120.14 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.85/120.14 apply zenon_Hd2. apply sym_equal. exact zenon_Hd5.
% 119.85/120.14 exact (zenon_Hd3 zenon_Hd0).
% 119.85/120.14 apply zenon_H76. apply refl_equal.
% 119.85/120.14 apply (zenon_L184_); trivial.
% 119.85/120.14 (* end of lemma zenon_L185_ *)
% 119.85/120.14 assert (zenon_L186_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.14 do 0 intro. intros zenon_H66 zenon_H249 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.14 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.85/120.14 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.85/120.14 apply (zenon_L185_); trivial.
% 119.85/120.14 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1e6 ].
% 119.85/120.14 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.85/120.14 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.85/120.14 generalize (zenon_H78 (n3)). zenon_intro zenon_H20f.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H20f); [ zenon_intro zenon_H6f | zenon_intro zenon_H210 ].
% 119.85/120.14 exact (zenon_H6f zenon_H67).
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H210); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H211 ].
% 119.85/120.14 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.14 cut ((gt (succ (loopcounter)) (n3)) = (gt (succ (n0)) (n3))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H249.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H211.
% 119.85/120.14 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.85/120.14 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.85/120.14 congruence.
% 119.85/120.14 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.85/120.14 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.85/120.14 apply zenon_Hd2. apply sym_equal. exact zenon_Hd5.
% 119.85/120.14 apply zenon_Hd3. zenon_intro zenon_Hd6.
% 119.85/120.14 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.85/120.14 generalize (zenon_H8e (succ (loopcounter))). zenon_intro zenon_Hd7.
% 119.85/120.14 generalize (zenon_Hd7 (n3)). zenon_intro zenon_H388.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H388); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H389 ].
% 119.85/120.14 exact (zenon_Hd0 zenon_Hd6).
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H389); [ zenon_intro zenon_H21a | zenon_intro zenon_H248 ].
% 119.85/120.14 exact (zenon_H21a zenon_H211).
% 119.85/120.14 exact (zenon_H249 zenon_H248).
% 119.85/120.14 apply zenon_H201. apply refl_equal.
% 119.85/120.14 apply (zenon_L171_); trivial.
% 119.85/120.14 (* end of lemma zenon_L186_ *)
% 119.85/120.14 assert (zenon_L187_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> (~(gt (succ (n0)) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.14 do 0 intro. intros zenon_H155 zenon_H67 zenon_H7d zenon_H240 zenon_H66.
% 119.85/120.14 elim (classic ((n3) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H21c | zenon_intro zenon_H99 ].
% 119.85/120.14 elim (classic (gt (succ (n0)) (n3))); [ zenon_intro zenon_H248 | zenon_intro zenon_H249 ].
% 119.85/120.14 cut ((gt (succ (n0)) (n3)) = (gt (succ (n0)) (succ (succ (succ (n0)))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H240.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H248.
% 119.85/120.14 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 119.85/120.14 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.14 congruence.
% 119.85/120.14 apply zenon_H8c. apply refl_equal.
% 119.85/120.14 exact (zenon_H99 zenon_H21c).
% 119.85/120.14 apply (zenon_L186_); trivial.
% 119.85/120.14 elim (classic ((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ].
% 119.85/120.14 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0))))) = ((n3) = (succ (succ (succ (n0)))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H99.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H21d.
% 119.85/120.14 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.85/120.14 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_H21f successor_3).
% 119.85/120.14 apply zenon_H21e. apply refl_equal.
% 119.85/120.14 apply zenon_H21e. apply refl_equal.
% 119.85/120.14 (* end of lemma zenon_L187_ *)
% 119.85/120.14 assert (zenon_L188_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (n1))) -> False).
% 119.85/120.14 do 0 intro. intros zenon_H66 zenon_H205.
% 119.85/120.14 elim (classic ((~((succ (succ (n0))) = (n2)))/\(~(gt (succ (succ (n0))) (n2))))); [ zenon_intro zenon_H38a | zenon_intro zenon_H38b ].
% 119.85/120.14 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_H105. zenon_intro zenon_H38c.
% 119.85/120.14 exact (zenon_H105 successor_2).
% 119.85/120.14 cut ((gt (n2) (n1)) = (gt (succ (succ (n0))) (n1))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H205.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact gt_2_1.
% 119.85/120.14 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.85/120.14 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.85/120.14 congruence.
% 119.85/120.14 apply (zenon_notand_s _ _ zenon_H38b); [ zenon_intro zenon_H38e | zenon_intro zenon_H38d ].
% 119.85/120.14 apply zenon_H38e. zenon_intro successor_2.
% 119.85/120.14 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.85/120.14 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H102.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H103.
% 119.85/120.14 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.14 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_H105 successor_2).
% 119.85/120.14 apply zenon_H104. apply refl_equal.
% 119.85/120.14 apply zenon_H104. apply refl_equal.
% 119.85/120.14 apply zenon_H38d. zenon_intro zenon_H38f.
% 119.85/120.14 generalize (zenon_H66 (succ (succ (n0)))). zenon_intro zenon_H206.
% 119.85/120.14 generalize (zenon_H206 (n2)). zenon_intro zenon_H390.
% 119.85/120.14 generalize (zenon_H390 (n1)). zenon_intro zenon_H391.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H391); [ zenon_intro zenon_H38c | zenon_intro zenon_H392 ].
% 119.85/120.14 exact (zenon_H38c zenon_H38f).
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H392); [ zenon_intro zenon_Hba | zenon_intro zenon_H204 ].
% 119.85/120.14 exact (zenon_Hba gt_2_1).
% 119.85/120.14 exact (zenon_H205 zenon_H204).
% 119.85/120.14 apply zenon_H64. apply refl_equal.
% 119.85/120.14 (* end of lemma zenon_L188_ *)
% 119.85/120.14 assert (zenon_L189_ : (~(gt (succ (succ (n0))) (succ (succ (succ (n0)))))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.85/120.14 do 0 intro. intros zenon_H21b zenon_H7d zenon_H67 zenon_H155 zenon_H66.
% 119.85/120.14 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.85/120.14 elim (classic (gt (succ (succ (n0))) (n1))); [ zenon_intro zenon_H204 | zenon_intro zenon_H205 ].
% 119.85/120.14 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_Hfd | zenon_intro zenon_Hfe ].
% 119.85/120.14 elim (classic (gt (succ (n0)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H246 | zenon_intro zenon_H240 ].
% 119.85/120.14 generalize (zenon_H66 (succ (succ (n0)))). zenon_intro zenon_H206.
% 119.85/120.14 generalize (zenon_H206 (succ (n0))). zenon_intro zenon_H393.
% 119.85/120.14 generalize (zenon_H393 (succ (succ (succ (n0))))). zenon_intro zenon_H394.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H394); [ zenon_intro zenon_Hfe | zenon_intro zenon_H395 ].
% 119.85/120.14 exact (zenon_Hfe zenon_Hfd).
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H395); [ zenon_intro zenon_H240 | zenon_intro zenon_H233 ].
% 119.85/120.14 exact (zenon_H240 zenon_H246).
% 119.85/120.14 exact (zenon_H21b zenon_H233).
% 119.85/120.14 apply (zenon_L187_); trivial.
% 119.85/120.14 cut ((gt (succ (succ (n0))) (n1)) = (gt (succ (succ (n0))) (succ (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_Hfe.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H204.
% 119.85/120.14 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.85/120.14 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.85/120.14 congruence.
% 119.85/120.14 apply zenon_H104. apply refl_equal.
% 119.85/120.14 exact (zenon_H88 zenon_Hd1).
% 119.85/120.14 apply (zenon_L188_); trivial.
% 119.85/120.14 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.85/120.14 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H88.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact zenon_H8b.
% 119.85/120.14 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.85/120.14 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.85/120.14 congruence.
% 119.85/120.14 exact (zenon_H87 successor_1).
% 119.85/120.14 apply zenon_H8c. apply refl_equal.
% 119.85/120.14 apply zenon_H8c. apply refl_equal.
% 119.85/120.14 (* end of lemma zenon_L189_ *)
% 119.85/120.14 assert (zenon_L190_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.85/120.14 do 0 intro. intros zenon_H66 zenon_H220 zenon_H155 zenon_H7d zenon_H67.
% 119.85/120.14 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1e6 ].
% 119.85/120.14 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.85/120.14 generalize (zenon_H1a6 (n1)). zenon_intro zenon_H1a7.
% 119.85/120.14 generalize (zenon_H1a7 (n3)). zenon_intro zenon_H221.
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H221); [ zenon_intro zenon_Hba | zenon_intro zenon_H222 ].
% 119.85/120.14 exact (zenon_Hba gt_2_1).
% 119.85/120.14 apply (zenon_imply_s _ _ zenon_H222); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H223 ].
% 119.85/120.14 exact (zenon_H1e6 zenon_H1ee).
% 119.85/120.14 exact (zenon_H220 zenon_H223).
% 119.85/120.14 apply (zenon_L171_); trivial.
% 119.85/120.14 (* end of lemma zenon_L190_ *)
% 119.85/120.14 assert (zenon_L191_ : ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> False).
% 119.85/120.14 do 0 intro. intros zenon_H155 zenon_H7d zenon_H67 zenon_H66 zenon_H1a5.
% 119.85/120.14 elim (classic ((~((n2) = (n3)))/\(~(gt (n2) (n3))))); [ zenon_intro zenon_H224 | zenon_intro zenon_H225 ].
% 119.85/120.14 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H226. zenon_intro zenon_H220.
% 119.85/120.14 apply (zenon_L190_); trivial.
% 119.85/120.14 cut ((gt (n3) (n2)) = (gt (n2) (n2))).
% 119.85/120.14 intro zenon_D_pnotp.
% 119.85/120.14 apply zenon_H1a5.
% 119.85/120.14 rewrite <- zenon_D_pnotp.
% 119.85/120.14 exact gt_3_2.
% 119.85/120.14 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.85/120.14 cut (((n3) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H227].
% 119.85/120.14 congruence.
% 119.85/120.14 apply (zenon_notand_s _ _ zenon_H225); [ zenon_intro zenon_H229 | zenon_intro zenon_H228 ].
% 119.90/120.14 apply zenon_H229. zenon_intro zenon_H22a.
% 119.90/120.14 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H22b | zenon_intro zenon_H63 ].
% 119.90/120.14 cut (((n2) = (n2)) = ((n3) = (n2))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H227.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H22b.
% 119.90/120.14 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.90/120.14 cut (((n2) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H226].
% 119.90/120.14 congruence.
% 119.90/120.14 exact (zenon_H226 zenon_H22a).
% 119.90/120.14 apply zenon_H63. apply refl_equal.
% 119.90/120.14 apply zenon_H63. apply refl_equal.
% 119.90/120.14 apply zenon_H228. zenon_intro zenon_H223.
% 119.90/120.14 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.90/120.14 generalize (zenon_H1a6 (n3)). zenon_intro zenon_H22c.
% 119.90/120.14 generalize (zenon_H22c (n2)). zenon_intro zenon_H22d.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H22d); [ zenon_intro zenon_H220 | zenon_intro zenon_H22e ].
% 119.90/120.14 exact (zenon_H220 zenon_H223).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H22e); [ zenon_intro zenon_H22f | zenon_intro zenon_H1aa ].
% 119.90/120.14 exact (zenon_H22f gt_3_2).
% 119.90/120.14 exact (zenon_H1a5 zenon_H1aa).
% 119.90/120.14 apply zenon_H63. apply refl_equal.
% 119.90/120.14 (* end of lemma zenon_L191_ *)
% 119.90/120.14 assert (zenon_L192_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (loopcounter)))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.14 do 0 intro. intros zenon_H66 zenon_H16c zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.14 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H176 | zenon_intro zenon_H168 ].
% 119.90/120.14 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_H177 | zenon_intro zenon_H178 ].
% 119.90/120.14 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.90/120.14 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.90/120.14 generalize (zenon_H171 (n0)). zenon_intro zenon_H179.
% 119.90/120.14 generalize (zenon_H179 (succ (loopcounter))). zenon_intro zenon_H2eb.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H2eb); [ zenon_intro zenon_H178 | zenon_intro zenon_H2ec ].
% 119.90/120.14 exact (zenon_H178 zenon_H177).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H2ec); [ zenon_intro zenon_H140 | zenon_intro zenon_H175 ].
% 119.90/120.14 exact (zenon_H140 zenon_H146).
% 119.90/120.14 exact (zenon_H16c zenon_H175).
% 119.90/120.14 apply (zenon_L125_); trivial.
% 119.90/120.14 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H178.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H176.
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 exact (zenon_H16b succ_tptp_minus_1).
% 119.90/120.14 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.90/120.14 cut ((gt (n0) (succ (loopcounter))) = (gt (succ (tptp_minus_1)) (succ (loopcounter)))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H16c.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H146.
% 119.90/120.14 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.90/120.14 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.90/120.14 congruence.
% 119.90/120.14 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H167.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H16a.
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.14 congruence.
% 119.90/120.14 exact (zenon_H16b succ_tptp_minus_1).
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 apply zenon_H76. apply refl_equal.
% 119.90/120.14 apply (zenon_L123_); trivial.
% 119.90/120.14 (* end of lemma zenon_L192_ *)
% 119.90/120.14 assert (zenon_L193_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n1))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.14 do 0 intro. intros zenon_H66 zenon_Hee zenon_H67 zenon_H7d zenon_H155.
% 119.90/120.14 elim (classic ((~((loopcounter) = (n3)))/\(~(gt (loopcounter) (n3))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ].
% 119.90/120.14 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hc2. zenon_intro zenon_H1f5.
% 119.90/120.14 apply (zenon_L170_); trivial.
% 119.90/120.14 cut ((gt (n3) (n1)) = (gt (loopcounter) (n1))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_Hee.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact gt_3_1.
% 119.90/120.14 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.90/120.14 cut (((n3) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 119.90/120.14 congruence.
% 119.90/120.14 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f7 ].
% 119.90/120.14 apply zenon_H1f8. zenon_intro zenon_Hcb.
% 119.90/120.14 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.90/120.14 cut (((loopcounter) = (loopcounter)) = ((n3) = (loopcounter))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H1f6.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_Hed.
% 119.90/120.14 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.14 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.90/120.14 congruence.
% 119.90/120.14 exact (zenon_Hc2 zenon_Hcb).
% 119.90/120.14 apply zenon_H7c. apply refl_equal.
% 119.90/120.14 apply zenon_H7c. apply refl_equal.
% 119.90/120.14 apply zenon_H1f7. zenon_intro zenon_H1f9.
% 119.90/120.14 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.14 generalize (zenon_H13b (n3)). zenon_intro zenon_H1fa.
% 119.90/120.14 generalize (zenon_H1fa (n1)). zenon_intro zenon_H1fb.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H1fb); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1fc ].
% 119.90/120.14 exact (zenon_H1f5 zenon_H1f9).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H1fc); [ zenon_intro zenon_H1f2 | zenon_intro zenon_Hf1 ].
% 119.90/120.14 exact (zenon_H1f2 gt_3_1).
% 119.90/120.14 exact (zenon_Hee zenon_Hf1).
% 119.90/120.14 apply zenon_H64. apply refl_equal.
% 119.90/120.14 (* end of lemma zenon_L193_ *)
% 119.90/120.14 assert (zenon_L194_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (succ (succ (succ (n0)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.14 do 0 intro. intros zenon_H66 zenon_H23c zenon_H67 zenon_H7d zenon_H155.
% 119.90/120.14 elim (classic (gt (loopcounter) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H237 | zenon_intro zenon_H230 ].
% 119.90/120.14 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.14 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.14 generalize (zenon_Hf3 (succ (succ (succ (n0))))). zenon_intro zenon_H23d.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H23d); [ zenon_intro zenon_H92 | zenon_intro zenon_H23e ].
% 119.90/120.14 exact (zenon_H92 zenon_H7d).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H230 | zenon_intro zenon_H23f ].
% 119.90/120.14 exact (zenon_H230 zenon_H237).
% 119.90/120.14 exact (zenon_H23c zenon_H23f).
% 119.90/120.14 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H88 ].
% 119.90/120.14 elim (classic (gt (loopcounter) (n1))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hee ].
% 119.90/120.14 elim (classic (gt (loopcounter) (succ (n0)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Heb ].
% 119.90/120.14 elim (classic (gt (succ (n0)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H246 | zenon_intro zenon_H240 ].
% 119.90/120.14 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.14 generalize (zenon_H13b (succ (n0))). zenon_intro zenon_H147.
% 119.90/120.14 generalize (zenon_H147 (succ (succ (succ (n0))))). zenon_intro zenon_H396.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H396); [ zenon_intro zenon_Heb | zenon_intro zenon_H397 ].
% 119.90/120.14 exact (zenon_Heb zenon_Hef).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H397); [ zenon_intro zenon_H240 | zenon_intro zenon_H237 ].
% 119.90/120.14 exact (zenon_H240 zenon_H246).
% 119.90/120.14 exact (zenon_H230 zenon_H237).
% 119.90/120.14 apply (zenon_L187_); trivial.
% 119.90/120.14 cut ((gt (loopcounter) (n1)) = (gt (loopcounter) (succ (n0)))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_Heb.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_Hf1.
% 119.90/120.14 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 119.90/120.14 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H7c. apply refl_equal.
% 119.90/120.14 exact (zenon_H88 zenon_Hd1).
% 119.90/120.14 apply (zenon_L193_); trivial.
% 119.90/120.14 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.90/120.14 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H88.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H8b.
% 119.90/120.14 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.90/120.14 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.90/120.14 congruence.
% 119.90/120.14 exact (zenon_H87 successor_1).
% 119.90/120.14 apply zenon_H8c. apply refl_equal.
% 119.90/120.14 apply zenon_H8c. apply refl_equal.
% 119.90/120.14 (* end of lemma zenon_L194_ *)
% 119.90/120.14 assert (zenon_L195_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.14 do 0 intro. intros zenon_H66 zenon_H255 zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.14 elim (classic ((~((succ (tptp_minus_1)) = (succ (loopcounter))))/\(~(gt (succ (tptp_minus_1)) (succ (loopcounter)))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ].
% 119.90/120.14 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H25f. zenon_intro zenon_H16c.
% 119.90/120.14 apply (zenon_L192_); trivial.
% 119.90/120.14 elim (classic (gt (n1) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H23f | zenon_intro zenon_H23c ].
% 119.90/120.14 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.14 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.14 generalize (zenon_H78 (succ (succ (succ (n0))))). zenon_intro zenon_H241.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H241); [ zenon_intro zenon_H6f | zenon_intro zenon_H242 ].
% 119.90/120.14 exact (zenon_H6f zenon_H67).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H242); [ zenon_intro zenon_H23c | zenon_intro zenon_H243 ].
% 119.90/120.14 exact (zenon_H23c zenon_H23f).
% 119.90/120.14 cut ((gt (succ (loopcounter)) (succ (succ (succ (n0))))) = (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H255.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H243.
% 119.90/120.14 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.90/120.14 cut (((succ (loopcounter)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H260].
% 119.90/120.14 congruence.
% 119.90/120.14 apply (zenon_notand_s _ _ zenon_H25e); [ zenon_intro zenon_H262 | zenon_intro zenon_H261 ].
% 119.90/120.14 apply zenon_H262. zenon_intro zenon_H263.
% 119.90/120.14 apply zenon_H260. apply sym_equal. exact zenon_H263.
% 119.90/120.14 apply zenon_H261. zenon_intro zenon_H175.
% 119.90/120.14 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.90/120.14 generalize (zenon_H171 (succ (loopcounter))). zenon_intro zenon_H264.
% 119.90/120.14 generalize (zenon_H264 (succ (succ (succ (n0))))). zenon_intro zenon_H326.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H326); [ zenon_intro zenon_H16c | zenon_intro zenon_H327 ].
% 119.90/120.14 exact (zenon_H16c zenon_H175).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H327); [ zenon_intro zenon_H247 | zenon_intro zenon_H258 ].
% 119.90/120.14 exact (zenon_H247 zenon_H243).
% 119.90/120.14 exact (zenon_H255 zenon_H258).
% 119.90/120.14 apply zenon_H21e. apply refl_equal.
% 119.90/120.14 apply (zenon_L194_); trivial.
% 119.90/120.14 (* end of lemma zenon_L195_ *)
% 119.90/120.14 assert (zenon_L196_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (n0))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.14 do 0 intro. intros zenon_H66 zenon_H1da zenon_H67 zenon_H7d zenon_H155.
% 119.90/120.14 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H258 | zenon_intro zenon_H255 ].
% 119.90/120.14 elim (classic (gt (succ (tptp_minus_1)) (n3))); [ zenon_intro zenon_H267 | zenon_intro zenon_H25b ].
% 119.90/120.14 elim (classic (gt (n3) (succ (succ (n0))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H202 ].
% 119.90/120.14 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.90/120.14 generalize (zenon_H171 (n3)). zenon_intro zenon_H26c.
% 119.90/120.14 generalize (zenon_H26c (succ (succ (n0)))). zenon_intro zenon_H398.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H398); [ zenon_intro zenon_H25b | zenon_intro zenon_H399 ].
% 119.90/120.14 exact (zenon_H25b zenon_H267).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H399); [ zenon_intro zenon_H202 | zenon_intro zenon_H1dd ].
% 119.90/120.14 exact (zenon_H202 zenon_H24a).
% 119.90/120.14 exact (zenon_H1da zenon_H1dd).
% 119.90/120.14 apply (zenon_L86_); trivial.
% 119.90/120.14 cut ((gt (succ (tptp_minus_1)) (succ (succ (succ (n0))))) = (gt (succ (tptp_minus_1)) (n3))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H25b.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H258.
% 119.90/120.14 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 exact (zenon_H21f successor_3).
% 119.90/120.14 apply (zenon_L195_); trivial.
% 119.90/120.14 (* end of lemma zenon_L196_ *)
% 119.90/120.14 assert (zenon_L197_ : forall (zenon_TG_dq : zenon_U), ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n0) zenon_TG_dq)) -> (~(gt (succ (n3)) zenon_TG_dq)) -> (gt (succ zenon_TG_dq) (n0)) -> (gt (succ (n4)) zenon_TG_dq) -> (~((n0) = zenon_TG_dq)) -> (~((n1) = zenon_TG_dq)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.90/120.14 do 1 intro. intros zenon_H155 zenon_H7d zenon_H67 zenon_H39a zenon_H39b zenon_H5c zenon_H32e zenon_H334 zenon_H335 zenon_H66.
% 119.90/120.14 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.90/120.14 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.90/120.14 elim (classic (gt (n0) (succ (tptp_minus_1)))); [ zenon_intro zenon_H163 | zenon_intro zenon_H15d ].
% 119.90/120.14 elim (classic (gt (succ (tptp_minus_1)) zenon_TG_dq)); [ zenon_intro zenon_H39c | zenon_intro zenon_H39d ].
% 119.90/120.14 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.90/120.14 generalize (zenon_H142 (succ (tptp_minus_1))). zenon_intro zenon_H39e.
% 119.90/120.14 generalize (zenon_H39e zenon_TG_dq). zenon_intro zenon_H39f.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H39f); [ zenon_intro zenon_H15d | zenon_intro zenon_H3a0 ].
% 119.90/120.14 exact (zenon_H15d zenon_H163).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3a0); [ zenon_intro zenon_H39d | zenon_intro zenon_H3a1 ].
% 119.90/120.14 exact (zenon_H39d zenon_H39c).
% 119.90/120.14 exact (zenon_H39a zenon_H3a1).
% 119.90/120.14 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1da ].
% 119.90/120.14 elim (classic (gt (succ (tptp_minus_1)) (n2))); [ zenon_intro zenon_H1de | zenon_intro zenon_H1df ].
% 119.90/120.14 cut ((gt (succ (tptp_minus_1)) (n2)) = (gt (succ (tptp_minus_1)) zenon_TG_dq)).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H39d.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H1de.
% 119.90/120.14 cut (((n2) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H336].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 elim (classic (gt (n2) zenon_TG_dq)); [ zenon_intro zenon_H3a2 | zenon_intro zenon_H3a3 ].
% 119.90/120.14 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.90/120.14 generalize (zenon_H171 (n2)). zenon_intro zenon_H1e0.
% 119.90/120.14 generalize (zenon_H1e0 zenon_TG_dq). zenon_intro zenon_H3a4.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3a4); [ zenon_intro zenon_H1df | zenon_intro zenon_H3a5 ].
% 119.90/120.14 exact (zenon_H1df zenon_H1de).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3a5); [ zenon_intro zenon_H3a3 | zenon_intro zenon_H39c ].
% 119.90/120.14 exact (zenon_H3a3 zenon_H3a2).
% 119.90/120.14 exact (zenon_H39d zenon_H39c).
% 119.90/120.14 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.90/120.14 elim (classic (gt (n2) (n2))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1a5 ].
% 119.90/120.14 elim (classic (gt (n2) (succ (succ (n0))))); [ zenon_intro zenon_H314 | zenon_intro zenon_H315 ].
% 119.90/120.14 elim (classic (gt (succ (succ (n0))) zenon_TG_dq)); [ zenon_intro zenon_H3a6 | zenon_intro zenon_H3a7 ].
% 119.90/120.14 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.90/120.14 generalize (zenon_H1a6 (succ (succ (n0)))). zenon_intro zenon_H323.
% 119.90/120.14 generalize (zenon_H323 zenon_TG_dq). zenon_intro zenon_H3a8.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3a8); [ zenon_intro zenon_H315 | zenon_intro zenon_H3a9 ].
% 119.90/120.14 exact (zenon_H315 zenon_H314).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3a9); [ zenon_intro zenon_H3a7 | zenon_intro zenon_H3a2 ].
% 119.90/120.14 exact (zenon_H3a7 zenon_H3a6).
% 119.90/120.14 exact (zenon_H3a3 zenon_H3a2).
% 119.90/120.14 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H233 | zenon_intro zenon_H21b ].
% 119.90/120.14 elim (classic (gt (succ (succ (n0))) (n3))); [ zenon_intro zenon_H219 | zenon_intro zenon_H20b ].
% 119.90/120.14 cut ((gt (succ (succ (n0))) (n3)) = (gt (succ (succ (n0))) zenon_TG_dq)).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H3a7.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H219.
% 119.90/120.14 cut (((n3) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H337].
% 119.90/120.14 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H104. apply refl_equal.
% 119.90/120.14 elim (classic (gt (succ (n3)) (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_H3aa | zenon_intro zenon_H383 ].
% 119.90/120.14 elim (classic (gt (succ (n3)) (n4))); [ zenon_intro zenon_H3ab | zenon_intro zenon_H3ac ].
% 119.90/120.14 cut ((gt (succ (n3)) (n4)) = (gt (succ (n3)) zenon_TG_dq)).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H39b.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H3ab.
% 119.90/120.14 cut (((n4) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H338].
% 119.90/120.14 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H9f. apply refl_equal.
% 119.90/120.14 elim (classic (gt (n4) zenon_TG_dq)); [ zenon_intro zenon_H3ad | zenon_intro zenon_H344 ].
% 119.90/120.14 generalize (zenon_H66 (succ (n3))). zenon_intro zenon_Hb5.
% 119.90/120.14 generalize (zenon_Hb5 (n4)). zenon_intro zenon_H3ae.
% 119.90/120.14 generalize (zenon_H3ae zenon_TG_dq). zenon_intro zenon_H3af.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3af); [ zenon_intro zenon_H3ac | zenon_intro zenon_H3b0 ].
% 119.90/120.14 exact (zenon_H3ac zenon_H3ab).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3b0); [ zenon_intro zenon_H344 | zenon_intro zenon_H3b1 ].
% 119.90/120.14 exact (zenon_H344 zenon_H3ad).
% 119.90/120.14 exact (zenon_H39b zenon_H3b1).
% 119.90/120.14 apply (zenon_L175_ zenon_TG_dq); trivial.
% 119.90/120.14 cut ((gt (succ (n3)) (succ (succ (succ (succ (n0)))))) = (gt (succ (n3)) (n4))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H3ac.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H3aa.
% 119.90/120.14 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 119.90/120.14 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H9f. apply refl_equal.
% 119.90/120.14 exact (zenon_Ha3 successor_4).
% 119.90/120.14 generalize (finite_domain_0 (loopcounter)). zenon_intro zenon_H94.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ].
% 119.90/120.14 apply (zenon_notand_s _ _ zenon_H96); [ zenon_intro zenon_H68 | zenon_intro zenon_H7e ].
% 119.90/120.14 apply (zenon_L5_); trivial.
% 119.90/120.14 apply (zenon_L7_); trivial.
% 119.90/120.14 generalize (finite_domain_0 (n1)). zenon_intro zenon_H107.
% 119.90/120.14 generalize (finite_domain_4 zenon_TG_dq). zenon_intro zenon_H339.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H339); [ zenon_intro zenon_H33b | zenon_intro zenon_H33a ].
% 119.90/120.14 apply (zenon_notand_s _ _ zenon_H33b); [ zenon_intro zenon_H5d | zenon_intro zenon_H32f ].
% 119.90/120.14 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.14 apply (zenon_L173_ zenon_TG_dq); trivial.
% 119.90/120.14 apply (zenon_or_s _ _ zenon_H33a); [ zenon_intro zenon_H33d | zenon_intro zenon_H33c ].
% 119.90/120.14 apply zenon_H334. apply sym_equal. exact zenon_H33d.
% 119.90/120.14 apply (zenon_or_s _ _ zenon_H33c); [ zenon_intro zenon_H33f | zenon_intro zenon_H33e ].
% 119.90/120.14 apply zenon_H335. apply sym_equal. exact zenon_H33f.
% 119.90/120.14 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H341 | zenon_intro zenon_H340 ].
% 119.90/120.14 apply zenon_H336. apply sym_equal. exact zenon_H341.
% 119.90/120.14 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H343 | zenon_intro zenon_H342 ].
% 119.90/120.14 apply zenon_H337. apply sym_equal. exact zenon_H343.
% 119.90/120.14 apply (zenon_L183_ zenon_TG_dq); trivial.
% 119.90/120.14 cut ((gt (succ (succ (n0))) (succ (succ (succ (n0))))) = (gt (succ (succ (n0))) (n3))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H20b.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H233.
% 119.90/120.14 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.90/120.14 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H104. apply refl_equal.
% 119.90/120.14 exact (zenon_H21f successor_3).
% 119.90/120.14 apply (zenon_L189_); trivial.
% 119.90/120.14 cut ((gt (n2) (n2)) = (gt (n2) (succ (succ (n0))))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H315.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H1aa.
% 119.90/120.14 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.90/120.14 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H63. apply refl_equal.
% 119.90/120.14 exact (zenon_H102 zenon_H1b9).
% 119.90/120.14 apply (zenon_L191_); trivial.
% 119.90/120.14 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.90/120.14 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H102.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H103.
% 119.90/120.14 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.90/120.14 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.90/120.14 congruence.
% 119.90/120.14 exact (zenon_H105 successor_2).
% 119.90/120.14 apply zenon_H104. apply refl_equal.
% 119.90/120.14 apply zenon_H104. apply refl_equal.
% 119.90/120.14 cut ((gt (succ (tptp_minus_1)) (succ (succ (n0)))) = (gt (succ (tptp_minus_1)) (n2))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H1df.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H1dd.
% 119.90/120.14 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 exact (zenon_H105 successor_2).
% 119.90/120.14 apply (zenon_L196_); trivial.
% 119.90/120.14 cut ((gt (n0) (n0)) = (gt (n0) (succ (tptp_minus_1)))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H15d.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H141.
% 119.90/120.14 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.90/120.14 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.90/120.14 congruence.
% 119.90/120.14 apply zenon_H65. apply refl_equal.
% 119.90/120.14 exact (zenon_H167 zenon_H180).
% 119.90/120.14 apply (zenon_L146_); trivial.
% 119.90/120.14 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H167.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H16a.
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.14 congruence.
% 119.90/120.14 exact (zenon_H16b succ_tptp_minus_1).
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 (* end of lemma zenon_L197_ *)
% 119.90/120.14 assert (zenon_L198_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(leq (n0) (tptp_minus_1))) -> False).
% 119.90/120.14 do 0 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H3b2.
% 119.90/120.14 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 119.90/120.14 generalize (zenon_H5f (tptp_minus_1)). zenon_intro zenon_H3b3.
% 119.90/120.14 apply (zenon_equiv_s _ _ zenon_H3b3); [ zenon_intro zenon_H3b2; zenon_intro zenon_H178 | zenon_intro zenon_H3b4; zenon_intro zenon_H177 ].
% 119.90/120.14 elim (classic ((~((succ (tptp_minus_1)) = (n3)))/\(~(gt (succ (tptp_minus_1)) (n3))))); [ zenon_intro zenon_H259 | zenon_intro zenon_H25a ].
% 119.90/120.14 apply (zenon_and_s _ _ zenon_H259). zenon_intro zenon_H25c. zenon_intro zenon_H25b.
% 119.90/120.14 elim (classic ((~((succ (tptp_minus_1)) = (succ (loopcounter))))/\(~(gt (succ (tptp_minus_1)) (succ (loopcounter)))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ].
% 119.90/120.14 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H25f. zenon_intro zenon_H16c.
% 119.90/120.14 apply (zenon_L192_); trivial.
% 119.90/120.14 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1e6 ].
% 119.90/120.14 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.14 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.14 generalize (zenon_H78 (n3)). zenon_intro zenon_H20f.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H20f); [ zenon_intro zenon_H6f | zenon_intro zenon_H210 ].
% 119.90/120.14 exact (zenon_H6f zenon_H67).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H210); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H211 ].
% 119.90/120.14 exact (zenon_H1e6 zenon_H1ee).
% 119.90/120.14 cut ((gt (succ (loopcounter)) (n3)) = (gt (succ (tptp_minus_1)) (n3))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H25b.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H211.
% 119.90/120.14 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.90/120.14 cut (((succ (loopcounter)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H260].
% 119.90/120.14 congruence.
% 119.90/120.14 apply (zenon_notand_s _ _ zenon_H25e); [ zenon_intro zenon_H262 | zenon_intro zenon_H261 ].
% 119.90/120.14 apply zenon_H262. zenon_intro zenon_H263.
% 119.90/120.14 apply zenon_H260. apply sym_equal. exact zenon_H263.
% 119.90/120.14 apply zenon_H261. zenon_intro zenon_H175.
% 119.90/120.14 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.90/120.14 generalize (zenon_H171 (succ (loopcounter))). zenon_intro zenon_H264.
% 119.90/120.14 generalize (zenon_H264 (n3)). zenon_intro zenon_H265.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H265); [ zenon_intro zenon_H16c | zenon_intro zenon_H266 ].
% 119.90/120.14 exact (zenon_H16c zenon_H175).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H266); [ zenon_intro zenon_H21a | zenon_intro zenon_H267 ].
% 119.90/120.14 exact (zenon_H21a zenon_H211).
% 119.90/120.14 exact (zenon_H25b zenon_H267).
% 119.90/120.14 apply zenon_H201. apply refl_equal.
% 119.90/120.14 apply (zenon_L171_); trivial.
% 119.90/120.14 cut ((gt (n3) (n0)) = (gt (succ (tptp_minus_1)) (n0))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H178.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact gt_3_0.
% 119.90/120.14 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.90/120.14 cut (((n3) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H268].
% 119.90/120.14 congruence.
% 119.90/120.14 apply (zenon_notand_s _ _ zenon_H25a); [ zenon_intro zenon_H26a | zenon_intro zenon_H269 ].
% 119.90/120.14 apply zenon_H26a. zenon_intro zenon_H26b.
% 119.90/120.14 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n3) = (succ (tptp_minus_1)))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H268.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H16a.
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.14 cut (((succ (tptp_minus_1)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H25c].
% 119.90/120.14 congruence.
% 119.90/120.14 exact (zenon_H25c zenon_H26b).
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 apply zenon_H169. apply refl_equal.
% 119.90/120.14 apply zenon_H269. zenon_intro zenon_H267.
% 119.90/120.14 generalize (zenon_H66 (succ (tptp_minus_1))). zenon_intro zenon_H171.
% 119.90/120.14 generalize (zenon_H171 (n3)). zenon_intro zenon_H26c.
% 119.90/120.14 generalize (zenon_H26c (n0)). zenon_intro zenon_H3b5.
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3b5); [ zenon_intro zenon_H25b | zenon_intro zenon_H3b6 ].
% 119.90/120.14 exact (zenon_H25b zenon_H267).
% 119.90/120.14 apply (zenon_imply_s _ _ zenon_H3b6); [ zenon_intro zenon_H291 | zenon_intro zenon_H177 ].
% 119.90/120.14 exact (zenon_H291 gt_3_0).
% 119.90/120.14 exact (zenon_H178 zenon_H177).
% 119.90/120.14 apply zenon_H65. apply refl_equal.
% 119.90/120.14 exact (zenon_H3b2 zenon_H3b4).
% 119.90/120.14 (* end of lemma zenon_L198_ *)
% 119.90/120.14 assert (zenon_L199_ : (~((tptp_minus_1) = (tptp_minus_1))) -> False).
% 119.90/120.14 do 0 intro. intros zenon_H3b7.
% 119.90/120.14 apply zenon_H3b7. apply refl_equal.
% 119.90/120.14 (* end of lemma zenon_L199_ *)
% 119.90/120.14 assert (zenon_L200_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(leq (tptp_minus_1) (n3))) -> False).
% 119.90/120.14 do 0 intro. intros zenon_H66 zenon_H3b8.
% 119.90/120.14 generalize (leq_succ_gt_equiv (tptp_minus_1)). zenon_intro zenon_H3b9.
% 119.90/120.14 generalize (zenon_H3b9 (n3)). zenon_intro zenon_H3ba.
% 119.90/120.14 apply (zenon_equiv_s _ _ zenon_H3ba); [ zenon_intro zenon_H3b8; zenon_intro zenon_H3bd | zenon_intro zenon_H3bc; zenon_intro zenon_H3bb ].
% 119.90/120.14 elim (classic ((~((succ (n3)) = (n2)))/\(~(gt (succ (n3)) (n2))))); [ zenon_intro zenon_Had | zenon_intro zenon_Hae ].
% 119.90/120.14 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_Haf. zenon_intro zenon_H9a.
% 119.90/120.14 apply (zenon_L11_); trivial.
% 119.90/120.14 cut ((gt (n2) (tptp_minus_1)) = (gt (succ (n3)) (tptp_minus_1))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_H3bd.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact gt_2_tptp_minus_1.
% 119.90/120.14 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.14 cut (((n2) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 119.90/120.14 congruence.
% 119.90/120.14 apply (zenon_notand_s _ _ zenon_Hae); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb1 ].
% 119.90/120.14 apply zenon_Hb2. zenon_intro zenon_Hb3.
% 119.90/120.14 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ].
% 119.90/120.14 cut (((succ (n3)) = (succ (n3))) = ((n2) = (succ (n3)))).
% 119.90/120.14 intro zenon_D_pnotp.
% 119.90/120.14 apply zenon_Hb0.
% 119.90/120.14 rewrite <- zenon_D_pnotp.
% 119.90/120.14 exact zenon_H9e.
% 119.90/120.14 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.90/120.14 cut (((succ (n3)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 119.90/120.14 congruence.
% 119.90/120.14 exact (zenon_Haf zenon_Hb3).
% 119.90/120.14 apply zenon_H9f. apply refl_equal.
% 119.90/120.14 apply zenon_H9f. apply refl_equal.
% 119.90/120.15 apply zenon_Hb1. zenon_intro zenon_Hb4.
% 119.90/120.15 generalize (zenon_H66 (succ (n3))). zenon_intro zenon_Hb5.
% 119.90/120.15 generalize (zenon_Hb5 (n2)). zenon_intro zenon_Hb6.
% 119.90/120.15 generalize (zenon_Hb6 (tptp_minus_1)). zenon_intro zenon_H3be.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3be); [ zenon_intro zenon_H9a | zenon_intro zenon_H3bf ].
% 119.90/120.15 exact (zenon_H9a zenon_Hb4).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3bf); [ zenon_intro zenon_H3c0 | zenon_intro zenon_H3bb ].
% 119.90/120.15 exact (zenon_H3c0 gt_2_tptp_minus_1).
% 119.90/120.15 exact (zenon_H3bd zenon_H3bb).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 exact (zenon_H3b8 zenon_H3bc).
% 119.90/120.15 (* end of lemma zenon_L200_ *)
% 119.90/120.15 assert (zenon_L201_ : ((tptp_minus_1) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (tptp_minus_1))) -> False).
% 119.90/120.15 do 0 intro. intros zenon_H3c1 zenon_H66 zenon_H3c2.
% 119.90/120.15 elim (classic ((~((tptp_minus_1) = (n0)))/\(~(gt (tptp_minus_1) (n0))))); [ zenon_intro zenon_H3c3 | zenon_intro zenon_H3c4 ].
% 119.90/120.15 apply (zenon_and_s _ _ zenon_H3c3). zenon_intro zenon_H3c6. zenon_intro zenon_H3c5.
% 119.90/120.15 exact (zenon_H3c6 zenon_H3c1).
% 119.90/120.15 cut ((gt (n0) (tptp_minus_1)) = (gt (tptp_minus_1) (tptp_minus_1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3c2.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact gt_0_tptp_minus_1.
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 cut (((n0) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3c7].
% 119.90/120.15 congruence.
% 119.90/120.15 apply (zenon_notand_s _ _ zenon_H3c4); [ zenon_intro zenon_H3c9 | zenon_intro zenon_H3c8 ].
% 119.90/120.15 apply zenon_H3c9. zenon_intro zenon_H3c1.
% 119.90/120.15 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3b7 ].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n0) = (tptp_minus_1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3c7.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3ca.
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3c6].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H3c6 zenon_H3c1).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H3c8. zenon_intro zenon_H3cb.
% 119.90/120.15 generalize (zenon_H66 (tptp_minus_1)). zenon_intro zenon_H3cc.
% 119.90/120.15 generalize (zenon_H3cc (n0)). zenon_intro zenon_H3cd.
% 119.90/120.15 generalize (zenon_H3cd (tptp_minus_1)). zenon_intro zenon_H3ce.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3ce); [ zenon_intro zenon_H3c5 | zenon_intro zenon_H3cf ].
% 119.90/120.15 exact (zenon_H3c5 zenon_H3cb).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3cf); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3d0 ].
% 119.90/120.15 exact (zenon_H3d1 gt_0_tptp_minus_1).
% 119.90/120.15 exact (zenon_H3c2 zenon_H3d0).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 (* end of lemma zenon_L201_ *)
% 119.90/120.15 assert (zenon_L202_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TG_dq zenon_TG_dq)) -> ((tptp_minus_1) = (n0)) -> (zenon_TG_dq = (n0)) -> False).
% 119.90/120.15 do 1 intro. intros zenon_H66 zenon_H3d2 zenon_H3c1 zenon_H33d.
% 119.90/120.15 elim (classic (gt (n0) zenon_TG_dq)); [ zenon_intro zenon_H3a1 | zenon_intro zenon_H39a ].
% 119.90/120.15 cut ((gt (n0) zenon_TG_dq) = (gt zenon_TG_dq zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3d2.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3a1.
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.15 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.15 congruence.
% 119.90/120.15 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq) = ((n0) = zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H334.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3d4.
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.15 cut ((zenon_TG_dq = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3d5].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H3d5 zenon_H33d).
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 elim (classic (gt (tptp_minus_1) zenon_TG_dq)); [ zenon_intro zenon_H3d6 | zenon_intro zenon_H3d7 ].
% 119.90/120.15 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.90/120.15 generalize (zenon_H142 (tptp_minus_1)). zenon_intro zenon_H3d8.
% 119.90/120.15 generalize (zenon_H3d8 zenon_TG_dq). zenon_intro zenon_H3d9.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3d9); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3da ].
% 119.90/120.15 exact (zenon_H3d1 gt_0_tptp_minus_1).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3da); [ zenon_intro zenon_H3d7 | zenon_intro zenon_H3a1 ].
% 119.90/120.15 exact (zenon_H3d7 zenon_H3d6).
% 119.90/120.15 exact (zenon_H39a zenon_H3a1).
% 119.90/120.15 elim (classic (gt (tptp_minus_1) (tptp_minus_1))); [ zenon_intro zenon_H3d0 | zenon_intro zenon_H3c2 ].
% 119.90/120.15 elim (classic (gt (tptp_minus_1) (n0))); [ zenon_intro zenon_H3cb | zenon_intro zenon_H3c5 ].
% 119.90/120.15 cut ((gt (tptp_minus_1) (n0)) = (gt (tptp_minus_1) zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3d7.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3cb.
% 119.90/120.15 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H334. apply sym_equal. exact zenon_H33d.
% 119.90/120.15 cut ((gt (tptp_minus_1) (tptp_minus_1)) = (gt (tptp_minus_1) (n0))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3c5.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3d0.
% 119.90/120.15 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3c6].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 exact (zenon_H3c6 zenon_H3c1).
% 119.90/120.15 apply (zenon_L201_); trivial.
% 119.90/120.15 (* end of lemma zenon_L202_ *)
% 119.90/120.15 assert (zenon_L203_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((tptp_minus_1) = (n0)) -> (zenon_TG_dq = (n0)) -> False).
% 119.90/120.15 do 1 intro. intros zenon_H66 zenon_H3c1 zenon_H33d.
% 119.90/120.15 generalize (irreflexivity_gt zenon_TG_dq). zenon_intro zenon_H3d2.
% 119.90/120.15 apply (zenon_L202_ zenon_TG_dq); trivial.
% 119.90/120.15 (* end of lemma zenon_L203_ *)
% 119.90/120.15 assert (zenon_L204_ : ((tptp_minus_1) = (n1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (tptp_minus_1))) -> False).
% 119.90/120.15 do 0 intro. intros zenon_H3db zenon_H66 zenon_H3c2.
% 119.90/120.15 elim (classic ((~((tptp_minus_1) = (n1)))/\(~(gt (tptp_minus_1) (n1))))); [ zenon_intro zenon_H3dc | zenon_intro zenon_H3dd ].
% 119.90/120.15 apply (zenon_and_s _ _ zenon_H3dc). zenon_intro zenon_H3df. zenon_intro zenon_H3de.
% 119.90/120.15 exact (zenon_H3df zenon_H3db).
% 119.90/120.15 cut ((gt (n1) (tptp_minus_1)) = (gt (tptp_minus_1) (tptp_minus_1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3c2.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact gt_1_tptp_minus_1.
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 cut (((n1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3e0].
% 119.90/120.15 congruence.
% 119.90/120.15 apply (zenon_notand_s _ _ zenon_H3dd); [ zenon_intro zenon_H3e2 | zenon_intro zenon_H3e1 ].
% 119.90/120.15 apply zenon_H3e2. zenon_intro zenon_H3db.
% 119.90/120.15 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3b7 ].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n1) = (tptp_minus_1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3e0.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3ca.
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 cut (((tptp_minus_1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H3df].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H3df zenon_H3db).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H3e1. zenon_intro zenon_H3e3.
% 119.90/120.15 generalize (zenon_H66 (tptp_minus_1)). zenon_intro zenon_H3cc.
% 119.90/120.15 generalize (zenon_H3cc (n1)). zenon_intro zenon_H3e4.
% 119.90/120.15 generalize (zenon_H3e4 (tptp_minus_1)). zenon_intro zenon_H3e5.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3e5); [ zenon_intro zenon_H3de | zenon_intro zenon_H3e6 ].
% 119.90/120.15 exact (zenon_H3de zenon_H3e3).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3e6); [ zenon_intro zenon_H3e7 | zenon_intro zenon_H3d0 ].
% 119.90/120.15 exact (zenon_H3e7 gt_1_tptp_minus_1).
% 119.90/120.15 exact (zenon_H3c2 zenon_H3d0).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 (* end of lemma zenon_L204_ *)
% 119.90/120.15 assert (zenon_L205_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(leq (tptp_minus_1) (n0))) -> False).
% 119.90/120.15 do 0 intro. intros zenon_H66 zenon_H7d zenon_H67 zenon_H155 zenon_H3e8.
% 119.90/120.15 generalize (leq_succ_gt_equiv (tptp_minus_1)). zenon_intro zenon_H3b9.
% 119.90/120.15 generalize (zenon_H3b9 (n0)). zenon_intro zenon_H3e9.
% 119.90/120.15 apply (zenon_equiv_s _ _ zenon_H3e9); [ zenon_intro zenon_H3e8; zenon_intro zenon_H3ec | zenon_intro zenon_H3eb; zenon_intro zenon_H3ea ].
% 119.90/120.15 elim (classic ((~((succ (n0)) = (n3)))/\(~(gt (succ (n0)) (n3))))); [ zenon_intro zenon_H3ed | zenon_intro zenon_H3ee ].
% 119.90/120.15 apply (zenon_and_s _ _ zenon_H3ed). zenon_intro zenon_H3ef. zenon_intro zenon_H249.
% 119.90/120.15 apply (zenon_L186_); trivial.
% 119.90/120.15 cut ((gt (n3) (tptp_minus_1)) = (gt (succ (n0)) (tptp_minus_1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3ec.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact gt_3_tptp_minus_1.
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 cut (((n3) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H3f0].
% 119.90/120.15 congruence.
% 119.90/120.15 apply (zenon_notand_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f2 | zenon_intro zenon_H3f1 ].
% 119.90/120.15 apply zenon_H3f2. zenon_intro zenon_H3f3.
% 119.90/120.15 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.90/120.15 cut (((succ (n0)) = (succ (n0))) = ((n3) = (succ (n0)))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3f0.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H8b.
% 119.90/120.15 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.90/120.15 cut (((succ (n0)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H3ef].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H3ef zenon_H3f3).
% 119.90/120.15 apply zenon_H8c. apply refl_equal.
% 119.90/120.15 apply zenon_H8c. apply refl_equal.
% 119.90/120.15 apply zenon_H3f1. zenon_intro zenon_H248.
% 119.90/120.15 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.90/120.15 generalize (zenon_H8e (n3)). zenon_intro zenon_H24b.
% 119.90/120.15 generalize (zenon_H24b (tptp_minus_1)). zenon_intro zenon_H3f4.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3f4); [ zenon_intro zenon_H249 | zenon_intro zenon_H3f5 ].
% 119.90/120.15 exact (zenon_H249 zenon_H248).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3f5); [ zenon_intro zenon_H3f6 | zenon_intro zenon_H3ea ].
% 119.90/120.15 exact (zenon_H3f6 gt_3_tptp_minus_1).
% 119.90/120.15 exact (zenon_H3ec zenon_H3ea).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 exact (zenon_H3e8 zenon_H3eb).
% 119.90/120.15 (* end of lemma zenon_L205_ *)
% 119.90/120.15 assert (zenon_L206_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TG_dq zenon_TG_dq)) -> ((tptp_minus_1) = (n1)) -> (zenon_TG_dq = (n0)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.15 do 1 intro. intros zenon_H66 zenon_H3d2 zenon_H3db zenon_H33d zenon_H3c1.
% 119.90/120.15 elim (classic (gt (n0) zenon_TG_dq)); [ zenon_intro zenon_H3a1 | zenon_intro zenon_H39a ].
% 119.90/120.15 cut ((gt (n0) zenon_TG_dq) = (gt zenon_TG_dq zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3d2.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3a1.
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.15 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.15 congruence.
% 119.90/120.15 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq) = ((n0) = zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H334.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3d4.
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.15 cut ((zenon_TG_dq = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3d5].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H3d5 zenon_H33d).
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 elim (classic (gt (tptp_minus_1) zenon_TG_dq)); [ zenon_intro zenon_H3d6 | zenon_intro zenon_H3d7 ].
% 119.90/120.15 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.90/120.15 generalize (zenon_H142 (tptp_minus_1)). zenon_intro zenon_H3d8.
% 119.90/120.15 generalize (zenon_H3d8 zenon_TG_dq). zenon_intro zenon_H3d9.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3d9); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3da ].
% 119.90/120.15 exact (zenon_H3d1 gt_0_tptp_minus_1).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3da); [ zenon_intro zenon_H3d7 | zenon_intro zenon_H3a1 ].
% 119.90/120.15 exact (zenon_H3d7 zenon_H3d6).
% 119.90/120.15 exact (zenon_H39a zenon_H3a1).
% 119.90/120.15 elim (classic (gt (tptp_minus_1) (tptp_minus_1))); [ zenon_intro zenon_H3d0 | zenon_intro zenon_H3c2 ].
% 119.90/120.15 elim (classic (gt (tptp_minus_1) (n0))); [ zenon_intro zenon_H3cb | zenon_intro zenon_H3c5 ].
% 119.90/120.15 cut ((gt (tptp_minus_1) (n0)) = (gt (tptp_minus_1) zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3d7.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3cb.
% 119.90/120.15 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H334. apply sym_equal. exact zenon_H33d.
% 119.90/120.15 cut ((gt (tptp_minus_1) (tptp_minus_1)) = (gt (tptp_minus_1) (n0))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3c5.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3d0.
% 119.90/120.15 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3c6].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 exact (zenon_H3c6 zenon_H3c1).
% 119.90/120.15 apply (zenon_L204_); trivial.
% 119.90/120.15 (* end of lemma zenon_L206_ *)
% 119.90/120.15 assert (zenon_L207_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((tptp_minus_1) = (n1)) -> (zenon_TG_dq = (n0)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.15 do 1 intro. intros zenon_H66 zenon_H3db zenon_H33d zenon_H3c1.
% 119.90/120.15 generalize (irreflexivity_gt zenon_TG_dq). zenon_intro zenon_H3d2.
% 119.90/120.15 apply (zenon_L206_ zenon_TG_dq); trivial.
% 119.90/120.15 (* end of lemma zenon_L207_ *)
% 119.90/120.15 assert (zenon_L208_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((tptp_minus_1) = (n1)) -> (zenon_TG_dq = (n0)) -> False).
% 119.90/120.15 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H3db zenon_H33d.
% 119.90/120.15 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H3f7.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3f7); [ zenon_intro zenon_H3f8 | zenon_intro zenon_H3c1 ].
% 119.90/120.15 apply (zenon_notand_s _ _ zenon_H3f8); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3e8 ].
% 119.90/120.15 apply (zenon_L198_); trivial.
% 119.90/120.15 apply (zenon_L205_); trivial.
% 119.90/120.15 apply (zenon_L207_ zenon_TG_dq); trivial.
% 119.90/120.15 (* end of lemma zenon_L208_ *)
% 119.90/120.15 assert (zenon_L209_ : ((tptp_minus_1) = (n2)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (tptp_minus_1))) -> False).
% 119.90/120.15 do 0 intro. intros zenon_H3f9 zenon_H66 zenon_H3c2.
% 119.90/120.15 elim (classic ((~((tptp_minus_1) = (n2)))/\(~(gt (tptp_minus_1) (n2))))); [ zenon_intro zenon_H3fa | zenon_intro zenon_H3fb ].
% 119.90/120.15 apply (zenon_and_s _ _ zenon_H3fa). zenon_intro zenon_H3fd. zenon_intro zenon_H3fc.
% 119.90/120.15 exact (zenon_H3fd zenon_H3f9).
% 119.90/120.15 cut ((gt (n2) (tptp_minus_1)) = (gt (tptp_minus_1) (tptp_minus_1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3c2.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact gt_2_tptp_minus_1.
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 cut (((n2) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3fe].
% 119.90/120.15 congruence.
% 119.90/120.15 apply (zenon_notand_s _ _ zenon_H3fb); [ zenon_intro zenon_H400 | zenon_intro zenon_H3ff ].
% 119.90/120.15 apply zenon_H400. zenon_intro zenon_H3f9.
% 119.90/120.15 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3b7 ].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n2) = (tptp_minus_1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3fe.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3ca.
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 cut (((tptp_minus_1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H3fd].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H3fd zenon_H3f9).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H3ff. zenon_intro zenon_H401.
% 119.90/120.15 generalize (zenon_H66 (tptp_minus_1)). zenon_intro zenon_H3cc.
% 119.90/120.15 generalize (zenon_H3cc (n2)). zenon_intro zenon_H402.
% 119.90/120.15 generalize (zenon_H402 (tptp_minus_1)). zenon_intro zenon_H403.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H403); [ zenon_intro zenon_H3fc | zenon_intro zenon_H404 ].
% 119.90/120.15 exact (zenon_H3fc zenon_H401).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H404); [ zenon_intro zenon_H3c0 | zenon_intro zenon_H3d0 ].
% 119.90/120.15 exact (zenon_H3c0 gt_2_tptp_minus_1).
% 119.90/120.15 exact (zenon_H3c2 zenon_H3d0).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 (* end of lemma zenon_L209_ *)
% 119.90/120.15 assert (zenon_L210_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(leq (tptp_minus_1) (n0))) -> False).
% 119.90/120.15 do 0 intro. intros zenon_H66 zenon_H7d zenon_H67 zenon_H155 zenon_H3e8.
% 119.90/120.15 generalize (leq_succ_gt_equiv (tptp_minus_1)). zenon_intro zenon_H3b9.
% 119.90/120.15 generalize (zenon_H3b9 (n0)). zenon_intro zenon_H3e9.
% 119.90/120.15 apply (zenon_equiv_s _ _ zenon_H3e9); [ zenon_intro zenon_H3e8; zenon_intro zenon_H3ec | zenon_intro zenon_H3eb; zenon_intro zenon_H3ea ].
% 119.90/120.15 elim (classic ((~((succ (n0)) = (n3)))/\(~(gt (succ (n0)) (n3))))); [ zenon_intro zenon_H3ed | zenon_intro zenon_H3ee ].
% 119.90/120.15 apply (zenon_and_s _ _ zenon_H3ed). zenon_intro zenon_H3ef. zenon_intro zenon_H249.
% 119.90/120.15 apply (zenon_L186_); trivial.
% 119.90/120.15 cut ((gt (n3) (tptp_minus_1)) = (gt (succ (n0)) (tptp_minus_1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3ec.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact gt_3_tptp_minus_1.
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 cut (((n3) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H3f0].
% 119.90/120.15 congruence.
% 119.90/120.15 apply (zenon_notand_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f2 | zenon_intro zenon_H3f1 ].
% 119.90/120.15 apply zenon_H3f2. zenon_intro zenon_H3f3.
% 119.90/120.15 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.90/120.15 cut (((succ (n0)) = (succ (n0))) = ((n3) = (succ (n0)))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3f0.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H8b.
% 119.90/120.15 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.90/120.15 cut (((succ (n0)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H3ef].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H3ef zenon_H3f3).
% 119.90/120.15 apply zenon_H8c. apply refl_equal.
% 119.90/120.15 apply zenon_H8c. apply refl_equal.
% 119.90/120.15 apply zenon_H3f1. zenon_intro zenon_H248.
% 119.90/120.15 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.90/120.15 generalize (zenon_H8e (n3)). zenon_intro zenon_H24b.
% 119.90/120.15 generalize (zenon_H24b (tptp_minus_1)). zenon_intro zenon_H3f4.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3f4); [ zenon_intro zenon_H249 | zenon_intro zenon_H3f5 ].
% 119.90/120.15 exact (zenon_H249 zenon_H248).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3f5); [ zenon_intro zenon_H3f6 | zenon_intro zenon_H3ea ].
% 119.90/120.15 exact (zenon_H3f6 gt_3_tptp_minus_1).
% 119.90/120.15 exact (zenon_H3ec zenon_H3ea).
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 exact (zenon_H3e8 zenon_H3eb).
% 119.90/120.15 (* end of lemma zenon_L210_ *)
% 119.90/120.15 assert (zenon_L211_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TG_dq zenon_TG_dq)) -> ((tptp_minus_1) = (n2)) -> (zenon_TG_dq = (n0)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.15 do 1 intro. intros zenon_H66 zenon_H3d2 zenon_H3f9 zenon_H33d zenon_H3c1.
% 119.90/120.15 elim (classic (gt (n0) zenon_TG_dq)); [ zenon_intro zenon_H3a1 | zenon_intro zenon_H39a ].
% 119.90/120.15 cut ((gt (n0) zenon_TG_dq) = (gt zenon_TG_dq zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3d2.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3a1.
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.15 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.15 congruence.
% 119.90/120.15 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq) = ((n0) = zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H334.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3d4.
% 119.90/120.15 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.15 cut ((zenon_TG_dq = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3d5].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H3d5 zenon_H33d).
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 apply zenon_H3d3. apply refl_equal.
% 119.90/120.15 elim (classic (gt (tptp_minus_1) zenon_TG_dq)); [ zenon_intro zenon_H3d6 | zenon_intro zenon_H3d7 ].
% 119.90/120.15 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.90/120.15 generalize (zenon_H142 (tptp_minus_1)). zenon_intro zenon_H3d8.
% 119.90/120.15 generalize (zenon_H3d8 zenon_TG_dq). zenon_intro zenon_H3d9.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3d9); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3da ].
% 119.90/120.15 exact (zenon_H3d1 gt_0_tptp_minus_1).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3da); [ zenon_intro zenon_H3d7 | zenon_intro zenon_H3a1 ].
% 119.90/120.15 exact (zenon_H3d7 zenon_H3d6).
% 119.90/120.15 exact (zenon_H39a zenon_H3a1).
% 119.90/120.15 elim (classic (gt (tptp_minus_1) (tptp_minus_1))); [ zenon_intro zenon_H3d0 | zenon_intro zenon_H3c2 ].
% 119.90/120.15 elim (classic (gt (tptp_minus_1) (n0))); [ zenon_intro zenon_H3cb | zenon_intro zenon_H3c5 ].
% 119.90/120.15 cut ((gt (tptp_minus_1) (n0)) = (gt (tptp_minus_1) zenon_TG_dq)).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3d7.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3cb.
% 119.90/120.15 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 apply zenon_H334. apply sym_equal. exact zenon_H33d.
% 119.90/120.15 cut ((gt (tptp_minus_1) (tptp_minus_1)) = (gt (tptp_minus_1) (n0))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H3c5.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H3d0.
% 119.90/120.15 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3c6].
% 119.90/120.15 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H3b7. apply refl_equal.
% 119.90/120.15 exact (zenon_H3c6 zenon_H3c1).
% 119.90/120.15 apply (zenon_L209_); trivial.
% 119.90/120.15 (* end of lemma zenon_L211_ *)
% 119.90/120.15 assert (zenon_L212_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((tptp_minus_1) = (n2)) -> (zenon_TG_dq = (n0)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.15 do 1 intro. intros zenon_H66 zenon_H3f9 zenon_H33d zenon_H3c1.
% 119.90/120.15 generalize (irreflexivity_gt zenon_TG_dq). zenon_intro zenon_H3d2.
% 119.90/120.15 apply (zenon_L211_ zenon_TG_dq); trivial.
% 119.90/120.15 (* end of lemma zenon_L212_ *)
% 119.90/120.15 assert (zenon_L213_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((tptp_minus_1) = (n2)) -> (zenon_TG_dq = (n0)) -> False).
% 119.90/120.15 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H3f9 zenon_H33d.
% 119.90/120.15 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H3f7.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H3f7); [ zenon_intro zenon_H3f8 | zenon_intro zenon_H3c1 ].
% 119.90/120.15 apply (zenon_notand_s _ _ zenon_H3f8); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3e8 ].
% 119.90/120.15 apply (zenon_L198_); trivial.
% 119.90/120.15 apply (zenon_L210_); trivial.
% 119.90/120.15 apply (zenon_L212_ zenon_TG_dq); trivial.
% 119.90/120.15 (* end of lemma zenon_L213_ *)
% 119.90/120.15 assert (zenon_L214_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n2)) (succ (loopcounter)))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.15 do 0 intro. intros zenon_H66 zenon_H405 zenon_H67 zenon_H7d zenon_H155.
% 119.90/120.15 elim (classic (gt (succ (n2)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H406 | zenon_intro zenon_H407 ].
% 119.90/120.15 elim (classic (gt (succ (n2)) (n0))); [ zenon_intro zenon_H408 | zenon_intro zenon_H409 ].
% 119.90/120.15 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.90/120.15 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.15 generalize (zenon_H40a (n0)). zenon_intro zenon_H40b.
% 119.90/120.15 generalize (zenon_H40b (succ (loopcounter))). zenon_intro zenon_H40c.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H40c); [ zenon_intro zenon_H409 | zenon_intro zenon_H40d ].
% 119.90/120.15 exact (zenon_H409 zenon_H408).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H40d); [ zenon_intro zenon_H140 | zenon_intro zenon_H40e ].
% 119.90/120.15 exact (zenon_H140 zenon_H146).
% 119.90/120.15 exact (zenon_H405 zenon_H40e).
% 119.90/120.15 apply (zenon_L127_); trivial.
% 119.90/120.15 cut ((gt (succ (n2)) (succ (tptp_minus_1))) = (gt (succ (n2)) (n0))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H409.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H406.
% 119.90/120.15 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.15 cut (((succ (n2)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H40f].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H40f. apply refl_equal.
% 119.90/120.15 exact (zenon_H16b succ_tptp_minus_1).
% 119.90/120.15 elim (classic (gt (succ (n2)) (succ (n0)))); [ zenon_intro zenon_H410 | zenon_intro zenon_H411 ].
% 119.90/120.15 elim (classic (gt (succ (n2)) (n1))); [ zenon_intro zenon_H412 | zenon_intro zenon_H413 ].
% 119.90/120.15 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H297 | zenon_intro zenon_H295 ].
% 119.90/120.15 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.15 generalize (zenon_H40a (n1)). zenon_intro zenon_H414.
% 119.90/120.15 generalize (zenon_H414 (succ (tptp_minus_1))). zenon_intro zenon_H415.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H415); [ zenon_intro zenon_H413 | zenon_intro zenon_H416 ].
% 119.90/120.15 exact (zenon_H413 zenon_H412).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H416); [ zenon_intro zenon_H295 | zenon_intro zenon_H406 ].
% 119.90/120.15 exact (zenon_H295 zenon_H297).
% 119.90/120.15 exact (zenon_H407 zenon_H406).
% 119.90/120.15 apply (zenon_L129_); trivial.
% 119.90/120.15 cut ((gt (succ (n2)) (succ (n0))) = (gt (succ (n2)) (n1))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H413.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H410.
% 119.90/120.15 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 119.90/120.15 cut (((succ (n2)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H40f].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H40f. apply refl_equal.
% 119.90/120.15 exact (zenon_H87 successor_1).
% 119.90/120.15 elim (classic (gt (succ (n2)) (succ (succ (n0))))); [ zenon_intro zenon_H417 | zenon_intro zenon_H418 ].
% 119.90/120.15 elim (classic (gt (succ (n2)) (n2))); [ zenon_intro zenon_H419 | zenon_intro zenon_H41a ].
% 119.90/120.15 elim (classic (gt (n2) (succ (n0)))); [ zenon_intro zenon_Hfc | zenon_intro zenon_Hf9 ].
% 119.90/120.15 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.15 generalize (zenon_H40a (n2)). zenon_intro zenon_H41b.
% 119.90/120.15 generalize (zenon_H41b (succ (n0))). zenon_intro zenon_H41c.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H41c); [ zenon_intro zenon_H41a | zenon_intro zenon_H41d ].
% 119.90/120.15 exact (zenon_H41a zenon_H419).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H41d); [ zenon_intro zenon_Hf9 | zenon_intro zenon_H410 ].
% 119.90/120.15 exact (zenon_Hf9 zenon_Hfc).
% 119.90/120.15 exact (zenon_H411 zenon_H410).
% 119.90/120.15 apply (zenon_L25_); trivial.
% 119.90/120.15 cut ((gt (succ (n2)) (succ (succ (n0)))) = (gt (succ (n2)) (n2))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H41a.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H417.
% 119.90/120.15 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.90/120.15 cut (((succ (n2)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H40f].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H40f. apply refl_equal.
% 119.90/120.15 exact (zenon_H105 successor_2).
% 119.90/120.15 elim (classic (gt (n3) (succ (succ (n0))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H202 ].
% 119.90/120.15 elim (classic (gt (succ (succ (succ (n0)))) (succ (succ (n0))))); [ zenon_intro zenon_H41e | zenon_intro zenon_H41f ].
% 119.90/120.15 cut ((gt (succ (succ (succ (n0)))) (succ (succ (n0)))) = (gt (succ (n2)) (succ (succ (n0))))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H418.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H41e.
% 119.90/120.15 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.90/120.15 cut (((succ (succ (succ (n0)))) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H420].
% 119.90/120.15 congruence.
% 119.90/120.15 elim (classic ((succ (n2)) = (succ (n2)))); [ zenon_intro zenon_H421 | zenon_intro zenon_H40f ].
% 119.90/120.15 cut (((succ (n2)) = (succ (n2))) = ((succ (succ (succ (n0)))) = (succ (n2)))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H420.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H421.
% 119.90/120.15 cut (((succ (n2)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H40f].
% 119.90/120.15 cut (((succ (n2)) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H422].
% 119.90/120.15 congruence.
% 119.90/120.15 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.90/120.15 congruence.
% 119.90/120.15 apply zenon_H102. apply sym_equal. exact successor_2.
% 119.90/120.15 apply zenon_H40f. apply refl_equal.
% 119.90/120.15 apply zenon_H40f. apply refl_equal.
% 119.90/120.15 apply zenon_H104. apply refl_equal.
% 119.90/120.15 cut ((gt (n3) (succ (succ (n0)))) = (gt (succ (succ (succ (n0)))) (succ (succ (n0))))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H41f.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H24a.
% 119.90/120.15 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.90/120.15 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 119.90/120.15 congruence.
% 119.90/120.15 elim (classic ((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ].
% 119.90/120.15 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0))))) = ((n3) = (succ (succ (succ (n0)))))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H99.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H21d.
% 119.90/120.15 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.90/120.15 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.90/120.15 congruence.
% 119.90/120.15 exact (zenon_H21f successor_3).
% 119.90/120.15 apply zenon_H21e. apply refl_equal.
% 119.90/120.15 apply zenon_H21e. apply refl_equal.
% 119.90/120.15 apply zenon_H104. apply refl_equal.
% 119.90/120.15 apply (zenon_L86_); trivial.
% 119.90/120.15 (* end of lemma zenon_L214_ *)
% 119.90/120.15 assert (zenon_L215_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n2)) (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.15 do 0 intro. intros zenon_H66 zenon_H423 zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.15 elim (classic ((~((succ (n2)) = (succ (loopcounter))))/\(~(gt (succ (n2)) (succ (loopcounter)))))); [ zenon_intro zenon_H424 | zenon_intro zenon_H425 ].
% 119.90/120.15 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H426. zenon_intro zenon_H405.
% 119.90/120.15 apply (zenon_L214_); trivial.
% 119.90/120.15 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1e6 ].
% 119.90/120.15 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.15 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.15 generalize (zenon_H78 (n3)). zenon_intro zenon_H20f.
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H20f); [ zenon_intro zenon_H6f | zenon_intro zenon_H210 ].
% 119.90/120.15 exact (zenon_H6f zenon_H67).
% 119.90/120.15 apply (zenon_imply_s _ _ zenon_H210); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H211 ].
% 119.90/120.15 exact (zenon_H1e6 zenon_H1ee).
% 119.90/120.15 cut ((gt (succ (loopcounter)) (n3)) = (gt (succ (n2)) (n3))).
% 119.90/120.15 intro zenon_D_pnotp.
% 119.90/120.15 apply zenon_H423.
% 119.90/120.15 rewrite <- zenon_D_pnotp.
% 119.90/120.15 exact zenon_H211.
% 119.90/120.15 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.90/120.16 cut (((succ (loopcounter)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H427].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H425); [ zenon_intro zenon_H429 | zenon_intro zenon_H428 ].
% 119.90/120.16 apply zenon_H429. zenon_intro zenon_H42a.
% 119.90/120.16 apply zenon_H427. apply sym_equal. exact zenon_H42a.
% 119.90/120.16 apply zenon_H428. zenon_intro zenon_H40e.
% 119.90/120.16 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.16 generalize (zenon_H40a (succ (loopcounter))). zenon_intro zenon_H42b.
% 119.90/120.16 generalize (zenon_H42b (n3)). zenon_intro zenon_H42c.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H42c); [ zenon_intro zenon_H405 | zenon_intro zenon_H42d ].
% 119.90/120.16 exact (zenon_H405 zenon_H40e).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H42d); [ zenon_intro zenon_H21a | zenon_intro zenon_H42e ].
% 119.90/120.16 exact (zenon_H21a zenon_H211).
% 119.90/120.16 exact (zenon_H423 zenon_H42e).
% 119.90/120.16 apply zenon_H201. apply refl_equal.
% 119.90/120.16 apply (zenon_L171_); trivial.
% 119.90/120.16 (* end of lemma zenon_L215_ *)
% 119.90/120.16 assert (zenon_L216_ : ((tptp_minus_1) = (n3)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (tptp_minus_1))) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H42f zenon_H66 zenon_H3c2.
% 119.90/120.16 elim (classic ((~((tptp_minus_1) = (n3)))/\(~(gt (tptp_minus_1) (n3))))); [ zenon_intro zenon_H430 | zenon_intro zenon_H431 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H430). zenon_intro zenon_H433. zenon_intro zenon_H432.
% 119.90/120.16 exact (zenon_H433 zenon_H42f).
% 119.90/120.16 cut ((gt (n3) (tptp_minus_1)) = (gt (tptp_minus_1) (tptp_minus_1))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H3c2.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact gt_3_tptp_minus_1.
% 119.90/120.16 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.16 cut (((n3) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H434].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H431); [ zenon_intro zenon_H436 | zenon_intro zenon_H435 ].
% 119.90/120.16 apply zenon_H436. zenon_intro zenon_H42f.
% 119.90/120.16 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3b7 ].
% 119.90/120.16 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n3) = (tptp_minus_1))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H434.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H3ca.
% 119.90/120.16 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.16 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H433].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H433 zenon_H42f).
% 119.90/120.16 apply zenon_H3b7. apply refl_equal.
% 119.90/120.16 apply zenon_H3b7. apply refl_equal.
% 119.90/120.16 apply zenon_H435. zenon_intro zenon_H437.
% 119.90/120.16 generalize (zenon_H66 (tptp_minus_1)). zenon_intro zenon_H3cc.
% 119.90/120.16 generalize (zenon_H3cc (n3)). zenon_intro zenon_H438.
% 119.90/120.16 generalize (zenon_H438 (tptp_minus_1)). zenon_intro zenon_H439.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H439); [ zenon_intro zenon_H432 | zenon_intro zenon_H43a ].
% 119.90/120.16 exact (zenon_H432 zenon_H437).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H43a); [ zenon_intro zenon_H3f6 | zenon_intro zenon_H3d0 ].
% 119.90/120.16 exact (zenon_H3f6 gt_3_tptp_minus_1).
% 119.90/120.16 exact (zenon_H3c2 zenon_H3d0).
% 119.90/120.16 apply zenon_H3b7. apply refl_equal.
% 119.90/120.16 (* end of lemma zenon_L216_ *)
% 119.90/120.16 assert (zenon_L217_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(leq (tptp_minus_1) (n2))) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H43b.
% 119.90/120.16 generalize (leq_succ_gt_equiv (tptp_minus_1)). zenon_intro zenon_H3b9.
% 119.90/120.16 generalize (zenon_H3b9 (n2)). zenon_intro zenon_H43c.
% 119.90/120.16 apply (zenon_equiv_s _ _ zenon_H43c); [ zenon_intro zenon_H43b; zenon_intro zenon_H43f | zenon_intro zenon_H43e; zenon_intro zenon_H43d ].
% 119.90/120.16 elim (classic ((~((succ (n2)) = (n3)))/\(~(gt (succ (n2)) (n3))))); [ zenon_intro zenon_H440 | zenon_intro zenon_H441 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H440). zenon_intro zenon_H442. zenon_intro zenon_H423.
% 119.90/120.16 apply (zenon_L215_); trivial.
% 119.90/120.16 cut ((gt (n3) (tptp_minus_1)) = (gt (succ (n2)) (tptp_minus_1))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H43f.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact gt_3_tptp_minus_1.
% 119.90/120.16 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.16 cut (((n3) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H443].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H441); [ zenon_intro zenon_H445 | zenon_intro zenon_H444 ].
% 119.90/120.16 apply zenon_H445. zenon_intro zenon_H446.
% 119.90/120.16 elim (classic ((succ (n2)) = (succ (n2)))); [ zenon_intro zenon_H421 | zenon_intro zenon_H40f ].
% 119.90/120.16 cut (((succ (n2)) = (succ (n2))) = ((n3) = (succ (n2)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H443.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H421.
% 119.90/120.16 cut (((succ (n2)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H40f].
% 119.90/120.16 cut (((succ (n2)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H442].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H442 zenon_H446).
% 119.90/120.16 apply zenon_H40f. apply refl_equal.
% 119.90/120.16 apply zenon_H40f. apply refl_equal.
% 119.90/120.16 apply zenon_H444. zenon_intro zenon_H42e.
% 119.90/120.16 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.16 generalize (zenon_H40a (n3)). zenon_intro zenon_H447.
% 119.90/120.16 generalize (zenon_H447 (tptp_minus_1)). zenon_intro zenon_H448.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H448); [ zenon_intro zenon_H423 | zenon_intro zenon_H449 ].
% 119.90/120.16 exact (zenon_H423 zenon_H42e).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H449); [ zenon_intro zenon_H3f6 | zenon_intro zenon_H43d ].
% 119.90/120.16 exact (zenon_H3f6 gt_3_tptp_minus_1).
% 119.90/120.16 exact (zenon_H43f zenon_H43d).
% 119.90/120.16 apply zenon_H3b7. apply refl_equal.
% 119.90/120.16 exact (zenon_H43b zenon_H43e).
% 119.90/120.16 (* end of lemma zenon_L217_ *)
% 119.90/120.16 assert (zenon_L218_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TG_dq zenon_TG_dq)) -> ((tptp_minus_1) = (n3)) -> (zenon_TG_dq = (n0)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H3d2 zenon_H42f zenon_H33d zenon_H3c1.
% 119.90/120.16 elim (classic (gt (n0) zenon_TG_dq)); [ zenon_intro zenon_H3a1 | zenon_intro zenon_H39a ].
% 119.90/120.16 cut ((gt (n0) zenon_TG_dq) = (gt zenon_TG_dq zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H3d2.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H3a1.
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.16 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.16 congruence.
% 119.90/120.16 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq) = ((n0) = zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H334.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H3d4.
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.16 cut ((zenon_TG_dq = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3d5].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H3d5 zenon_H33d).
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 elim (classic (gt (tptp_minus_1) zenon_TG_dq)); [ zenon_intro zenon_H3d6 | zenon_intro zenon_H3d7 ].
% 119.90/120.16 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.90/120.16 generalize (zenon_H142 (tptp_minus_1)). zenon_intro zenon_H3d8.
% 119.90/120.16 generalize (zenon_H3d8 zenon_TG_dq). zenon_intro zenon_H3d9.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H3d9); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3da ].
% 119.90/120.16 exact (zenon_H3d1 gt_0_tptp_minus_1).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H3da); [ zenon_intro zenon_H3d7 | zenon_intro zenon_H3a1 ].
% 119.90/120.16 exact (zenon_H3d7 zenon_H3d6).
% 119.90/120.16 exact (zenon_H39a zenon_H3a1).
% 119.90/120.16 elim (classic (gt (tptp_minus_1) (tptp_minus_1))); [ zenon_intro zenon_H3d0 | zenon_intro zenon_H3c2 ].
% 119.90/120.16 elim (classic (gt (tptp_minus_1) (n0))); [ zenon_intro zenon_H3cb | zenon_intro zenon_H3c5 ].
% 119.90/120.16 cut ((gt (tptp_minus_1) (n0)) = (gt (tptp_minus_1) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H3d7.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H3cb.
% 119.90/120.16 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.16 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H3b7. apply refl_equal.
% 119.90/120.16 apply zenon_H334. apply sym_equal. exact zenon_H33d.
% 119.90/120.16 cut ((gt (tptp_minus_1) (tptp_minus_1)) = (gt (tptp_minus_1) (n0))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H3c5.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H3d0.
% 119.90/120.16 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H3c6].
% 119.90/120.16 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3b7].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H3b7. apply refl_equal.
% 119.90/120.16 exact (zenon_H3c6 zenon_H3c1).
% 119.90/120.16 apply (zenon_L216_); trivial.
% 119.90/120.16 (* end of lemma zenon_L218_ *)
% 119.90/120.16 assert (zenon_L219_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((tptp_minus_1) = (n3)) -> (zenon_TG_dq = (n0)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H42f zenon_H33d zenon_H3c1.
% 119.90/120.16 generalize (irreflexivity_gt zenon_TG_dq). zenon_intro zenon_H3d2.
% 119.90/120.16 apply (zenon_L218_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L219_ *)
% 119.90/120.16 assert (zenon_L220_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n0)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H33d.
% 119.90/120.16 generalize (finite_domain_3 (tptp_minus_1)). zenon_intro zenon_H44a.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H44a); [ zenon_intro zenon_H44c | zenon_intro zenon_H44b ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H44c); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3b8 ].
% 119.90/120.16 apply (zenon_L198_); trivial.
% 119.90/120.16 apply (zenon_L200_); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H44b); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H44d ].
% 119.90/120.16 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H44d); [ zenon_intro zenon_H3db | zenon_intro zenon_H44e ].
% 119.90/120.16 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H44e); [ zenon_intro zenon_H3f9 | zenon_intro zenon_H42f ].
% 119.90/120.16 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.16 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.16 apply (zenon_L198_); trivial.
% 119.90/120.16 apply (zenon_L217_); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.16 apply (zenon_L219_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.16 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L220_ *)
% 119.90/120.16 assert (zenon_L221_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n1)) -> (~(leq zenon_TG_dq (n0))) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H7d zenon_H67 zenon_H33f zenon_H453.
% 119.90/120.16 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.16 generalize (zenon_H330 (n0)). zenon_intro zenon_H454.
% 119.90/120.16 apply (zenon_equiv_s _ _ zenon_H454); [ zenon_intro zenon_H453; zenon_intro zenon_H457 | zenon_intro zenon_H456; zenon_intro zenon_H455 ].
% 119.90/120.16 elim (classic ((~((succ (n0)) = (succ (loopcounter))))/\(~(gt (succ (n0)) (succ (loopcounter)))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H97. zenon_intro zenon_Hd0.
% 119.90/120.16 apply (zenon_L9_); trivial.
% 119.90/120.16 elim (classic ((n1) = zenon_TG_dq)); [ zenon_intro zenon_H458 | zenon_intro zenon_H335 ].
% 119.90/120.16 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (n0)) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H457.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H67.
% 119.90/120.16 cut (((n1) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H335].
% 119.90/120.16 cut (((succ (loopcounter)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ].
% 119.90/120.16 apply zenon_Hd4. zenon_intro zenon_Hd5.
% 119.90/120.16 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 119.90/120.16 cut (((succ (n0)) = (succ (n0))) = ((succ (loopcounter)) = (succ (n0)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_Hd2.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H8b.
% 119.90/120.16 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.90/120.16 cut (((succ (n0)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H97 zenon_Hd5).
% 119.90/120.16 apply zenon_H8c. apply refl_equal.
% 119.90/120.16 apply zenon_H8c. apply refl_equal.
% 119.90/120.16 apply zenon_Hd3. zenon_intro zenon_Hd6.
% 119.90/120.16 generalize (zenon_H66 (succ (n0))). zenon_intro zenon_H8e.
% 119.90/120.16 generalize (zenon_H8e (succ (loopcounter))). zenon_intro zenon_Hd7.
% 119.90/120.16 generalize (zenon_Hd7 (n1)). zenon_intro zenon_Hd8.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_Hd8); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd9 ].
% 119.90/120.16 exact (zenon_Hd0 zenon_Hd6).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_Hd9); [ zenon_intro zenon_H6f | zenon_intro zenon_H8d ].
% 119.90/120.16 exact (zenon_H6f zenon_H67).
% 119.90/120.16 cut ((gt (succ (n0)) (n1)) = (gt (succ (n0)) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H457.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H8d.
% 119.90/120.16 cut (((n1) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H335].
% 119.90/120.16 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H8c. apply refl_equal.
% 119.90/120.16 exact (zenon_H335 zenon_H458).
% 119.90/120.16 exact (zenon_H335 zenon_H458).
% 119.90/120.16 apply zenon_H335. apply sym_equal. exact zenon_H33f.
% 119.90/120.16 exact (zenon_H453 zenon_H456).
% 119.90/120.16 (* end of lemma zenon_L221_ *)
% 119.90/120.16 assert (zenon_L222_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n1)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H5c zenon_H7d zenon_H67 zenon_H33f zenon_H3c1.
% 119.90/120.16 generalize (finite_domain_0 zenon_TG_dq). zenon_intro zenon_H459.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H459); [ zenon_intro zenon_H45a | zenon_intro zenon_H33d ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H45a); [ zenon_intro zenon_H5d | zenon_intro zenon_H453 ].
% 119.90/120.16 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L221_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L222_ *)
% 119.90/120.16 assert (zenon_L223_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((tptp_minus_1) = (n1)) -> (gt (succ zenon_TG_dq) (n0)) -> (zenon_TG_dq = (n1)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H3db zenon_H5c zenon_H33f.
% 119.90/120.16 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H3f7.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H3f7); [ zenon_intro zenon_H3f8 | zenon_intro zenon_H3c1 ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H3f8); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3e8 ].
% 119.90/120.16 apply (zenon_L198_); trivial.
% 119.90/120.16 apply (zenon_L205_); trivial.
% 119.90/120.16 generalize (finite_domain_0 zenon_TG_dq). zenon_intro zenon_H459.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H459); [ zenon_intro zenon_H45a | zenon_intro zenon_H33d ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H45a); [ zenon_intro zenon_H5d | zenon_intro zenon_H453 ].
% 119.90/120.16 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L221_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L207_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L223_ *)
% 119.90/120.16 assert (zenon_L224_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((tptp_minus_1) = (n2)) -> (gt (succ zenon_TG_dq) (n0)) -> (zenon_TG_dq = (n1)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H3f9 zenon_H5c zenon_H33f.
% 119.90/120.16 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H3f7.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H3f7); [ zenon_intro zenon_H3f8 | zenon_intro zenon_H3c1 ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H3f8); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3e8 ].
% 119.90/120.16 apply (zenon_L198_); trivial.
% 119.90/120.16 apply (zenon_L210_); trivial.
% 119.90/120.16 generalize (finite_domain_0 zenon_TG_dq). zenon_intro zenon_H459.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H459); [ zenon_intro zenon_H45a | zenon_intro zenon_H33d ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H45a); [ zenon_intro zenon_H5d | zenon_intro zenon_H453 ].
% 119.90/120.16 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L221_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L212_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L224_ *)
% 119.90/120.16 assert (zenon_L225_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n1)) -> ((tptp_minus_1) = (n3)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H5c zenon_H7d zenon_H67 zenon_H33f zenon_H42f zenon_H3c1.
% 119.90/120.16 generalize (finite_domain_0 zenon_TG_dq). zenon_intro zenon_H459.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H459); [ zenon_intro zenon_H45a | zenon_intro zenon_H33d ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H45a); [ zenon_intro zenon_H5d | zenon_intro zenon_H453 ].
% 119.90/120.16 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L221_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L219_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L225_ *)
% 119.90/120.16 assert (zenon_L226_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (gt (succ zenon_TG_dq) (n0)) -> (zenon_TG_dq = (n1)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H5c zenon_H33f.
% 119.90/120.16 generalize (finite_domain_3 (tptp_minus_1)). zenon_intro zenon_H44a.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H44a); [ zenon_intro zenon_H44c | zenon_intro zenon_H44b ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H44c); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3b8 ].
% 119.90/120.16 apply (zenon_L198_); trivial.
% 119.90/120.16 apply (zenon_L200_); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H44b); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H44d ].
% 119.90/120.16 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H44d); [ zenon_intro zenon_H3db | zenon_intro zenon_H44e ].
% 119.90/120.16 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H44e); [ zenon_intro zenon_H3f9 | zenon_intro zenon_H42f ].
% 119.90/120.16 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.16 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.16 apply (zenon_L198_); trivial.
% 119.90/120.16 apply (zenon_L217_); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.16 apply (zenon_L225_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.16 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L226_ *)
% 119.90/120.16 assert (zenon_L227_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n3) (n3))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H66 zenon_H24e zenon_H67 zenon_H7d zenon_H155.
% 119.90/120.16 elim (classic (gt (n2) (n3))); [ zenon_intro zenon_H223 | zenon_intro zenon_H220 ].
% 119.90/120.16 generalize (zenon_H66 (n3)). zenon_intro zenon_H24f.
% 119.90/120.16 generalize (zenon_H24f (n2)). zenon_intro zenon_H250.
% 119.90/120.16 generalize (zenon_H250 (n3)). zenon_intro zenon_H251.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H251); [ zenon_intro zenon_H22f | zenon_intro zenon_H252 ].
% 119.90/120.16 exact (zenon_H22f gt_3_2).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H252); [ zenon_intro zenon_H220 | zenon_intro zenon_H253 ].
% 119.90/120.16 exact (zenon_H220 zenon_H223).
% 119.90/120.16 exact (zenon_H24e zenon_H253).
% 119.90/120.16 apply (zenon_L190_); trivial.
% 119.90/120.16 (* end of lemma zenon_L227_ *)
% 119.90/120.16 assert (zenon_L228_ : (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H67 zenon_H7d zenon_H155 zenon_H272 zenon_H66.
% 119.90/120.16 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H167 ].
% 119.90/120.16 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H258 | zenon_intro zenon_H255 ].
% 119.90/120.16 elim (classic (gt (n0) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H273 | zenon_intro zenon_H274 ].
% 119.90/120.16 cut ((gt (n0) (succ (succ (succ (n0))))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H272.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H273.
% 119.90/120.16 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.90/120.16 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.90/120.16 congruence.
% 119.90/120.16 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.90/120.16 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H159.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H15a.
% 119.90/120.16 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.90/120.16 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H15b zenon_H155).
% 119.90/120.16 apply zenon_H158. apply refl_equal.
% 119.90/120.16 apply zenon_H158. apply refl_equal.
% 119.90/120.16 apply zenon_H21e. apply refl_equal.
% 119.90/120.16 cut ((gt (succ (tptp_minus_1)) (succ (succ (succ (n0))))) = (gt (n0) (succ (succ (succ (n0)))))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H274.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H258.
% 119.90/120.16 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.16 congruence.
% 119.90/120.16 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H136 | zenon_intro zenon_H65 ].
% 119.90/120.16 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H16b.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H136.
% 119.90/120.16 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.90/120.16 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H167 zenon_H180).
% 119.90/120.16 apply zenon_H65. apply refl_equal.
% 119.90/120.16 apply zenon_H65. apply refl_equal.
% 119.90/120.16 apply zenon_H21e. apply refl_equal.
% 119.90/120.16 apply (zenon_L195_); trivial.
% 119.90/120.16 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H167.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H16a.
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H16b succ_tptp_minus_1).
% 119.90/120.16 apply zenon_H169. apply refl_equal.
% 119.90/120.16 apply zenon_H169. apply refl_equal.
% 119.90/120.16 (* end of lemma zenon_L228_ *)
% 119.90/120.16 assert (zenon_L229_ : (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(gt (n0) (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H7d zenon_H67 zenon_H254 zenon_H66 zenon_H155.
% 119.90/120.16 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15c | zenon_intro zenon_H159 ].
% 119.90/120.16 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H141 | zenon_intro zenon_H12f ].
% 119.90/120.16 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 119.90/120.16 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n3))); [ zenon_intro zenon_H27e | zenon_intro zenon_H275 ].
% 119.90/120.16 generalize (zenon_H66 (n0)). zenon_intro zenon_H142.
% 119.90/120.16 generalize (zenon_H142 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H160.
% 119.90/120.16 generalize (zenon_H160 (n3)). zenon_intro zenon_H45b.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H45b); [ zenon_intro zenon_H157 | zenon_intro zenon_H45c ].
% 119.90/120.16 exact (zenon_H157 zenon_H156).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H45c); [ zenon_intro zenon_H275 | zenon_intro zenon_H28b ].
% 119.90/120.16 exact (zenon_H275 zenon_H27e).
% 119.90/120.16 exact (zenon_H254 zenon_H28b).
% 119.90/120.16 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H276 | zenon_intro zenon_H272 ].
% 119.90/120.16 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0))))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n3))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H275.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H276.
% 119.90/120.16 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.90/120.16 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H158. apply refl_equal.
% 119.90/120.16 exact (zenon_H21f successor_3).
% 119.90/120.16 apply (zenon_L228_); trivial.
% 119.90/120.16 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H157.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H141.
% 119.90/120.16 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 119.90/120.16 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H65. apply refl_equal.
% 119.90/120.16 exact (zenon_H159 zenon_H15c).
% 119.90/120.16 apply (zenon_L146_); trivial.
% 119.90/120.16 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_H15a | zenon_intro zenon_H158 ].
% 119.90/120.16 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H159.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H15a.
% 119.90/120.16 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 119.90/120.16 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H15b zenon_H155).
% 119.90/120.16 apply zenon_H158. apply refl_equal.
% 119.90/120.16 apply zenon_H158. apply refl_equal.
% 119.90/120.16 (* end of lemma zenon_L229_ *)
% 119.90/120.16 assert (zenon_L230_ : (gt (succ (loopcounter)) (n1)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (loopcounter))) -> (gt (n1) (loopcounter)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H67 zenon_H155 zenon_H66 zenon_H135 zenon_H7d.
% 119.90/120.16 elim (classic ((~((loopcounter) = (n1)))/\(~(gt (loopcounter) (n1))))); [ zenon_intro zenon_H137 | zenon_intro zenon_H138 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H137). zenon_intro zenon_Hc4. zenon_intro zenon_Hee.
% 119.90/120.16 apply (zenon_L193_); trivial.
% 119.90/120.16 cut ((gt (n1) (loopcounter)) = (gt (loopcounter) (loopcounter))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H135.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H7d.
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 119.90/120.16 apply zenon_H13a. zenon_intro zenon_Hca.
% 119.90/120.16 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.90/120.16 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_Hec.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_Hed.
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_Hc4 zenon_Hca).
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H139. zenon_intro zenon_Hf1.
% 119.90/120.16 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.16 generalize (zenon_H13b (n1)). zenon_intro zenon_H13c.
% 119.90/120.16 generalize (zenon_H13c (loopcounter)). zenon_intro zenon_H13d.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H13d); [ zenon_intro zenon_Hee | zenon_intro zenon_H13e ].
% 119.90/120.16 exact (zenon_Hee zenon_Hf1).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H92 | zenon_intro zenon_H134 ].
% 119.90/120.16 exact (zenon_H92 zenon_H7d).
% 119.90/120.16 exact (zenon_H135 zenon_H134).
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 (* end of lemma zenon_L230_ *)
% 119.90/120.16 assert (zenon_L231_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((loopcounter) = (n0)) -> (~(gt (loopcounter) (n3))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H66 zenon_H95 zenon_H1f5 zenon_H67 zenon_H7d zenon_H155.
% 119.90/120.16 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.90/120.16 elim (classic (gt (loopcounter) (n0))); [ zenon_intro zenon_H2fd | zenon_intro zenon_H2fa ].
% 119.90/120.16 elim (classic (gt (n0) (n3))); [ zenon_intro zenon_H28b | zenon_intro zenon_H254 ].
% 119.90/120.16 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.16 generalize (zenon_H13b (n0)). zenon_intro zenon_H45d.
% 119.90/120.16 generalize (zenon_H45d (n3)). zenon_intro zenon_H45e.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H45e); [ zenon_intro zenon_H2fa | zenon_intro zenon_H45f ].
% 119.90/120.16 exact (zenon_H2fa zenon_H2fd).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H45f); [ zenon_intro zenon_H254 | zenon_intro zenon_H1f9 ].
% 119.90/120.16 exact (zenon_H254 zenon_H28b).
% 119.90/120.16 exact (zenon_H1f5 zenon_H1f9).
% 119.90/120.16 apply (zenon_L229_); trivial.
% 119.90/120.16 cut ((gt (loopcounter) (loopcounter)) = (gt (loopcounter) (n0))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H2fa.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H134.
% 119.90/120.16 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 exact (zenon_H132 zenon_H95).
% 119.90/120.16 apply (zenon_L230_); trivial.
% 119.90/120.16 (* end of lemma zenon_L231_ *)
% 119.90/120.16 assert (zenon_L232_ : ((loopcounter) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H95 zenon_H66 zenon_H19d zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.16 elim (classic ((~((loopcounter) = (n3)))/\(~(gt (loopcounter) (n3))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hc2. zenon_intro zenon_H1f5.
% 119.90/120.16 apply (zenon_L231_); trivial.
% 119.90/120.16 cut ((gt (n3) (n2)) = (gt (loopcounter) (n2))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H19d.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact gt_3_2.
% 119.90/120.16 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.90/120.16 cut (((n3) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f7 ].
% 119.90/120.16 apply zenon_H1f8. zenon_intro zenon_Hcb.
% 119.90/120.16 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.90/120.16 cut (((loopcounter) = (loopcounter)) = ((n3) = (loopcounter))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H1f6.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_Hed.
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_Hc2 zenon_Hcb).
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H1f7. zenon_intro zenon_H1f9.
% 119.90/120.16 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.16 generalize (zenon_H13b (n3)). zenon_intro zenon_H1fa.
% 119.90/120.16 generalize (zenon_H1fa (n2)). zenon_intro zenon_H23a.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H23a); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23b ].
% 119.90/120.16 exact (zenon_H1f5 zenon_H1f9).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H22f | zenon_intro zenon_H1a1 ].
% 119.90/120.16 exact (zenon_H22f gt_3_2).
% 119.90/120.16 exact (zenon_H19d zenon_H1a1).
% 119.90/120.16 apply zenon_H63. apply refl_equal.
% 119.90/120.16 (* end of lemma zenon_L232_ *)
% 119.90/120.16 assert (zenon_L233_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> ((loopcounter) = (n0)) -> (zenon_TG_dq = (n2)) -> (~(leq zenon_TG_dq (n1))) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H95 zenon_H341 zenon_H460.
% 119.90/120.16 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.16 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.16 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.16 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.16 apply (zenon_L138_); trivial.
% 119.90/120.16 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.16 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.16 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.16 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.16 exact (zenon_H6f zenon_H67).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.16 exact (zenon_H466 zenon_H465).
% 119.90/120.16 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H464.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H469.
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.16 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.16 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.16 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.16 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.16 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.16 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.16 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.16 exact (zenon_H116 zenon_H11e).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.16 exact (zenon_H46c zenon_H469).
% 119.90/120.16 exact (zenon_H464 zenon_H462).
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.16 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.16 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.16 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.16 exact (zenon_H92 zenon_H7d).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.16 exact (zenon_H46e zenon_H46d).
% 119.90/120.16 exact (zenon_H466 zenon_H465).
% 119.90/120.16 elim (classic ((n2) = zenon_TG_dq)); [ zenon_intro zenon_H471 | zenon_intro zenon_H336 ].
% 119.90/120.16 elim (classic (gt (loopcounter) (n2))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H19d ].
% 119.90/120.16 cut ((gt (loopcounter) (n2)) = (gt (loopcounter) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H46e.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H1a1.
% 119.90/120.16 cut (((n2) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H336].
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 exact (zenon_H336 zenon_H471).
% 119.90/120.16 apply (zenon_L232_); trivial.
% 119.90/120.16 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq) = ((n2) = zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H336.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H3d4.
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.16 cut ((zenon_TG_dq = (n2))); [idtac | apply NNPP; zenon_intro zenon_H472].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H472 zenon_H341).
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 exact (zenon_H460 zenon_H463).
% 119.90/120.16 (* end of lemma zenon_L233_ *)
% 119.90/120.16 assert (zenon_L234_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (succ (n1)) (succ (loopcounter)))) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H116.
% 119.90/120.16 elim (classic (gt (succ (n1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2bd | zenon_intro zenon_H2ba ].
% 119.90/120.16 elim (classic (gt (succ (n1)) (n0))); [ zenon_intro zenon_H10d | zenon_intro zenon_H10f ].
% 119.90/120.16 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.90/120.16 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.16 generalize (zenon_H11a (n0)). zenon_intro zenon_H2be.
% 119.90/120.16 generalize (zenon_H2be (succ (loopcounter))). zenon_intro zenon_H2bf.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H2bf); [ zenon_intro zenon_H10f | zenon_intro zenon_H2c0 ].
% 119.90/120.16 exact (zenon_H10f zenon_H10d).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H2c0); [ zenon_intro zenon_H140 | zenon_intro zenon_H11e ].
% 119.90/120.16 exact (zenon_H140 zenon_H146).
% 119.90/120.16 exact (zenon_H116 zenon_H11e).
% 119.90/120.16 apply (zenon_L127_); trivial.
% 119.90/120.16 cut ((gt (succ (n1)) (succ (tptp_minus_1))) = (gt (succ (n1)) (n0))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H10f.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H2bd.
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.16 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H101. apply refl_equal.
% 119.90/120.16 exact (zenon_H16b succ_tptp_minus_1).
% 119.90/120.16 apply (zenon_L137_); trivial.
% 119.90/120.16 (* end of lemma zenon_L234_ *)
% 119.90/120.16 assert (zenon_L235_ : (~(gt (n0) (n2))) -> ((tptp_minus_1) = (n2)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H1ab zenon_H3f9.
% 119.90/120.16 cut ((gt (n0) (tptp_minus_1)) = (gt (n0) (n2))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H1ab.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact gt_0_tptp_minus_1.
% 119.90/120.16 cut (((tptp_minus_1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H3fd].
% 119.90/120.16 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H65. apply refl_equal.
% 119.90/120.16 exact (zenon_H3fd zenon_H3f9).
% 119.90/120.16 (* end of lemma zenon_L235_ *)
% 119.90/120.16 assert (zenon_L236_ : ((loopcounter) = (n0)) -> (~(gt (loopcounter) (n2))) -> ((tptp_minus_1) = (n2)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H95 zenon_H19d zenon_H3f9.
% 119.90/120.16 elim (classic (gt (n0) (n2))); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1ab ].
% 119.90/120.16 cut ((gt (n0) (n2)) = (gt (loopcounter) (n2))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H19d.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H1b3.
% 119.90/120.16 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.90/120.16 cut (((n0) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 119.90/120.16 congruence.
% 119.90/120.16 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.90/120.16 cut (((loopcounter) = (loopcounter)) = ((n0) = (loopcounter))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H93.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_Hed.
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H132 zenon_H95).
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H63. apply refl_equal.
% 119.90/120.16 apply (zenon_L235_); trivial.
% 119.90/120.16 (* end of lemma zenon_L236_ *)
% 119.90/120.16 assert (zenon_L237_ : forall (zenon_TG_dq : zenon_U), ((tptp_minus_1) = (n2)) -> ((loopcounter) = (n0)) -> (~(gt (loopcounter) zenon_TG_dq)) -> (zenon_TG_dq = (n2)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H3f9 zenon_H95 zenon_H46e zenon_H341.
% 119.90/120.16 elim (classic ((n2) = zenon_TG_dq)); [ zenon_intro zenon_H471 | zenon_intro zenon_H336 ].
% 119.90/120.16 elim (classic (gt (loopcounter) (n2))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H19d ].
% 119.90/120.16 cut ((gt (loopcounter) (n2)) = (gt (loopcounter) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H46e.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H1a1.
% 119.90/120.16 cut (((n2) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H336].
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 exact (zenon_H336 zenon_H471).
% 119.90/120.16 apply (zenon_L236_); trivial.
% 119.90/120.16 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq) = ((n2) = zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H336.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H3d4.
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.16 cut ((zenon_TG_dq = (n2))); [idtac | apply NNPP; zenon_intro zenon_H472].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H472 zenon_H341).
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 (* end of lemma zenon_L237_ *)
% 119.90/120.16 assert (zenon_L238_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((loopcounter) = (n0)) -> ((tptp_minus_1) = (n2)) -> (zenon_TG_dq = (n2)) -> (~(leq zenon_TG_dq (n1))) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H95 zenon_H3f9 zenon_H341 zenon_H460.
% 119.90/120.16 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.16 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.16 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.16 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.16 apply (zenon_L234_); trivial.
% 119.90/120.16 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.16 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.16 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.16 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.16 exact (zenon_H6f zenon_H67).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.16 exact (zenon_H466 zenon_H465).
% 119.90/120.16 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H464.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H469.
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.16 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.16 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.16 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.16 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.16 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.16 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.16 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.16 exact (zenon_H116 zenon_H11e).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.16 exact (zenon_H46c zenon_H469).
% 119.90/120.16 exact (zenon_H464 zenon_H462).
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.16 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.16 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.16 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.16 exact (zenon_H92 zenon_H7d).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.16 exact (zenon_H46e zenon_H46d).
% 119.90/120.16 exact (zenon_H466 zenon_H465).
% 119.90/120.16 apply (zenon_L237_ zenon_TG_dq); trivial.
% 119.90/120.16 exact (zenon_H460 zenon_H463).
% 119.90/120.16 (* end of lemma zenon_L238_ *)
% 119.90/120.16 assert (zenon_L239_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((loopcounter) = (n0)) -> ((tptp_minus_1) = (n2)) -> (zenon_TG_dq = (n2)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H95 zenon_H3f9 zenon_H341.
% 119.90/120.16 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.16 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L238_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.16 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L239_ *)
% 119.90/120.16 assert (zenon_L240_ : (~(gt (n0) (n3))) -> ((tptp_minus_1) = (n3)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H254 zenon_H42f.
% 119.90/120.16 cut ((gt (n0) (tptp_minus_1)) = (gt (n0) (n3))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H254.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact gt_0_tptp_minus_1.
% 119.90/120.16 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H433].
% 119.90/120.16 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H65. apply refl_equal.
% 119.90/120.16 exact (zenon_H433 zenon_H42f).
% 119.90/120.16 (* end of lemma zenon_L240_ *)
% 119.90/120.16 assert (zenon_L241_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((tptp_minus_1) = (n3)) -> ((loopcounter) = (n0)) -> (~(gt (loopcounter) (n3))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H66 zenon_H42f zenon_H95 zenon_H1f5 zenon_H67 zenon_H7d zenon_H155.
% 119.90/120.16 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.90/120.16 elim (classic (gt (loopcounter) (n0))); [ zenon_intro zenon_H2fd | zenon_intro zenon_H2fa ].
% 119.90/120.16 elim (classic (gt (n0) (n3))); [ zenon_intro zenon_H28b | zenon_intro zenon_H254 ].
% 119.90/120.16 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.16 generalize (zenon_H13b (n0)). zenon_intro zenon_H45d.
% 119.90/120.16 generalize (zenon_H45d (n3)). zenon_intro zenon_H45e.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H45e); [ zenon_intro zenon_H2fa | zenon_intro zenon_H45f ].
% 119.90/120.16 exact (zenon_H2fa zenon_H2fd).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H45f); [ zenon_intro zenon_H254 | zenon_intro zenon_H1f9 ].
% 119.90/120.16 exact (zenon_H254 zenon_H28b).
% 119.90/120.16 exact (zenon_H1f5 zenon_H1f9).
% 119.90/120.16 apply (zenon_L240_); trivial.
% 119.90/120.16 cut ((gt (loopcounter) (loopcounter)) = (gt (loopcounter) (n0))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H2fa.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H134.
% 119.90/120.16 cut (((loopcounter) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 exact (zenon_H132 zenon_H95).
% 119.90/120.16 apply (zenon_L230_); trivial.
% 119.90/120.16 (* end of lemma zenon_L241_ *)
% 119.90/120.16 assert (zenon_L242_ : ((tptp_minus_1) = (n3)) -> ((loopcounter) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (loopcounter) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H42f zenon_H95 zenon_H66 zenon_H19d zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.16 elim (classic ((~((loopcounter) = (n3)))/\(~(gt (loopcounter) (n3))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hc2. zenon_intro zenon_H1f5.
% 119.90/120.16 apply (zenon_L241_); trivial.
% 119.90/120.16 cut ((gt (n3) (n2)) = (gt (loopcounter) (n2))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H19d.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact gt_3_2.
% 119.90/120.16 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.90/120.16 cut (((n3) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f7 ].
% 119.90/120.16 apply zenon_H1f8. zenon_intro zenon_Hcb.
% 119.90/120.16 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.90/120.16 cut (((loopcounter) = (loopcounter)) = ((n3) = (loopcounter))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H1f6.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_Hed.
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_Hc2 zenon_Hcb).
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H1f7. zenon_intro zenon_H1f9.
% 119.90/120.16 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.16 generalize (zenon_H13b (n3)). zenon_intro zenon_H1fa.
% 119.90/120.16 generalize (zenon_H1fa (n2)). zenon_intro zenon_H23a.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H23a); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23b ].
% 119.90/120.16 exact (zenon_H1f5 zenon_H1f9).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H22f | zenon_intro zenon_H1a1 ].
% 119.90/120.16 exact (zenon_H22f gt_3_2).
% 119.90/120.16 exact (zenon_H19d zenon_H1a1).
% 119.90/120.16 apply zenon_H63. apply refl_equal.
% 119.90/120.16 (* end of lemma zenon_L242_ *)
% 119.90/120.16 assert (zenon_L243_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) zenon_TG_dq)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n0)) -> ((tptp_minus_1) = (n3)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H466 zenon_H341 zenon_H95 zenon_H42f zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.16 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.16 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.16 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.16 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.16 exact (zenon_H92 zenon_H7d).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.16 exact (zenon_H46e zenon_H46d).
% 119.90/120.16 exact (zenon_H466 zenon_H465).
% 119.90/120.16 elim (classic ((n2) = zenon_TG_dq)); [ zenon_intro zenon_H471 | zenon_intro zenon_H336 ].
% 119.90/120.16 elim (classic (gt (loopcounter) (n2))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H19d ].
% 119.90/120.16 cut ((gt (loopcounter) (n2)) = (gt (loopcounter) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H46e.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H1a1.
% 119.90/120.16 cut (((n2) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H336].
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 exact (zenon_H336 zenon_H471).
% 119.90/120.16 apply (zenon_L242_); trivial.
% 119.90/120.16 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq) = ((n2) = zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H336.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H3d4.
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.16 cut ((zenon_TG_dq = (n2))); [idtac | apply NNPP; zenon_intro zenon_H472].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H472 zenon_H341).
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 (* end of lemma zenon_L243_ *)
% 119.90/120.16 assert (zenon_L244_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n1)) (succ (loopcounter)))) -> ((tptp_minus_1) = (n1)) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H66 zenon_H116 zenon_H3db zenon_H67 zenon_H7d zenon_H155.
% 119.90/120.16 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.90/120.16 elim (classic (gt (succ (tptp_minus_1)) (succ (loopcounter)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H16c ].
% 119.90/120.16 cut ((gt (succ (tptp_minus_1)) (succ (loopcounter))) = (gt (succ (n1)) (succ (loopcounter)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H116.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H175.
% 119.90/120.16 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H476].
% 119.90/120.16 congruence.
% 119.90/120.16 elim (classic ((succ (n1)) = (succ (n1)))); [ zenon_intro zenon_H100 | zenon_intro zenon_H101 ].
% 119.90/120.16 cut (((succ (n1)) = (succ (n1))) = ((succ (tptp_minus_1)) = (succ (n1)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H476.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H100.
% 119.90/120.16 cut (((succ (n1)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H101].
% 119.90/120.16 cut (((succ (n1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H477].
% 119.90/120.16 congruence.
% 119.90/120.16 cut (((n1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3e0].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H3e0. apply sym_equal. exact zenon_H3db.
% 119.90/120.16 apply zenon_H101. apply refl_equal.
% 119.90/120.16 apply zenon_H101. apply refl_equal.
% 119.90/120.16 apply zenon_H76. apply refl_equal.
% 119.90/120.16 cut ((gt (n0) (succ (loopcounter))) = (gt (succ (tptp_minus_1)) (succ (loopcounter)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H16c.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H146.
% 119.90/120.16 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.90/120.16 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.90/120.16 congruence.
% 119.90/120.16 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H167.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H16a.
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.16 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H16b succ_tptp_minus_1).
% 119.90/120.16 apply zenon_H169. apply refl_equal.
% 119.90/120.16 apply zenon_H169. apply refl_equal.
% 119.90/120.16 apply zenon_H76. apply refl_equal.
% 119.90/120.16 apply (zenon_L127_); trivial.
% 119.90/120.16 (* end of lemma zenon_L244_ *)
% 119.90/120.16 assert (zenon_L245_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (~(leq (loopcounter) (n2))) -> False).
% 119.90/120.16 do 0 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H478.
% 119.90/120.16 generalize (leq_succ_gt_equiv (loopcounter)). zenon_intro zenon_H7f.
% 119.90/120.16 generalize (zenon_H7f (n2)). zenon_intro zenon_H479.
% 119.90/120.16 apply (zenon_equiv_s _ _ zenon_H479); [ zenon_intro zenon_H478; zenon_intro zenon_H47c | zenon_intro zenon_H47b; zenon_intro zenon_H47a ].
% 119.90/120.16 elim (classic ((~((succ (n2)) = (n1)))/\(~(gt (succ (n2)) (n1))))); [ zenon_intro zenon_H47d | zenon_intro zenon_H47e ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H47d). zenon_intro zenon_H47f. zenon_intro zenon_H413.
% 119.90/120.16 elim (classic ((~((succ (n2)) = (n3)))/\(~(gt (succ (n2)) (n3))))); [ zenon_intro zenon_H440 | zenon_intro zenon_H441 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H440). zenon_intro zenon_H442. zenon_intro zenon_H423.
% 119.90/120.16 apply (zenon_L215_); trivial.
% 119.90/120.16 cut ((gt (n3) (n1)) = (gt (succ (n2)) (n1))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H413.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact gt_3_1.
% 119.90/120.16 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.90/120.16 cut (((n3) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H443].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H441); [ zenon_intro zenon_H445 | zenon_intro zenon_H444 ].
% 119.90/120.16 apply zenon_H445. zenon_intro zenon_H446.
% 119.90/120.16 elim (classic ((succ (n2)) = (succ (n2)))); [ zenon_intro zenon_H421 | zenon_intro zenon_H40f ].
% 119.90/120.16 cut (((succ (n2)) = (succ (n2))) = ((n3) = (succ (n2)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H443.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H421.
% 119.90/120.16 cut (((succ (n2)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H40f].
% 119.90/120.16 cut (((succ (n2)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H442].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H442 zenon_H446).
% 119.90/120.16 apply zenon_H40f. apply refl_equal.
% 119.90/120.16 apply zenon_H40f. apply refl_equal.
% 119.90/120.16 apply zenon_H444. zenon_intro zenon_H42e.
% 119.90/120.16 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.16 generalize (zenon_H40a (n3)). zenon_intro zenon_H447.
% 119.90/120.16 generalize (zenon_H447 (n1)). zenon_intro zenon_H480.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H480); [ zenon_intro zenon_H423 | zenon_intro zenon_H481 ].
% 119.90/120.16 exact (zenon_H423 zenon_H42e).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H481); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H412 ].
% 119.90/120.16 exact (zenon_H1f2 gt_3_1).
% 119.90/120.16 exact (zenon_H413 zenon_H412).
% 119.90/120.16 apply zenon_H64. apply refl_equal.
% 119.90/120.16 cut ((gt (n1) (loopcounter)) = (gt (succ (n2)) (loopcounter))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H47c.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H7d.
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 cut (((n1) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H482].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H47e); [ zenon_intro zenon_H484 | zenon_intro zenon_H483 ].
% 119.90/120.16 apply zenon_H484. zenon_intro zenon_H485.
% 119.90/120.16 elim (classic ((succ (n2)) = (succ (n2)))); [ zenon_intro zenon_H421 | zenon_intro zenon_H40f ].
% 119.90/120.16 cut (((succ (n2)) = (succ (n2))) = ((n1) = (succ (n2)))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H482.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H421.
% 119.90/120.16 cut (((succ (n2)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H40f].
% 119.90/120.16 cut (((succ (n2)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H47f].
% 119.90/120.16 congruence.
% 119.90/120.16 exact (zenon_H47f zenon_H485).
% 119.90/120.16 apply zenon_H40f. apply refl_equal.
% 119.90/120.16 apply zenon_H40f. apply refl_equal.
% 119.90/120.16 apply zenon_H483. zenon_intro zenon_H412.
% 119.90/120.16 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.16 generalize (zenon_H40a (n1)). zenon_intro zenon_H414.
% 119.90/120.16 generalize (zenon_H414 (loopcounter)). zenon_intro zenon_H486.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H486); [ zenon_intro zenon_H413 | zenon_intro zenon_H487 ].
% 119.90/120.16 exact (zenon_H413 zenon_H412).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H487); [ zenon_intro zenon_H92 | zenon_intro zenon_H47a ].
% 119.90/120.16 exact (zenon_H92 zenon_H7d).
% 119.90/120.16 exact (zenon_H47c zenon_H47a).
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 exact (zenon_H478 zenon_H47b).
% 119.90/120.16 (* end of lemma zenon_L245_ *)
% 119.90/120.16 assert (zenon_L246_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n2)) -> (~(leq zenon_TG_dq (n1))) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H341 zenon_Hcc zenon_H460.
% 119.90/120.16 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.16 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.16 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.16 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.16 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.16 apply (zenon_L234_); trivial.
% 119.90/120.16 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.16 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.16 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.16 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.16 exact (zenon_H6f zenon_H67).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.16 exact (zenon_H466 zenon_H465).
% 119.90/120.16 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H464.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H469.
% 119.90/120.16 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.16 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.16 congruence.
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.16 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.16 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.16 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.16 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.16 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.16 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.16 exact (zenon_H116 zenon_H11e).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.16 exact (zenon_H46c zenon_H469).
% 119.90/120.16 exact (zenon_H464 zenon_H462).
% 119.90/120.16 apply zenon_H3d3. apply refl_equal.
% 119.90/120.16 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.16 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.16 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.16 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.16 exact (zenon_H92 zenon_H7d).
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.16 exact (zenon_H46e zenon_H46d).
% 119.90/120.16 exact (zenon_H466 zenon_H465).
% 119.90/120.16 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.90/120.16 elim (classic (gt (loopcounter) (n2))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H19d ].
% 119.90/120.16 cut ((gt (loopcounter) (n2)) = (gt (loopcounter) zenon_TG_dq)).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H46e.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H1a1.
% 119.90/120.16 cut (((n2) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H336].
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 apply zenon_H336. apply sym_equal. exact zenon_H341.
% 119.90/120.16 cut ((gt (loopcounter) (loopcounter)) = (gt (loopcounter) (n2))).
% 119.90/120.16 intro zenon_D_pnotp.
% 119.90/120.16 apply zenon_H19d.
% 119.90/120.16 rewrite <- zenon_D_pnotp.
% 119.90/120.16 exact zenon_H134.
% 119.90/120.16 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.90/120.16 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.16 congruence.
% 119.90/120.16 apply zenon_H7c. apply refl_equal.
% 119.90/120.16 exact (zenon_Hc3 zenon_Hcc).
% 119.90/120.16 apply (zenon_L230_); trivial.
% 119.90/120.16 exact (zenon_H460 zenon_H463).
% 119.90/120.16 (* end of lemma zenon_L246_ *)
% 119.90/120.16 assert (zenon_L247_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n2)) -> ((tptp_minus_1) = (n2)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H341 zenon_Hcc zenon_H3f9.
% 119.90/120.16 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.16 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L246_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.16 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L247_ *)
% 119.90/120.16 assert (zenon_L248_ : forall (zenon_TG_dq : zenon_U), (((leq (n0) (loopcounter))/\(leq (loopcounter) (n2)))->(((loopcounter) = (n0))\/(((loopcounter) = (n1))\/((loopcounter) = (n2))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n2)) -> ((tptp_minus_1) = (n2)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H488 zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H341 zenon_H3f9.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H488); [ zenon_intro zenon_H48a | zenon_intro zenon_H489 ].
% 119.90/120.16 apply (zenon_notand_s _ _ zenon_H48a); [ zenon_intro zenon_H68 | zenon_intro zenon_H478 ].
% 119.90/120.16 apply (zenon_L5_); trivial.
% 119.90/120.16 apply (zenon_L245_); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H489); [ zenon_intro zenon_H95 | zenon_intro zenon_H48b ].
% 119.90/120.16 apply (zenon_L239_ zenon_TG_dq); trivial.
% 119.90/120.16 apply (zenon_or_s _ _ zenon_H48b); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcc ].
% 119.90/120.16 apply (zenon_L141_); trivial.
% 119.90/120.16 apply (zenon_L247_ zenon_TG_dq); trivial.
% 119.90/120.16 (* end of lemma zenon_L248_ *)
% 119.90/120.16 assert (zenon_L249_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n2)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.16 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H341 zenon_Hcc zenon_H3c1.
% 119.90/120.16 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.16 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L246_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L249_ *)
% 119.90/120.17 assert (zenon_L250_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n2)) -> ((tptp_minus_1) = (n1)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H341 zenon_Hcc zenon_H3db.
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L246_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L250_ *)
% 119.90/120.17 assert (zenon_L251_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (gt (succ zenon_TG_dq) (n0)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n2)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H5c zenon_H341 zenon_Hcc.
% 119.90/120.17 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L217_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.17 apply (zenon_L249_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.17 apply (zenon_L250_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L247_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L251_ *)
% 119.90/120.17 assert (zenon_L252_ : forall (zenon_TG_dq : zenon_U), (~(gt (n3) zenon_TG_dq)) -> (zenon_TG_dq = (n2)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H48c zenon_H341.
% 119.90/120.17 elim (classic ((n2) = zenon_TG_dq)); [ zenon_intro zenon_H471 | zenon_intro zenon_H336 ].
% 119.90/120.17 cut ((gt (n3) (n2)) = (gt (n3) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H48c.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact gt_3_2.
% 119.90/120.17 cut (((n2) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H336].
% 119.90/120.17 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H201. apply refl_equal.
% 119.90/120.17 exact (zenon_H336 zenon_H471).
% 119.90/120.17 apply zenon_H336. apply sym_equal. exact zenon_H341.
% 119.90/120.17 (* end of lemma zenon_L252_ *)
% 119.90/120.17 assert (zenon_L253_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) zenon_TG_dq)) -> ((loopcounter) = (n3)) -> (zenon_TG_dq = (n2)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H466 zenon_Hcb zenon_H341 zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.17 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.17 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.17 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.17 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.17 exact (zenon_H92 zenon_H7d).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.17 exact (zenon_H46e zenon_H46d).
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.90/120.17 elim (classic (gt (loopcounter) (n3))); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H1f5 ].
% 119.90/120.17 elim (classic (gt (n3) zenon_TG_dq)); [ zenon_intro zenon_H48d | zenon_intro zenon_H48c ].
% 119.90/120.17 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.17 generalize (zenon_H13b (n3)). zenon_intro zenon_H1fa.
% 119.90/120.17 generalize (zenon_H1fa zenon_TG_dq). zenon_intro zenon_H48e.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H48e); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H48f ].
% 119.90/120.17 exact (zenon_H1f5 zenon_H1f9).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H48f); [ zenon_intro zenon_H48c | zenon_intro zenon_H46d ].
% 119.90/120.17 exact (zenon_H48c zenon_H48d).
% 119.90/120.17 exact (zenon_H46e zenon_H46d).
% 119.90/120.17 apply (zenon_L252_ zenon_TG_dq); trivial.
% 119.90/120.17 cut ((gt (loopcounter) (loopcounter)) = (gt (loopcounter) (n3))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H1f5.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H134.
% 119.90/120.17 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.90/120.17 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H7c. apply refl_equal.
% 119.90/120.17 exact (zenon_Hc2 zenon_Hcb).
% 119.90/120.17 apply (zenon_L230_); trivial.
% 119.90/120.17 (* end of lemma zenon_L253_ *)
% 119.90/120.17 assert (zenon_L254_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> ((loopcounter) = (n0)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n3)) -> (~(leq zenon_TG_dq (n1))) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H95 zenon_H341 zenon_Hcb zenon_H460.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L138_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L253_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 (* end of lemma zenon_L254_ *)
% 119.90/120.17 assert (zenon_L255_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> ((loopcounter) = (n0)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n3)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H67 zenon_H7d zenon_H155 zenon_H95 zenon_H341 zenon_Hcb zenon_H3c1.
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L254_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L255_ *)
% 119.90/120.17 assert (zenon_L256_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((tptp_minus_1) = (n1)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n3)) -> (~(leq zenon_TG_dq (n1))) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H3db zenon_H341 zenon_Hcb zenon_H460.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L244_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L253_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 (* end of lemma zenon_L256_ *)
% 119.90/120.17 assert (zenon_L257_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> ((tptp_minus_1) = (n1)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n3)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H3db zenon_H341 zenon_Hcb.
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L256_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L257_ *)
% 119.90/120.17 assert (zenon_L258_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ zenon_TG_dq) (n0)) -> (zenon_TG_dq = (n2)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H5c zenon_H341.
% 119.90/120.17 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.90/120.17 apply (zenon_L5_); trivial.
% 119.90/120.17 apply (zenon_L12_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.90/120.17 generalize (finite_domain_3 (tptp_minus_1)). zenon_intro zenon_H44a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44a); [ zenon_intro zenon_H44c | zenon_intro zenon_H44b ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H44c); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3b8 ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L200_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44b); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H44d ].
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L233_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44d); [ zenon_intro zenon_H3db | zenon_intro zenon_H44e ].
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L233_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44e); [ zenon_intro zenon_H3f9 | zenon_intro zenon_H42f ].
% 119.90/120.17 apply (zenon_L239_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_2 (loopcounter)). zenon_intro zenon_H488.
% 119.90/120.17 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L217_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L234_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L243_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L219_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L225_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L244_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L243_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L248_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.90/120.17 apply (zenon_L141_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.90/120.17 apply (zenon_L251_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_2 (loopcounter)). zenon_intro zenon_H488.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H488); [ zenon_intro zenon_H48a | zenon_intro zenon_H489 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H48a); [ zenon_intro zenon_H68 | zenon_intro zenon_H478 ].
% 119.90/120.17 apply (zenon_L5_); trivial.
% 119.90/120.17 apply (zenon_L245_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H489); [ zenon_intro zenon_H95 | zenon_intro zenon_H48b ].
% 119.90/120.17 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L217_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.17 apply (zenon_L255_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.17 apply (zenon_L257_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L239_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H48b); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcc ].
% 119.90/120.17 apply (zenon_L141_); trivial.
% 119.90/120.17 apply (zenon_L251_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L258_ *)
% 119.90/120.17 assert (zenon_L259_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) zenon_TG_dq)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H466 zenon_H343 zenon_H95 zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.17 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.17 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.17 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.17 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.17 exact (zenon_H92 zenon_H7d).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.17 exact (zenon_H46e zenon_H46d).
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 elim (classic ((n3) = zenon_TG_dq)); [ zenon_intro zenon_H345 | zenon_intro zenon_H337 ].
% 119.90/120.17 elim (classic (gt (loopcounter) (n3))); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H1f5 ].
% 119.90/120.17 cut ((gt (loopcounter) (n3)) = (gt (loopcounter) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H46e.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H1f9.
% 119.90/120.17 cut (((n3) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H337].
% 119.90/120.17 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H7c. apply refl_equal.
% 119.90/120.17 exact (zenon_H337 zenon_H345).
% 119.90/120.17 apply (zenon_L231_); trivial.
% 119.90/120.17 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq) = ((n3) = zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H337.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H3d4.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut ((zenon_TG_dq = (n3))); [idtac | apply NNPP; zenon_intro zenon_H490].
% 119.90/120.17 congruence.
% 119.90/120.17 exact (zenon_H490 zenon_H343).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 (* end of lemma zenon_L259_ *)
% 119.90/120.17 assert (zenon_L260_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n2)) (succ (loopcounter)))) -> ((tptp_minus_1) = (n2)) -> ((loopcounter) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.17 do 0 intro. intros zenon_H66 zenon_H405 zenon_H3f9 zenon_H95 zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.17 elim (classic (gt (n0) (succ (loopcounter)))); [ zenon_intro zenon_H146 | zenon_intro zenon_H140 ].
% 119.90/120.17 elim (classic (gt (succ (tptp_minus_1)) (succ (loopcounter)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H16c ].
% 119.90/120.17 cut ((gt (succ (tptp_minus_1)) (succ (loopcounter))) = (gt (succ (n2)) (succ (loopcounter)))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H405.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H175.
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.90/120.17 cut (((succ (tptp_minus_1)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H491].
% 119.90/120.17 congruence.
% 119.90/120.17 elim (classic ((succ (n2)) = (succ (n2)))); [ zenon_intro zenon_H421 | zenon_intro zenon_H40f ].
% 119.90/120.17 cut (((succ (n2)) = (succ (n2))) = ((succ (tptp_minus_1)) = (succ (n2)))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H491.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H421.
% 119.90/120.17 cut (((succ (n2)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H40f].
% 119.90/120.17 cut (((succ (n2)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H492].
% 119.90/120.17 congruence.
% 119.90/120.17 cut (((n2) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H3fe].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H3fe. apply sym_equal. exact zenon_H3f9.
% 119.90/120.17 apply zenon_H40f. apply refl_equal.
% 119.90/120.17 apply zenon_H40f. apply refl_equal.
% 119.90/120.17 apply zenon_H76. apply refl_equal.
% 119.90/120.17 cut ((gt (n0) (succ (loopcounter))) = (gt (succ (tptp_minus_1)) (succ (loopcounter)))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H16c.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H146.
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 119.90/120.17 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 119.90/120.17 congruence.
% 119.90/120.17 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 119.90/120.17 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H167.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H16a.
% 119.90/120.17 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 119.90/120.17 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 119.90/120.17 congruence.
% 119.90/120.17 exact (zenon_H16b succ_tptp_minus_1).
% 119.90/120.17 apply zenon_H169. apply refl_equal.
% 119.90/120.17 apply zenon_H169. apply refl_equal.
% 119.90/120.17 apply zenon_H76. apply refl_equal.
% 119.90/120.17 apply (zenon_L100_); trivial.
% 119.90/120.17 (* end of lemma zenon_L260_ *)
% 119.90/120.17 assert (zenon_L261_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) zenon_TG_dq)) -> (zenon_TG_dq = (n3)) -> ((tptp_minus_1) = (n3)) -> ((loopcounter) = (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H466 zenon_H343 zenon_H42f zenon_H95 zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.17 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.17 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.17 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.17 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.17 exact (zenon_H92 zenon_H7d).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.17 exact (zenon_H46e zenon_H46d).
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 elim (classic ((n3) = zenon_TG_dq)); [ zenon_intro zenon_H345 | zenon_intro zenon_H337 ].
% 119.90/120.17 elim (classic (gt (loopcounter) (n3))); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H1f5 ].
% 119.90/120.17 cut ((gt (loopcounter) (n3)) = (gt (loopcounter) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H46e.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H1f9.
% 119.90/120.17 cut (((n3) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H337].
% 119.90/120.17 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H7c. apply refl_equal.
% 119.90/120.17 exact (zenon_H337 zenon_H345).
% 119.90/120.17 apply (zenon_L241_); trivial.
% 119.90/120.17 elim (classic (zenon_TG_dq = zenon_TG_dq)); [ zenon_intro zenon_H3d4 | zenon_intro zenon_H3d3 ].
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq) = ((n3) = zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H337.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H3d4.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut ((zenon_TG_dq = (n3))); [idtac | apply NNPP; zenon_intro zenon_H490].
% 119.90/120.17 congruence.
% 119.90/120.17 exact (zenon_H490 zenon_H343).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 (* end of lemma zenon_L261_ *)
% 119.90/120.17 assert (zenon_L262_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n2)) -> (~(leq zenon_TG_dq (n2))) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H343 zenon_Hcc zenon_H493.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n2)). zenon_intro zenon_H494.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H494); [ zenon_intro zenon_H493; zenon_intro zenon_H497 | zenon_intro zenon_H496; zenon_intro zenon_H495 ].
% 119.90/120.17 elim (classic ((~((succ (n2)) = (succ (loopcounter))))/\(~(gt (succ (n2)) (succ (loopcounter)))))); [ zenon_intro zenon_H424 | zenon_intro zenon_H425 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H426. zenon_intro zenon_H405.
% 119.90/120.17 apply (zenon_L214_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n2)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H497.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H427].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H425); [ zenon_intro zenon_H429 | zenon_intro zenon_H428 ].
% 119.90/120.17 apply zenon_H429. zenon_intro zenon_H42a.
% 119.90/120.17 apply zenon_H427. apply sym_equal. exact zenon_H42a.
% 119.90/120.17 apply zenon_H428. zenon_intro zenon_H40e.
% 119.90/120.17 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.17 generalize (zenon_H40a (succ (loopcounter))). zenon_intro zenon_H42b.
% 119.90/120.17 generalize (zenon_H42b zenon_TG_dq). zenon_intro zenon_H498.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H498); [ zenon_intro zenon_H405 | zenon_intro zenon_H499 ].
% 119.90/120.17 exact (zenon_H405 zenon_H40e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H499); [ zenon_intro zenon_H46c | zenon_intro zenon_H495 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H497 zenon_H495).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.17 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.17 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.17 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.17 exact (zenon_H92 zenon_H7d).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.17 exact (zenon_H46e zenon_H46d).
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.90/120.17 elim (classic (gt (loopcounter) (n2))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H19d ].
% 119.90/120.17 elim (classic (gt (n2) zenon_TG_dq)); [ zenon_intro zenon_H3a2 | zenon_intro zenon_H3a3 ].
% 119.90/120.17 generalize (zenon_H66 (loopcounter)). zenon_intro zenon_H13b.
% 119.90/120.17 generalize (zenon_H13b (n2)). zenon_intro zenon_H1a2.
% 119.90/120.17 generalize (zenon_H1a2 zenon_TG_dq). zenon_intro zenon_H49a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49a); [ zenon_intro zenon_H19d | zenon_intro zenon_H49b ].
% 119.90/120.17 exact (zenon_H19d zenon_H1a1).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49b); [ zenon_intro zenon_H3a3 | zenon_intro zenon_H46d ].
% 119.90/120.17 exact (zenon_H3a3 zenon_H3a2).
% 119.90/120.17 exact (zenon_H46e zenon_H46d).
% 119.90/120.17 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H102 ].
% 119.90/120.17 elim (classic (gt (n2) (n2))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1a5 ].
% 119.90/120.17 elim (classic (gt (n2) (succ (succ (n0))))); [ zenon_intro zenon_H314 | zenon_intro zenon_H315 ].
% 119.90/120.17 elim (classic (gt (succ (succ (n0))) zenon_TG_dq)); [ zenon_intro zenon_H3a6 | zenon_intro zenon_H3a7 ].
% 119.90/120.17 generalize (zenon_H66 (n2)). zenon_intro zenon_H1a6.
% 119.90/120.17 generalize (zenon_H1a6 (succ (succ (n0)))). zenon_intro zenon_H323.
% 119.90/120.17 generalize (zenon_H323 zenon_TG_dq). zenon_intro zenon_H3a8.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H3a8); [ zenon_intro zenon_H315 | zenon_intro zenon_H3a9 ].
% 119.90/120.17 exact (zenon_H315 zenon_H314).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H3a9); [ zenon_intro zenon_H3a7 | zenon_intro zenon_H3a2 ].
% 119.90/120.17 exact (zenon_H3a7 zenon_H3a6).
% 119.90/120.17 exact (zenon_H3a3 zenon_H3a2).
% 119.90/120.17 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H233 | zenon_intro zenon_H21b ].
% 119.90/120.17 elim (classic (gt (succ (succ (n0))) (n3))); [ zenon_intro zenon_H219 | zenon_intro zenon_H20b ].
% 119.90/120.17 cut ((gt (succ (succ (n0))) (n3)) = (gt (succ (succ (n0))) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H3a7.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H219.
% 119.90/120.17 cut (((n3) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H337].
% 119.90/120.17 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H104. apply refl_equal.
% 119.90/120.17 apply zenon_H337. apply sym_equal. exact zenon_H343.
% 119.90/120.17 cut ((gt (succ (succ (n0))) (succ (succ (succ (n0))))) = (gt (succ (succ (n0))) (n3))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H20b.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H233.
% 119.90/120.17 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 119.90/120.17 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H104. apply refl_equal.
% 119.90/120.17 exact (zenon_H21f successor_3).
% 119.90/120.17 apply (zenon_L189_); trivial.
% 119.90/120.17 cut ((gt (n2) (n2)) = (gt (n2) (succ (succ (n0))))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H315.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H1aa.
% 119.90/120.17 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 119.90/120.17 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H63. apply refl_equal.
% 119.90/120.17 exact (zenon_H102 zenon_H1b9).
% 119.90/120.17 apply (zenon_L191_); trivial.
% 119.90/120.17 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 119.90/120.17 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H102.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H103.
% 119.90/120.17 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H104].
% 119.90/120.17 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 119.90/120.17 congruence.
% 119.90/120.17 exact (zenon_H105 successor_2).
% 119.90/120.17 apply zenon_H104. apply refl_equal.
% 119.90/120.17 apply zenon_H104. apply refl_equal.
% 119.90/120.17 cut ((gt (loopcounter) (loopcounter)) = (gt (loopcounter) (n2))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H19d.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H134.
% 119.90/120.17 cut (((loopcounter) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 119.90/120.17 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H7c. apply refl_equal.
% 119.90/120.17 exact (zenon_Hc3 zenon_Hcc).
% 119.90/120.17 apply (zenon_L230_); trivial.
% 119.90/120.17 exact (zenon_H493 zenon_H496).
% 119.90/120.17 (* end of lemma zenon_L262_ *)
% 119.90/120.17 assert (zenon_L263_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n2)) -> ((tptp_minus_1) = (n1)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H343 zenon_Hcc zenon_H3db.
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L262_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L250_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L263_ *)
% 119.90/120.17 assert (zenon_L264_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n2)) -> ((tptp_minus_1) = (n2)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H343 zenon_Hcc zenon_H3f9.
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L262_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L247_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L264_ *)
% 119.90/120.17 assert (zenon_L265_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n2)) -> ((tptp_minus_1) = (n3)) -> ((tptp_minus_1) = (n0)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H341 zenon_Hcc zenon_H42f zenon_H3c1.
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L246_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L219_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L225_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L265_ *)
% 119.90/120.17 assert (zenon_L266_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) zenon_TG_dq)) -> ((loopcounter) = (n3)) -> (zenon_TG_dq = (n3)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H466 zenon_Hcb zenon_H343 zenon_H155 zenon_H7d zenon_H67.
% 119.90/120.17 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.17 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.17 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.17 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.17 exact (zenon_H92 zenon_H7d).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.17 exact (zenon_H46e zenon_H46d).
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 elim (classic (gt (loopcounter) (loopcounter))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 119.90/120.17 elim (classic (gt (loopcounter) (n3))); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H1f5 ].
% 119.90/120.17 cut ((gt (loopcounter) (n3)) = (gt (loopcounter) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H46e.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H1f9.
% 119.90/120.17 cut (((n3) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H337].
% 119.90/120.17 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H7c. apply refl_equal.
% 119.90/120.17 apply zenon_H337. apply sym_equal. exact zenon_H343.
% 119.90/120.17 cut ((gt (loopcounter) (loopcounter)) = (gt (loopcounter) (n3))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H1f5.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H134.
% 119.90/120.17 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.90/120.17 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H7c. apply refl_equal.
% 119.90/120.17 exact (zenon_Hc2 zenon_Hcb).
% 119.90/120.17 apply (zenon_L230_); trivial.
% 119.90/120.17 (* end of lemma zenon_L266_ *)
% 119.90/120.17 assert (zenon_L267_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n3)) -> (~(leq zenon_TG_dq (n2))) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H343 zenon_Hcb zenon_H493.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n2)). zenon_intro zenon_H494.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H494); [ zenon_intro zenon_H493; zenon_intro zenon_H497 | zenon_intro zenon_H496; zenon_intro zenon_H495 ].
% 119.90/120.17 elim (classic ((~((succ (n2)) = (succ (loopcounter))))/\(~(gt (succ (n2)) (succ (loopcounter)))))); [ zenon_intro zenon_H424 | zenon_intro zenon_H425 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H426. zenon_intro zenon_H405.
% 119.90/120.17 apply (zenon_L214_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n2)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H497.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H427].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H425); [ zenon_intro zenon_H429 | zenon_intro zenon_H428 ].
% 119.90/120.17 apply zenon_H429. zenon_intro zenon_H42a.
% 119.90/120.17 apply zenon_H427. apply sym_equal. exact zenon_H42a.
% 119.90/120.17 apply zenon_H428. zenon_intro zenon_H40e.
% 119.90/120.17 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.17 generalize (zenon_H40a (succ (loopcounter))). zenon_intro zenon_H42b.
% 119.90/120.17 generalize (zenon_H42b zenon_TG_dq). zenon_intro zenon_H498.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H498); [ zenon_intro zenon_H405 | zenon_intro zenon_H499 ].
% 119.90/120.17 exact (zenon_H405 zenon_H40e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H499); [ zenon_intro zenon_H46c | zenon_intro zenon_H495 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H497 zenon_H495).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L266_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H493 zenon_H496).
% 119.90/120.17 (* end of lemma zenon_L267_ *)
% 119.90/120.17 assert (zenon_L268_ : forall (zenon_TG_dq : zenon_U), ((loopcounter) = (n3)) -> (~(gt (loopcounter) zenon_TG_dq)) -> (zenon_TG_dq = (n2)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_Hcb zenon_H46e zenon_H341.
% 119.90/120.17 elim (classic (gt (n3) zenon_TG_dq)); [ zenon_intro zenon_H48d | zenon_intro zenon_H48c ].
% 119.90/120.17 cut ((gt (n3) zenon_TG_dq) = (gt (loopcounter) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H46e.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H48d.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((n3) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 119.90/120.17 congruence.
% 119.90/120.17 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_Hed | zenon_intro zenon_H7c ].
% 119.90/120.17 cut (((loopcounter) = (loopcounter)) = ((n3) = (loopcounter))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H1f6.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_Hed.
% 119.90/120.17 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 119.90/120.17 cut (((loopcounter) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 119.90/120.17 congruence.
% 119.90/120.17 exact (zenon_Hc2 zenon_Hcb).
% 119.90/120.17 apply zenon_H7c. apply refl_equal.
% 119.90/120.17 apply zenon_H7c. apply refl_equal.
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L252_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L268_ *)
% 119.90/120.17 assert (zenon_L269_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n2)) -> ((loopcounter) = (n3)) -> (~(leq zenon_TG_dq (n1))) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H155 zenon_H7d zenon_H67 zenon_H341 zenon_Hcb zenon_H460.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L234_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 elim (classic (gt (loopcounter) zenon_TG_dq)); [ zenon_intro zenon_H46d | zenon_intro zenon_H46e ].
% 119.90/120.17 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.17 generalize (zenon_He4 (loopcounter)). zenon_intro zenon_Hf3.
% 119.90/120.17 generalize (zenon_Hf3 zenon_TG_dq). zenon_intro zenon_H46f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46f); [ zenon_intro zenon_H92 | zenon_intro zenon_H470 ].
% 119.90/120.17 exact (zenon_H92 zenon_H7d).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H470); [ zenon_intro zenon_H46e | zenon_intro zenon_H465 ].
% 119.90/120.17 exact (zenon_H46e zenon_H46d).
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 apply (zenon_L268_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 (* end of lemma zenon_L269_ *)
% 119.90/120.17 assert (zenon_L270_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n3)) -> ((tptp_minus_1) = (n1)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H343 zenon_Hcb zenon_H3db.
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L267_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L269_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L270_ *)
% 119.90/120.17 assert (zenon_L271_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> ((loopcounter) = (n0)) -> ((tptp_minus_1) = (n2)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n3)) -> (~(leq zenon_TG_dq (n2))) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H95 zenon_H3f9 zenon_H343 zenon_Hcb zenon_H493.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n2)). zenon_intro zenon_H494.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H494); [ zenon_intro zenon_H493; zenon_intro zenon_H497 | zenon_intro zenon_H496; zenon_intro zenon_H495 ].
% 119.90/120.17 elim (classic ((~((succ (n2)) = (succ (loopcounter))))/\(~(gt (succ (n2)) (succ (loopcounter)))))); [ zenon_intro zenon_H424 | zenon_intro zenon_H425 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H426. zenon_intro zenon_H405.
% 119.90/120.17 apply (zenon_L260_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n2)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H497.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H427].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H425); [ zenon_intro zenon_H429 | zenon_intro zenon_H428 ].
% 119.90/120.17 apply zenon_H429. zenon_intro zenon_H42a.
% 119.90/120.17 apply zenon_H427. apply sym_equal. exact zenon_H42a.
% 119.90/120.17 apply zenon_H428. zenon_intro zenon_H40e.
% 119.90/120.17 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.17 generalize (zenon_H40a (succ (loopcounter))). zenon_intro zenon_H42b.
% 119.90/120.17 generalize (zenon_H42b zenon_TG_dq). zenon_intro zenon_H498.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H498); [ zenon_intro zenon_H405 | zenon_intro zenon_H499 ].
% 119.90/120.17 exact (zenon_H405 zenon_H40e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H499); [ zenon_intro zenon_H46c | zenon_intro zenon_H495 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H497 zenon_H495).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L266_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H493 zenon_H496).
% 119.90/120.17 (* end of lemma zenon_L271_ *)
% 119.90/120.17 assert (zenon_L272_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> ((loopcounter) = (n0)) -> ((tptp_minus_1) = (n2)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n3)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H67 zenon_H7d zenon_H155 zenon_H95 zenon_H3f9 zenon_H343 zenon_Hcb.
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L271_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L269_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L272_ *)
% 119.90/120.17 assert (zenon_L273_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TG_dq) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (n1) (loopcounter)) -> (gt (succ (loopcounter)) (n1)) -> (zenon_TG_dq = (n3)) -> ((loopcounter) = (n3)) -> ((tptp_minus_1) = (n2)) -> ((loopcounter) = (n2)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H5c zenon_H155 zenon_H7d zenon_H67 zenon_H343 zenon_Hcb zenon_H3f9 zenon_Hcc.
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L267_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L247_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L273_ *)
% 119.90/120.17 assert (zenon_L274_ : forall (zenon_TG_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (loopcounter)) (n1)) -> (gt (n1) (loopcounter)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ zenon_TG_dq) (n0)) -> (zenon_TG_dq = (n3)) -> False).
% 119.90/120.17 do 1 intro. intros zenon_H66 zenon_H67 zenon_H7d zenon_H155 zenon_H5c zenon_H343.
% 119.90/120.17 generalize (finite_domain_3 (loopcounter)). zenon_intro zenon_Hc5.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha4 ].
% 119.90/120.17 apply (zenon_L5_); trivial.
% 119.90/120.17 apply (zenon_L12_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc8 ].
% 119.90/120.17 generalize (finite_domain_3 (tptp_minus_1)). zenon_intro zenon_H44a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44a); [ zenon_intro zenon_H44c | zenon_intro zenon_H44b ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H44c); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3b8 ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L200_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44b); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H44d ].
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L234_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L259_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44d); [ zenon_intro zenon_H3db | zenon_intro zenon_H44e ].
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L244_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L259_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44e); [ zenon_intro zenon_H3f9 | zenon_intro zenon_H42f ].
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n2)). zenon_intro zenon_H494.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H494); [ zenon_intro zenon_H493; zenon_intro zenon_H497 | zenon_intro zenon_H496; zenon_intro zenon_H495 ].
% 119.90/120.17 elim (classic ((~((succ (n2)) = (succ (loopcounter))))/\(~(gt (succ (n2)) (succ (loopcounter)))))); [ zenon_intro zenon_H424 | zenon_intro zenon_H425 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H426. zenon_intro zenon_H405.
% 119.90/120.17 apply (zenon_L260_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n2)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H497.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H427].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H425); [ zenon_intro zenon_H429 | zenon_intro zenon_H428 ].
% 119.90/120.17 apply zenon_H429. zenon_intro zenon_H42a.
% 119.90/120.17 apply zenon_H427. apply sym_equal. exact zenon_H42a.
% 119.90/120.17 apply zenon_H428. zenon_intro zenon_H40e.
% 119.90/120.17 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.17 generalize (zenon_H40a (succ (loopcounter))). zenon_intro zenon_H42b.
% 119.90/120.17 generalize (zenon_H42b zenon_TG_dq). zenon_intro zenon_H498.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H498); [ zenon_intro zenon_H405 | zenon_intro zenon_H499 ].
% 119.90/120.17 exact (zenon_H405 zenon_H40e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H499); [ zenon_intro zenon_H46c | zenon_intro zenon_H495 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H497 zenon_H495).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L259_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H493 zenon_H496).
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L239_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L217_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L234_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L261_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n1)). zenon_intro zenon_H461.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H461); [ zenon_intro zenon_H460; zenon_intro zenon_H464 | zenon_intro zenon_H463; zenon_intro zenon_H462 ].
% 119.90/120.17 elim (classic ((~((succ (n1)) = (succ (loopcounter))))/\(~(gt (succ (n1)) (succ (loopcounter)))))); [ zenon_intro zenon_H114 | zenon_intro zenon_H115 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H114). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 119.90/120.17 apply (zenon_L244_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n1)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H464.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n1)))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 119.90/120.17 apply zenon_H121. zenon_intro zenon_H122.
% 119.90/120.17 apply zenon_H11f. apply sym_equal. exact zenon_H122.
% 119.90/120.17 apply zenon_H120. zenon_intro zenon_H11e.
% 119.90/120.17 generalize (zenon_H66 (succ (n1))). zenon_intro zenon_H11a.
% 119.90/120.17 generalize (zenon_H11a (succ (loopcounter))). zenon_intro zenon_H123.
% 119.90/120.17 generalize (zenon_H123 zenon_TG_dq). zenon_intro zenon_H46a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46a); [ zenon_intro zenon_H116 | zenon_intro zenon_H46b ].
% 119.90/120.17 exact (zenon_H116 zenon_H11e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H46b); [ zenon_intro zenon_H46c | zenon_intro zenon_H462 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H464 zenon_H462).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L261_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H460 zenon_H463).
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n2)). zenon_intro zenon_H494.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H494); [ zenon_intro zenon_H493; zenon_intro zenon_H497 | zenon_intro zenon_H496; zenon_intro zenon_H495 ].
% 119.90/120.17 elim (classic ((~((succ (n2)) = (succ (loopcounter))))/\(~(gt (succ (n2)) (succ (loopcounter)))))); [ zenon_intro zenon_H424 | zenon_intro zenon_H425 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H426. zenon_intro zenon_H405.
% 119.90/120.17 apply (zenon_L260_); trivial.
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n2)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H497.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n2)))); [idtac | apply NNPP; zenon_intro zenon_H427].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H425); [ zenon_intro zenon_H429 | zenon_intro zenon_H428 ].
% 119.90/120.17 apply zenon_H429. zenon_intro zenon_H42a.
% 119.90/120.17 apply zenon_H427. apply sym_equal. exact zenon_H42a.
% 119.90/120.17 apply zenon_H428. zenon_intro zenon_H40e.
% 119.90/120.17 generalize (zenon_H66 (succ (n2))). zenon_intro zenon_H40a.
% 119.90/120.17 generalize (zenon_H40a (succ (loopcounter))). zenon_intro zenon_H42b.
% 119.90/120.17 generalize (zenon_H42b zenon_TG_dq). zenon_intro zenon_H498.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H498); [ zenon_intro zenon_H405 | zenon_intro zenon_H499 ].
% 119.90/120.17 exact (zenon_H405 zenon_H40e).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H499); [ zenon_intro zenon_H46c | zenon_intro zenon_H495 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H497 zenon_H495).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 apply (zenon_L261_ zenon_TG_dq); trivial.
% 119.90/120.17 exact (zenon_H493 zenon_H496).
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L213_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L224_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L239_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 119.90/120.17 apply (zenon_L141_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 119.90/120.17 generalize (finite_domain_3 (tptp_minus_1)). zenon_intro zenon_H44a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44a); [ zenon_intro zenon_H44c | zenon_intro zenon_H44b ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H44c); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3b8 ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L200_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44b); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H44d ].
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L262_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L249_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44d); [ zenon_intro zenon_H3db | zenon_intro zenon_H44e ].
% 119.90/120.17 apply (zenon_L263_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44e); [ zenon_intro zenon_H3f9 | zenon_intro zenon_H42f ].
% 119.90/120.17 apply (zenon_L264_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L217_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L262_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L225_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L265_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.17 apply (zenon_L263_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L264_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_3 (tptp_minus_1)). zenon_intro zenon_H44a.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44a); [ zenon_intro zenon_H44c | zenon_intro zenon_H44b ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H44c); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3b8 ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L200_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44b); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H44d ].
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L267_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L269_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L203_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L222_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44d); [ zenon_intro zenon_H3db | zenon_intro zenon_H44e ].
% 119.90/120.17 apply (zenon_L270_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H44e); [ zenon_intro zenon_H3f9 | zenon_intro zenon_H42f ].
% 119.90/120.17 generalize (finite_domain_2 (loopcounter)). zenon_intro zenon_H488.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H488); [ zenon_intro zenon_H48a | zenon_intro zenon_H489 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H48a); [ zenon_intro zenon_H68 | zenon_intro zenon_H478 ].
% 119.90/120.17 apply (zenon_L5_); trivial.
% 119.90/120.17 apply (zenon_L245_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H489); [ zenon_intro zenon_H95 | zenon_intro zenon_H48b ].
% 119.90/120.17 apply (zenon_L272_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H48b); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcc ].
% 119.90/120.17 apply (zenon_L141_); trivial.
% 119.90/120.17 apply (zenon_L273_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_2 (loopcounter)). zenon_intro zenon_H488.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H488); [ zenon_intro zenon_H48a | zenon_intro zenon_H489 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H48a); [ zenon_intro zenon_H68 | zenon_intro zenon_H478 ].
% 119.90/120.17 apply (zenon_L5_); trivial.
% 119.90/120.17 apply (zenon_L245_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H489); [ zenon_intro zenon_H95 | zenon_intro zenon_H48b ].
% 119.90/120.17 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L217_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L267_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L219_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L225_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (finite_domain_1 zenon_TG_dq). zenon_intro zenon_H473.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H473); [ zenon_intro zenon_H475 | zenon_intro zenon_H474 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H475); [ zenon_intro zenon_H5d | zenon_intro zenon_H460 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L269_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H474); [ zenon_intro zenon_H33d | zenon_intro zenon_H33f ].
% 119.90/120.17 apply (zenon_L219_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L225_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.17 apply (zenon_L270_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L272_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H48b); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcc ].
% 119.90/120.17 apply (zenon_L141_); trivial.
% 119.90/120.17 generalize (finite_domain_2 (tptp_minus_1)). zenon_intro zenon_H44f.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H44f); [ zenon_intro zenon_H451 | zenon_intro zenon_H450 ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H43b ].
% 119.90/120.17 apply (zenon_L198_); trivial.
% 119.90/120.17 apply (zenon_L217_); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H452 ].
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L267_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L219_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L225_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L265_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H452); [ zenon_intro zenon_H3db | zenon_intro zenon_H3f9 ].
% 119.90/120.17 generalize (finite_domain_2 zenon_TG_dq). zenon_intro zenon_H49c.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H49c); [ zenon_intro zenon_H49e | zenon_intro zenon_H49d ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H49e); [ zenon_intro zenon_H5d | zenon_intro zenon_H493 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L267_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49d); [ zenon_intro zenon_H33d | zenon_intro zenon_H49f ].
% 119.90/120.17 apply (zenon_L208_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_or_s _ _ zenon_H49f); [ zenon_intro zenon_H33f | zenon_intro zenon_H341 ].
% 119.90/120.17 apply (zenon_L223_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L250_ zenon_TG_dq); trivial.
% 119.90/120.17 apply (zenon_L273_ zenon_TG_dq); trivial.
% 119.90/120.17 (* end of lemma zenon_L274_ *)
% 119.90/120.17 apply NNPP. intro zenon_G.
% 119.90/120.17 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_H66 | zenon_intro zenon_H4a0 ].
% 119.90/120.17 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H4a2. zenon_intro zenon_H4a1.
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H4a2). zenon_intro zenon_H4a4. zenon_intro zenon_H4a3.
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H4a3). zenon_intro zenon_H4a6. zenon_intro zenon_H4a5.
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H4a5). zenon_intro zenon_H7d. zenon_intro zenon_H4a7.
% 119.90/120.17 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H12c.
% 119.90/120.17 generalize (zenon_H12c (loopcounter)). zenon_intro zenon_H4a8.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H4a8); [ zenon_intro zenon_H4a9; zenon_intro zenon_H6f | zenon_intro zenon_H4a6; zenon_intro zenon_H67 ].
% 119.90/120.17 exact (zenon_H4a9 zenon_H4a6).
% 119.90/120.17 apply (zenon_notallex_s (fun G : zenon_U => (((leq (n0) G)/\(leq G (n4)))->((a_select2 (muold_init) G) = (init)))) zenon_H4a1); [ zenon_intro zenon_H4aa; idtac ].
% 119.90/120.17 elim zenon_H4aa. zenon_intro zenon_TG_dq. zenon_intro zenon_H4ab.
% 119.90/120.17 apply (zenon_notimply_s _ _ zenon_H4ab). zenon_intro zenon_H4ad. zenon_intro zenon_H4ac.
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H4ad). zenon_intro zenon_H61. zenon_intro zenon_H332.
% 119.90/120.17 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 119.90/120.17 generalize (zenon_H5f zenon_TG_dq). zenon_intro zenon_H60.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H5d; zenon_intro zenon_H62 | zenon_intro zenon_H61; zenon_intro zenon_H5c ].
% 119.90/120.17 exact (zenon_H5d zenon_H61).
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n4)). zenon_intro zenon_H331.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H331); [ zenon_intro zenon_H32f; zenon_intro zenon_H333 | zenon_intro zenon_H332; zenon_intro zenon_H32e ].
% 119.90/120.17 exact (zenon_H32f zenon_H332).
% 119.90/120.17 generalize (sum_plus_base zenon_E). zenon_intro zenon_H155.
% 119.90/120.17 generalize (finite_domain_3 zenon_TG_dq). zenon_intro zenon_H4ae.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H4ae); [ zenon_intro zenon_H4b0 | zenon_intro zenon_H4af ].
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H4b0); [ zenon_intro zenon_H5d | zenon_intro zenon_H4b1 ].
% 119.90/120.17 apply (zenon_L1_ zenon_TG_dq); trivial.
% 119.90/120.17 generalize (leq_succ_gt_equiv zenon_TG_dq). zenon_intro zenon_H330.
% 119.90/120.17 generalize (zenon_H330 (n3)). zenon_intro zenon_H4b2.
% 119.90/120.17 apply (zenon_equiv_s _ _ zenon_H4b2); [ zenon_intro zenon_H4b1; zenon_intro zenon_H39b | zenon_intro zenon_H4b3; zenon_intro zenon_H3b1 ].
% 119.90/120.17 elim (classic ((~((succ (n3)) = (succ (loopcounter))))/\(~(gt (succ (n3)) (succ (loopcounter)))))); [ zenon_intro zenon_H4b4 | zenon_intro zenon_H4b5 ].
% 119.90/120.17 apply (zenon_and_s _ _ zenon_H4b4). zenon_intro zenon_H4b6. zenon_intro zenon_H2a9.
% 119.90/120.17 apply (zenon_L134_); trivial.
% 119.90/120.17 elim (classic ((n1) = zenon_TG_dq)); [ zenon_intro zenon_H458 | zenon_intro zenon_H335 ].
% 119.90/120.17 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (n3)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H39b.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H67.
% 119.90/120.17 cut (((n1) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H335].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H4b7].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H4b5); [ zenon_intro zenon_H4b9 | zenon_intro zenon_H4b8 ].
% 119.90/120.17 apply zenon_H4b9. zenon_intro zenon_H4ba.
% 119.90/120.17 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ].
% 119.90/120.17 cut (((succ (n3)) = (succ (n3))) = ((succ (loopcounter)) = (succ (n3)))).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H4b7.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H9e.
% 119.90/120.17 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.90/120.17 cut (((succ (n3)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H4b6].
% 119.90/120.17 congruence.
% 119.90/120.17 exact (zenon_H4b6 zenon_H4ba).
% 119.90/120.17 apply zenon_H9f. apply refl_equal.
% 119.90/120.17 apply zenon_H9f. apply refl_equal.
% 119.90/120.17 apply zenon_H4b8. zenon_intro zenon_H2b0.
% 119.90/120.17 generalize (zenon_H66 (succ (n3))). zenon_intro zenon_Hb5.
% 119.90/120.17 generalize (zenon_Hb5 (succ (loopcounter))). zenon_intro zenon_H4bb.
% 119.90/120.17 generalize (zenon_H4bb (n1)). zenon_intro zenon_H4bc.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H4bc); [ zenon_intro zenon_H2a9 | zenon_intro zenon_H4bd ].
% 119.90/120.17 exact (zenon_H2a9 zenon_H2b0).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H4bd); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb9 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 cut ((gt (succ (n3)) (n1)) = (gt (succ (n3)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H39b.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_Hb9.
% 119.90/120.17 cut (((n1) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H335].
% 119.90/120.17 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H9f. apply refl_equal.
% 119.90/120.17 exact (zenon_H335 zenon_H458).
% 119.90/120.17 exact (zenon_H335 zenon_H458).
% 119.90/120.17 elim (classic (gt (n1) zenon_TG_dq)); [ zenon_intro zenon_H465 | zenon_intro zenon_H466 ].
% 119.90/120.17 generalize (zenon_H66 (succ (loopcounter))). zenon_intro zenon_H77.
% 119.90/120.17 generalize (zenon_H77 (n1)). zenon_intro zenon_H78.
% 119.90/120.17 generalize (zenon_H78 zenon_TG_dq). zenon_intro zenon_H467.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H467); [ zenon_intro zenon_H6f | zenon_intro zenon_H468 ].
% 119.90/120.17 exact (zenon_H6f zenon_H67).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H468); [ zenon_intro zenon_H466 | zenon_intro zenon_H469 ].
% 119.90/120.17 exact (zenon_H466 zenon_H465).
% 119.90/120.17 cut ((gt (succ (loopcounter)) zenon_TG_dq) = (gt (succ (n3)) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H39b.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact zenon_H469.
% 119.90/120.17 cut ((zenon_TG_dq = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H3d3].
% 119.90/120.17 cut (((succ (loopcounter)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H4b7].
% 119.90/120.17 congruence.
% 119.90/120.17 apply (zenon_notand_s _ _ zenon_H4b5); [ zenon_intro zenon_H4b9 | zenon_intro zenon_H4b8 ].
% 119.90/120.17 apply zenon_H4b9. zenon_intro zenon_H4ba.
% 119.90/120.17 apply zenon_H4b7. apply sym_equal. exact zenon_H4ba.
% 119.90/120.17 apply zenon_H4b8. zenon_intro zenon_H2b0.
% 119.90/120.17 generalize (zenon_H66 (succ (n3))). zenon_intro zenon_Hb5.
% 119.90/120.17 generalize (zenon_Hb5 (succ (loopcounter))). zenon_intro zenon_H4bb.
% 119.90/120.17 generalize (zenon_H4bb zenon_TG_dq). zenon_intro zenon_H4be.
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H4be); [ zenon_intro zenon_H2a9 | zenon_intro zenon_H4bf ].
% 119.90/120.17 exact (zenon_H2a9 zenon_H2b0).
% 119.90/120.17 apply (zenon_imply_s _ _ zenon_H4bf); [ zenon_intro zenon_H46c | zenon_intro zenon_H3b1 ].
% 119.90/120.17 exact (zenon_H46c zenon_H469).
% 119.90/120.17 exact (zenon_H39b zenon_H3b1).
% 119.90/120.17 apply zenon_H3d3. apply refl_equal.
% 119.90/120.17 elim (classic ((n0) = zenon_TG_dq)); [ zenon_intro zenon_H4c0 | zenon_intro zenon_H334 ].
% 119.90/120.17 cut ((gt (n1) (n0)) = (gt (n1) zenon_TG_dq)).
% 119.90/120.17 intro zenon_D_pnotp.
% 119.90/120.17 apply zenon_H466.
% 119.90/120.17 rewrite <- zenon_D_pnotp.
% 119.90/120.17 exact gt_1_0.
% 119.90/120.17 cut (((n0) = zenon_TG_dq)); [idtac | apply NNPP; zenon_intro zenon_H334].
% 119.90/120.17 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 119.90/120.17 congruence.
% 119.90/120.17 apply zenon_H64. apply refl_equal.
% 119.90/120.17 exact (zenon_H334 zenon_H4c0).
% 119.90/120.18 elim (classic (gt (n0) zenon_TG_dq)); [ zenon_intro zenon_H3a1 | zenon_intro zenon_H39a ].
% 119.90/120.18 generalize (zenon_H66 (n1)). zenon_intro zenon_He4.
% 119.90/120.18 generalize (zenon_He4 (n0)). zenon_intro zenon_H385.
% 119.90/120.18 generalize (zenon_H385 zenon_TG_dq). zenon_intro zenon_H4c1.
% 119.90/120.18 apply (zenon_imply_s _ _ zenon_H4c1); [ zenon_intro zenon_H7b | zenon_intro zenon_H4c2 ].
% 119.90/120.18 exact (zenon_H7b gt_1_0).
% 119.90/120.18 apply (zenon_imply_s _ _ zenon_H4c2); [ zenon_intro zenon_H39a | zenon_intro zenon_H465 ].
% 119.90/120.18 exact (zenon_H39a zenon_H3a1).
% 119.90/120.18 exact (zenon_H466 zenon_H465).
% 119.90/120.18 apply (zenon_L197_ zenon_TG_dq); trivial.
% 119.90/120.18 exact (zenon_H4b1 zenon_H4b3).
% 119.90/120.18 apply (zenon_or_s _ _ zenon_H4af); [ zenon_intro zenon_H33d | zenon_intro zenon_H4c3 ].
% 119.90/120.18 apply (zenon_L220_ zenon_TG_dq); trivial.
% 119.90/120.18 apply (zenon_or_s _ _ zenon_H4c3); [ zenon_intro zenon_H33f | zenon_intro zenon_H4c4 ].
% 119.90/120.18 apply (zenon_L226_ zenon_TG_dq); trivial.
% 119.90/120.18 apply (zenon_or_s _ _ zenon_H4c4); [ zenon_intro zenon_H341 | zenon_intro zenon_H343 ].
% 119.90/120.18 apply (zenon_L258_ zenon_TG_dq); trivial.
% 119.90/120.18 apply (zenon_L274_ zenon_TG_dq); trivial.
% 119.90/120.18 apply zenon_H4a0. zenon_intro zenon_Tx_buz. apply NNPP. zenon_intro zenon_H4c6.
% 119.90/120.18 apply zenon_H4c6. zenon_intro zenon_Ty_bvb. apply NNPP. zenon_intro zenon_H4c8.
% 119.90/120.18 apply zenon_H4c8. zenon_intro zenon_Tz_bvd. apply NNPP. zenon_intro zenon_H4ca.
% 119.90/120.18 apply (zenon_notimply_s _ _ zenon_H4ca). zenon_intro zenon_H4cc. zenon_intro zenon_H4cb.
% 119.90/120.18 apply (zenon_notimply_s _ _ zenon_H4cb). zenon_intro zenon_H4ce. zenon_intro zenon_H4cd.
% 119.90/120.18 generalize (transitivity_gt zenon_Tx_buz). zenon_intro zenon_H4cf.
% 119.90/120.18 generalize (zenon_H4cf zenon_Ty_bvb). zenon_intro zenon_H4d0.
% 119.90/120.18 generalize (zenon_H4d0 zenon_Tz_bvd). zenon_intro zenon_H4d1.
% 119.90/120.18 apply (zenon_imply_s _ _ zenon_H4d1); [ zenon_intro zenon_H4d3 | zenon_intro zenon_H4d2 ].
% 119.90/120.18 apply (zenon_notand_s _ _ zenon_H4d3); [ zenon_intro zenon_H4d5 | zenon_intro zenon_H4d4 ].
% 119.90/120.18 exact (zenon_H4d5 zenon_H4cc).
% 119.90/120.18 exact (zenon_H4d4 zenon_H4ce).
% 119.90/120.18 exact (zenon_H4cd zenon_H4d2).
% 119.90/120.18 Qed.
% 119.90/120.18 % SZS output end Proof
% 119.90/120.18 (* END-PROOF *)
% 119.90/120.18 nodes searched: 7794005
% 119.90/120.18 max branch formulas: 14852
% 119.90/120.18 proof nodes created: 20373
% 119.90/120.18 formulas created: 2854394
% 119.90/120.18
%------------------------------------------------------------------------------