TSTP Solution File: SWV205+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV205+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n017.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 23:03:18 EDT 2022
% Result : Theorem 8.12s 8.35s
% Output : Proof 8.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV205+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.12/0.14 % Command : run_zenon %s %d
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 15 23:05:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 8.12/8.35 (* PROOF-FOUND *)
% 8.12/8.35 % SZS status Theorem
% 8.12/8.35 (* BEGIN-PROOF *)
% 8.12/8.35 % SZS output start Proof
% 8.12/8.35 Theorem quaternion_ds1_inuse_0016 : ((((a_select2 (rho_defuse) (n0)) = (use))/\(((a_select2 (rho_defuse) (n1)) = (use))/\(((a_select2 (rho_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n0)) = (use))/\(((a_select2 (sigma_defuse) (n1)) = (use))/\(((a_select2 (sigma_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n3)) = (use))/\(((a_select2 (sigma_defuse) (n4)) = (use))/\(((a_select2 (sigma_defuse) (n5)) = (use))/\(((a_select3 (u_defuse) (n0) (n0)) = (use))/\(((a_select3 (u_defuse) (n1) (n0)) = (use))/\(((a_select3 (u_defuse) (n2) (n0)) = (use))/\(((a_select2 (xinit_defuse) (n3)) = (use))/\(((a_select2 (xinit_defuse) (n4)) = (use))/\(((a_select2 (xinit_defuse) (n5)) = (use))/\(((a_select2 (xinit_mean_defuse) (n0)) = (use))/\(((a_select2 (xinit_mean_defuse) (n1)) = (use))/\(((a_select2 (xinit_mean_defuse) (n2)) = (use))/\(((a_select2 (xinit_mean_defuse) (n3)) = (use))/\(((a_select2 (xinit_mean_defuse) (n4)) = (use))/\(((a_select2 (xinit_mean_defuse) (n5)) = (use))/\(((a_select2 (xinit_noise_defuse) (n0)) = (use))/\(((a_select2 (xinit_noise_defuse) (n1)) = (use))/\(((a_select2 (xinit_noise_defuse) (n2)) = (use))/\(((a_select2 (xinit_noise_defuse) (n3)) = (use))/\(((a_select2 (xinit_noise_defuse) (n4)) = (use))/\(((a_select2 (xinit_noise_defuse) (n5)) = (use))/\((forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n2))/\(leq B (n998)))))->((a_select3 (u_defuse) A B) = (use)))))/\(forall C : zenon_U, (forall D : zenon_U, (((leq (n0) C)/\((leq (n0) D)/\((leq C (n2))/\(leq D (n998)))))->((a_select3 (z_defuse) C D) = (use)))))))))))))))))))))))))))))))))->(forall E : zenon_U, (((leq (n0) E)/\(leq E (n5)))->((a_select2 (sigma_defuse) E) = (use))))).
% 8.12/8.35 Proof.
% 8.12/8.35 assert (zenon_L1_ : forall (zenon_TE_dq : zenon_U), (gt (succ zenon_TE_dq) (n0)) -> (~(leq (n0) zenon_TE_dq)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H5c zenon_H5d.
% 8.12/8.35 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 8.12/8.35 generalize (zenon_H5f zenon_TE_dq). zenon_intro zenon_H60.
% 8.12/8.35 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H5d; zenon_intro zenon_H62 | zenon_intro zenon_H61; zenon_intro zenon_H5c ].
% 8.12/8.35 exact (zenon_H62 zenon_H5c).
% 8.12/8.35 exact (zenon_H5d zenon_H61).
% 8.12/8.35 (* end of lemma zenon_L1_ *)
% 8.12/8.35 assert (zenon_L2_ : (~((n4) = (n4))) -> False).
% 8.12/8.35 do 0 intro. intros zenon_H63.
% 8.12/8.35 apply zenon_H63. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L2_ *)
% 8.12/8.35 assert (zenon_L3_ : (~((n3) = (n3))) -> False).
% 8.12/8.35 do 0 intro. intros zenon_H64.
% 8.12/8.35 apply zenon_H64. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L3_ *)
% 8.12/8.35 assert (zenon_L4_ : (~((n2) = (n2))) -> False).
% 8.12/8.35 do 0 intro. intros zenon_H65.
% 8.12/8.35 apply zenon_H65. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L4_ *)
% 8.12/8.35 assert (zenon_L5_ : (~((sigma_defuse) = (sigma_defuse))) -> False).
% 8.12/8.35 do 0 intro. intros zenon_H66.
% 8.12/8.35 apply zenon_H66. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L5_ *)
% 8.12/8.35 assert (zenon_L6_ : forall (zenon_TE_dq : zenon_U), (gt (succ (n5)) zenon_TE_dq) -> (~(leq zenon_TE_dq (n5))) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H67 zenon_H68.
% 8.12/8.35 generalize (leq_succ_gt_equiv zenon_TE_dq). zenon_intro zenon_H69.
% 8.12/8.35 generalize (zenon_H69 (n5)). zenon_intro zenon_H6a.
% 8.12/8.35 apply (zenon_equiv_s _ _ zenon_H6a); [ zenon_intro zenon_H68; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H67 ].
% 8.12/8.35 exact (zenon_H6c zenon_H67).
% 8.12/8.35 exact (zenon_H68 zenon_H6b).
% 8.12/8.35 (* end of lemma zenon_L6_ *)
% 8.12/8.35 assert (zenon_L7_ : forall (zenon_TE_dq : zenon_U), (gt (succ zenon_TE_dq) (n0)) -> (gt (succ (n5)) zenon_TE_dq) -> (~((n0) = zenon_TE_dq)) -> (~((n1) = zenon_TE_dq)) -> (~((n2) = zenon_TE_dq)) -> (~((n3) = zenon_TE_dq)) -> (~(zenon_TE_dq = (n4))) -> (~(zenon_TE_dq = (n5))) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H5c zenon_H67 zenon_H6d zenon_H6e zenon_H6f zenon_H70 zenon_H71 zenon_H72.
% 8.12/8.35 generalize (finite_domain_5 zenon_TE_dq). zenon_intro zenon_H73.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ].
% 8.12/8.35 apply (zenon_notand_s _ _ zenon_H75); [ zenon_intro zenon_H5d | zenon_intro zenon_H68 ].
% 8.12/8.35 apply (zenon_L1_ zenon_TE_dq); trivial.
% 8.12/8.35 apply (zenon_L6_ zenon_TE_dq); trivial.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ].
% 8.12/8.35 apply zenon_H6d. apply sym_equal. exact zenon_H77.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H79 | zenon_intro zenon_H78 ].
% 8.12/8.35 apply zenon_H6e. apply sym_equal. exact zenon_H79.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ].
% 8.12/8.35 apply zenon_H6f. apply sym_equal. exact zenon_H7b.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_H7a); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ].
% 8.12/8.35 apply zenon_H70. apply sym_equal. exact zenon_H7d.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_H7c); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ].
% 8.12/8.35 exact (zenon_H71 zenon_H7f).
% 8.12/8.35 exact (zenon_H72 zenon_H7e).
% 8.12/8.35 (* end of lemma zenon_L7_ *)
% 8.12/8.35 assert (zenon_L8_ : forall (zenon_TE_dq : zenon_U), (~((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) (n4)))) -> (~(zenon_TE_dq = (n5))) -> (~((n3) = zenon_TE_dq)) -> (~((n2) = zenon_TE_dq)) -> (~((n1) = zenon_TE_dq)) -> (~((n0) = zenon_TE_dq)) -> (gt (succ (n5)) zenon_TE_dq) -> (gt (succ zenon_TE_dq) (n0)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H80 zenon_H72 zenon_H70 zenon_H6f zenon_H6e zenon_H6d zenon_H67 zenon_H5c.
% 8.12/8.35 cut ((zenon_TE_dq = (n4))); [idtac | apply NNPP; zenon_intro zenon_H71].
% 8.12/8.35 cut (((sigma_defuse) = (sigma_defuse))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H66. apply refl_equal.
% 8.12/8.35 apply (zenon_L7_ zenon_TE_dq); trivial.
% 8.12/8.35 (* end of lemma zenon_L8_ *)
% 8.12/8.35 assert (zenon_L9_ : (~((use) = (use))) -> False).
% 8.12/8.35 do 0 intro. intros zenon_H81.
% 8.12/8.35 apply zenon_H81. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L9_ *)
% 8.12/8.35 assert (zenon_L10_ : forall (zenon_TE_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 (n4) zenon_TE_dq)) -> ((a_select2 (sigma_defuse) (n4)) = (use)) -> (gt (succ zenon_TE_dq) (n0)) -> (gt (succ (n5)) zenon_TE_dq) -> (~((n0) = zenon_TE_dq)) -> ((a_select2 (sigma_defuse) (n5)) = (use)) -> (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H82 zenon_H83 zenon_H84 zenon_H5c zenon_H67 zenon_H6d zenon_H85 zenon_H86.
% 8.12/8.35 elim (classic ((n3) = zenon_TE_dq)); [ zenon_intro zenon_H87 | zenon_intro zenon_H70 ].
% 8.12/8.35 cut ((gt (n4) (n3)) = (gt (n4) zenon_TE_dq)).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H83.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact gt_4_3.
% 8.12/8.35 cut (((n3) = zenon_TE_dq)); [idtac | apply NNPP; zenon_intro zenon_H70].
% 8.12/8.35 cut (((n4) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H63. apply refl_equal.
% 8.12/8.35 exact (zenon_H70 zenon_H87).
% 8.12/8.35 elim (classic (gt (n3) zenon_TE_dq)); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ].
% 8.12/8.35 generalize (zenon_H82 (n4)). zenon_intro zenon_H8a.
% 8.12/8.35 generalize (zenon_H8a (n3)). zenon_intro zenon_H8b.
% 8.12/8.35 generalize (zenon_H8b zenon_TE_dq). zenon_intro zenon_H8c.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_H8c); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ].
% 8.12/8.35 exact (zenon_H8e gt_4_3).
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8f ].
% 8.12/8.35 exact (zenon_H89 zenon_H88).
% 8.12/8.35 exact (zenon_H83 zenon_H8f).
% 8.12/8.35 elim (classic ((n2) = zenon_TE_dq)); [ zenon_intro zenon_H90 | zenon_intro zenon_H6f ].
% 8.12/8.35 cut ((gt (n3) (n2)) = (gt (n3) zenon_TE_dq)).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H89.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact gt_3_2.
% 8.12/8.35 cut (((n2) = zenon_TE_dq)); [idtac | apply NNPP; zenon_intro zenon_H6f].
% 8.12/8.35 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H64. apply refl_equal.
% 8.12/8.35 exact (zenon_H6f zenon_H90).
% 8.12/8.35 elim (classic (gt (n2) zenon_TE_dq)); [ zenon_intro zenon_H91 | zenon_intro zenon_H92 ].
% 8.12/8.35 generalize (zenon_H82 (n3)). zenon_intro zenon_H93.
% 8.12/8.35 generalize (zenon_H93 (n2)). zenon_intro zenon_H94.
% 8.12/8.35 generalize (zenon_H94 zenon_TE_dq). zenon_intro zenon_H95.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ].
% 8.12/8.35 exact (zenon_H97 gt_3_2).
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_H96); [ zenon_intro zenon_H92 | zenon_intro zenon_H88 ].
% 8.12/8.35 exact (zenon_H92 zenon_H91).
% 8.12/8.35 exact (zenon_H89 zenon_H88).
% 8.12/8.35 elim (classic ((n1) = zenon_TE_dq)); [ zenon_intro zenon_H98 | zenon_intro zenon_H6e ].
% 8.12/8.35 cut ((gt (n2) (n1)) = (gt (n2) zenon_TE_dq)).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H92.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact gt_2_1.
% 8.12/8.35 cut (((n1) = zenon_TE_dq)); [idtac | apply NNPP; zenon_intro zenon_H6e].
% 8.12/8.35 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H65. apply refl_equal.
% 8.12/8.35 exact (zenon_H6e zenon_H98).
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n4)) = (use)) = ((a_select2 (sigma_defuse) zenon_TE_dq) = (use))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H86.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H84.
% 8.12/8.35 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n4)) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq)) = ((a_select2 (sigma_defuse) (n4)) = (a_select2 (sigma_defuse) zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H99.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H9a.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) (n4)))); [idtac | apply NNPP; zenon_intro zenon_H80].
% 8.12/8.35 congruence.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n5)) = (use)) = ((a_select2 (sigma_defuse) zenon_TE_dq) = (use))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H86.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H85.
% 8.12/8.35 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n5)) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H9c].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq)) = ((a_select2 (sigma_defuse) (n5)) = (a_select2 (sigma_defuse) zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H9c.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H9a.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) (n5)))); [idtac | apply NNPP; zenon_intro zenon_H9d].
% 8.12/8.35 congruence.
% 8.12/8.35 cut ((zenon_TE_dq = (n5))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 8.12/8.35 cut (((sigma_defuse) = (sigma_defuse))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H66. apply refl_equal.
% 8.12/8.35 apply (zenon_L8_ zenon_TE_dq); trivial.
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H81. apply refl_equal.
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H81. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L10_ *)
% 8.12/8.35 assert (zenon_L11_ : (~((succ (n3)) = (succ (succ (succ (succ (n0))))))) -> False).
% 8.12/8.35 do 0 intro. intros zenon_H9e.
% 8.12/8.35 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H9f. apply sym_equal. exact successor_3.
% 8.12/8.35 (* end of lemma zenon_L11_ *)
% 8.12/8.35 assert (zenon_L12_ : forall (zenon_TE_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)) zenon_TE_dq)) -> (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> ((a_select2 (sigma_defuse) (n5)) = (use)) -> (~((n0) = zenon_TE_dq)) -> (gt (succ (n5)) zenon_TE_dq) -> (gt (succ zenon_TE_dq) (n0)) -> ((a_select2 (sigma_defuse) (n4)) = (use)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H82 zenon_Ha0 zenon_H86 zenon_H85 zenon_H6d zenon_H67 zenon_H5c zenon_H84.
% 8.12/8.35 elim (classic (gt (n4) zenon_TE_dq)); [ zenon_intro zenon_H8f | zenon_intro zenon_H83 ].
% 8.12/8.35 elim (classic (gt (succ (succ (succ (succ (n0))))) zenon_TE_dq)); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ].
% 8.12/8.35 cut ((gt (succ (succ (succ (succ (n0))))) zenon_TE_dq) = (gt (succ (n3)) zenon_TE_dq)).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Ha0.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Ha1.
% 8.12/8.35 cut ((zenon_TE_dq = zenon_TE_dq)); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 8.12/8.35 cut (((succ (succ (succ (succ (n0))))) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ].
% 8.12/8.35 cut (((succ (n3)) = (succ (n3))) = ((succ (succ (succ (succ (n0))))) = (succ (n3)))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Ha4.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Ha5.
% 8.12/8.35 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6].
% 8.12/8.35 cut (((succ (n3)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H9e].
% 8.12/8.35 congruence.
% 8.12/8.35 apply (zenon_L11_); trivial.
% 8.12/8.35 apply zenon_Ha6. apply refl_equal.
% 8.12/8.35 apply zenon_Ha6. apply refl_equal.
% 8.12/8.35 apply zenon_Ha3. apply refl_equal.
% 8.12/8.35 cut ((gt (n4) zenon_TE_dq) = (gt (succ (succ (succ (succ (n0))))) zenon_TE_dq)).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Ha2.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H8f.
% 8.12/8.35 cut ((zenon_TE_dq = zenon_TE_dq)); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 8.12/8.35 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha7].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ].
% 8.12/8.35 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Ha7.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Ha8.
% 8.12/8.35 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha9].
% 8.12/8.35 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Haa].
% 8.12/8.35 congruence.
% 8.12/8.35 exact (zenon_Haa successor_4).
% 8.12/8.35 apply zenon_Ha9. apply refl_equal.
% 8.12/8.35 apply zenon_Ha9. apply refl_equal.
% 8.12/8.35 apply zenon_Ha3. apply refl_equal.
% 8.12/8.35 apply (zenon_L10_ zenon_TE_dq); trivial.
% 8.12/8.35 (* end of lemma zenon_L12_ *)
% 8.12/8.35 assert (zenon_L13_ : forall (zenon_TE_dq : zenon_U), (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> ((a_select2 (sigma_defuse) (n1)) = (use)) -> (zenon_TE_dq = (n1)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H86 zenon_Hab zenon_H79.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n1)) = (use)) = ((a_select2 (sigma_defuse) zenon_TE_dq) = (use))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H86.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hab.
% 8.12/8.35 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n1)) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_Hac].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq)) = ((a_select2 (sigma_defuse) (n1)) = (a_select2 (sigma_defuse) zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hac.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H9a.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) (n1)))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 8.12/8.35 congruence.
% 8.12/8.35 cut ((zenon_TE_dq = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae].
% 8.12/8.35 cut (((sigma_defuse) = (sigma_defuse))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H66. apply refl_equal.
% 8.12/8.35 exact (zenon_Hae zenon_H79).
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H81. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L13_ *)
% 8.12/8.35 assert (zenon_L14_ : forall (zenon_TE_dq : zenon_U), (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> ((a_select2 (sigma_defuse) (n2)) = (use)) -> (zenon_TE_dq = (n2)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H86 zenon_Haf zenon_H7b.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n2)) = (use)) = ((a_select2 (sigma_defuse) zenon_TE_dq) = (use))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H86.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Haf.
% 8.12/8.35 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n2)) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq)) = ((a_select2 (sigma_defuse) (n2)) = (a_select2 (sigma_defuse) zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hb0.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H9a.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) (n2)))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 8.12/8.35 congruence.
% 8.12/8.35 cut ((zenon_TE_dq = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb2].
% 8.12/8.35 cut (((sigma_defuse) = (sigma_defuse))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H66. apply refl_equal.
% 8.12/8.35 exact (zenon_Hb2 zenon_H7b).
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H81. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L14_ *)
% 8.12/8.35 assert (zenon_L15_ : forall (zenon_TE_dq : zenon_U), (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> ((a_select2 (sigma_defuse) (n3)) = (use)) -> (zenon_TE_dq = (n3)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H86 zenon_Hb3 zenon_H7d.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n3)) = (use)) = ((a_select2 (sigma_defuse) zenon_TE_dq) = (use))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H86.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hb3.
% 8.12/8.35 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n3)) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_Hb4].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq)) = ((a_select2 (sigma_defuse) (n3)) = (a_select2 (sigma_defuse) zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hb4.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H9a.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) (n3)))); [idtac | apply NNPP; zenon_intro zenon_Hb5].
% 8.12/8.35 congruence.
% 8.12/8.35 cut ((zenon_TE_dq = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6].
% 8.12/8.35 cut (((sigma_defuse) = (sigma_defuse))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H66. apply refl_equal.
% 8.12/8.35 exact (zenon_Hb6 zenon_H7d).
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H81. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L15_ *)
% 8.12/8.35 assert (zenon_L16_ : forall (zenon_TE_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_TE_dq) (n0)) -> (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> ((a_select2 (sigma_defuse) (n5)) = (use)) -> (~((n0) = zenon_TE_dq)) -> (gt (succ (n5)) zenon_TE_dq) -> ((a_select2 (sigma_defuse) (n4)) = (use)) -> ((a_select2 (sigma_defuse) (n1)) = (use)) -> ((a_select2 (sigma_defuse) (n2)) = (use)) -> ((a_select2 (sigma_defuse) (n3)) = (use)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H82 zenon_H5c zenon_H86 zenon_H85 zenon_H6d zenon_H67 zenon_H84 zenon_Hab zenon_Haf zenon_Hb3.
% 8.12/8.35 generalize (finite_domain_3 zenon_TE_dq). zenon_intro zenon_Hb7.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ].
% 8.12/8.35 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_H5d | zenon_intro zenon_Hba ].
% 8.12/8.35 apply (zenon_L1_ zenon_TE_dq); trivial.
% 8.12/8.35 generalize (leq_succ_gt_equiv zenon_TE_dq). zenon_intro zenon_H69.
% 8.12/8.35 generalize (zenon_H69 (n3)). zenon_intro zenon_Hbb.
% 8.12/8.35 apply (zenon_equiv_s _ _ zenon_Hbb); [ zenon_intro zenon_Hba; zenon_intro zenon_Ha0 | zenon_intro zenon_Hbd; zenon_intro zenon_Hbc ].
% 8.12/8.35 apply (zenon_L12_ zenon_TE_dq); trivial.
% 8.12/8.35 exact (zenon_Hba zenon_Hbd).
% 8.12/8.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hbe ].
% 8.12/8.35 apply zenon_H6d. apply sym_equal. exact zenon_H77.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H79 | zenon_intro zenon_Hbf ].
% 8.12/8.35 apply (zenon_L13_ zenon_TE_dq); trivial.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7b | zenon_intro zenon_H7d ].
% 8.12/8.35 apply (zenon_L14_ zenon_TE_dq); trivial.
% 8.12/8.35 apply (zenon_L15_ zenon_TE_dq); trivial.
% 8.12/8.35 (* end of lemma zenon_L16_ *)
% 8.12/8.35 assert (zenon_L17_ : forall (zenon_TE_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((succ (n0)) = (succ zenon_TE_dq))) -> ((a_select2 (sigma_defuse) (n3)) = (use)) -> ((a_select2 (sigma_defuse) (n2)) = (use)) -> ((a_select2 (sigma_defuse) (n1)) = (use)) -> ((a_select2 (sigma_defuse) (n4)) = (use)) -> (gt (succ (n5)) zenon_TE_dq) -> ((a_select2 (sigma_defuse) (n5)) = (use)) -> (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> (gt (succ zenon_TE_dq) (n0)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H82 zenon_Hc0 zenon_Hb3 zenon_Haf zenon_Hab zenon_H84 zenon_H67 zenon_H85 zenon_H86 zenon_H5c.
% 8.12/8.35 cut (((n0) = zenon_TE_dq)); [idtac | apply NNPP; zenon_intro zenon_H6d].
% 8.12/8.35 congruence.
% 8.12/8.35 apply (zenon_L16_ zenon_TE_dq); trivial.
% 8.12/8.35 (* end of lemma zenon_L17_ *)
% 8.12/8.35 assert (zenon_L18_ : (~((n1) = (n1))) -> False).
% 8.12/8.35 do 0 intro. intros zenon_Hc1.
% 8.12/8.35 apply zenon_Hc1. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L18_ *)
% 8.12/8.35 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 (succ (n0))) (n1))) -> False).
% 8.12/8.35 do 0 intro. intros zenon_H82 zenon_Hc2.
% 8.12/8.35 elim (classic ((~((succ (succ (n0))) = (n2)))/\(~(gt (succ (succ (n0))) (n2))))); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc4 ].
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc6. zenon_intro zenon_Hc5.
% 8.12/8.35 exact (zenon_Hc6 successor_2).
% 8.12/8.35 cut ((gt (n2) (n1)) = (gt (succ (succ (n0))) (n1))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hc2.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact gt_2_1.
% 8.12/8.35 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hc1].
% 8.12/8.35 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hc7].
% 8.12/8.35 congruence.
% 8.12/8.35 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hc8 ].
% 8.12/8.35 apply zenon_Hc9. zenon_intro successor_2.
% 8.12/8.35 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ].
% 8.12/8.35 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hc7.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hca.
% 8.12/8.35 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 8.12/8.35 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc6].
% 8.12/8.35 congruence.
% 8.12/8.35 exact (zenon_Hc6 successor_2).
% 8.12/8.35 apply zenon_Hcb. apply refl_equal.
% 8.12/8.35 apply zenon_Hcb. apply refl_equal.
% 8.12/8.35 apply zenon_Hc8. zenon_intro zenon_Hcc.
% 8.12/8.35 generalize (zenon_H82 (succ (succ (n0)))). zenon_intro zenon_Hcd.
% 8.12/8.35 generalize (zenon_Hcd (n2)). zenon_intro zenon_Hce.
% 8.12/8.35 generalize (zenon_Hce (n1)). zenon_intro zenon_Hcf.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_Hcf); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hd0 ].
% 8.12/8.35 exact (zenon_Hc5 zenon_Hcc).
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_Hd0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd1 ].
% 8.12/8.35 exact (zenon_Hd2 gt_2_1).
% 8.12/8.35 exact (zenon_Hc2 zenon_Hd1).
% 8.12/8.35 apply zenon_Hc1. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L19_ *)
% 8.12/8.35 assert (zenon_L20_ : forall (zenon_TE_dq : zenon_U), (~(gt (succ (succ (n0))) (succ zenon_TE_dq))) -> (gt (succ zenon_TE_dq) (n0)) -> (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> ((a_select2 (sigma_defuse) (n5)) = (use)) -> (gt (succ (n5)) zenon_TE_dq) -> ((a_select2 (sigma_defuse) (n4)) = (use)) -> ((a_select2 (sigma_defuse) (n1)) = (use)) -> ((a_select2 (sigma_defuse) (n2)) = (use)) -> ((a_select2 (sigma_defuse) (n3)) = (use)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 8.12/8.35 do 1 intro. intros zenon_Hd3 zenon_H5c zenon_H86 zenon_H85 zenon_H67 zenon_H84 zenon_Hab zenon_Haf zenon_Hb3 zenon_H82.
% 8.12/8.35 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ].
% 8.12/8.35 elim (classic (gt (succ (succ (n0))) (n1))); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hc2 ].
% 8.12/8.35 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ].
% 8.12/8.35 cut ((gt (succ (succ (n0))) (succ (n0))) = (gt (succ (succ (n0))) (succ zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hd3.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hd6.
% 8.12/8.35 cut (((succ (n0)) = (succ zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_Hc0].
% 8.12/8.35 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_Hcb. apply refl_equal.
% 8.12/8.35 apply (zenon_L17_ zenon_TE_dq); trivial.
% 8.12/8.35 cut ((gt (succ (succ (n0))) (n1)) = (gt (succ (succ (n0))) (succ (n0)))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hd7.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hd1.
% 8.12/8.35 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd5].
% 8.12/8.35 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_Hcb. apply refl_equal.
% 8.12/8.35 exact (zenon_Hd5 zenon_Hd4).
% 8.12/8.35 apply (zenon_L19_); trivial.
% 8.12/8.35 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ].
% 8.12/8.35 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hd5.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hd8.
% 8.12/8.35 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 8.12/8.35 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 8.12/8.35 congruence.
% 8.12/8.35 exact (zenon_Hda successor_1).
% 8.12/8.35 apply zenon_Hd9. apply refl_equal.
% 8.12/8.35 apply zenon_Hd9. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L20_ *)
% 8.12/8.35 assert (zenon_L21_ : forall (zenon_TE_dq : zenon_U), ((a_select2 (sigma_defuse) (n3)) = (use)) -> ((a_select2 (sigma_defuse) (n2)) = (use)) -> ((a_select2 (sigma_defuse) (n1)) = (use)) -> ((a_select2 (sigma_defuse) (n4)) = (use)) -> (gt (succ (n5)) zenon_TE_dq) -> ((a_select2 (sigma_defuse) (n5)) = (use)) -> (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> (gt (succ zenon_TE_dq) (n0)) -> (~(gt (n2) (succ zenon_TE_dq))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False).
% 8.12/8.35 do 1 intro. intros zenon_Hb3 zenon_Haf zenon_Hab zenon_H84 zenon_H67 zenon_H85 zenon_H86 zenon_H5c zenon_Hdb zenon_H82.
% 8.12/8.35 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hc7 ].
% 8.12/8.35 elim (classic (gt (succ (succ (n0))) (succ zenon_TE_dq))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hd3 ].
% 8.12/8.35 cut ((gt (succ (succ (n0))) (succ zenon_TE_dq)) = (gt (n2) (succ zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hdb.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hdd.
% 8.12/8.35 cut (((succ zenon_TE_dq) = (succ zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 8.12/8.35 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc6].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((n2) = (n2))); [ zenon_intro zenon_Hdf | zenon_intro zenon_H65 ].
% 8.12/8.35 cut (((n2) = (n2)) = ((succ (succ (n0))) = (n2))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hc6.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hdf.
% 8.12/8.35 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 8.12/8.35 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hc7].
% 8.12/8.35 congruence.
% 8.12/8.35 exact (zenon_Hc7 zenon_Hdc).
% 8.12/8.35 apply zenon_H65. apply refl_equal.
% 8.12/8.35 apply zenon_H65. apply refl_equal.
% 8.12/8.35 apply zenon_Hde. apply refl_equal.
% 8.12/8.35 apply (zenon_L20_ zenon_TE_dq); trivial.
% 8.12/8.35 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ].
% 8.12/8.35 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hc7.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Hca.
% 8.12/8.35 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 8.12/8.35 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc6].
% 8.12/8.35 congruence.
% 8.12/8.35 exact (zenon_Hc6 successor_2).
% 8.12/8.35 apply zenon_Hcb. apply refl_equal.
% 8.12/8.35 apply zenon_Hcb. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L21_ *)
% 8.12/8.35 assert (zenon_L22_ : forall (zenon_TE_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 (n4) (succ zenon_TE_dq))) -> (gt (succ zenon_TE_dq) (n0)) -> (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> ((a_select2 (sigma_defuse) (n5)) = (use)) -> (gt (succ (n5)) zenon_TE_dq) -> ((a_select2 (sigma_defuse) (n4)) = (use)) -> ((a_select2 (sigma_defuse) (n1)) = (use)) -> ((a_select2 (sigma_defuse) (n2)) = (use)) -> ((a_select2 (sigma_defuse) (n3)) = (use)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H82 zenon_He0 zenon_H5c zenon_H86 zenon_H85 zenon_H67 zenon_H84 zenon_Hab zenon_Haf zenon_Hb3.
% 8.12/8.35 elim (classic (gt (n3) (succ zenon_TE_dq))); [ zenon_intro zenon_He1 | zenon_intro zenon_He2 ].
% 8.12/8.35 generalize (zenon_H82 (n4)). zenon_intro zenon_H8a.
% 8.12/8.35 generalize (zenon_H8a (n3)). zenon_intro zenon_H8b.
% 8.12/8.35 generalize (zenon_H8b (succ zenon_TE_dq)). zenon_intro zenon_He3.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_He3); [ zenon_intro zenon_H8e | zenon_intro zenon_He4 ].
% 8.12/8.35 exact (zenon_H8e gt_4_3).
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_He4); [ zenon_intro zenon_He2 | zenon_intro zenon_He5 ].
% 8.12/8.35 exact (zenon_He2 zenon_He1).
% 8.12/8.35 exact (zenon_He0 zenon_He5).
% 8.12/8.35 elim (classic (gt (n2) (succ zenon_TE_dq))); [ zenon_intro zenon_He6 | zenon_intro zenon_Hdb ].
% 8.12/8.35 generalize (zenon_H82 (n3)). zenon_intro zenon_H93.
% 8.12/8.35 generalize (zenon_H93 (n2)). zenon_intro zenon_H94.
% 8.12/8.35 generalize (zenon_H94 (succ zenon_TE_dq)). zenon_intro zenon_He7.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_He7); [ zenon_intro zenon_H97 | zenon_intro zenon_He8 ].
% 8.12/8.35 exact (zenon_H97 gt_3_2).
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_He8); [ zenon_intro zenon_Hdb | zenon_intro zenon_He1 ].
% 8.12/8.35 exact (zenon_Hdb zenon_He6).
% 8.12/8.35 exact (zenon_He2 zenon_He1).
% 8.12/8.35 apply (zenon_L21_ zenon_TE_dq); trivial.
% 8.12/8.35 (* end of lemma zenon_L22_ *)
% 8.12/8.35 assert (zenon_L23_ : forall (zenon_TE_dq : zenon_U), (~((a_select2 (sigma_defuse) zenon_TE_dq) = (use))) -> ((a_select2 (sigma_defuse) (n0)) = (use)) -> (zenon_TE_dq = (n0)) -> False).
% 8.12/8.35 do 1 intro. intros zenon_H86 zenon_He9 zenon_H77.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n0)) = (use)) = ((a_select2 (sigma_defuse) zenon_TE_dq) = (use))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H86.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_He9.
% 8.12/8.35 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) (n0)) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_Hea].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq)) = ((a_select2 (sigma_defuse) (n0)) = (a_select2 (sigma_defuse) zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Hea.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H9a.
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 8.12/8.35 cut (((a_select2 (sigma_defuse) zenon_TE_dq) = (a_select2 (sigma_defuse) (n0)))); [idtac | apply NNPP; zenon_intro zenon_Heb].
% 8.12/8.35 congruence.
% 8.12/8.35 cut ((zenon_TE_dq = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 8.12/8.35 cut (((sigma_defuse) = (sigma_defuse))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_H66. apply refl_equal.
% 8.12/8.35 exact (zenon_Hec zenon_H77).
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H9b. apply refl_equal.
% 8.12/8.35 apply zenon_H81. apply refl_equal.
% 8.12/8.35 (* end of lemma zenon_L23_ *)
% 8.12/8.35 apply NNPP. intro zenon_G.
% 8.12/8.35 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_H82 | zenon_intro zenon_Hed ].
% 8.12/8.35 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_Hef. zenon_intro zenon_Hee.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hef). zenon_intro zenon_Hf1. zenon_intro zenon_Hf0.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hf0). zenon_intro zenon_Hf3. zenon_intro zenon_Hf2.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Hf5. zenon_intro zenon_Hf4.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hf4). zenon_intro zenon_He9. zenon_intro zenon_Hf6.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hf6). zenon_intro zenon_Hab. zenon_intro zenon_Hf7.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hf7). zenon_intro zenon_Haf. zenon_intro zenon_Hf8.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_Hb3. zenon_intro zenon_Hf9.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_H84. zenon_intro zenon_Hfa.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hfa). zenon_intro zenon_H85. zenon_intro zenon_Hfb.
% 8.12/8.35 apply (zenon_notallex_s (fun E : zenon_U => (((leq (n0) E)/\(leq E (n5)))->((a_select2 (sigma_defuse) E) = (use)))) zenon_Hee); [ zenon_intro zenon_Hfc; idtac ].
% 8.12/8.35 elim zenon_Hfc. zenon_intro zenon_TE_dq. zenon_intro zenon_Hfd.
% 8.12/8.35 apply (zenon_notimply_s _ _ zenon_Hfd). zenon_intro zenon_Hfe. zenon_intro zenon_H86.
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_H61. zenon_intro zenon_H6b.
% 8.12/8.35 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 8.12/8.35 generalize (zenon_H5f zenon_TE_dq). zenon_intro zenon_H60.
% 8.12/8.35 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H5d; zenon_intro zenon_H62 | zenon_intro zenon_H61; zenon_intro zenon_H5c ].
% 8.12/8.35 exact (zenon_H5d zenon_H61).
% 8.12/8.35 generalize (leq_succ_gt_equiv zenon_TE_dq). zenon_intro zenon_H69.
% 8.12/8.35 generalize (zenon_H69 (n5)). zenon_intro zenon_H6a.
% 8.12/8.35 apply (zenon_equiv_s _ _ zenon_H6a); [ zenon_intro zenon_H68; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H67 ].
% 8.12/8.35 exact (zenon_H68 zenon_H6b).
% 8.12/8.35 generalize (finite_domain_3 zenon_TE_dq). zenon_intro zenon_Hb7.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ].
% 8.12/8.35 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_H5d | zenon_intro zenon_Hba ].
% 8.12/8.35 apply (zenon_L1_ zenon_TE_dq); trivial.
% 8.12/8.35 generalize (leq_succ_gt_equiv zenon_TE_dq). zenon_intro zenon_H69.
% 8.12/8.35 generalize (zenon_H69 (n3)). zenon_intro zenon_Hbb.
% 8.12/8.35 apply (zenon_equiv_s _ _ zenon_Hbb); [ zenon_intro zenon_Hba; zenon_intro zenon_Ha0 | zenon_intro zenon_Hbd; zenon_intro zenon_Hbc ].
% 8.12/8.35 elim (classic ((~((succ (n3)) = (succ zenon_TE_dq)))/\(~(gt (succ (n3)) (succ zenon_TE_dq))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ].
% 8.12/8.35 apply (zenon_and_s _ _ zenon_Hff). zenon_intro zenon_H102. zenon_intro zenon_H101.
% 8.12/8.35 elim (classic (gt (n4) (succ zenon_TE_dq))); [ zenon_intro zenon_He5 | zenon_intro zenon_He0 ].
% 8.12/8.35 elim (classic (gt (succ (succ (succ (succ (n0))))) (succ zenon_TE_dq))); [ zenon_intro zenon_H103 | zenon_intro zenon_H104 ].
% 8.12/8.35 cut ((gt (succ (succ (succ (succ (n0))))) (succ zenon_TE_dq)) = (gt (succ (n3)) (succ zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H101.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H103.
% 8.12/8.35 cut (((succ zenon_TE_dq) = (succ zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 8.12/8.35 cut (((succ (succ (succ (succ (n0))))) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ].
% 8.12/8.35 cut (((succ (n3)) = (succ (n3))) = ((succ (succ (succ (succ (n0))))) = (succ (n3)))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Ha4.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Ha5.
% 8.12/8.35 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6].
% 8.12/8.35 cut (((succ (n3)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H9e].
% 8.12/8.35 congruence.
% 8.12/8.35 apply (zenon_L11_); trivial.
% 8.12/8.35 apply zenon_Ha6. apply refl_equal.
% 8.12/8.35 apply zenon_Ha6. apply refl_equal.
% 8.12/8.35 apply zenon_Hde. apply refl_equal.
% 8.12/8.35 cut ((gt (n4) (succ zenon_TE_dq)) = (gt (succ (succ (succ (succ (n0))))) (succ zenon_TE_dq))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H104.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_He5.
% 8.12/8.35 cut (((succ zenon_TE_dq) = (succ zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 8.12/8.35 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha7].
% 8.12/8.35 congruence.
% 8.12/8.35 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ].
% 8.12/8.35 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Ha7.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Ha8.
% 8.12/8.35 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_Ha9].
% 8.12/8.35 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Haa].
% 8.12/8.35 congruence.
% 8.12/8.35 exact (zenon_Haa successor_4).
% 8.12/8.35 apply zenon_Ha9. apply refl_equal.
% 8.12/8.35 apply zenon_Ha9. apply refl_equal.
% 8.12/8.35 apply zenon_Hde. apply refl_equal.
% 8.12/8.35 apply (zenon_L22_ zenon_TE_dq); trivial.
% 8.12/8.35 elim (classic ((n0) = zenon_TE_dq)); [ zenon_intro zenon_H105 | zenon_intro zenon_H6d ].
% 8.12/8.35 cut ((gt (succ zenon_TE_dq) (n0)) = (gt (succ (n3)) zenon_TE_dq)).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Ha0.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H5c.
% 8.12/8.35 cut (((n0) = zenon_TE_dq)); [idtac | apply NNPP; zenon_intro zenon_H6d].
% 8.12/8.35 cut (((succ zenon_TE_dq) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 8.12/8.35 congruence.
% 8.12/8.35 apply (zenon_notand_s _ _ zenon_H100); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ].
% 8.12/8.35 apply zenon_H108. zenon_intro zenon_H109.
% 8.12/8.35 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ].
% 8.12/8.35 cut (((succ (n3)) = (succ (n3))) = ((succ zenon_TE_dq) = (succ (n3)))).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_H106.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_Ha5.
% 8.12/8.35 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6].
% 8.12/8.35 cut (((succ (n3)) = (succ zenon_TE_dq))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 8.12/8.35 congruence.
% 8.12/8.35 exact (zenon_H102 zenon_H109).
% 8.12/8.35 apply zenon_Ha6. apply refl_equal.
% 8.12/8.35 apply zenon_Ha6. apply refl_equal.
% 8.12/8.35 apply zenon_H107. zenon_intro zenon_H10a.
% 8.12/8.35 generalize (zenon_H82 (succ (n3))). zenon_intro zenon_H10b.
% 8.12/8.35 generalize (zenon_H10b (succ zenon_TE_dq)). zenon_intro zenon_H10c.
% 8.12/8.35 generalize (zenon_H10c (n0)). zenon_intro zenon_H10d.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_H10d); [ zenon_intro zenon_H101 | zenon_intro zenon_H10e ].
% 8.12/8.35 exact (zenon_H101 zenon_H10a).
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_H10e); [ zenon_intro zenon_H62 | zenon_intro zenon_H10f ].
% 8.12/8.35 exact (zenon_H62 zenon_H5c).
% 8.12/8.35 cut ((gt (succ (n3)) (n0)) = (gt (succ (n3)) zenon_TE_dq)).
% 8.12/8.35 intro zenon_D_pnotp.
% 8.12/8.35 apply zenon_Ha0.
% 8.12/8.35 rewrite <- zenon_D_pnotp.
% 8.12/8.35 exact zenon_H10f.
% 8.12/8.35 cut (((n0) = zenon_TE_dq)); [idtac | apply NNPP; zenon_intro zenon_H6d].
% 8.12/8.35 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6].
% 8.12/8.35 congruence.
% 8.12/8.35 apply zenon_Ha6. apply refl_equal.
% 8.12/8.35 exact (zenon_H6d zenon_H105).
% 8.12/8.35 exact (zenon_H6d zenon_H105).
% 8.12/8.35 apply (zenon_L12_ zenon_TE_dq); trivial.
% 8.12/8.35 exact (zenon_Hba zenon_Hbd).
% 8.12/8.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hbe ].
% 8.12/8.35 apply (zenon_L23_ zenon_TE_dq); trivial.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H79 | zenon_intro zenon_Hbf ].
% 8.12/8.35 apply (zenon_L13_ zenon_TE_dq); trivial.
% 8.12/8.35 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7b | zenon_intro zenon_H7d ].
% 8.12/8.35 apply (zenon_L14_ zenon_TE_dq); trivial.
% 8.12/8.35 apply (zenon_L15_ zenon_TE_dq); trivial.
% 8.12/8.35 apply zenon_Hed. zenon_intro zenon_Tx_km. apply NNPP. zenon_intro zenon_H111.
% 8.12/8.35 apply zenon_H111. zenon_intro zenon_Ty_ko. apply NNPP. zenon_intro zenon_H113.
% 8.12/8.35 apply zenon_H113. zenon_intro zenon_Tz_kq. apply NNPP. zenon_intro zenon_H115.
% 8.12/8.35 apply (zenon_notimply_s _ _ zenon_H115). zenon_intro zenon_H117. zenon_intro zenon_H116.
% 8.12/8.35 apply (zenon_notimply_s _ _ zenon_H116). zenon_intro zenon_H119. zenon_intro zenon_H118.
% 8.12/8.35 generalize (transitivity_gt zenon_Tx_km). zenon_intro zenon_H11a.
% 8.12/8.35 generalize (zenon_H11a zenon_Ty_ko). zenon_intro zenon_H11b.
% 8.12/8.35 generalize (zenon_H11b zenon_Tz_kq). zenon_intro zenon_H11c.
% 8.12/8.35 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_H11e | zenon_intro zenon_H11d ].
% 8.12/8.35 apply (zenon_notand_s _ _ zenon_H11e); [ zenon_intro zenon_H120 | zenon_intro zenon_H11f ].
% 8.12/8.35 exact (zenon_H120 zenon_H117).
% 8.12/8.35 exact (zenon_H11f zenon_H119).
% 8.12/8.35 exact (zenon_H118 zenon_H11d).
% 8.12/8.35 Qed.
% 8.12/8.35 % SZS output end Proof
% 8.12/8.35 (* END-PROOF *)
% 8.12/8.35 nodes searched: 518389
% 8.12/8.35 max branch formulas: 3213
% 8.12/8.35 proof nodes created: 1225
% 8.12/8.35 formulas created: 308684
% 8.12/8.35
%------------------------------------------------------------------------------