TSTP Solution File: ALG139+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : ALG139+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n023.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 : Thu Jul 14 18:30:13 EDT 2022
% Result : Unsatisfiable 3.14s 3.35s
% Output : Proof 3.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG139+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 9 07:15:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.14/3.35 (* PROOF-FOUND *)
% 3.14/3.35 % SZS status Unsatisfiable
% 3.14/3.35 (* BEGIN-PROOF *)
% 3.14/3.35 % SZS output start Proof
% 3.14/3.35 Theorem zenon_thm : False.
% 3.14/3.35 Proof.
% 3.14/3.35 assert (zenon_L1_ : (((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H1d.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 3.14/3.35 exact (zenon_H1e zenon_H1f).
% 3.14/3.35 (* end of lemma zenon_L1_ *)
% 3.14/3.35 assert (zenon_L2_ : (~((e2) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H20.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L2_ *)
% 3.14/3.35 assert (zenon_L3_ : (((op (e0) (e0)) = (e3))/\(~((op (e3) (e3)) = (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H21 zenon_H22 zenon_H23.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 3.14/3.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ].
% 3.14/3.35 cut (((e3) = (e3)) = ((e2) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H23.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H26.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e0) (e0)) = (e2)) = ((e3) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H28.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H22.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H29 zenon_H25).
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L3_ *)
% 3.14/3.35 assert (zenon_L4_ : (~((e3) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H27.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L4_ *)
% 3.14/3.35 assert (zenon_L5_ : (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H2a zenon_H2b zenon_H2c.
% 3.14/3.35 cut (((op (e1) (e1)) = (e3)) = ((e0) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H2a.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H2b.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2d].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H2d zenon_H2c).
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L5_ *)
% 3.14/3.35 assert (zenon_L6_ : (((op (e1) (e1)) = (e3))/\(~((op (e3) (e3)) = (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H2e zenon_H2c zenon_H2a.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H2b. zenon_intro zenon_H2f.
% 3.14/3.35 apply (zenon_L5_); trivial.
% 3.14/3.35 (* end of lemma zenon_L6_ *)
% 3.14/3.35 assert (zenon_L7_ : (~((e1) = (e1))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H30.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L7_ *)
% 3.14/3.35 assert (zenon_L8_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H31 zenon_H32 zenon_H33.
% 3.14/3.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ].
% 3.14/3.35 cut (((e3) = (e3)) = ((e1) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H33.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H26.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H34].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e1)) = ((e3) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H34.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H31.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H35 zenon_H32).
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L8_ *)
% 3.14/3.35 assert (zenon_L9_ : (((op (e2) (e2)) = (e3))/\(~((op (e3) (e3)) = (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H36 zenon_H31 zenon_H33.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H32. zenon_intro zenon_H37.
% 3.14/3.35 apply (zenon_L8_); trivial.
% 3.14/3.35 (* end of lemma zenon_L9_ *)
% 3.14/3.35 assert (zenon_L10_ : (((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H38.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H3a. zenon_intro zenon_H39.
% 3.14/3.35 exact (zenon_H39 zenon_H3a).
% 3.14/3.35 (* end of lemma zenon_L10_ *)
% 3.14/3.35 assert (zenon_L11_ : (((op (e1) (e1)) = (e2))/\(~((op (e2) (e2)) = (e1)))) -> (~((op (e1) (e1)) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H3b zenon_H3c.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 3.14/3.35 exact (zenon_H3c zenon_H3e).
% 3.14/3.35 (* end of lemma zenon_L11_ *)
% 3.14/3.35 assert (zenon_L12_ : (((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H3f.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40.
% 3.14/3.35 exact (zenon_H40 zenon_H41).
% 3.14/3.35 (* end of lemma zenon_L12_ *)
% 3.14/3.35 assert (zenon_L13_ : ((op (e3) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H42 zenon_H43 zenon_H44.
% 3.14/3.35 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H45 | zenon_intro zenon_H46 ].
% 3.14/3.35 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H44.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H45.
% 3.14/3.35 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 3.14/3.35 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H47].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e2) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H47.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H42.
% 3.14/3.35 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H48].
% 3.14/3.35 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H46. apply refl_equal.
% 3.14/3.35 apply zenon_H48. apply sym_equal. exact zenon_H43.
% 3.14/3.35 apply zenon_H46. apply refl_equal.
% 3.14/3.35 apply zenon_H46. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L13_ *)
% 3.14/3.35 assert (zenon_L14_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H49 zenon_H2c zenon_H4a.
% 3.14/3.35 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e3) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H49.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H2c.
% 3.14/3.35 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4b].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 apply zenon_H4b. apply sym_equal. exact zenon_H4a.
% 3.14/3.35 (* end of lemma zenon_L14_ *)
% 3.14/3.35 assert (zenon_L15_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H4d zenon_H42 zenon_H4e.
% 3.14/3.35 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H4d.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H42.
% 3.14/3.35 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 3.14/3.35 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H46. apply refl_equal.
% 3.14/3.35 apply zenon_H4f. apply sym_equal. exact zenon_H4e.
% 3.14/3.35 (* end of lemma zenon_L15_ *)
% 3.14/3.35 assert (zenon_L16_ : (~((e0) = (e0))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H50.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L16_ *)
% 3.14/3.35 assert (zenon_L17_ : (~((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H51 zenon_H25.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H29 zenon_H25).
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L17_ *)
% 3.14/3.35 assert (zenon_L18_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H52 zenon_H25.
% 3.14/3.35 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 3.14/3.35 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H29 zenon_H25).
% 3.14/3.35 exact (zenon_H29 zenon_H25).
% 3.14/3.35 (* end of lemma zenon_L18_ *)
% 3.14/3.35 assert (zenon_L19_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H53 zenon_H54 zenon_H25.
% 3.14/3.35 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e1) = (op (op (e0) (e0)) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H56.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H57.
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H59.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H53.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5a].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H5a.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H57.
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H51].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L17_); trivial.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ].
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H5d | zenon_intro zenon_H5e ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H5c.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H5d.
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H5f.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H54.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H5d | zenon_intro zenon_H5e ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H60.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H5d.
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H52].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L18_); trivial.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H5b. apply sym_equal. exact zenon_H25.
% 3.14/3.35 (* end of lemma zenon_L19_ *)
% 3.14/3.35 assert (zenon_L20_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H54 zenon_H61 zenon_H62.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H62.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H65.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H54.
% 3.14/3.35 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H66. apply sym_equal. exact zenon_H61.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L20_ *)
% 3.14/3.35 assert (zenon_L21_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H67 zenon_H25 zenon_H68.
% 3.14/3.35 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e3) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H67.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H25.
% 3.14/3.35 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H69].
% 3.14/3.35 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H6a. apply refl_equal.
% 3.14/3.35 apply zenon_H69. apply sym_equal. exact zenon_H68.
% 3.14/3.35 (* end of lemma zenon_L21_ *)
% 3.14/3.35 assert (zenon_L22_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H6b zenon_H4e zenon_H4d zenon_H62 zenon_H54 zenon_H67 zenon_H25.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H42 | zenon_intro zenon_H6c ].
% 3.14/3.35 apply (zenon_L15_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H53 | zenon_intro zenon_H6d ].
% 3.14/3.35 apply (zenon_L19_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6d); [ zenon_intro zenon_H61 | zenon_intro zenon_H68 ].
% 3.14/3.35 apply (zenon_L20_); trivial.
% 3.14/3.35 apply (zenon_L21_); trivial.
% 3.14/3.35 (* end of lemma zenon_L22_ *)
% 3.14/3.35 assert (zenon_L23_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H6e zenon_H44 zenon_H43 zenon_H2c zenon_H49 zenon_H25 zenon_H67 zenon_H54 zenon_H62 zenon_H4d zenon_H6b zenon_H24.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H42 | zenon_intro zenon_H6f ].
% 3.14/3.35 apply (zenon_L13_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H4a | zenon_intro zenon_H70 ].
% 3.14/3.35 apply (zenon_L14_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H4e | zenon_intro zenon_H71 ].
% 3.14/3.35 apply (zenon_L22_); trivial.
% 3.14/3.35 exact (zenon_H24 zenon_H71).
% 3.14/3.35 (* end of lemma zenon_L23_ *)
% 3.14/3.35 assert (zenon_L24_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H72 zenon_H2c zenon_H73.
% 3.14/3.35 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e2) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H72.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H2c.
% 3.14/3.35 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H74].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 apply zenon_H74. apply sym_equal. exact zenon_H73.
% 3.14/3.35 (* end of lemma zenon_L24_ *)
% 3.14/3.35 assert (zenon_L25_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H75 zenon_H31 zenon_H76.
% 3.14/3.35 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H77 | zenon_intro zenon_H30 ].
% 3.14/3.35 cut (((e1) = (e1)) = ((e0) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H76.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H77.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H78].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e0)) = ((e1) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H78.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H75.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H3d].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H3d zenon_H31).
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L25_ *)
% 3.14/3.35 assert (zenon_L26_ : (~((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H79 zenon_H54.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H37 zenon_H54).
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L26_ *)
% 3.14/3.35 assert (zenon_L27_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H7a zenon_H54.
% 3.14/3.35 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 3.14/3.35 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H37 zenon_H54).
% 3.14/3.35 exact (zenon_H37 zenon_H54).
% 3.14/3.35 (* end of lemma zenon_L27_ *)
% 3.14/3.35 assert (zenon_L28_ : ((op (e2) (e3)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H7b zenon_H31 zenon_H54.
% 3.14/3.35 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ].
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e0) = (op (op (e3) (e3)) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H7d.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H7e.
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H80].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H80.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H7b.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H81.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H7e.
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H79].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L26_); trivial.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ].
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H83.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H84.
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H86].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H86.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H31.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H87.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H84.
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7a].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L27_); trivial.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H82. apply sym_equal. exact zenon_H54.
% 3.14/3.35 (* end of lemma zenon_L28_ *)
% 3.14/3.35 assert (zenon_L29_ : (((op (e2) (e2)) = (e3))/\(~((op (e3) (e3)) = (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H36 zenon_H35.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H32. zenon_intro zenon_H37.
% 3.14/3.35 exact (zenon_H35 zenon_H32).
% 3.14/3.35 (* end of lemma zenon_L29_ *)
% 3.14/3.35 assert (zenon_L30_ : (((op (e1) (e1)) = (e3))/\(~((op (e3) (e3)) = (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H2e zenon_H88.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H2b. zenon_intro zenon_H2f.
% 3.14/3.35 exact (zenon_H88 zenon_H2b).
% 3.14/3.35 (* end of lemma zenon_L30_ *)
% 3.14/3.35 assert (zenon_L31_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H89 zenon_H22 zenon_H8a.
% 3.14/3.35 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e0) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H89.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H22.
% 3.14/3.35 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b].
% 3.14/3.35 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H6a. apply refl_equal.
% 3.14/3.35 apply zenon_H8b. apply sym_equal. exact zenon_H8a.
% 3.14/3.35 (* end of lemma zenon_L31_ *)
% 3.14/3.35 assert (zenon_L32_ : (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H8c zenon_H3e zenon_H2c.
% 3.14/3.35 cut (((op (e1) (e1)) = (e2)) = ((e0) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H8c.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H3e.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2d].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H2d zenon_H2c).
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L32_ *)
% 3.14/3.35 assert (zenon_L33_ : ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (op (op (e0) (e0)) (e0)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H8d zenon_H22 zenon_H56.
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e1) = (op (op (e0) (e0)) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H56.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H57.
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H59.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H8d.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8e].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H8e.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H57.
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H90].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H90 zenon_H22).
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L33_ *)
% 3.14/3.35 assert (zenon_L34_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H8d zenon_H32 zenon_H22.
% 3.14/3.35 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_H56 | zenon_intro zenon_H91 ].
% 3.14/3.35 apply (zenon_L33_); trivial.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H5d | zenon_intro zenon_H5e ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e3) = (op (op (e0) (e0)) (op (e0) (e0))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H93.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H5d.
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e3)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H94.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H32.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H95].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H5d | zenon_intro zenon_H5e ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H95.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H5d.
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H90].
% 3.14/3.35 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H90].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H90 zenon_H22).
% 3.14/3.35 exact (zenon_H90 zenon_H22).
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H92. apply sym_equal. exact zenon_H22.
% 3.14/3.35 (* end of lemma zenon_L34_ *)
% 3.14/3.35 assert (zenon_L35_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H97 zenon_H8d zenon_H98.
% 3.14/3.35 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e2) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H97.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H8d.
% 3.14/3.35 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 3.14/3.35 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H9a. apply refl_equal.
% 3.14/3.35 apply zenon_H99. apply sym_equal. exact zenon_H98.
% 3.14/3.35 (* end of lemma zenon_L35_ *)
% 3.14/3.35 assert (zenon_L36_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H97 zenon_H9b zenon_H9c.
% 3.14/3.35 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H97.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H9b.
% 3.14/3.35 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9d].
% 3.14/3.35 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H9a. apply refl_equal.
% 3.14/3.35 apply zenon_H9d. apply sym_equal. exact zenon_H9c.
% 3.14/3.35 (* end of lemma zenon_L36_ *)
% 3.14/3.35 assert (zenon_L37_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H32 zenon_H9e zenon_H9f.
% 3.14/3.35 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha1 ].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H9f.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Ha0.
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Ha2.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H32.
% 3.14/3.35 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 apply zenon_Ha3. apply sym_equal. exact zenon_H9e.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L37_ *)
% 3.14/3.35 assert (zenon_L38_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Ha4 zenon_H44 zenon_H42 zenon_H98 zenon_H9c zenon_H97 zenon_H32 zenon_H9f.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H43 | zenon_intro zenon_Ha5 ].
% 3.14/3.35 apply (zenon_L13_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H8d | zenon_intro zenon_Ha6 ].
% 3.14/3.35 apply (zenon_L35_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Ha6); [ zenon_intro zenon_H9b | zenon_intro zenon_H9e ].
% 3.14/3.35 apply (zenon_L36_); trivial.
% 3.14/3.35 apply (zenon_L37_); trivial.
% 3.14/3.35 (* end of lemma zenon_L38_ *)
% 3.14/3.35 assert (zenon_L39_ : (~((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Ha7 zenon_H32.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H35 zenon_H32).
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L39_ *)
% 3.14/3.35 assert (zenon_L40_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Ha8 zenon_H32.
% 3.14/3.35 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 3.14/3.35 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H35 zenon_H32).
% 3.14/3.35 exact (zenon_H35 zenon_H32).
% 3.14/3.35 (* end of lemma zenon_L40_ *)
% 3.14/3.35 assert (zenon_L41_ : ((op (e3) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H4e zenon_Ha9 zenon_H32.
% 3.14/3.35 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ].
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hab.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hac.
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hae].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hae.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H4e.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Haf.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hac.
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha7].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L39_); trivial.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ].
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb1.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hb2.
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb4].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb4.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Ha9.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hb5].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb5.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hb2.
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha8].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L40_); trivial.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_Hb0. apply sym_equal. exact zenon_H32.
% 3.14/3.35 (* end of lemma zenon_L41_ *)
% 3.14/3.35 assert (zenon_L42_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H71 zenon_Ha9 zenon_H76.
% 3.14/3.35 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H77 | zenon_intro zenon_H30 ].
% 3.14/3.35 cut (((e1) = (e1)) = ((e0) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H76.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H77.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H78].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e0)) = ((e1) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H78.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H71.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H2f zenon_Ha9).
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L42_ *)
% 3.14/3.35 assert (zenon_L43_ : (((op (e3) (e3)) = (e1))/\(~((op (e1) (e1)) = (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hb6 zenon_H71 zenon_H76.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_Ha9. zenon_intro zenon_H88.
% 3.14/3.35 apply (zenon_L42_); trivial.
% 3.14/3.35 (* end of lemma zenon_L43_ *)
% 3.14/3.35 assert (zenon_L44_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e3)) = (e1))/\(~((op (e1) (e1)) = (e3)))) -> (~((e0) = (e1))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H6e zenon_H9f zenon_H97 zenon_H9c zenon_H98 zenon_H44 zenon_Ha4 zenon_H2c zenon_H49 zenon_H32 zenon_Ha9 zenon_Hb6 zenon_H76.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H42 | zenon_intro zenon_H6f ].
% 3.14/3.35 apply (zenon_L38_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H4a | zenon_intro zenon_H70 ].
% 3.14/3.35 apply (zenon_L14_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H4e | zenon_intro zenon_H71 ].
% 3.14/3.35 apply (zenon_L41_); trivial.
% 3.14/3.35 apply (zenon_L43_); trivial.
% 3.14/3.35 (* end of lemma zenon_L44_ *)
% 3.14/3.35 assert (zenon_L45_ : ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Ha9 zenon_Hb7 zenon_Hb8.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb8.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb9].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e2) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb9.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Ha9.
% 3.14/3.35 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hba].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_Hba. apply sym_equal. exact zenon_Hb7.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L45_ *)
% 3.14/3.35 assert (zenon_L46_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Ha9 zenon_Hbb zenon_Hbc.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hbc.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbd].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hbd.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Ha9.
% 3.14/3.35 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_Hbe. apply sym_equal. exact zenon_Hbb.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L46_ *)
% 3.14/3.35 assert (zenon_L47_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hbf zenon_Hc0 zenon_Hc1.
% 3.14/3.35 cut (((op (e3) (e1)) = (e2)) = ((op (e3) (e1)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hbf.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hc0.
% 3.14/3.35 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 3.14/3.35 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Hc3. apply refl_equal.
% 3.14/3.35 apply zenon_Hc2. apply sym_equal. exact zenon_Hc1.
% 3.14/3.35 (* end of lemma zenon_L47_ *)
% 3.14/3.35 assert (zenon_L48_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hc4 zenon_H32 zenon_Hc5.
% 3.14/3.35 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hc4.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H32.
% 3.14/3.35 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc6].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 apply zenon_Hc6. apply sym_equal. exact zenon_Hc5.
% 3.14/3.35 (* end of lemma zenon_L48_ *)
% 3.14/3.35 assert (zenon_L49_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hc7 zenon_Hbc zenon_Ha9 zenon_Hc0 zenon_Hbf zenon_Hc4 zenon_H32.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H4e | zenon_intro zenon_Hc8 ].
% 3.14/3.35 apply (zenon_L41_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc9 ].
% 3.14/3.35 apply (zenon_L46_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hc5 ].
% 3.14/3.35 apply (zenon_L47_); trivial.
% 3.14/3.35 apply (zenon_L48_); trivial.
% 3.14/3.35 (* end of lemma zenon_L49_ *)
% 3.14/3.35 assert (zenon_L50_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Ha9 zenon_H54 zenon_Hca.
% 3.14/3.35 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hcb | zenon_intro zenon_H20 ].
% 3.14/3.35 cut (((e2) = (e2)) = ((e1) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hca.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hcb.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcc].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e1)) = ((e2) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hcc.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Ha9.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H37 zenon_H54).
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L50_ *)
% 3.14/3.35 assert (zenon_L51_ : (((op (e3) (e3)) = (e2))/\(~((op (e2) (e2)) = (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hcd zenon_Ha9 zenon_Hca.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_H54. zenon_intro zenon_H35.
% 3.14/3.35 apply (zenon_L50_); trivial.
% 3.14/3.35 (* end of lemma zenon_L51_ *)
% 3.14/3.35 assert (zenon_L52_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hce zenon_H22 zenon_Hca.
% 3.14/3.35 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hcb | zenon_intro zenon_H20 ].
% 3.14/3.35 cut (((e2) = (e2)) = ((e1) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hca.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hcb.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcc].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e0) (e0)) = (e1)) = ((e2) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hcc.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hce.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H90].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H90 zenon_H22).
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L52_ *)
% 3.14/3.35 assert (zenon_L53_ : (((op (e0) (e0)) = (e2))/\(~((op (e2) (e2)) = (e0)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hcf zenon_Hce zenon_Hca.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_H22. zenon_intro zenon_Hd0.
% 3.14/3.35 apply (zenon_L52_); trivial.
% 3.14/3.35 (* end of lemma zenon_L53_ *)
% 3.14/3.35 assert (zenon_L54_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hce zenon_H25 zenon_H33.
% 3.14/3.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ].
% 3.14/3.35 cut (((e3) = (e3)) = ((e1) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H33.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H26.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H34].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e0) (e0)) = (e1)) = ((e3) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H34.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hce.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H29 zenon_H25).
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L54_ *)
% 3.14/3.35 assert (zenon_L55_ : (((op (e0) (e0)) = (e3))/\(~((op (e3) (e3)) = (e0)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H21 zenon_Hce zenon_H33.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 3.14/3.35 apply (zenon_L54_); trivial.
% 3.14/3.35 (* end of lemma zenon_L55_ *)
% 3.14/3.35 assert (zenon_L56_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H3e zenon_H2b zenon_H23.
% 3.14/3.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ].
% 3.14/3.35 cut (((e3) = (e3)) = ((e2) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H23.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H26.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e1) (e1)) = (e2)) = ((e3) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H28.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H3e.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H88 zenon_H2b).
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L56_ *)
% 3.14/3.35 assert (zenon_L57_ : (((op (e1) (e1)) = (e3))/\(~((op (e3) (e3)) = (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H2e zenon_H3e zenon_H23.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H2b. zenon_intro zenon_H2f.
% 3.14/3.35 apply (zenon_L56_); trivial.
% 3.14/3.35 (* end of lemma zenon_L57_ *)
% 3.14/3.35 assert (zenon_L58_ : (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H2a zenon_H32 zenon_H75.
% 3.14/3.35 cut (((op (e2) (e2)) = (e3)) = ((e0) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H2a.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H32.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hd0].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_Hd0 zenon_H75).
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L58_ *)
% 3.14/3.35 assert (zenon_L59_ : (((op (e2) (e2)) = (e3))/\(~((op (e3) (e3)) = (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H36 zenon_H75 zenon_H2a.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H32. zenon_intro zenon_H37.
% 3.14/3.35 apply (zenon_L58_); trivial.
% 3.14/3.35 (* end of lemma zenon_L59_ *)
% 3.14/3.35 assert (zenon_L60_ : ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H2b zenon_Hd1 zenon_Hd2.
% 3.14/3.35 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H4c ].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hd2.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hd3.
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd4].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e0) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hd4.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H2b.
% 3.14/3.35 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd5].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 apply zenon_Hd5. apply sym_equal. exact zenon_Hd1.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L60_ *)
% 3.14/3.35 assert (zenon_L61_ : (~((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hd6 zenon_H2b.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H88 zenon_H2b).
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L61_ *)
% 3.14/3.35 assert (zenon_L62_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hd7 zenon_H2b.
% 3.14/3.35 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 3.14/3.35 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H88 zenon_H2b).
% 3.14/3.35 exact (zenon_H88 zenon_H2b).
% 3.14/3.35 (* end of lemma zenon_L62_ *)
% 3.14/3.35 assert (zenon_L63_ : ((op (e3) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H4a zenon_H54 zenon_H2b.
% 3.14/3.35 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hd8 ].
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hd9.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hda.
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdc].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hdc.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H4a.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdd].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hdd.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hda.
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd6].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L61_); trivial.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_Hd8); [ zenon_intro zenon_Hdf | zenon_intro zenon_Hde ].
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hdf.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_He0.
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_He2].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_He2.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H54.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_He3].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_He3.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_He0.
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L62_); trivial.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_Hde. apply sym_equal. exact zenon_H2b.
% 3.14/3.35 (* end of lemma zenon_L63_ *)
% 3.14/3.35 assert (zenon_L64_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hbf zenon_He4 zenon_Hbb.
% 3.14/3.35 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hbf.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_He4.
% 3.14/3.35 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 3.14/3.35 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc3].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Hc3. apply refl_equal.
% 3.14/3.35 apply zenon_Hbe. apply sym_equal. exact zenon_Hbb.
% 3.14/3.35 (* end of lemma zenon_L64_ *)
% 3.14/3.35 assert (zenon_L65_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H54 zenon_Hc1 zenon_Hbc.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hbc.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbd].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hbd.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H54.
% 3.14/3.35 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_Hc2. apply sym_equal. exact zenon_Hc1.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L65_ *)
% 3.14/3.35 assert (zenon_L66_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_He5 zenon_He6 zenon_Hc5.
% 3.14/3.35 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_He5.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_He6.
% 3.14/3.35 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc6].
% 3.14/3.35 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_He7].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_He7. apply refl_equal.
% 3.14/3.35 apply zenon_Hc6. apply sym_equal. exact zenon_Hc5.
% 3.14/3.35 (* end of lemma zenon_L66_ *)
% 3.14/3.35 assert (zenon_L67_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hc7 zenon_H75 zenon_Hc4 zenon_He4 zenon_Hbf zenon_Hbc zenon_H54 zenon_He5 zenon_He6.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H4e | zenon_intro zenon_Hc8 ].
% 3.14/3.35 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hc4.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H75.
% 3.14/3.35 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 apply zenon_H4f. apply sym_equal. exact zenon_H4e.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc9 ].
% 3.14/3.35 apply (zenon_L64_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hc5 ].
% 3.14/3.35 apply (zenon_L65_); trivial.
% 3.14/3.35 apply (zenon_L66_); trivial.
% 3.14/3.35 (* end of lemma zenon_L67_ *)
% 3.14/3.35 assert (zenon_L68_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H54 zenon_Hc0 zenon_He8.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_He8.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He9].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_He9.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H54.
% 3.14/3.35 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hea].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_Hea. apply sym_equal. exact zenon_Hc0.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L68_ *)
% 3.14/3.35 assert (zenon_L69_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H49 zenon_H2b zenon_Heb.
% 3.14/3.35 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e3) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H49.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H2b.
% 3.14/3.35 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hec].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 apply zenon_Hec. apply sym_equal. exact zenon_Heb.
% 3.14/3.35 (* end of lemma zenon_L69_ *)
% 3.14/3.35 assert (zenon_L70_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hed zenon_He6 zenon_He5 zenon_Hbc zenon_Hbf zenon_Hc4 zenon_H75 zenon_Hc7 zenon_He8 zenon_H54 zenon_H49 zenon_H2b.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H4a | zenon_intro zenon_Hee ].
% 3.14/3.35 apply (zenon_L63_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_He4 | zenon_intro zenon_Hef ].
% 3.14/3.35 apply (zenon_L67_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Heb ].
% 3.14/3.35 apply (zenon_L68_); trivial.
% 3.14/3.35 apply (zenon_L69_); trivial.
% 3.14/3.35 (* end of lemma zenon_L70_ *)
% 3.14/3.35 assert (zenon_L71_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hf0 zenon_Hf1 zenon_H33.
% 3.14/3.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ].
% 3.14/3.35 cut (((e3) = (e3)) = ((e1) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H33.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H26.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H34].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e0) (e3)) = (e1)) = ((e3) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H34.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hf0.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hf2].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_Hf2 zenon_Hf1).
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L71_ *)
% 3.14/3.35 assert (zenon_L72_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hf3 zenon_H75 zenon_H7b.
% 3.14/3.35 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hf3.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H75.
% 3.14/3.35 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf4].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 apply zenon_Hf4. apply sym_equal. exact zenon_H7b.
% 3.14/3.35 (* end of lemma zenon_L72_ *)
% 3.14/3.35 assert (zenon_L73_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hf5 zenon_Hf6 zenon_Hb7.
% 3.14/3.35 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hf5.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hf6.
% 3.14/3.35 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hba].
% 3.14/3.35 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf7].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Hf7. apply refl_equal.
% 3.14/3.35 apply zenon_Hba. apply sym_equal. exact zenon_Hb7.
% 3.14/3.35 (* end of lemma zenon_L73_ *)
% 3.14/3.35 assert (zenon_L74_ : ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H54 zenon_Hf8 zenon_Hb8.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb8.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb9].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e2) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb9.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H54.
% 3.14/3.35 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_Hf9. apply sym_equal. exact zenon_Hf8.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L74_ *)
% 3.14/3.35 assert (zenon_L75_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hfa zenon_Hf1 zenon_Hfb.
% 3.14/3.35 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hfa.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hf1.
% 3.14/3.35 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfc].
% 3.14/3.35 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfd].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Hfd. apply refl_equal.
% 3.14/3.35 apply zenon_Hfc. apply sym_equal. exact zenon_Hfb.
% 3.14/3.35 (* end of lemma zenon_L75_ *)
% 3.14/3.35 assert (zenon_L76_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hfe zenon_H75 zenon_Hf3 zenon_Hf6 zenon_Hf5 zenon_Hb8 zenon_H54 zenon_Hfa zenon_Hf1.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H7b | zenon_intro zenon_Hff ].
% 3.14/3.35 apply (zenon_L72_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H100 ].
% 3.14/3.35 apply (zenon_L73_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf8 | zenon_intro zenon_Hfb ].
% 3.14/3.35 apply (zenon_L74_); trivial.
% 3.14/3.35 apply (zenon_L75_); trivial.
% 3.14/3.35 (* end of lemma zenon_L76_ *)
% 3.14/3.35 assert (zenon_L77_ : ((op (e2) (e3)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hb7 zenon_H75 zenon_H54.
% 3.14/3.35 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H102 | zenon_intro zenon_H101 ].
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H102.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H7e.
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H103].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H103.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hb7.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H81.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H7e.
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H79].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L26_); trivial.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H101); [ zenon_intro zenon_H104 | zenon_intro zenon_H82 ].
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H104.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H84.
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H105].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H105.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H75.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H87.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H84.
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7a].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L27_); trivial.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H82. apply sym_equal. exact zenon_H54.
% 3.14/3.35 (* end of lemma zenon_L77_ *)
% 3.14/3.35 assert (zenon_L78_ : (((op (e2) (e2)) = (e1))/\(~((op (e1) (e1)) = (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H106 zenon_H75 zenon_H76.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H31. zenon_intro zenon_H3c.
% 3.14/3.35 apply (zenon_L25_); trivial.
% 3.14/3.35 (* end of lemma zenon_L78_ *)
% 3.14/3.35 assert (zenon_L79_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H107 zenon_H108 zenon_H109.
% 3.14/3.35 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H10a | zenon_intro zenon_Hfd ].
% 3.14/3.35 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H109.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H10a.
% 3.14/3.35 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfd].
% 3.14/3.35 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10b].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H10b.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H107.
% 3.14/3.35 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10c].
% 3.14/3.35 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfd].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Hfd. apply refl_equal.
% 3.14/3.35 apply zenon_H10c. apply sym_equal. exact zenon_H108.
% 3.14/3.35 apply zenon_Hfd. apply refl_equal.
% 3.14/3.35 apply zenon_Hfd. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L79_ *)
% 3.14/3.35 assert (zenon_L80_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H75 zenon_H73 zenon_H10d.
% 3.14/3.35 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha1 ].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H10d.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Ha0.
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10e].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H10e.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H75.
% 3.14/3.35 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H74].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 apply zenon_H74. apply sym_equal. exact zenon_H73.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 apply zenon_Ha1. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L80_ *)
% 3.14/3.35 assert (zenon_L81_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H10f zenon_H42 zenon_H4a.
% 3.14/3.35 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H10f.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H42.
% 3.14/3.35 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4b].
% 3.14/3.35 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H46. apply refl_equal.
% 3.14/3.35 apply zenon_H4b. apply sym_equal. exact zenon_H4a.
% 3.14/3.35 (* end of lemma zenon_L81_ *)
% 3.14/3.35 assert (zenon_L82_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H110 zenon_H109 zenon_H107 zenon_H3e zenon_H8c zenon_H10d zenon_H75 zenon_H10f zenon_H42.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H108 | zenon_intro zenon_H111 ].
% 3.14/3.35 apply (zenon_L79_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H2c | zenon_intro zenon_H112 ].
% 3.14/3.35 apply (zenon_L32_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_H73 | zenon_intro zenon_H4a ].
% 3.14/3.35 apply (zenon_L80_); trivial.
% 3.14/3.35 apply (zenon_L81_); trivial.
% 3.14/3.35 (* end of lemma zenon_L82_ *)
% 3.14/3.35 assert (zenon_L83_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Ha9 zenon_H53 zenon_H62.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H62.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H65.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Ha9.
% 3.14/3.35 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H113. apply sym_equal. exact zenon_H53.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L83_ *)
% 3.14/3.35 assert (zenon_L84_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (op (op (e0) (e0)) (e0)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H61 zenon_H25 zenon_H114.
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e2) = (op (op (e0) (e0)) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H114.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H57.
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H115].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H115.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H61.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5a].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H5a.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H57.
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 3.14/3.35 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H51].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L17_); trivial.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 apply zenon_H58. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L84_ *)
% 3.14/3.35 assert (zenon_L85_ : ((op (e3) (e0)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H61 zenon_Ha9 zenon_H25.
% 3.14/3.35 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_H114 | zenon_intro zenon_H116 ].
% 3.14/3.35 apply (zenon_L84_); trivial.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H116); [ zenon_intro zenon_H117 | zenon_intro zenon_H5b ].
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H5d | zenon_intro zenon_H5e ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H117.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H5d.
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H118].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H118.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Ha9.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H5d | zenon_intro zenon_H5e ].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H60.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H5d.
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 3.14/3.35 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H52].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L18_); trivial.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H5e. apply refl_equal.
% 3.14/3.35 apply zenon_H5b. apply sym_equal. exact zenon_H25.
% 3.14/3.35 (* end of lemma zenon_L85_ *)
% 3.14/3.35 assert (zenon_L86_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H6b zenon_H10f zenon_H75 zenon_H10d zenon_H8c zenon_H3e zenon_H107 zenon_H109 zenon_H110 zenon_H62 zenon_Ha9 zenon_H67 zenon_H25.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H42 | zenon_intro zenon_H6c ].
% 3.14/3.35 apply (zenon_L82_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H53 | zenon_intro zenon_H6d ].
% 3.14/3.35 apply (zenon_L83_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H6d); [ zenon_intro zenon_H61 | zenon_intro zenon_H68 ].
% 3.14/3.35 apply (zenon_L85_); trivial.
% 3.14/3.35 apply (zenon_L21_); trivial.
% 3.14/3.35 (* end of lemma zenon_L86_ *)
% 3.14/3.35 assert (zenon_L87_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H119 zenon_H3e zenon_Ha9.
% 3.14/3.35 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H7d | zenon_intro zenon_H11a ].
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e0) = (op (op (e3) (e3)) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H7d.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H7e.
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H80].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e1) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H80.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H119.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H11b.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H7e.
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 3.14/3.35 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H2f zenon_Ha9).
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply zenon_H7f. apply refl_equal.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H11a); [ zenon_intro zenon_H11e | zenon_intro zenon_H11d ].
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H11e.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H84.
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H11f].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e1) (e1)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H11f.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H3e.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H120].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H120.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H84.
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 3.14/3.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H121].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 3.14/3.35 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H2f zenon_Ha9).
% 3.14/3.35 exact (zenon_H2f zenon_Ha9).
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H85. apply refl_equal.
% 3.14/3.35 apply zenon_H11d. apply sym_equal. exact zenon_Ha9.
% 3.14/3.35 (* end of lemma zenon_L87_ *)
% 3.14/3.35 assert (zenon_L88_ : (((op (e0) (e0)) = (e3))/\(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e0)) = (e3))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H21 zenon_H29.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 3.14/3.35 exact (zenon_H29 zenon_H25).
% 3.14/3.35 (* end of lemma zenon_L88_ *)
% 3.14/3.35 assert (zenon_L89_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H3e zenon_H122 zenon_H123.
% 3.14/3.35 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H4c ].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H123.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hd3.
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H124].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e0)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H124.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H3e.
% 3.14/3.35 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H125].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 apply zenon_H125. apply sym_equal. exact zenon_H122.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 apply zenon_H4c. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L89_ *)
% 3.14/3.35 assert (zenon_L90_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H43 zenon_H9b zenon_H8c.
% 3.14/3.35 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hcb | zenon_intro zenon_H20 ].
% 3.14/3.35 cut (((e2) = (e2)) = ((e0) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H8c.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hcb.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H126].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e0)) = (e0)) = ((e2) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H126.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H43.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H127].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H127 zenon_H9b).
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L90_ *)
% 3.14/3.35 assert (zenon_L91_ : ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (op (op (e1) (e1)) (e1)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H73 zenon_H3e zenon_Hd9.
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hd9.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hda.
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdc].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hdc.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H73.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H128].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H128.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hda.
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H129].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H3c].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H3c zenon_H3e).
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L91_ *)
% 3.14/3.35 assert (zenon_L92_ : ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H73 zenon_H32 zenon_H3e.
% 3.14/3.35 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_Hd9 | zenon_intro zenon_H12a ].
% 3.14/3.35 apply (zenon_L91_); trivial.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H12a); [ zenon_intro zenon_H12c | zenon_intro zenon_H12b ].
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e3) = (op (op (e1) (e1)) (op (e1) (e1))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H12c.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_He0.
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H12d].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H12d.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H32.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H12e].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H12e.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_He0.
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H12f].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H3c].
% 3.14/3.35 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H3c].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H3c zenon_H3e).
% 3.14/3.35 exact (zenon_H3c zenon_H3e).
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_H12b. apply sym_equal. exact zenon_H3e.
% 3.14/3.35 (* end of lemma zenon_L92_ *)
% 3.14/3.35 assert (zenon_L93_ : ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H71 zenon_H7b zenon_Hb8.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb8.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb9].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e2) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb9.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H71.
% 3.14/3.35 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf4].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_Hf4. apply sym_equal. exact zenon_H7b.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L93_ *)
% 3.14/3.35 assert (zenon_L94_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H71 zenon_H4e zenon_Hbc.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hbc.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbd].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hbd.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H71.
% 3.14/3.35 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H4f. apply sym_equal. exact zenon_H4e.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L94_ *)
% 3.14/3.35 assert (zenon_L95_ : ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hbb zenon_H32 zenon_H130.
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H130.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hac.
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H131].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H131.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hbb.
% 3.14/3.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 3.14/3.35 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Haf.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hac.
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha7].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L39_); trivial.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_H30. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L95_ *)
% 3.14/3.35 assert (zenon_L96_ : ((op (e3) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hbb zenon_H71 zenon_H32.
% 3.14/3.35 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H130 | zenon_intro zenon_H132 ].
% 3.14/3.35 apply (zenon_L95_); trivial.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H132); [ zenon_intro zenon_H133 | zenon_intro zenon_Hb0 ].
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H133.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hb2.
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H134].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H134.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H71.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hb5].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hb5.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hb2.
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha8].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L40_); trivial.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_Hb0. apply sym_equal. exact zenon_H32.
% 3.14/3.35 (* end of lemma zenon_L96_ *)
% 3.14/3.35 assert (zenon_L97_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H4d zenon_H61 zenon_Hc1.
% 3.14/3.35 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (e0)) = (op (e3) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H4d.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H61.
% 3.14/3.35 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 3.14/3.35 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H46. apply refl_equal.
% 3.14/3.35 apply zenon_Hc2. apply sym_equal. exact zenon_Hc1.
% 3.14/3.35 (* end of lemma zenon_L97_ *)
% 3.14/3.35 assert (zenon_L98_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hc7 zenon_Hbc zenon_H71 zenon_H61 zenon_H4d zenon_Hc4 zenon_H32.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H4e | zenon_intro zenon_Hc8 ].
% 3.14/3.35 apply (zenon_L94_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc9 ].
% 3.14/3.35 apply (zenon_L96_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hc5 ].
% 3.14/3.35 apply (zenon_L97_); trivial.
% 3.14/3.35 apply (zenon_L48_); trivial.
% 3.14/3.35 (* end of lemma zenon_L98_ *)
% 3.14/3.35 assert (zenon_L99_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H71 zenon_H54 zenon_H8c.
% 3.14/3.35 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hcb | zenon_intro zenon_H20 ].
% 3.14/3.35 cut (((e2) = (e2)) = ((e0) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H8c.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hcb.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H126].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e0)) = ((e2) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H126.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H71.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H37 zenon_H54).
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L99_ *)
% 3.14/3.35 assert (zenon_L100_ : (((op (e3) (e3)) = (e2))/\(~((op (e2) (e2)) = (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hcd zenon_H71 zenon_H8c.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_H54. zenon_intro zenon_H35.
% 3.14/3.35 apply (zenon_L99_); trivial.
% 3.14/3.35 (* end of lemma zenon_L100_ *)
% 3.14/3.35 assert (zenon_L101_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H135 zenon_H108 zenon_H136.
% 3.14/3.35 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H137 | zenon_intro zenon_He7 ].
% 3.14/3.35 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H136.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H137.
% 3.14/3.35 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_He7].
% 3.14/3.35 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H138].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H138.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H135.
% 3.14/3.35 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10c].
% 3.14/3.35 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_He7].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_He7. apply refl_equal.
% 3.14/3.35 apply zenon_H10c. apply sym_equal. exact zenon_H108.
% 3.14/3.35 apply zenon_He7. apply refl_equal.
% 3.14/3.35 apply zenon_He7. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L101_ *)
% 3.14/3.35 assert (zenon_L102_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H71 zenon_H4a zenon_He8.
% 3.14/3.35 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_He8.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H63.
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He9].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_He9.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H71.
% 3.14/3.35 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4b].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H4b. apply sym_equal. exact zenon_H4a.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 apply zenon_H64. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L102_ *)
% 3.14/3.35 assert (zenon_L103_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H139 zenon_H13a zenon_He4.
% 3.14/3.35 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H139.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H13a.
% 3.14/3.35 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 3.14/3.35 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13c].
% 3.14/3.35 congruence.
% 3.14/3.35 apply zenon_H13c. apply refl_equal.
% 3.14/3.35 apply zenon_H13b. apply sym_equal. exact zenon_He4.
% 3.14/3.35 (* end of lemma zenon_L103_ *)
% 3.14/3.35 assert (zenon_L104_ : ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (op (op (e1) (e1)) (e1)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hc0 zenon_H2b zenon_H13d.
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e2) = (op (op (e1) (e1)) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H13d.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hda.
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13e].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H13e.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hc0.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdd].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hdd.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hda.
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 3.14/3.35 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd6].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L61_); trivial.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 apply zenon_Hdb. apply refl_equal.
% 3.14/3.35 (* end of lemma zenon_L104_ *)
% 3.14/3.35 assert (zenon_L105_ : ((op (e3) (e1)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hc0 zenon_H71 zenon_H2b.
% 3.14/3.35 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H13d | zenon_intro zenon_H13f ].
% 3.14/3.35 apply (zenon_L104_); trivial.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H13f); [ zenon_intro zenon_H140 | zenon_intro zenon_Hde ].
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H140.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_He0.
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H141].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e3) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H141.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H71.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_He3].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_He3.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_He0.
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 3.14/3.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7].
% 3.14/3.35 congruence.
% 3.14/3.35 apply (zenon_L62_); trivial.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_He1. apply refl_equal.
% 3.14/3.35 apply zenon_Hde. apply sym_equal. exact zenon_H2b.
% 3.14/3.35 (* end of lemma zenon_L105_ *)
% 3.14/3.35 assert (zenon_L106_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_Hed zenon_He8 zenon_H13a zenon_H139 zenon_H71 zenon_H49 zenon_H2b.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H4a | zenon_intro zenon_Hee ].
% 3.14/3.35 apply (zenon_L102_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_He4 | zenon_intro zenon_Hef ].
% 3.14/3.35 apply (zenon_L103_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Heb ].
% 3.14/3.35 apply (zenon_L105_); trivial.
% 3.14/3.35 apply (zenon_L69_); trivial.
% 3.14/3.35 (* end of lemma zenon_L106_ *)
% 3.14/3.35 assert (zenon_L107_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H142 zenon_H136 zenon_H135 zenon_H49 zenon_H71 zenon_H139 zenon_He8 zenon_Hed zenon_H22 zenon_H89 zenon_H2b zenon_Hd2.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H108 | zenon_intro zenon_H143 ].
% 3.14/3.35 apply (zenon_L101_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H13a | zenon_intro zenon_H144 ].
% 3.14/3.35 apply (zenon_L106_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H8a | zenon_intro zenon_Hd1 ].
% 3.14/3.35 apply (zenon_L31_); trivial.
% 3.14/3.35 apply (zenon_L60_); trivial.
% 3.14/3.35 (* end of lemma zenon_L107_ *)
% 3.14/3.35 assert (zenon_L108_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False).
% 3.14/3.35 do 0 intro. intros zenon_H145 zenon_H2b zenon_H31.
% 3.14/3.35 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_Hab | zenon_intro zenon_H146 ].
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hab.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hac.
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hae].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e1) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_Hae.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H145.
% 3.14/3.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.14/3.35 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H147].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H147.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hac.
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 3.14/3.35 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H148].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 3.14/3.35 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H3d].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H3d zenon_H31).
% 3.14/3.35 apply zenon_H20. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_H50. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply zenon_Had. apply refl_equal.
% 3.14/3.35 apply (zenon_notand_s _ _ zenon_H146); [ zenon_intro zenon_H14a | zenon_intro zenon_H149 ].
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e3) = (op (op (e2) (e2)) (op (e2) (e2))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H14a.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hb2.
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H14b].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e1) (e1)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H14b.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_H2b.
% 3.14/3.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 3.14/3.35 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 3.14/3.35 congruence.
% 3.14/3.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))).
% 3.14/3.35 intro zenon_D_pnotp.
% 3.14/3.35 apply zenon_H14c.
% 3.14/3.35 rewrite <- zenon_D_pnotp.
% 3.14/3.35 exact zenon_Hb2.
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 3.14/3.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d].
% 3.14/3.35 congruence.
% 3.14/3.35 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H3d].
% 3.14/3.35 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H3d].
% 3.14/3.35 congruence.
% 3.14/3.35 exact (zenon_H3d zenon_H31).
% 3.14/3.35 exact (zenon_H3d zenon_H31).
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_H27. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_Hb3. apply refl_equal.
% 3.14/3.35 apply zenon_H149. apply sym_equal. exact zenon_H31.
% 3.14/3.35 (* end of lemma zenon_L108_ *)
% 3.14/3.35 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H14f. zenon_intro zenon_H14e.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H14e). zenon_intro zenon_H142. zenon_intro zenon_H150.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H150). zenon_intro zenon_H152. zenon_intro zenon_H151.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H151). zenon_intro zenon_H154. zenon_intro zenon_H153.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H153). zenon_intro zenon_H156. zenon_intro zenon_H155.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H155). zenon_intro zenon_H158. zenon_intro zenon_H157.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H157). zenon_intro zenon_H15a. zenon_intro zenon_H159.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H159). zenon_intro zenon_H15c. zenon_intro zenon_H15b.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H15b). zenon_intro zenon_Ha4. zenon_intro zenon_H15d.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H15d). zenon_intro zenon_H15f. zenon_intro zenon_H15e.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H15e). zenon_intro zenon_H161. zenon_intro zenon_H160.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H160). zenon_intro zenon_Hfe. zenon_intro zenon_H162.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H162). zenon_intro zenon_H6b. zenon_intro zenon_H163.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H163). zenon_intro zenon_Hed. zenon_intro zenon_H164.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H164). zenon_intro zenon_Hc7. zenon_intro zenon_H165.
% 3.14/3.35 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H167. zenon_intro zenon_H166.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H166). zenon_intro zenon_H169. zenon_intro zenon_H168.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H168). zenon_intro zenon_H16b. zenon_intro zenon_H16a.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_H16d. zenon_intro zenon_H16c.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H16c). zenon_intro zenon_H16f. zenon_intro zenon_H16e.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H16e). zenon_intro zenon_H171. zenon_intro zenon_H170.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_H173. zenon_intro zenon_H172.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H172). zenon_intro zenon_H175. zenon_intro zenon_H174.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H174). zenon_intro zenon_H177. zenon_intro zenon_H176.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H110. zenon_intro zenon_H178.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_H17a. zenon_intro zenon_H179.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H17c. zenon_intro zenon_H17b.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H17e. zenon_intro zenon_H17d.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H180. zenon_intro zenon_H17f.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H182. zenon_intro zenon_H181.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H184. zenon_intro zenon_H183.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H186. zenon_intro zenon_H185.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H185). zenon_intro zenon_H188. zenon_intro zenon_H187.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H18a. zenon_intro zenon_H189.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H18c. zenon_intro zenon_H18b.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H18b). zenon_intro zenon_H18e. zenon_intro zenon_H18d.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H18d). zenon_intro zenon_H190. zenon_intro zenon_H18f.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H192. zenon_intro zenon_H191.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H191). zenon_intro zenon_H194. zenon_intro zenon_H193.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H193). zenon_intro zenon_H6e. zenon_intro zenon_H195.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H197. zenon_intro zenon_H196.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H196). zenon_intro zenon_H199. zenon_intro zenon_H198.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_H19b. zenon_intro zenon_H19a.
% 3.14/3.35 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H19d. zenon_intro zenon_H19c.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H19c). zenon_intro zenon_H19f. zenon_intro zenon_H19e.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H67. zenon_intro zenon_H1a0.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H1a2. zenon_intro zenon_H1a1.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H1a4. zenon_intro zenon_H1a3.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_H44. zenon_intro zenon_H1a5.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_Hd2. zenon_intro zenon_H1a6.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H1a8. zenon_intro zenon_H1a7.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H139. zenon_intro zenon_H1a9.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H72. zenon_intro zenon_H1aa.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_H49. zenon_intro zenon_H1ab.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1ab). zenon_intro zenon_H1ad. zenon_intro zenon_H1ac.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_H1af. zenon_intro zenon_H1ae.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H1b1. zenon_intro zenon_H1b0.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_He5. zenon_intro zenon_H1b2.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H1b4. zenon_intro zenon_H1b3.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H1b6. zenon_intro zenon_H1b5.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_Hc4. zenon_intro zenon_H1b7.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H1b9. zenon_intro zenon_H1b8.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_Hfa. zenon_intro zenon_H1ba.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1ba). zenon_intro zenon_H1bc. zenon_intro zenon_H1bb.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_Hf5. zenon_intro zenon_H1bd.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H1bf. zenon_intro zenon_H1be.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hb8. zenon_intro zenon_H1c0.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H89. zenon_intro zenon_H1c1.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H1c3. zenon_intro zenon_H1c2.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H1c5. zenon_intro zenon_H1c4.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1c4). zenon_intro zenon_H136. zenon_intro zenon_H1c6.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1c6). zenon_intro zenon_H109. zenon_intro zenon_H1c7.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_H1c9. zenon_intro zenon_H1c8.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H123. zenon_intro zenon_H1ca.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_H1cc. zenon_intro zenon_H1cb.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H1ce. zenon_intro zenon_H1cd.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1cd). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d4. zenon_intro zenon_H1d3.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_H97. zenon_intro zenon_H1d5.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H9f. zenon_intro zenon_H1d6.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H10d. zenon_intro zenon_H1d9.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H1db. zenon_intro zenon_H1da.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_Hf3. zenon_intro zenon_H1dc.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1dc). zenon_intro zenon_H10f. zenon_intro zenon_H1dd.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1dd). zenon_intro zenon_H4d. zenon_intro zenon_H1de.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1de). zenon_intro zenon_H62. zenon_intro zenon_H1df.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1df). zenon_intro zenon_Hbf. zenon_intro zenon_H1e0.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1e0). zenon_intro zenon_He8. zenon_intro zenon_Hbc.
% 3.14/3.35 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H76. zenon_intro zenon_H1e1.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H8c. zenon_intro zenon_H1e2.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H2a. zenon_intro zenon_H1e3.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_Hca. zenon_intro zenon_H1e4.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H33. zenon_intro zenon_H23.
% 3.14/3.35 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H1e6. zenon_intro zenon_H1e5.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1e5). zenon_intro zenon_H1e8. zenon_intro zenon_H1e7.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1ea. zenon_intro zenon_H1e9.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1ec | zenon_intro zenon_H1eb ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H1ed.
% 3.14/3.35 exact (zenon_H1ed zenon_H1ee).
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1eb); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1ef ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H2c. zenon_intro zenon_H1f1.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f2 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hce. zenon_intro zenon_H2d.
% 3.14/3.35 exact (zenon_H1f1 zenon_Hce).
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1f4 ].
% 3.14/3.35 apply (zenon_L1_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H106 | zenon_intro zenon_Hb6 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H31. zenon_intro zenon_H3c.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f5 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_H22. zenon_intro zenon_Hd0.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 3.14/3.35 apply (zenon_L3_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H2e | zenon_intro zenon_H1f7 ].
% 3.14/3.35 apply (zenon_L6_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H36 | zenon_intro zenon_H38 ].
% 3.14/3.35 apply (zenon_L9_); trivial.
% 3.14/3.35 apply (zenon_L10_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H3b | zenon_intro zenon_H1f8 ].
% 3.14/3.35 apply (zenon_L11_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H3f | zenon_intro zenon_Hcd ].
% 3.14/3.35 apply (zenon_L12_); trivial.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_H54. zenon_intro zenon_H35.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H43 | zenon_intro zenon_H1f9 ].
% 3.14/3.35 apply (zenon_L23_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H73 | zenon_intro zenon_H1fa ].
% 3.14/3.35 apply (zenon_L24_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H75 | zenon_intro zenon_H7b ].
% 3.14/3.35 apply (zenon_L25_); trivial.
% 3.14/3.35 apply (zenon_L28_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H2e | zenon_intro zenon_H1f7 ].
% 3.14/3.35 apply (zenon_L6_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H36 | zenon_intro zenon_H38 ].
% 3.14/3.35 apply (zenon_L29_); trivial.
% 3.14/3.35 apply (zenon_L10_); trivial.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_Ha9. zenon_intro zenon_H88.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f5 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_H22. zenon_intro zenon_Hd0.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 3.14/3.35 apply (zenon_L3_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H2e | zenon_intro zenon_H1f7 ].
% 3.14/3.35 apply (zenon_L30_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H36 | zenon_intro zenon_H38 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H32. zenon_intro zenon_H37.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H8a | zenon_intro zenon_H1fb ].
% 3.14/3.35 apply (zenon_L31_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H3e | zenon_intro zenon_H1fc ].
% 3.14/3.35 apply (zenon_L32_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H9c | zenon_intro zenon_Hc0 ].
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H8d | zenon_intro zenon_H1fd ].
% 3.14/3.35 apply (zenon_L34_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H98 | zenon_intro zenon_H1fe ].
% 3.14/3.35 apply (zenon_L44_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H31 | zenon_intro zenon_Hb7 ].
% 3.14/3.35 apply (zenon_L9_); trivial.
% 3.14/3.35 apply (zenon_L45_); trivial.
% 3.14/3.35 apply (zenon_L49_); trivial.
% 3.14/3.35 apply (zenon_L10_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H3b | zenon_intro zenon_H1f8 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 3.14/3.35 apply (zenon_L32_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H3f | zenon_intro zenon_Hcd ].
% 3.14/3.35 apply (zenon_L12_); trivial.
% 3.14/3.35 apply (zenon_L51_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H200 | zenon_intro zenon_H1ff ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H75. zenon_intro zenon_H90.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f2 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hce. zenon_intro zenon_H2d.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f5 ].
% 3.14/3.35 apply (zenon_L53_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H3b | zenon_intro zenon_H1f8 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 3.14/3.35 apply (zenon_L55_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H2e | zenon_intro zenon_H1f7 ].
% 3.14/3.35 apply (zenon_L57_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H36 | zenon_intro zenon_H38 ].
% 3.14/3.35 apply (zenon_L59_); trivial.
% 3.14/3.35 apply (zenon_L10_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H3f | zenon_intro zenon_Hcd ].
% 3.14/3.35 apply (zenon_L12_); trivial.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_H54. zenon_intro zenon_H35.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 3.14/3.35 apply (zenon_L55_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H2e | zenon_intro zenon_H1f7 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H2b. zenon_intro zenon_H2f.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H25 | zenon_intro zenon_H201 ].
% 3.14/3.35 apply (zenon_L54_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H202 ].
% 3.14/3.35 apply (zenon_L60_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_He6 | zenon_intro zenon_Hf1 ].
% 3.14/3.35 apply (zenon_L70_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H203 ].
% 3.14/3.35 apply (zenon_L71_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H204 ].
% 3.14/3.35 apply (zenon_L76_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Ha9 ].
% 3.14/3.35 apply (zenon_L77_); trivial.
% 3.14/3.35 exact (zenon_H2f zenon_Ha9).
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H36 | zenon_intro zenon_H38 ].
% 3.14/3.35 apply (zenon_L59_); trivial.
% 3.14/3.35 apply (zenon_L10_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1f4 ].
% 3.14/3.35 apply (zenon_L1_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H106 | zenon_intro zenon_Hb6 ].
% 3.14/3.35 apply (zenon_L78_); trivial.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_Ha9. zenon_intro zenon_H88.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f5 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_H22. zenon_intro zenon_Hd0.
% 3.14/3.35 exact (zenon_H90 zenon_H22).
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H3b | zenon_intro zenon_H1f8 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H107 | zenon_intro zenon_H205 ].
% 3.14/3.35 apply (zenon_L86_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H119 | zenon_intro zenon_H206 ].
% 3.14/3.35 apply (zenon_L87_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H7b | zenon_intro zenon_H71 ].
% 3.14/3.35 apply (zenon_L72_); trivial.
% 3.14/3.35 exact (zenon_H24 zenon_H71).
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H2e | zenon_intro zenon_H1f7 ].
% 3.14/3.35 apply (zenon_L57_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H36 | zenon_intro zenon_H38 ].
% 3.14/3.35 apply (zenon_L59_); trivial.
% 3.14/3.35 apply (zenon_L10_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H3f | zenon_intro zenon_Hcd ].
% 3.14/3.35 apply (zenon_L12_); trivial.
% 3.14/3.35 apply (zenon_L51_); trivial.
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H71. zenon_intro zenon_H29.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f2 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_Hce. zenon_intro zenon_H2d.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f5 ].
% 3.14/3.35 apply (zenon_L53_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H3b | zenon_intro zenon_H1f8 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 3.14/3.35 apply (zenon_L88_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H2e | zenon_intro zenon_H1f7 ].
% 3.14/3.35 apply (zenon_L57_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H36 | zenon_intro zenon_H38 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H32. zenon_intro zenon_H37.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H22 | zenon_intro zenon_H207 ].
% 3.14/3.35 apply (zenon_L52_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H122 | zenon_intro zenon_H208 ].
% 3.14/3.35 apply (zenon_L89_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H9b | zenon_intro zenon_H61 ].
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H43 | zenon_intro zenon_H1f9 ].
% 3.14/3.35 apply (zenon_L90_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H73 | zenon_intro zenon_H1fa ].
% 3.14/3.35 apply (zenon_L92_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H75 | zenon_intro zenon_H7b ].
% 3.14/3.35 apply (zenon_L58_); trivial.
% 3.14/3.35 apply (zenon_L93_); trivial.
% 3.14/3.35 apply (zenon_L98_); trivial.
% 3.14/3.35 apply (zenon_L10_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H3f | zenon_intro zenon_Hcd ].
% 3.14/3.35 apply (zenon_L12_); trivial.
% 3.14/3.35 apply (zenon_L100_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1f4 ].
% 3.14/3.35 apply (zenon_L1_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H106 | zenon_intro zenon_Hb6 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H31. zenon_intro zenon_H3c.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f5 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_H22. zenon_intro zenon_Hd0.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 3.14/3.35 apply (zenon_L88_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H2e | zenon_intro zenon_H1f7 ].
% 3.14/3.35 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H2b. zenon_intro zenon_H2f.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H188); [ zenon_intro zenon_H135 | zenon_intro zenon_H209 ].
% 3.14/3.35 apply (zenon_L107_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H145 | zenon_intro zenon_H20a ].
% 3.14/3.35 apply (zenon_L108_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H75 | zenon_intro zenon_H4e ].
% 3.14/3.35 exact (zenon_Hd0 zenon_H75).
% 3.14/3.35 apply (zenon_L94_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H36 | zenon_intro zenon_H38 ].
% 3.14/3.35 apply (zenon_L9_); trivial.
% 3.14/3.35 apply (zenon_L10_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H3b | zenon_intro zenon_H1f8 ].
% 3.14/3.35 apply (zenon_L11_); trivial.
% 3.14/3.35 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H3f | zenon_intro zenon_Hcd ].
% 3.14/3.35 apply (zenon_L12_); trivial.
% 3.14/3.35 apply (zenon_L100_); trivial.
% 3.14/3.35 apply (zenon_L43_); trivial.
% 3.14/3.35 Qed.
% 3.14/3.35 % SZS output end Proof
% 3.14/3.35 (* END-PROOF *)
% 3.14/3.35 nodes searched: 114549
% 3.14/3.35 max branch formulas: 284
% 3.14/3.35 proof nodes created: 5795
% 3.14/3.35 formulas created: 34338
% 3.14/3.35
%------------------------------------------------------------------------------