TSTP Solution File: GEO222+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n011.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 : Sat Jul 16 07:01:02 EDT 2022
% Result : Theorem 106.02s 106.20s
% Output : Proof 106.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jun 17 20:56:07 EDT 2022
% 0.14/0.35 % CPUTime :
% 106.02/106.20 (* PROOF-FOUND *)
% 106.02/106.20 % SZS status Theorem
% 106.02/106.20 (* BEGIN-PROOF *)
% 106.02/106.20 % SZS output start Proof
% 106.02/106.20 Theorem con : (forall A : zenon_U, (forall L : zenon_U, (~(convergent_lines L (orthogonal_through_point (orthogonal_through_point L A) A))))).
% 106.02/106.20 Proof.
% 106.02/106.20 assert (zenon_L1_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H17 zenon_H18.
% 106.02/106.20 generalize (occu1 (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H1b.
% 106.02/106.20 generalize (zenon_H1b (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H1c.
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 106.02/106.20 exact (zenon_H18 zenon_H1e).
% 106.02/106.20 exact (zenon_H17 zenon_H1d).
% 106.02/106.20 (* end of lemma zenon_L1_ *)
% 106.02/106.20 assert (zenon_L2_ : forall (zenon_TL_ba : zenon_U) (zenon_TA_z : zenon_U), (forall L : zenon_U, (~(unorthogonal_lines (orthogonal_through_point L zenon_TA_z) L))) -> (~(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H1f zenon_H18.
% 106.02/106.20 generalize (zenon_H1f (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H17.
% 106.02/106.20 apply (zenon_L1_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 (* end of lemma zenon_L2_ *)
% 106.02/106.20 assert (zenon_L3_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) Y)->((distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) Z)\/(distinct_lines Y Z))))) -> (~(distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H20 zenon_H21 zenon_H22 zenon_H23.
% 106.02/106.20 generalize (zenon_H20 (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H24.
% 106.02/106.20 generalize (zenon_H24 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H25.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 106.02/106.20 exact (zenon_H27 zenon_H23).
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 106.02/106.20 exact (zenon_H22 zenon_H29).
% 106.02/106.20 exact (zenon_H21 zenon_H28).
% 106.02/106.20 (* end of lemma zenon_L3_ *)
% 106.02/106.20 assert (zenon_L4_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), (forall Z : zenon_U, ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))->((distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) Z)\/(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) Z)))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) Y)->((distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) Z)\/(distinct_lines Y Z))))) -> (~(distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z))) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H2a zenon_H1e zenon_H20 zenon_H21 zenon_H22 zenon_H2b.
% 106.02/106.20 generalize (zenon_H2a (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H2c.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H18 | zenon_intro zenon_H2d ].
% 106.02/106.20 exact (zenon_H18 zenon_H1e).
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H23 | zenon_intro zenon_H2e ].
% 106.02/106.20 apply (zenon_L3_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 exact (zenon_H2b zenon_H2e).
% 106.02/106.20 (* end of lemma zenon_L4_ *)
% 106.02/106.20 assert (zenon_L5_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), (~(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z))) -> (~(distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z)) -> (forall Z : zenon_U, ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))->((distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) Z)\/(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) Z)))) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H2b zenon_H22 zenon_H21 zenon_H1e zenon_H2a.
% 106.02/106.20 generalize (apart5 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H20.
% 106.02/106.20 apply (zenon_L4_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 (* end of lemma zenon_L5_ *)
% 106.02/106.20 assert (zenon_L6_ : forall (zenon_TL_ba : zenon_U) (zenon_TA_z : zenon_U), (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((distinct_lines L M)->((apart_point_and_line zenon_TA_z L)\/((apart_point_and_line zenon_TA_z M)\/((unorthogonal_lines L N)\/(unorthogonal_lines M N)))))))) -> (distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z)) -> (~(apart_point_and_line zenon_TA_z (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z))) -> (~(apart_point_and_line zenon_TA_z (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba)) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TL_ba)) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H2f zenon_H28 zenon_H30 zenon_H31 zenon_H32 zenon_H33.
% 106.02/106.20 generalize (zenon_H2f (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H34.
% 106.02/106.20 generalize (zenon_H34 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H35.
% 106.02/106.20 generalize (zenon_H35 zenon_TL_ba). zenon_intro zenon_H36.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H21 | zenon_intro zenon_H37 ].
% 106.02/106.20 exact (zenon_H21 zenon_H28).
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 106.02/106.20 exact (zenon_H30 zenon_H39).
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 106.02/106.20 exact (zenon_H31 zenon_H3b).
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 106.02/106.20 exact (zenon_H32 zenon_H3d).
% 106.02/106.20 exact (zenon_H33 zenon_H3c).
% 106.02/106.20 (* end of lemma zenon_L6_ *)
% 106.02/106.20 assert (zenon_L7_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), (forall Z : zenon_U, ((distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))->((distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) Z)\/(distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) Z)))) -> (~(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z))) -> (~(distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z)) -> (forall Z : zenon_U, ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))->((distinct_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) Z)\/(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) Z)))) -> (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((distinct_lines L M)->((apart_point_and_line zenon_TA_z L)\/((apart_point_and_line zenon_TA_z M)\/((unorthogonal_lines L N)\/(unorthogonal_lines M N)))))))) -> (~(apart_point_and_line zenon_TA_z (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z))) -> (~(apart_point_and_line zenon_TA_z (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba)) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TL_ba)) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H3e zenon_H2b zenon_H22 zenon_H1e zenon_H2a zenon_H2f zenon_H30 zenon_H31 zenon_H32 zenon_H33.
% 106.02/106.20 generalize (zenon_H3e (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H3f.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H21 | zenon_intro zenon_H40 ].
% 106.02/106.20 apply (zenon_L5_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ].
% 106.02/106.20 apply (zenon_L6_ zenon_TL_ba zenon_TA_z); trivial.
% 106.02/106.20 exact (zenon_H22 zenon_H29).
% 106.02/106.20 (* end of lemma zenon_L7_ *)
% 106.02/106.20 assert (zenon_L8_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H41 zenon_H17.
% 106.02/106.20 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H1e. zenon_intro zenon_H1d.
% 106.02/106.20 exact (zenon_H17 zenon_H1d).
% 106.02/106.20 (* end of lemma zenon_L8_ *)
% 106.02/106.20 assert (zenon_L9_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), (forall N : zenon_U, (((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba))->(((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) N)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) N))\/((convergent_lines zenon_TL_ba N)/\(unorthogonal_lines zenon_TL_ba N))))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba) -> (unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (~(unorthogonal_lines zenon_TL_ba (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H42 zenon_H43 zenon_H3d zenon_H17 zenon_H44.
% 106.02/106.20 generalize (zenon_H42 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H45.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 106.02/106.20 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H32 ].
% 106.02/106.20 exact (zenon_H48 zenon_H43).
% 106.02/106.20 exact (zenon_H32 zenon_H3d).
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H41 | zenon_intro zenon_H49 ].
% 106.02/106.20 apply (zenon_L8_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 106.02/106.20 exact (zenon_H44 zenon_H4a).
% 106.02/106.20 (* end of lemma zenon_L9_ *)
% 106.02/106.20 assert (zenon_L10_ : forall (zenon_TL_ba : zenon_U), ((convergent_lines zenon_TL_ba zenon_TL_ba)/\(unorthogonal_lines zenon_TL_ba zenon_TL_ba)) -> (~(convergent_lines zenon_TL_ba zenon_TL_ba)) -> False).
% 106.02/106.20 do 1 intro. intros zenon_H4c zenon_H4d.
% 106.02/106.20 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e.
% 106.02/106.20 exact (zenon_H4d zenon_H4f).
% 106.02/106.20 (* end of lemma zenon_L10_ *)
% 106.02/106.20 assert (zenon_L11_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), (forall M : zenon_U, (forall N : zenon_U, (((convergent_lines zenon_TL_ba M)/\(unorthogonal_lines zenon_TL_ba M))->(((convergent_lines zenon_TL_ba N)/\(unorthogonal_lines zenon_TL_ba N))\/((convergent_lines M N)/\(unorthogonal_lines M N)))))) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TL_ba)) -> (~(convergent_lines zenon_TL_ba zenon_TL_ba)) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) (orthogonal_through_point zenon_TL_ba zenon_TA_z))) -> (unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba) -> (forall N : zenon_U, (((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba))->(((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) N)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) N))\/((convergent_lines zenon_TL_ba N)/\(unorthogonal_lines zenon_TL_ba N))))) -> (convergent_lines zenon_TL_ba (orthogonal_through_point zenon_TL_ba zenon_TA_z)) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H50 zenon_H33 zenon_H4d zenon_H17 zenon_H3d zenon_H43 zenon_H42 zenon_H4b.
% 106.02/106.20 generalize (zenon_H50 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H51.
% 106.02/106.20 generalize (zenon_H51 zenon_TL_ba). zenon_intro zenon_H52.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 106.02/106.20 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H55 | zenon_intro zenon_H44 ].
% 106.02/106.20 exact (zenon_H55 zenon_H4b).
% 106.02/106.20 apply (zenon_L9_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H4c | zenon_intro zenon_H56 ].
% 106.02/106.20 apply (zenon_L10_ zenon_TL_ba); trivial.
% 106.02/106.20 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H57. zenon_intro zenon_H3c.
% 106.02/106.20 exact (zenon_H33 zenon_H3c).
% 106.02/106.20 (* end of lemma zenon_L11_ *)
% 106.02/106.20 assert (zenon_L12_ : forall (zenon_TA_z : zenon_U) (zenon_TL_ba : zenon_U), ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba)) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba) -> (forall N : zenon_U, (((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) zenon_TL_ba))->(((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) N)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z) N))\/((convergent_lines zenon_TL_ba N)/\(unorthogonal_lines zenon_TL_ba N))))) -> (~(convergent_lines zenon_TL_ba zenon_TL_ba)) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TL_ba)) -> (forall M : zenon_U, (forall N : zenon_U, (((convergent_lines zenon_TL_ba M)/\(unorthogonal_lines zenon_TL_ba M))->(((convergent_lines zenon_TL_ba N)/\(unorthogonal_lines zenon_TL_ba N))\/((convergent_lines M N)/\(unorthogonal_lines M N)))))) -> (forall L : zenon_U, (~(unorthogonal_lines (orthogonal_through_point L zenon_TA_z) L))) -> False).
% 106.02/106.20 do 2 intro. intros zenon_H58 zenon_H43 zenon_H42 zenon_H4d zenon_H33 zenon_H50 zenon_H1f.
% 106.02/106.20 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H43. zenon_intro zenon_H3d.
% 106.02/106.20 generalize (zenon_H1f (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H17.
% 106.02/106.20 generalize (zenon_H42 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H45.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 106.02/106.20 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H32 ].
% 106.02/106.20 exact (zenon_H48 zenon_H43).
% 106.02/106.20 exact (zenon_H32 zenon_H3d).
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H41 | zenon_intro zenon_H49 ].
% 106.02/106.20 apply (zenon_L8_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 106.02/106.20 apply (zenon_L11_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 (* end of lemma zenon_L12_ *)
% 106.02/106.20 apply NNPP. intro zenon_G.
% 106.02/106.20 apply (zenon_notallex_s (fun A : zenon_U => (forall L : zenon_U, (~(convergent_lines L (orthogonal_through_point (orthogonal_through_point L A) A))))) zenon_G); [ zenon_intro zenon_H59; idtac ].
% 106.02/106.20 elim zenon_H59. zenon_intro zenon_TA_z. zenon_intro zenon_H5a.
% 106.02/106.20 apply (zenon_notallex_s (fun L : zenon_U => (~(convergent_lines L (orthogonal_through_point (orthogonal_through_point L zenon_TA_z) zenon_TA_z)))) zenon_H5a); [ zenon_intro zenon_H5b; idtac ].
% 106.02/106.20 elim zenon_H5b. zenon_intro zenon_TL_ba. zenon_intro zenon_H5c.
% 106.02/106.20 apply zenon_H5c. zenon_intro zenon_H5d.
% 106.02/106.20 generalize (apart3 (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H2b.
% 106.02/106.20 generalize (ax6 zenon_TL_ba). zenon_intro zenon_H5e.
% 106.02/106.20 generalize (ooc2 zenon_TA_z). zenon_intro zenon_H5f.
% 106.02/106.20 generalize (zenon_H5f (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H30.
% 106.02/106.20 generalize (zenon_H5e (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H60.
% 106.02/106.20 generalize (ceq3 (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H61.
% 106.02/106.20 generalize (apart3 zenon_TL_ba). zenon_intro zenon_H4d.
% 106.02/106.20 generalize (zenon_H60 zenon_TL_ba). zenon_intro zenon_H62.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 106.02/106.20 exact (zenon_H64 zenon_H5d).
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H4f | zenon_intro zenon_H43 ].
% 106.02/106.20 exact (zenon_H4d zenon_H4f).
% 106.02/106.20 generalize (apart5 (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H65.
% 106.02/106.20 generalize (oac1 zenon_TL_ba). zenon_intro zenon_H50.
% 106.02/106.20 generalize (oac1 (orthogonal_through_point (orthogonal_through_point zenon_TL_ba zenon_TA_z) zenon_TA_z)). zenon_intro zenon_H66.
% 106.02/106.20 generalize (ooc1 zenon_TA_z). zenon_intro zenon_H1f.
% 106.02/106.20 generalize (zenon_H66 zenon_TL_ba). zenon_intro zenon_H42.
% 106.02/106.20 generalize (zenon_H1f zenon_TL_ba). zenon_intro zenon_H33.
% 106.02/106.20 generalize (zenon_H42 zenon_TL_ba). zenon_intro zenon_H67.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H47 | zenon_intro zenon_H68 ].
% 106.02/106.20 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H32 ].
% 106.02/106.20 exact (zenon_H48 zenon_H43).
% 106.02/106.20 generalize (zenon_H5f zenon_TL_ba). zenon_intro zenon_H31.
% 106.02/106.20 generalize (ouo1 zenon_TA_z). zenon_intro zenon_H2f.
% 106.02/106.20 generalize (apart2 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H22.
% 106.02/106.20 generalize (zenon_H61 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H2a.
% 106.02/106.20 generalize (zenon_H65 (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H3e.
% 106.02/106.20 generalize (zenon_H2a (orthogonal_through_point zenon_TL_ba zenon_TA_z)). zenon_intro zenon_H69.
% 106.02/106.20 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H18 | zenon_intro zenon_H6a ].
% 106.02/106.20 apply (zenon_L2_ zenon_TL_ba zenon_TA_z); trivial.
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H29 | zenon_intro zenon_H1e ].
% 106.02/106.20 exact (zenon_H22 zenon_H29).
% 106.02/106.20 apply (zenon_L7_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H58 | zenon_intro zenon_H4c ].
% 106.02/106.20 apply (zenon_L12_ zenon_TA_z zenon_TL_ba); trivial.
% 106.02/106.20 apply (zenon_L10_ zenon_TL_ba); trivial.
% 106.02/106.20 Qed.
% 106.02/106.20 % SZS output end Proof
% 106.02/106.20 (* END-PROOF *)
% 106.02/106.20 nodes searched: 12264627
% 106.02/106.20 max branch formulas: 66469
% 106.02/106.20 proof nodes created: 138007
% 106.02/106.20 formulas created: 14984554
% 106.02/106.20
%------------------------------------------------------------------------------