TSTP Solution File: GEO231+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO231+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n024.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 07:01:08 EDT 2022
% Result : Theorem 0.49s 0.72s
% Output : Proof 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO231+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n024.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 : Sat Jun 18 01:38:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.49/0.72 (* PROOF-FOUND *)
% 0.49/0.72 % SZS status Theorem
% 0.49/0.72 (* BEGIN-PROOF *)
% 0.49/0.72 % SZS output start Proof
% 0.49/0.72 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, (((~(unequally_directed_lines L (reverse_line M)))/\(~(unequally_directed_lines L N)))->(~(unequally_directed_lines M (reverse_line N))))))).
% 0.49/0.72 Proof.
% 0.49/0.72 assert (zenon_L1_ : forall (zenon_TM_bi : zenon_U), ((unequally_directed_lines zenon_TM_bi zenon_TM_bi)/\(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> False).
% 0.49/0.72 do 1 intro. intros zenon_H20 zenon_H21.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 0.49/0.72 exact (zenon_H21 zenon_H24).
% 0.49/0.72 (* end of lemma zenon_L1_ *)
% 0.49/0.72 assert (zenon_L2_ : forall (zenon_TM_bi : zenon_U) (zenon_TL_bn : zenon_U), ((unequally_directed_lines zenon_TL_bn zenon_TM_bi)/\(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> False).
% 0.49/0.72 do 2 intro. intros zenon_H25 zenon_H26.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H29. zenon_intro zenon_H28.
% 0.49/0.72 exact (zenon_H26 zenon_H28).
% 0.49/0.72 (* end of lemma zenon_L2_ *)
% 0.49/0.72 assert (zenon_L3_ : forall (zenon_TN_bs : zenon_U), ((unequally_directed_lines zenon_TN_bs zenon_TN_bs)/\(unequally_directed_lines zenon_TN_bs (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> False).
% 0.49/0.72 do 1 intro. intros zenon_H2a zenon_H2b.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.49/0.72 exact (zenon_H2b zenon_H2e).
% 0.49/0.72 (* end of lemma zenon_L3_ *)
% 0.49/0.72 assert (zenon_L4_ : forall (zenon_TN_bs : zenon_U) (zenon_TL_bn : zenon_U), ((unequally_directed_lines zenon_TL_bn zenon_TN_bs)/\(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> False).
% 0.49/0.72 do 2 intro. intros zenon_H2f zenon_H30.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 0.49/0.72 exact (zenon_H30 zenon_H32).
% 0.49/0.72 (* end of lemma zenon_L4_ *)
% 0.49/0.72 assert (zenon_L5_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U), ((unequally_directed_lines zenon_TN_bs zenon_TL_bn)/\(unequally_directed_lines zenon_TN_bs (reverse_line zenon_TL_bn))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> False).
% 0.49/0.72 do 2 intro. intros zenon_H33 zenon_H30 zenon_H2b.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34.
% 0.49/0.72 generalize (oag7 zenon_TN_bs). zenon_intro zenon_H36.
% 0.49/0.72 generalize (zenon_H36 zenon_TL_bn). zenon_intro zenon_H37.
% 0.49/0.72 generalize (zenon_H37 zenon_TN_bs). zenon_intro zenon_H38.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 0.49/0.72 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 0.49/0.72 exact (zenon_H3c zenon_H35).
% 0.49/0.72 exact (zenon_H3b zenon_H34).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H2a | zenon_intro zenon_H2f ].
% 0.49/0.72 apply (zenon_L3_ zenon_TN_bs); trivial.
% 0.49/0.72 apply (zenon_L4_ zenon_TN_bs zenon_TL_bn); trivial.
% 0.49/0.72 (* end of lemma zenon_L5_ *)
% 0.49/0.72 assert (zenon_L6_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), (unequally_directed_lines zenon_TM_bi zenon_TN_bs) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (forall M : zenon_U, (forall N : zenon_U, (((unequally_directed_lines zenon_TM_bi M)/\(unequally_directed_lines zenon_TM_bi (reverse_line M)))->(((unequally_directed_lines zenon_TM_bi N)/\(unequally_directed_lines zenon_TM_bi (reverse_line N)))\/((unequally_directed_lines M N)/\(unequally_directed_lines M (reverse_line N))))))) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H3d zenon_H3e zenon_H26 zenon_H21 zenon_H3f zenon_H30 zenon_H2b zenon_H40.
% 0.49/0.72 generalize (zenon_H40 zenon_TN_bs). zenon_intro zenon_H41.
% 0.49/0.72 generalize (zenon_H40 zenon_TL_bn). zenon_intro zenon_H42.
% 0.49/0.72 generalize (zenon_H41 zenon_TL_bn). zenon_intro zenon_H43.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 0.49/0.72 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.49/0.72 exact (zenon_H47 zenon_H3d).
% 0.49/0.72 exact (zenon_H46 zenon_H3e).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H48 | zenon_intro zenon_H33 ].
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H3f. zenon_intro zenon_H49.
% 0.49/0.72 generalize (zenon_H42 zenon_TM_bi). zenon_intro zenon_H4a.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 0.49/0.72 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 0.49/0.72 exact (zenon_H4e zenon_H3f).
% 0.49/0.72 exact (zenon_H4d zenon_H49).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H20 | zenon_intro zenon_H25 ].
% 0.49/0.72 apply (zenon_L1_ zenon_TM_bi); trivial.
% 0.49/0.72 apply (zenon_L2_ zenon_TM_bi zenon_TL_bn); trivial.
% 0.49/0.72 apply (zenon_L5_ zenon_TL_bn zenon_TN_bs); trivial.
% 0.49/0.72 (* end of lemma zenon_L6_ *)
% 0.49/0.72 assert (zenon_L7_ : forall (zenon_TN_bs : zenon_U) (zenon_TL_bn : zenon_U) (zenon_TM_bi : zenon_U), (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi M)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines M N))))) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H3f zenon_H3e zenon_H26 zenon_H21 zenon_H30 zenon_H2b zenon_H4f.
% 0.49/0.72 generalize (oag7 zenon_TM_bi). zenon_intro zenon_H40.
% 0.49/0.72 generalize (zenon_H4f zenon_TL_bn). zenon_intro zenon_H50.
% 0.49/0.72 generalize (zenon_H50 zenon_TN_bs). zenon_intro zenon_H51.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H4e | zenon_intro zenon_H52 ].
% 0.49/0.72 exact (zenon_H4e zenon_H3f).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H3d | zenon_intro zenon_H32 ].
% 0.49/0.72 apply (zenon_L6_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial.
% 0.49/0.72 exact (zenon_H30 zenon_H32).
% 0.49/0.72 (* end of lemma zenon_L7_ *)
% 0.49/0.72 assert (zenon_L8_ : forall (zenon_TN_bs : zenon_U), ((unequally_directed_lines (reverse_line zenon_TN_bs) zenon_TN_bs)/\(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> False).
% 0.49/0.72 do 1 intro. intros zenon_H53 zenon_H54.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55.
% 0.49/0.72 exact (zenon_H54 zenon_H55).
% 0.49/0.72 (* end of lemma zenon_L8_ *)
% 0.49/0.72 assert (zenon_L9_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U), (unequally_directed_lines (reverse_line zenon_TN_bs) zenon_TL_bn) -> (unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TL_bn)) -> (~(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> False).
% 0.49/0.72 do 2 intro. intros zenon_H57 zenon_H58 zenon_H54 zenon_H30.
% 0.49/0.72 generalize (oag7 (reverse_line zenon_TN_bs)). zenon_intro zenon_H59.
% 0.49/0.72 generalize (zenon_H59 zenon_TL_bn). zenon_intro zenon_H5a.
% 0.49/0.72 generalize (zenon_H5a zenon_TN_bs). zenon_intro zenon_H5b.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ].
% 0.49/0.72 apply (zenon_notand_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ].
% 0.49/0.72 exact (zenon_H5f zenon_H57).
% 0.49/0.72 exact (zenon_H5e zenon_H58).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H53 | zenon_intro zenon_H2f ].
% 0.49/0.72 apply (zenon_L8_ zenon_TN_bs); trivial.
% 0.49/0.72 apply (zenon_L4_ zenon_TN_bs zenon_TL_bn); trivial.
% 0.49/0.72 (* end of lemma zenon_L9_ *)
% 0.49/0.72 assert (zenon_L10_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs))->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines (reverse_line zenon_TN_bs) N)))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TL_bn))) -> (unequally_directed_lines (reverse_line zenon_TN_bs) zenon_TL_bn) -> (~(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H60 zenon_H3e zenon_H4d zenon_H57 zenon_H54 zenon_H30.
% 0.49/0.72 generalize (zenon_H60 (reverse_line zenon_TL_bn)). zenon_intro zenon_H61.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H46 | zenon_intro zenon_H62 ].
% 0.49/0.72 exact (zenon_H46 zenon_H3e).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H49 | zenon_intro zenon_H58 ].
% 0.49/0.72 exact (zenon_H4d zenon_H49).
% 0.49/0.72 apply (zenon_L9_ zenon_TL_bn zenon_TN_bs); trivial.
% 0.49/0.72 (* end of lemma zenon_L10_ *)
% 0.49/0.72 assert (zenon_L11_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U), (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TN_bs M)->((unequally_directed_lines zenon_TN_bs N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (unequally_directed_lines zenon_TN_bs zenon_TL_bn) -> False).
% 0.49/0.72 do 2 intro. intros zenon_H63 zenon_H30 zenon_H2b zenon_H35.
% 0.49/0.72 generalize (zenon_H63 zenon_TL_bn). zenon_intro zenon_H64.
% 0.49/0.72 generalize (zenon_H64 zenon_TN_bs). zenon_intro zenon_H65.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H3c | zenon_intro zenon_H66 ].
% 0.49/0.72 exact (zenon_H3c zenon_H35).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H2e | zenon_intro zenon_H32 ].
% 0.49/0.72 exact (zenon_H2b zenon_H2e).
% 0.49/0.72 exact (zenon_H30 zenon_H32).
% 0.49/0.72 (* end of lemma zenon_L11_ *)
% 0.49/0.72 assert (zenon_L12_ : forall (zenon_TM_bi : zenon_U) (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U), (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (unequally_directed_lines zenon_TM_bi zenon_TN_bs) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H2b zenon_H30 zenon_H3f zenon_H21 zenon_H26 zenon_H3e zenon_H3d.
% 0.49/0.72 generalize (oag7 zenon_TM_bi). zenon_intro zenon_H40.
% 0.49/0.72 apply (zenon_L6_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial.
% 0.49/0.72 (* end of lemma zenon_L12_ *)
% 0.49/0.72 assert (zenon_L13_ : forall (zenon_TL_bn : zenon_U) (zenon_TM_bi : zenon_U) (zenon_TN_bs : zenon_U), (unequally_directed_lines zenon_TN_bs zenon_TM_bi) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H67 zenon_H30 zenon_H2b zenon_H21 zenon_H26 zenon_H3e.
% 0.49/0.72 generalize (oag6 zenon_TN_bs). zenon_intro zenon_H63.
% 0.49/0.72 generalize (zenon_H63 zenon_TM_bi). zenon_intro zenon_H68.
% 0.49/0.72 generalize (zenon_H68 zenon_TL_bn). zenon_intro zenon_H69.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ].
% 0.49/0.72 exact (zenon_H6b zenon_H67).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H35 | zenon_intro zenon_H3f ].
% 0.49/0.72 apply (zenon_L11_ zenon_TL_bn zenon_TN_bs); trivial.
% 0.49/0.72 generalize (zenon_H68 zenon_TN_bs). zenon_intro zenon_H6c.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H6b | zenon_intro zenon_H6d ].
% 0.49/0.72 exact (zenon_H6b zenon_H67).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H6d); [ zenon_intro zenon_H2e | zenon_intro zenon_H3d ].
% 0.49/0.72 exact (zenon_H2b zenon_H2e).
% 0.49/0.72 apply (zenon_L12_ zenon_TM_bi zenon_TL_bn zenon_TN_bs); trivial.
% 0.49/0.72 (* end of lemma zenon_L13_ *)
% 0.49/0.72 assert (zenon_L14_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi zenon_TN_bs)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines zenon_TN_bs N)))) -> (unequally_directed_lines zenon_TM_bi zenon_TN_bs) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H6e zenon_H3d zenon_H21 zenon_H30 zenon_H2b zenon_H26 zenon_H3e.
% 0.49/0.72 generalize (zenon_H6e zenon_TM_bi). zenon_intro zenon_H6f.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H47 | zenon_intro zenon_H70 ].
% 0.49/0.72 exact (zenon_H47 zenon_H3d).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H24 | zenon_intro zenon_H67 ].
% 0.49/0.72 exact (zenon_H21 zenon_H24).
% 0.49/0.72 apply (zenon_L13_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial.
% 0.49/0.72 (* end of lemma zenon_L14_ *)
% 0.49/0.72 assert (zenon_L15_ : forall (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), ((unequally_directed_lines zenon_TM_bi zenon_TN_bs)/\(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TN_bs)) -> False).
% 0.49/0.72 do 2 intro. intros zenon_H71 zenon_H47.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H3d. zenon_intro zenon_H3e.
% 0.49/0.72 exact (zenon_H47 zenon_H3d).
% 0.49/0.72 (* end of lemma zenon_L15_ *)
% 0.49/0.72 assert (zenon_L16_ : forall (zenon_TL_bn : zenon_U) (zenon_TM_bi : zenon_U) (zenon_TN_bs : zenon_U), ((unequally_directed_lines zenon_TN_bs zenon_TM_bi)/\(unequally_directed_lines zenon_TN_bs (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H72 zenon_H3e zenon_H26 zenon_H21 zenon_H2b zenon_H30.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H67. zenon_intro zenon_H73.
% 0.49/0.72 apply (zenon_L13_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial.
% 0.49/0.72 (* end of lemma zenon_L16_ *)
% 0.49/0.72 assert (zenon_L17_ : forall (zenon_TM_bi : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TL_bn : zenon_U), (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi M)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TL_bn (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H30 zenon_H2b zenon_H4f zenon_H54 zenon_H26 zenon_H31 zenon_H21 zenon_H3e.
% 0.49/0.72 generalize (oag6 zenon_TL_bn). zenon_intro zenon_H74.
% 0.49/0.72 generalize (oag7 zenon_TM_bi). zenon_intro zenon_H40.
% 0.49/0.72 generalize (zenon_H40 zenon_TN_bs). zenon_intro zenon_H41.
% 0.49/0.72 generalize (zenon_H41 zenon_TM_bi). zenon_intro zenon_H75.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H45 | zenon_intro zenon_H76 ].
% 0.49/0.72 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.49/0.72 generalize (zenon_H74 (reverse_line zenon_TN_bs)). zenon_intro zenon_H77.
% 0.49/0.72 generalize (zenon_H4f (reverse_line zenon_TN_bs)). zenon_intro zenon_H60.
% 0.49/0.72 generalize (zenon_H60 zenon_TM_bi). zenon_intro zenon_H78.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H46 | zenon_intro zenon_H79 ].
% 0.49/0.72 exact (zenon_H46 zenon_H3e).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H79); [ zenon_intro zenon_H24 | zenon_intro zenon_H7a ].
% 0.49/0.72 exact (zenon_H21 zenon_H24).
% 0.49/0.72 generalize (oag7 (reverse_line zenon_TN_bs)). zenon_intro zenon_H59.
% 0.49/0.72 generalize (zenon_H59 zenon_TM_bi). zenon_intro zenon_H7b.
% 0.49/0.72 generalize (zenon_H7b zenon_TN_bs). zenon_intro zenon_H7c.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ].
% 0.49/0.72 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ].
% 0.49/0.72 exact (zenon_H80 zenon_H7a).
% 0.49/0.72 generalize (zenon_H77 (reverse_line zenon_TM_bi)). zenon_intro zenon_H81.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ].
% 0.49/0.72 exact (zenon_H83 zenon_H31).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H28 | zenon_intro zenon_H84 ].
% 0.49/0.72 exact (zenon_H26 zenon_H28).
% 0.49/0.72 exact (zenon_H7f zenon_H84).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H53 | zenon_intro zenon_H71 ].
% 0.49/0.72 apply (zenon_L8_ zenon_TN_bs); trivial.
% 0.49/0.72 apply (zenon_L15_ zenon_TN_bs zenon_TM_bi); trivial.
% 0.49/0.72 exact (zenon_H46 zenon_H3e).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H20 | zenon_intro zenon_H72 ].
% 0.49/0.72 apply (zenon_L1_ zenon_TM_bi); trivial.
% 0.49/0.72 apply (zenon_L16_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial.
% 0.49/0.72 (* end of lemma zenon_L17_ *)
% 0.49/0.72 assert (zenon_L18_ : forall (zenon_TL_bn : zenon_U), ((unequally_directed_lines (reverse_line zenon_TL_bn) zenon_TL_bn)/\(unequally_directed_lines (reverse_line zenon_TL_bn) (reverse_line zenon_TL_bn))) -> (~(unequally_directed_lines (reverse_line zenon_TL_bn) (reverse_line zenon_TL_bn))) -> False).
% 0.49/0.72 do 1 intro. intros zenon_H85 zenon_H86.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 0.49/0.72 exact (zenon_H86 zenon_H87).
% 0.49/0.72 (* end of lemma zenon_L18_ *)
% 0.49/0.72 assert (zenon_L19_ : forall (zenon_TN_bs : zenon_U) (zenon_TL_bn : zenon_U) (zenon_TM_bi : zenon_U), (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi M)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi zenon_TN_bs)) -> (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H4f zenon_H30 zenon_H47 zenon_H3f.
% 0.49/0.72 generalize (zenon_H4f zenon_TL_bn). zenon_intro zenon_H50.
% 0.49/0.72 generalize (zenon_H50 zenon_TN_bs). zenon_intro zenon_H51.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H4e | zenon_intro zenon_H52 ].
% 0.49/0.72 exact (zenon_H4e zenon_H3f).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H3d | zenon_intro zenon_H32 ].
% 0.49/0.72 exact (zenon_H47 zenon_H3d).
% 0.49/0.72 exact (zenon_H30 zenon_H32).
% 0.49/0.72 (* end of lemma zenon_L19_ *)
% 0.49/0.72 assert (zenon_L20_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), ((unequally_directed_lines zenon_TM_bi zenon_TN_bs)->((unequally_directed_lines zenon_TM_bi zenon_TM_bi)\/(unequally_directed_lines zenon_TN_bs zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi M)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> False).
% 0.49/0.72 do 3 intro. intros zenon_H6f zenon_H3f zenon_H4f zenon_H30 zenon_H2b zenon_H21 zenon_H26 zenon_H3e.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H47 | zenon_intro zenon_H70 ].
% 0.49/0.72 apply (zenon_L19_ zenon_TN_bs zenon_TL_bn zenon_TM_bi); trivial.
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H24 | zenon_intro zenon_H67 ].
% 0.49/0.72 exact (zenon_H21 zenon_H24).
% 0.49/0.72 apply (zenon_L13_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial.
% 0.49/0.72 (* end of lemma zenon_L20_ *)
% 0.49/0.72 apply NNPP. intro zenon_G.
% 0.49/0.72 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, (((~(unequally_directed_lines L (reverse_line M)))/\(~(unequally_directed_lines L N)))->(~(unequally_directed_lines M (reverse_line N))))))) zenon_G); [ zenon_intro zenon_H89; idtac ].
% 0.49/0.72 elim zenon_H89. zenon_intro zenon_TL_bn. zenon_intro zenon_H8a.
% 0.49/0.72 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, (((~(unequally_directed_lines zenon_TL_bn (reverse_line M)))/\(~(unequally_directed_lines zenon_TL_bn N)))->(~(unequally_directed_lines M (reverse_line N)))))) zenon_H8a); [ zenon_intro zenon_H8b; idtac ].
% 0.49/0.72 elim zenon_H8b. zenon_intro zenon_TM_bi. zenon_intro zenon_H8c.
% 0.49/0.72 apply (zenon_notallex_s (fun N : zenon_U => (((~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi)))/\(~(unequally_directed_lines zenon_TL_bn N)))->(~(unequally_directed_lines zenon_TM_bi (reverse_line N))))) zenon_H8c); [ zenon_intro zenon_H8d; idtac ].
% 0.49/0.72 elim zenon_H8d. zenon_intro zenon_TN_bs. zenon_intro zenon_H8e.
% 0.49/0.72 apply (zenon_notimply_s _ _ zenon_H8e). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 0.49/0.72 apply zenon_H8f. zenon_intro zenon_H3e.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H26. zenon_intro zenon_H30.
% 0.49/0.72 generalize (oag5 zenon_TN_bs). zenon_intro zenon_H2b.
% 0.49/0.72 generalize (oag5 zenon_TM_bi). zenon_intro zenon_H21.
% 0.49/0.72 generalize (oag5 zenon_TL_bn). zenon_intro zenon_H91.
% 0.49/0.72 generalize (oag5 (reverse_line zenon_TN_bs)). zenon_intro zenon_H54.
% 0.49/0.72 generalize (oag6 zenon_TM_bi). zenon_intro zenon_H4f.
% 0.49/0.72 generalize (oag5 (reverse_line zenon_TL_bn)). zenon_intro zenon_H86.
% 0.49/0.72 generalize (zenon_H4f (reverse_line zenon_TN_bs)). zenon_intro zenon_H60.
% 0.49/0.72 generalize (zenon_H60 zenon_TL_bn). zenon_intro zenon_H92.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H92); [ zenon_intro zenon_H46 | zenon_intro zenon_H93 ].
% 0.49/0.72 exact (zenon_H46 zenon_H3e).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H3f | zenon_intro zenon_H57 ].
% 0.49/0.72 apply (zenon_L7_ zenon_TN_bs zenon_TL_bn zenon_TM_bi); trivial.
% 0.49/0.72 generalize (zenon_H4f (reverse_line zenon_TL_bn)). zenon_intro zenon_H94.
% 0.49/0.72 generalize (zenon_H94 zenon_TM_bi). zenon_intro zenon_H95.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H4d | zenon_intro zenon_H96 ].
% 0.49/0.72 apply (zenon_L10_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial.
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H24 | zenon_intro zenon_H97 ].
% 0.49/0.72 exact (zenon_H21 zenon_H24).
% 0.49/0.72 generalize (zenon_H94 zenon_TL_bn). zenon_intro zenon_H98.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H4d | zenon_intro zenon_H99 ].
% 0.49/0.72 apply (zenon_L10_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial.
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H3f | zenon_intro zenon_H88 ].
% 0.49/0.72 apply (zenon_L7_ zenon_TN_bs zenon_TL_bn zenon_TM_bi); trivial.
% 0.49/0.72 generalize (zenon_H94 zenon_TN_bs). zenon_intro zenon_H9a.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H4d | zenon_intro zenon_H9b ].
% 0.49/0.72 apply (zenon_L10_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial.
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H3d | zenon_intro zenon_H9c ].
% 0.49/0.72 generalize (zenon_H4f zenon_TN_bs). zenon_intro zenon_H6e.
% 0.49/0.72 apply (zenon_L14_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial.
% 0.49/0.72 generalize (zenon_H4f zenon_TN_bs). zenon_intro zenon_H6e.
% 0.49/0.72 generalize (zenon_H4f zenon_TL_bn). zenon_intro zenon_H50.
% 0.49/0.72 generalize (zenon_H6e zenon_TM_bi). zenon_intro zenon_H6f.
% 0.49/0.72 generalize (zenon_H50 zenon_TL_bn). zenon_intro zenon_H9d.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_H9d); [ zenon_intro zenon_H4e | zenon_intro zenon_H9e ].
% 0.49/0.72 generalize (oag7 (reverse_line zenon_TL_bn)). zenon_intro zenon_H9f.
% 0.49/0.72 generalize (zenon_H9f zenon_TM_bi). zenon_intro zenon_Ha0.
% 0.49/0.72 generalize (zenon_H9f zenon_TN_bs). zenon_intro zenon_Ha1.
% 0.49/0.72 generalize (zenon_Ha0 zenon_TL_bn). zenon_intro zenon_Ha2.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ].
% 0.49/0.72 apply (zenon_notand_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha5 ].
% 0.49/0.72 exact (zenon_Ha6 zenon_H97).
% 0.49/0.72 generalize (zenon_Ha1 zenon_TM_bi). zenon_intro zenon_Ha7.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8 ].
% 0.49/0.72 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ].
% 0.49/0.72 exact (zenon_Hab zenon_H9c).
% 0.49/0.72 generalize (oag6 (reverse_line zenon_TL_bn)). zenon_intro zenon_Hac.
% 0.49/0.72 generalize (zenon_Hac zenon_TL_bn). zenon_intro zenon_Had.
% 0.49/0.72 generalize (zenon_Had (reverse_line zenon_TN_bs)). zenon_intro zenon_Hae.
% 0.49/0.72 apply (zenon_imply_s _ _ zenon_Hae); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Haf ].
% 0.49/0.72 exact (zenon_Hb0 zenon_H88).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H31 ].
% 0.49/0.72 exact (zenon_Haa zenon_Hb1).
% 0.49/0.72 apply (zenon_L17_ zenon_TM_bi zenon_TN_bs zenon_TL_bn); trivial.
% 0.49/0.72 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H72 ].
% 0.49/0.72 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H97. zenon_intro zenon_Hb3.
% 0.49/0.72 exact (zenon_Ha5 zenon_Hb3).
% 0.49/0.72 apply (zenon_L16_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial.
% 0.49/0.72 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H85 | zenon_intro zenon_H48 ].
% 0.49/0.72 apply (zenon_L18_ zenon_TL_bn); trivial.
% 0.49/0.72 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H3f. zenon_intro zenon_H49.
% 0.49/0.72 exact (zenon_H4e zenon_H3f).
% 0.49/0.72 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H3f | zenon_intro zenon_Hb4 ].
% 0.49/0.72 apply (zenon_L20_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial.
% 0.49/0.72 exact (zenon_H91 zenon_Hb4).
% 0.49/0.72 Qed.
% 0.49/0.72 % SZS output end Proof
% 0.49/0.72 (* END-PROOF *)
% 0.49/0.72 nodes searched: 12921
% 0.49/0.72 max branch formulas: 1474
% 0.49/0.72 proof nodes created: 655
% 0.49/0.72 formulas created: 27116
% 0.49/0.72
%------------------------------------------------------------------------------