TSTP Solution File: GEO177+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n026.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 07:00:25 EDT 2022
% Result : Theorem 0.53s 0.76s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 17:55:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.53/0.76 (* PROOF-FOUND *)
% 0.53/0.76 % SZS status Theorem
% 0.53/0.76 (* BEGIN-PROOF *)
% 0.53/0.76 % SZS output start Proof
% 0.53/0.76 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\(distinct_points U V))->(((apart_point_and_line X (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting X Y))\/(apart_point_and_line V (line_connecting X Y))))))))).
% 0.53/0.76 Proof.
% 0.53/0.76 assert (zenon_L1_ : forall (zenon_TV_r : zenon_U) (zenon_TU_s : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TU_s zenon_TV_r)->((distinct_points zenon_TU_s Z)\/(distinct_points zenon_TV_r Z)))) -> (distinct_points zenon_TU_s zenon_TV_r) -> (~(distinct_points zenon_TU_s zenon_TU_s)) -> (~(distinct_points zenon_TV_r zenon_TU_s)) -> False).
% 0.53/0.76 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10.
% 0.53/0.76 generalize (zenon_Hd zenon_TU_s). zenon_intro zenon_H13.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ].
% 0.53/0.76 exact (zenon_H15 zenon_He).
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 0.53/0.76 exact (zenon_Hf zenon_H17).
% 0.53/0.76 exact (zenon_H10 zenon_H16).
% 0.53/0.76 (* end of lemma zenon_L1_ *)
% 0.53/0.76 assert (zenon_L2_ : forall (zenon_TU_s : zenon_U) (zenon_TV_r : zenon_U), (~(distinct_points zenon_TV_r zenon_TU_s)) -> (distinct_points zenon_TU_s zenon_TV_r) -> (forall Z : zenon_U, ((distinct_points zenon_TU_s zenon_TV_r)->((distinct_points zenon_TU_s Z)\/(distinct_points zenon_TV_r Z)))) -> False).
% 0.53/0.76 do 2 intro. intros zenon_H10 zenon_He zenon_Hd.
% 0.53/0.76 generalize (apart1 zenon_TU_s). zenon_intro zenon_Hf.
% 0.53/0.76 apply (zenon_L1_ zenon_TV_r zenon_TU_s); trivial.
% 0.53/0.76 (* end of lemma zenon_L2_ *)
% 0.53/0.76 assert (zenon_L3_ : forall (zenon_TY_be : zenon_U) (zenon_TX_bf : zenon_U) (zenon_TU_s : zenon_U) (zenon_TV_r : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TV_r zenon_TU_s)/\(distinct_lines U V))->((apart_point_and_line zenon_TV_r U)\/((apart_point_and_line zenon_TV_r V)\/((apart_point_and_line zenon_TU_s U)\/(apart_point_and_line zenon_TU_s V))))))) -> (~(apart_point_and_line zenon_TU_s (line_connecting zenon_TX_bf zenon_TY_be))) -> (~(apart_point_and_line zenon_TU_s (line_connecting zenon_TU_s zenon_TV_r))) -> (~(apart_point_and_line zenon_TV_r (line_connecting zenon_TX_bf zenon_TY_be))) -> (~(apart_point_and_line zenon_TV_r (line_connecting zenon_TU_s zenon_TV_r))) -> (distinct_lines (line_connecting zenon_TU_s zenon_TV_r) (line_connecting zenon_TX_bf zenon_TY_be)) -> (distinct_points zenon_TV_r zenon_TU_s) -> False).
% 0.53/0.76 do 4 intro. intros zenon_H18 zenon_H19 zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_H16.
% 0.53/0.76 generalize (zenon_H18 (line_connecting zenon_TU_s zenon_TV_r)). zenon_intro zenon_H20.
% 0.53/0.76 generalize (zenon_H20 (line_connecting zenon_TX_bf zenon_TY_be)). zenon_intro zenon_H21.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 0.53/0.76 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H10 | zenon_intro zenon_H24 ].
% 0.53/0.76 exact (zenon_H10 zenon_H16).
% 0.53/0.76 exact (zenon_H24 zenon_H1d).
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ].
% 0.53/0.76 exact (zenon_H1c zenon_H26).
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 0.53/0.76 exact (zenon_H1b zenon_H28).
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.53/0.76 exact (zenon_H1a zenon_H2a).
% 0.53/0.76 exact (zenon_H19 zenon_H29).
% 0.53/0.76 (* end of lemma zenon_L3_ *)
% 0.53/0.76 assert (zenon_L4_ : forall (zenon_TU_s : zenon_U) (zenon_TV_r : zenon_U) (zenon_TY_be : zenon_U) (zenon_TX_bf : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line zenon_TX_bf Y)->((distinct_lines Y Z)\/(apart_point_and_line zenon_TX_bf Z))))) -> (~(apart_point_and_line zenon_TX_bf (line_connecting zenon_TX_bf zenon_TY_be))) -> (distinct_points zenon_TV_r zenon_TU_s) -> (~(apart_point_and_line zenon_TV_r (line_connecting zenon_TU_s zenon_TV_r))) -> (~(apart_point_and_line zenon_TV_r (line_connecting zenon_TX_bf zenon_TY_be))) -> (~(apart_point_and_line zenon_TU_s (line_connecting zenon_TU_s zenon_TV_r))) -> (~(apart_point_and_line zenon_TU_s (line_connecting zenon_TX_bf zenon_TY_be))) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TV_r zenon_TU_s)/\(distinct_lines U V))->((apart_point_and_line zenon_TV_r U)\/((apart_point_and_line zenon_TV_r V)\/((apart_point_and_line zenon_TU_s U)\/(apart_point_and_line zenon_TU_s V))))))) -> (apart_point_and_line zenon_TX_bf (line_connecting zenon_TU_s zenon_TV_r)) -> False).
% 0.53/0.76 do 4 intro. intros zenon_H2b zenon_H2c zenon_H16 zenon_H1c zenon_H1b zenon_H1a zenon_H19 zenon_H18 zenon_H2d.
% 0.53/0.76 generalize (zenon_H2b (line_connecting zenon_TU_s zenon_TV_r)). zenon_intro zenon_H2e.
% 0.53/0.76 generalize (zenon_H2e (line_connecting zenon_TX_bf zenon_TY_be)). zenon_intro zenon_H2f.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ].
% 0.53/0.76 exact (zenon_H31 zenon_H2d).
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H1d | zenon_intro zenon_H32 ].
% 0.53/0.76 apply (zenon_L3_ zenon_TY_be zenon_TX_bf zenon_TU_s zenon_TV_r); trivial.
% 0.53/0.76 exact (zenon_H2c zenon_H32).
% 0.53/0.76 (* end of lemma zenon_L4_ *)
% 0.53/0.76 assert (zenon_L5_ : forall (zenon_TY_be : zenon_U) (zenon_TX_bf : zenon_U), ((distinct_points zenon_TX_bf zenon_TX_bf)/\(distinct_points zenon_TX_bf zenon_TY_be)) -> (~(distinct_points zenon_TX_bf zenon_TX_bf)) -> False).
% 0.53/0.76 do 2 intro. intros zenon_H33 zenon_H34.
% 0.53/0.76 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H36. zenon_intro zenon_H35.
% 0.53/0.76 exact (zenon_H34 zenon_H36).
% 0.53/0.76 (* end of lemma zenon_L5_ *)
% 0.53/0.76 assert (zenon_L6_ : forall (zenon_TV_r : zenon_U) (zenon_TU_s : zenon_U), ((distinct_points zenon_TU_s zenon_TU_s)/\(distinct_points zenon_TU_s zenon_TV_r)) -> (~(distinct_points zenon_TU_s zenon_TU_s)) -> False).
% 0.53/0.76 do 2 intro. intros zenon_H37 zenon_Hf.
% 0.53/0.76 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H17. zenon_intro zenon_He.
% 0.53/0.76 exact (zenon_Hf zenon_H17).
% 0.53/0.76 (* end of lemma zenon_L6_ *)
% 0.53/0.76 assert (zenon_L7_ : forall (zenon_TU_s : zenon_U) (zenon_TV_r : zenon_U), ((distinct_points zenon_TV_r zenon_TU_s)/\(distinct_points zenon_TV_r zenon_TV_r)) -> (~(distinct_points zenon_TV_r zenon_TV_r)) -> False).
% 0.53/0.76 do 2 intro. intros zenon_H38 zenon_H39.
% 0.53/0.76 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H16. zenon_intro zenon_H3a.
% 0.53/0.76 exact (zenon_H39 zenon_H3a).
% 0.53/0.76 (* end of lemma zenon_L7_ *)
% 0.53/0.76 assert (zenon_L8_ : forall (zenon_TX_bf : zenon_U) (zenon_TY_be : zenon_U), ((distinct_points zenon_TY_be zenon_TX_bf)/\(distinct_points zenon_TY_be zenon_TY_be)) -> (~(distinct_points zenon_TY_be zenon_TY_be)) -> False).
% 0.53/0.76 do 2 intro. intros zenon_H3b zenon_H3c.
% 0.53/0.76 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 0.53/0.76 exact (zenon_H3c zenon_H3d).
% 0.53/0.76 (* end of lemma zenon_L8_ *)
% 0.53/0.76 apply NNPP. intro zenon_G.
% 0.53/0.76 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\(distinct_points U V))->(((apart_point_and_line X (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting X Y))\/(apart_point_and_line V (line_connecting X Y))))))))) zenon_G); [ zenon_intro zenon_H3f; idtac ].
% 0.53/0.76 elim zenon_H3f. zenon_intro zenon_TX_bf. zenon_intro zenon_H40.
% 0.53/0.76 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bf Y)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_bf (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_bf Y))\/(apart_point_and_line V (line_connecting zenon_TX_bf Y)))))))) zenon_H40); [ zenon_intro zenon_H41; idtac ].
% 0.53/0.76 elim zenon_H41. zenon_intro zenon_TY_be. zenon_intro zenon_H42.
% 0.53/0.76 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bf zenon_TY_be)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_bf (line_connecting U V))\/(apart_point_and_line zenon_TY_be (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_bf zenon_TY_be))\/(apart_point_and_line V (line_connecting zenon_TX_bf zenon_TY_be))))))) zenon_H42); [ zenon_intro zenon_H43; idtac ].
% 0.53/0.76 elim zenon_H43. zenon_intro zenon_TU_s. zenon_intro zenon_H44.
% 0.53/0.76 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bf zenon_TY_be)/\(distinct_points zenon_TU_s V))->(((apart_point_and_line zenon_TX_bf (line_connecting zenon_TU_s V))\/(apart_point_and_line zenon_TY_be (line_connecting zenon_TU_s V)))->((apart_point_and_line zenon_TU_s (line_connecting zenon_TX_bf zenon_TY_be))\/(apart_point_and_line V (line_connecting zenon_TX_bf zenon_TY_be)))))) zenon_H44); [ zenon_intro zenon_H45; idtac ].
% 0.53/0.76 elim zenon_H45. zenon_intro zenon_TV_r. zenon_intro zenon_H46.
% 0.53/0.76 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47.
% 0.53/0.76 apply (zenon_notimply_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 0.53/0.76 apply (zenon_notor_s _ _ zenon_H49). zenon_intro zenon_H19. zenon_intro zenon_H1b.
% 0.53/0.76 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H35. zenon_intro zenon_He.
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H2d | zenon_intro zenon_H4b ].
% 0.53/0.76 generalize (apart1 zenon_TV_r). zenon_intro zenon_H39.
% 0.53/0.76 generalize (apart4 zenon_TU_s). zenon_intro zenon_H4c.
% 0.53/0.76 generalize (zenon_H4c zenon_TV_r). zenon_intro zenon_Hd.
% 0.53/0.76 generalize (con1 zenon_TU_s). zenon_intro zenon_H4d.
% 0.53/0.76 generalize (con1 zenon_TX_bf). zenon_intro zenon_H4e.
% 0.53/0.76 generalize (zenon_H4d zenon_TV_r). zenon_intro zenon_H4f.
% 0.53/0.76 generalize (apart4 zenon_TV_r). zenon_intro zenon_H50.
% 0.53/0.76 generalize (cu1 zenon_TV_r). zenon_intro zenon_H51.
% 0.53/0.76 generalize (zenon_H4f zenon_TV_r). zenon_intro zenon_H52.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H15 | zenon_intro zenon_H53 ].
% 0.53/0.76 exact (zenon_H15 zenon_He).
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H1c | zenon_intro zenon_H38 ].
% 0.53/0.76 generalize (zenon_H4e zenon_TY_be). zenon_intro zenon_H54.
% 0.53/0.76 generalize (apart1 zenon_TU_s). zenon_intro zenon_Hf.
% 0.53/0.76 generalize (apart1 zenon_TX_bf). zenon_intro zenon_H34.
% 0.53/0.76 generalize (ceq2 zenon_TX_bf). zenon_intro zenon_H2b.
% 0.53/0.76 generalize (zenon_H50 zenon_TU_s). zenon_intro zenon_H55.
% 0.53/0.76 generalize (zenon_H51 zenon_TU_s). zenon_intro zenon_H18.
% 0.53/0.76 generalize (zenon_H4f zenon_TU_s). zenon_intro zenon_H56.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H15 | zenon_intro zenon_H57 ].
% 0.53/0.76 exact (zenon_H15 zenon_He).
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H1a | zenon_intro zenon_H37 ].
% 0.53/0.76 generalize (zenon_H55 zenon_TU_s). zenon_intro zenon_H58.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H10 | zenon_intro zenon_H59 ].
% 0.53/0.76 apply (zenon_L2_ zenon_TU_s zenon_TV_r); trivial.
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H16 | zenon_intro zenon_H17 ].
% 0.53/0.76 generalize (zenon_H54 zenon_TX_bf). zenon_intro zenon_H5a.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ].
% 0.53/0.76 exact (zenon_H5c zenon_H35).
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H2c | zenon_intro zenon_H33 ].
% 0.53/0.76 apply (zenon_L4_ zenon_TU_s zenon_TV_r zenon_TY_be zenon_TX_bf); trivial.
% 0.53/0.76 apply (zenon_L5_ zenon_TY_be zenon_TX_bf); trivial.
% 0.53/0.76 exact (zenon_Hf zenon_H17).
% 0.53/0.76 apply (zenon_L6_ zenon_TV_r zenon_TU_s); trivial.
% 0.53/0.76 apply (zenon_L7_ zenon_TU_s zenon_TV_r); trivial.
% 0.53/0.76 generalize (apart1 zenon_TV_r). zenon_intro zenon_H39.
% 0.53/0.76 generalize (apart1 zenon_TY_be). zenon_intro zenon_H3c.
% 0.53/0.76 generalize (apart4 zenon_TU_s). zenon_intro zenon_H4c.
% 0.53/0.76 generalize (zenon_H4c zenon_TV_r). zenon_intro zenon_Hd.
% 0.53/0.76 generalize (con1 zenon_TU_s). zenon_intro zenon_H4d.
% 0.53/0.76 generalize (con1 zenon_TX_bf). zenon_intro zenon_H4e.
% 0.53/0.76 generalize (zenon_H4d zenon_TV_r). zenon_intro zenon_H4f.
% 0.53/0.76 generalize (apart4 zenon_TV_r). zenon_intro zenon_H50.
% 0.53/0.76 generalize (cu1 zenon_TV_r). zenon_intro zenon_H51.
% 0.53/0.76 generalize (zenon_H4f zenon_TV_r). zenon_intro zenon_H52.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H15 | zenon_intro zenon_H53 ].
% 0.53/0.76 exact (zenon_H15 zenon_He).
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H1c | zenon_intro zenon_H38 ].
% 0.53/0.76 generalize (zenon_H4e zenon_TY_be). zenon_intro zenon_H54.
% 0.53/0.76 generalize (apart1 zenon_TU_s). zenon_intro zenon_Hf.
% 0.53/0.76 generalize (ceq2 zenon_TY_be). zenon_intro zenon_H5d.
% 0.53/0.76 generalize (zenon_H50 zenon_TU_s). zenon_intro zenon_H55.
% 0.53/0.76 generalize (zenon_H51 zenon_TU_s). zenon_intro zenon_H18.
% 0.53/0.76 generalize (zenon_H54 zenon_TY_be). zenon_intro zenon_H5e.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5c | zenon_intro zenon_H5f ].
% 0.53/0.76 exact (zenon_H5c zenon_H35).
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H60 | zenon_intro zenon_H3b ].
% 0.53/0.76 generalize (zenon_H4f zenon_TU_s). zenon_intro zenon_H56.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H15 | zenon_intro zenon_H57 ].
% 0.53/0.76 exact (zenon_H15 zenon_He).
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H1a | zenon_intro zenon_H37 ].
% 0.53/0.76 generalize (zenon_H55 zenon_TU_s). zenon_intro zenon_H58.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H10 | zenon_intro zenon_H59 ].
% 0.53/0.76 apply (zenon_L2_ zenon_TU_s zenon_TV_r); trivial.
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H16 | zenon_intro zenon_H17 ].
% 0.53/0.76 generalize (zenon_H5d (line_connecting zenon_TU_s zenon_TV_r)). zenon_intro zenon_H61.
% 0.53/0.76 generalize (zenon_H61 (line_connecting zenon_TX_bf zenon_TY_be)). zenon_intro zenon_H62.
% 0.53/0.76 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 0.53/0.76 exact (zenon_H64 zenon_H4b).
% 0.53/0.76 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H1d | zenon_intro zenon_H65 ].
% 0.53/0.76 apply (zenon_L3_ zenon_TY_be zenon_TX_bf zenon_TU_s zenon_TV_r); trivial.
% 0.53/0.76 exact (zenon_H60 zenon_H65).
% 0.53/0.76 exact (zenon_Hf zenon_H17).
% 0.53/0.76 apply (zenon_L6_ zenon_TV_r zenon_TU_s); trivial.
% 0.53/0.76 apply (zenon_L8_ zenon_TX_bf zenon_TY_be); trivial.
% 0.53/0.76 apply (zenon_L7_ zenon_TU_s zenon_TV_r); trivial.
% 0.53/0.76 Qed.
% 0.53/0.76 % SZS output end Proof
% 0.53/0.76 (* END-PROOF *)
% 0.53/0.76 nodes searched: 19769
% 0.53/0.76 max branch formulas: 2779
% 0.53/0.76 proof nodes created: 1586
% 0.53/0.76 formulas created: 39938
% 0.53/0.76
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