TSTP Solution File: GEO196+2 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO196+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n006.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 07:00:40 EDT 2022
% Result : Theorem 2.88s 3.08s
% Output : Proof 2.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO196+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jun 18 04:10:10 EDT 2022
% 0.12/0.32 % CPUTime :
% 2.88/3.08 (* PROOF-FOUND *)
% 2.88/3.08 % SZS status Theorem
% 2.88/3.08 (* BEGIN-PROOF *)
% 2.88/3.08 % SZS output start Proof
% 2.88/3.08 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines X Y)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point X Y) U))/\(~(apart_point_and_line (intersection_point X Y) V)))))->((~(apart_point_and_line (intersection_point U V) X))/\(~(apart_point_and_line (intersection_point U V) Y)))))))).
% 2.88/3.08 Proof.
% 2.88/3.08 assert (zenon_L1_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TU_x zenon_TV_w) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) U)\/((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (distinct_points (intersection_point zenon_TU_x zenon_TV_w) (intersection_point zenon_TX_v zenon_TY_u)) -> (distinct_lines zenon_TU_x zenon_TV_w) -> (~(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TU_x)) -> (~(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TV_w)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> False).
% 2.88/3.08 do 4 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13.
% 2.88/3.08 generalize (zenon_Hd (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H18.
% 2.88/3.08 generalize (zenon_H18 zenon_TU_x). zenon_intro zenon_H19.
% 2.88/3.08 generalize (zenon_H19 zenon_TV_w). zenon_intro zenon_H1a.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 2.88/3.08 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 2.88/3.08 exact (zenon_H1e zenon_He).
% 2.88/3.08 exact (zenon_H1d zenon_Hf).
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ].
% 2.88/3.08 exact (zenon_H10 zenon_H20).
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ].
% 2.88/3.08 exact (zenon_H11 zenon_H22).
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ].
% 2.88/3.08 exact (zenon_H12 zenon_H24).
% 2.88/3.08 exact (zenon_H13 zenon_H23).
% 2.88/3.08 (* end of lemma zenon_L1_ *)
% 2.88/3.08 assert (zenon_L2_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (convergent_lines zenon_TU_x zenon_TV_w) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> (~(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TV_w)) -> (distinct_lines zenon_TU_x zenon_TV_w) -> (distinct_points (intersection_point zenon_TU_x zenon_TV_w) (intersection_point zenon_TX_v zenon_TY_u)) -> False).
% 2.88/3.08 do 4 intro. intros zenon_H25 zenon_H13 zenon_H12 zenon_H11 zenon_Hf zenon_He.
% 2.88/3.08 generalize (con2 zenon_TU_x). zenon_intro zenon_H26.
% 2.88/3.08 generalize (zenon_H26 zenon_TV_w). zenon_intro zenon_H27.
% 2.88/3.08 generalize (cu1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_Hd.
% 2.88/3.08 generalize (apart1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H28.
% 2.88/3.08 generalize (zenon_H27 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H29.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 2.88/3.08 exact (zenon_H2b zenon_H25).
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 2.88/3.08 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H10. zenon_intro zenon_H11.
% 2.88/3.08 apply (zenon_L1_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 exact (zenon_H28 zenon_H2c).
% 2.88/3.08 (* end of lemma zenon_L2_ *)
% 2.88/3.08 assert (zenon_L3_ : forall (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TV_w) -> (convergent_lines zenon_TU_x zenon_TV_w) -> False).
% 2.88/3.08 do 2 intro. intros zenon_H22 zenon_H25.
% 2.88/3.08 generalize (apart1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H28.
% 2.88/3.08 generalize (con2 zenon_TU_x). zenon_intro zenon_H26.
% 2.88/3.08 generalize (zenon_H26 zenon_TV_w). zenon_intro zenon_H27.
% 2.88/3.08 generalize (zenon_H27 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H29.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 2.88/3.08 exact (zenon_H2b zenon_H25).
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 2.88/3.08 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H10. zenon_intro zenon_H11.
% 2.88/3.08 exact (zenon_H11 zenon_H22).
% 2.88/3.08 exact (zenon_H28 zenon_H2c).
% 2.88/3.08 (* end of lemma zenon_L3_ *)
% 2.88/3.08 assert (zenon_L4_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U), (apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TY_u) -> (convergent_lines zenon_TX_v zenon_TY_u) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_v zenon_TY_u)->(((apart_point_and_line Z zenon_TX_v)\/(apart_point_and_line Z zenon_TY_u))->(distinct_points Z (intersection_point zenon_TX_v zenon_TY_u))))) -> False).
% 2.88/3.08 do 2 intro. intros zenon_H2e zenon_H2f zenon_H30.
% 2.88/3.08 generalize (apart1 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H31.
% 2.88/3.08 generalize (zenon_H30 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H32.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 2.88/3.08 exact (zenon_H34 zenon_H2f).
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 2.88/3.08 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37.
% 2.88/3.08 exact (zenon_H37 zenon_H2e).
% 2.88/3.08 exact (zenon_H31 zenon_H35).
% 2.88/3.08 (* end of lemma zenon_L4_ *)
% 2.88/3.08 assert (zenon_L5_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U), (apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TY_u) -> (convergent_lines zenon_TX_v zenon_TY_u) -> False).
% 2.88/3.08 do 2 intro. intros zenon_H2e zenon_H2f.
% 2.88/3.08 generalize (con2 zenon_TX_v). zenon_intro zenon_H39.
% 2.88/3.08 generalize (zenon_H39 zenon_TY_u). zenon_intro zenon_H30.
% 2.88/3.08 apply (zenon_L4_ zenon_TY_u zenon_TX_v); trivial.
% 2.88/3.08 (* end of lemma zenon_L5_ *)
% 2.88/3.08 assert (zenon_L6_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TU_x)->((distinct_points (intersection_point zenon_TU_x zenon_TV_w) (intersection_point zenon_TX_v zenon_TY_u))\/(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x))) -> (convergent_lines zenon_TX_v zenon_TY_u) -> (~(distinct_lines zenon_TY_u zenon_TY_u)) -> (apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TY_u) -> (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TY_u)->((distinct_points (intersection_point zenon_TU_x zenon_TV_w) Z)\/(apart_point_and_line Z zenon_TY_u)))) -> (distinct_lines zenon_TU_x zenon_TV_w) -> (~(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TV_w)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> (convergent_lines zenon_TU_x zenon_TV_w) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> False).
% 2.88/3.08 do 4 intro. intros zenon_H3a zenon_H2f zenon_H3b zenon_H3c zenon_H3d zenon_Hf zenon_H11 zenon_H13 zenon_H25 zenon_H12.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H10 | zenon_intro zenon_H3e ].
% 2.88/3.08 generalize (ceq2 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H3f.
% 2.88/3.08 generalize (zenon_H3f zenon_TY_u). zenon_intro zenon_H40.
% 2.88/3.08 generalize (zenon_H40 zenon_TY_u). zenon_intro zenon_H41.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H37 | zenon_intro zenon_H42 ].
% 2.88/3.08 generalize (zenon_H3d (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H43.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 2.88/3.08 exact (zenon_H45 zenon_H3c).
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_He | zenon_intro zenon_H2e ].
% 2.88/3.08 generalize (cu1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_Hd.
% 2.88/3.08 apply (zenon_L1_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 exact (zenon_H37 zenon_H2e).
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H46 | zenon_intro zenon_H2e ].
% 2.88/3.08 exact (zenon_H3b zenon_H46).
% 2.88/3.08 apply (zenon_L5_ zenon_TY_u zenon_TX_v); trivial.
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_He | zenon_intro zenon_H24 ].
% 2.88/3.08 apply (zenon_L2_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 exact (zenon_H12 zenon_H24).
% 2.88/3.08 (* end of lemma zenon_L6_ *)
% 2.88/3.08 assert (zenon_L7_ : forall (zenon_TX_v : zenon_U) (zenon_TY_u : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Y)->((distinct_points (intersection_point zenon_TU_x zenon_TV_w) Z)\/(apart_point_and_line Z Y))))) -> (~(distinct_lines zenon_TV_w zenon_TV_w)) -> (apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TY_u) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> (~(distinct_lines zenon_TY_u zenon_TY_u)) -> (convergent_lines zenon_TX_v zenon_TY_u) -> (convergent_lines zenon_TU_x zenon_TV_w) -> (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Z))))) -> False).
% 2.88/3.08 do 4 intro. intros zenon_H47 zenon_H48 zenon_H3c zenon_H13 zenon_H12 zenon_H3b zenon_H2f zenon_H25 zenon_H49.
% 2.88/3.08 generalize (zenon_H47 zenon_TY_u). zenon_intro zenon_H3d.
% 2.88/3.08 generalize (zenon_H49 zenon_TV_w). zenon_intro zenon_H4a.
% 2.88/3.08 generalize (zenon_H47 zenon_TU_x). zenon_intro zenon_H4b.
% 2.88/3.08 generalize (zenon_H4a zenon_TV_w). zenon_intro zenon_H4c.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H11 | zenon_intro zenon_H4d ].
% 2.88/3.08 generalize (zenon_H4b (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H3a.
% 2.88/3.08 generalize (ceq3 zenon_TU_x). zenon_intro zenon_H4e.
% 2.88/3.08 generalize (zenon_H4e zenon_TV_w). zenon_intro zenon_H4f.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H2b | zenon_intro zenon_Hf ].
% 2.88/3.08 exact (zenon_H2b zenon_H25).
% 2.88/3.08 apply (zenon_L6_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H50 | zenon_intro zenon_H22 ].
% 2.88/3.08 exact (zenon_H48 zenon_H50).
% 2.88/3.08 apply (zenon_L3_ zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 (* end of lemma zenon_L7_ *)
% 2.88/3.08 assert (zenon_L8_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Z))))) -> (convergent_lines zenon_TU_x zenon_TV_w) -> (convergent_lines zenon_TX_v zenon_TY_u) -> (~(distinct_lines zenon_TY_u zenon_TY_u)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> (apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TY_u) -> (~(distinct_lines zenon_TV_w zenon_TV_w)) -> False).
% 2.88/3.08 do 4 intro. intros zenon_H49 zenon_H25 zenon_H2f zenon_H3b zenon_H12 zenon_H13 zenon_H3c zenon_H48.
% 2.88/3.08 generalize (ceq1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H47.
% 2.88/3.08 apply (zenon_L7_ zenon_TX_v zenon_TY_u zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 (* end of lemma zenon_L8_ *)
% 2.88/3.08 apply NNPP. intro zenon_G.
% 2.88/3.08 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines X Y)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point X Y) U))/\(~(apart_point_and_line (intersection_point X Y) V)))))->((~(apart_point_and_line (intersection_point U V) X))/\(~(apart_point_and_line (intersection_point U V) Y)))))))) zenon_G); [ zenon_intro zenon_H51; idtac ].
% 2.88/3.08 elim zenon_H51. zenon_intro zenon_TX_v. zenon_intro zenon_H52.
% 2.88/3.08 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines zenon_TX_v Y)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point zenon_TX_v Y) U))/\(~(apart_point_and_line (intersection_point zenon_TX_v Y) V)))))->((~(apart_point_and_line (intersection_point U V) zenon_TX_v))/\(~(apart_point_and_line (intersection_point U V) Y))))))) zenon_H52); [ zenon_intro zenon_H53; idtac ].
% 2.88/3.08 elim zenon_H53. zenon_intro zenon_TY_u. zenon_intro zenon_H54.
% 2.88/3.08 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((convergent_lines zenon_TX_v zenon_TY_u)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) U))/\(~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) V)))))->((~(apart_point_and_line (intersection_point U V) zenon_TX_v))/\(~(apart_point_and_line (intersection_point U V) zenon_TY_u)))))) zenon_H54); [ zenon_intro zenon_H55; idtac ].
% 2.88/3.08 elim zenon_H55. zenon_intro zenon_TU_x. zenon_intro zenon_H56.
% 2.88/3.08 apply (zenon_notallex_s (fun V : zenon_U => (((convergent_lines zenon_TX_v zenon_TY_u)/\((convergent_lines zenon_TU_x V)/\((~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x))/\(~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) V)))))->((~(apart_point_and_line (intersection_point zenon_TU_x V) zenon_TX_v))/\(~(apart_point_and_line (intersection_point zenon_TU_x V) zenon_TY_u))))) zenon_H56); [ zenon_intro zenon_H57; idtac ].
% 2.88/3.08 elim zenon_H57. zenon_intro zenon_TV_w. zenon_intro zenon_H58.
% 2.88/3.08 apply (zenon_notimply_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59.
% 2.88/3.08 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H2f. zenon_intro zenon_H5b.
% 2.88/3.08 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H25. zenon_intro zenon_H5c.
% 2.88/3.08 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H12. zenon_intro zenon_H13.
% 2.88/3.08 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5e | zenon_intro zenon_H5d ].
% 2.88/3.08 apply zenon_H5e. zenon_intro zenon_H5f.
% 2.88/3.08 generalize (apart2 zenon_TV_w). zenon_intro zenon_H48.
% 2.88/3.08 generalize (ceq2 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H49.
% 2.88/3.08 generalize (ceq1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H47.
% 2.88/3.08 generalize (zenon_H47 zenon_TX_v). zenon_intro zenon_H60.
% 2.88/3.08 generalize (apart5 zenon_TU_x). zenon_intro zenon_H61.
% 2.88/3.08 generalize (zenon_H61 zenon_TV_w). zenon_intro zenon_H62.
% 2.88/3.08 generalize (zenon_H62 zenon_TV_w). zenon_intro zenon_H63.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H1d | zenon_intro zenon_H64 ].
% 2.88/3.08 generalize (ceq3 zenon_TU_x). zenon_intro zenon_H4e.
% 2.88/3.08 generalize (zenon_H4e zenon_TV_w). zenon_intro zenon_H4f.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H2b | zenon_intro zenon_Hf ].
% 2.88/3.08 exact (zenon_H2b zenon_H25).
% 2.88/3.08 exact (zenon_H1d zenon_Hf).
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_Hf | zenon_intro zenon_H50 ].
% 2.88/3.08 generalize (zenon_H49 zenon_TV_w). zenon_intro zenon_H4a.
% 2.88/3.08 generalize (zenon_H4a zenon_TV_w). zenon_intro zenon_H4c.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H11 | zenon_intro zenon_H4d ].
% 2.88/3.08 generalize (con2 zenon_TX_v). zenon_intro zenon_H39.
% 2.88/3.08 generalize (zenon_H39 zenon_TY_u). zenon_intro zenon_H30.
% 2.88/3.08 generalize (apart1 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H31.
% 2.88/3.08 generalize (zenon_H30 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H32.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 2.88/3.08 exact (zenon_H34 zenon_H2f).
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 2.88/3.08 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37.
% 2.88/3.08 generalize (zenon_H60 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H65.
% 2.88/3.08 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H67 | zenon_intro zenon_H66 ].
% 2.88/3.08 exact (zenon_H67 zenon_H5f).
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_He | zenon_intro zenon_H68 ].
% 2.88/3.08 apply (zenon_L2_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 exact (zenon_H38 zenon_H68).
% 2.88/3.08 exact (zenon_H31 zenon_H35).
% 2.88/3.08 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H50 | zenon_intro zenon_H22 ].
% 2.88/3.08 exact (zenon_H48 zenon_H50).
% 2.88/3.08 apply (zenon_L3_ zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 exact (zenon_H48 zenon_H50).
% 2.88/3.08 apply zenon_H5d. zenon_intro zenon_H3c.
% 2.88/3.08 generalize (apart2 zenon_TY_u). zenon_intro zenon_H3b.
% 2.88/3.08 generalize (apart2 zenon_TV_w). zenon_intro zenon_H48.
% 2.88/3.08 generalize (ceq2 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H49.
% 2.88/3.08 apply (zenon_L8_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial.
% 2.88/3.08 Qed.
% 2.88/3.08 % SZS output end Proof
% 2.88/3.08 (* END-PROOF *)
% 2.88/3.08 nodes searched: 409118
% 2.88/3.08 max branch formulas: 7190
% 2.88/3.08 proof nodes created: 6210
% 2.88/3.08 formulas created: 465272
% 2.88/3.08
%------------------------------------------------------------------------------