%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n029.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 102.51s 102.72s % Output : Proof 102.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n029.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 07:23:59 EDT 2022 % 0.13/0.34 % CPUTime : % 102.51/102.72 (* PROOF-FOUND *) % 102.51/102.72 % SZS status Theorem % 102.51/102.72 (* BEGIN-PROOF *) % 102.51/102.72 % SZS output start Proof % 102.51/102.72 Theorem con : (forall A : zenon_U, (forall L : zenon_U, (~(convergent_lines L (orthogonal_through_point (orthogonal_through_point L A) A))))). % 102.51/102.72 Proof. % 102.51/102.72 assert (zenon_L1_ : forall (zenon_TL_x : zenon_U) (zenon_TA_y : zenon_U), (forall L : zenon_U, (~(unorthogonal_lines (orthogonal_through_point L zenon_TA_y) L))) -> (~(convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> False). % 102.51/102.72 do 2 intro. intros zenon_H15 zenon_H16. % 102.51/102.72 generalize (zenon_H15 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H19. % 102.51/102.72 generalize (occu1 (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y)). zenon_intro zenon_H1a. % 102.51/102.72 generalize (zenon_H1a (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H1b. % 102.51/102.72 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 102.51/102.72 exact (zenon_H16 zenon_H1d). % 102.51/102.72 exact (zenon_H19 zenon_H1c). % 102.51/102.72 (* end of lemma zenon_L1_ *) % 102.51/102.72 assert (zenon_L2_ : forall (zenon_TA_y : zenon_U) (zenon_TL_x : zenon_U), (forall Y : zenon_U, ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) Y)->(distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) Y))) -> (forall L : zenon_U, (~(unorthogonal_lines (orthogonal_through_point L zenon_TA_y) L))) -> (~(distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> False). % 102.51/102.72 do 2 intro. intros zenon_H1e zenon_H15 zenon_H1f. % 102.51/102.72 generalize (zenon_H1e (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H20. % 102.51/102.72 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H16 | zenon_intro zenon_H21 ]. % 102.51/102.72 apply (zenon_L1_ zenon_TL_x zenon_TA_y); trivial. % 102.51/102.72 exact (zenon_H1f zenon_H21). % 102.51/102.72 (* end of lemma zenon_L2_ *) % 102.51/102.72 assert (zenon_L3_ : forall (zenon_TL_x : zenon_U) (zenon_TA_y : zenon_U), (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((distinct_lines L M)->((apart_point_and_line zenon_TA_y L)\/((apart_point_and_line zenon_TA_y M)\/((unorthogonal_lines L N)\/(unorthogonal_lines M N)))))))) -> (distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y)) -> (~(apart_point_and_line zenon_TA_y (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y))) -> (~(apart_point_and_line zenon_TA_y (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TL_x)) -> False). % 102.51/102.72 do 2 intro. intros zenon_H22 zenon_H21 zenon_H23 zenon_H24 zenon_H25 zenon_H26. % 102.51/102.72 generalize (zenon_H22 (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y)). zenon_intro zenon_H27. % 102.51/102.72 generalize (zenon_H27 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H28. % 102.51/102.72 generalize (zenon_H28 zenon_TL_x). zenon_intro zenon_H29. % 102.51/102.72 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H1f | zenon_intro zenon_H2a ]. % 102.51/102.72 exact (zenon_H1f zenon_H21). % 102.51/102.72 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 102.51/102.72 exact (zenon_H23 zenon_H2c). % 102.51/102.72 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 102.51/102.72 exact (zenon_H24 zenon_H2e). % 102.51/102.72 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 102.51/102.72 exact (zenon_H25 zenon_H30). % 102.51/102.72 exact (zenon_H26 zenon_H2f). % 102.51/102.72 (* end of lemma zenon_L3_ *) % 102.51/102.72 assert (zenon_L4_ : forall (zenon_TA_y : zenon_U) (zenon_TL_x : zenon_U), (forall Y : zenon_U, ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) Y)->(distinct_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) Y))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y)) -> (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((distinct_lines L M)->((apart_point_and_line zenon_TA_y L)\/((apart_point_and_line zenon_TA_y M)\/((unorthogonal_lines L N)\/(unorthogonal_lines M N)))))))) -> (~(apart_point_and_line zenon_TA_y (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y))) -> (~(apart_point_and_line zenon_TA_y (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TL_x)) -> False). % 102.51/102.72 do 2 intro. intros zenon_H1e zenon_H1d zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H26. % 102.51/102.72 generalize (zenon_H1e (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H20. % 102.51/102.72 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H16 | zenon_intro zenon_H21 ]. % 102.51/102.72 exact (zenon_H16 zenon_H1d). % 102.51/102.72 apply (zenon_L3_ zenon_TL_x zenon_TA_y); trivial. % 102.51/102.72 (* end of lemma zenon_L4_ *) % 102.51/102.72 assert (zenon_L5_ : forall (zenon_TA_y : zenon_U) (zenon_TL_x : zenon_U), ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y))/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> False). % 102.51/102.72 do 2 intro. intros zenon_H31 zenon_H19. % 102.51/102.72 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 102.51/102.72 exact (zenon_H19 zenon_H1c). % 102.51/102.72 (* end of lemma zenon_L5_ *) % 102.51/102.72 assert (zenon_L6_ : forall (zenon_TA_y : zenon_U) (zenon_TL_x : zenon_U), (forall N : zenon_U, (((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x))->(((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N))\/((convergent_lines zenon_TL_x N)/\(unorthogonal_lines zenon_TL_x N))))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> (~(convergent_lines zenon_TL_x (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> False). % 102.51/102.72 do 2 intro. intros zenon_H32 zenon_H33 zenon_H30 zenon_H19 zenon_H34. % 102.51/102.72 generalize (zenon_H32 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H35. % 102.51/102.72 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 102.51/102.72 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_H25 ]. % 102.51/102.72 exact (zenon_H38 zenon_H33). % 102.51/102.72 exact (zenon_H25 zenon_H30). % 102.51/102.72 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H31 | zenon_intro zenon_H39 ]. % 102.51/102.72 apply (zenon_L5_ zenon_TA_y zenon_TL_x); trivial. % 102.51/102.72 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 102.51/102.72 exact (zenon_H34 zenon_H3b). % 102.51/102.72 (* end of lemma zenon_L6_ *) % 102.51/102.72 assert (zenon_L7_ : forall (zenon_TL_x : zenon_U) (zenon_TA_y : zenon_U), (forall L : zenon_U, (~(unorthogonal_lines (orthogonal_through_point L zenon_TA_y) L))) -> (~(convergent_lines zenon_TL_x (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> (unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (forall N : zenon_U, (((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x))->(((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N))\/((convergent_lines zenon_TL_x N)/\(unorthogonal_lines zenon_TL_x N))))) -> False). % 102.51/102.72 do 2 intro. intros zenon_H15 zenon_H34 zenon_H30 zenon_H33 zenon_H32. % 102.51/102.72 generalize (zenon_H15 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H19. % 102.51/102.72 apply (zenon_L6_ zenon_TA_y zenon_TL_x); trivial. % 102.51/102.72 (* end of lemma zenon_L7_ *) % 102.51/102.72 assert (zenon_L8_ : forall (zenon_TA_y : zenon_U) (zenon_TL_x : zenon_U), (forall N : zenon_U, (((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x))->(((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N))\/((convergent_lines zenon_TL_x N)/\(unorthogonal_lines zenon_TL_x N))))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> (~(unorthogonal_lines zenon_TL_x (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> False). % 102.51/102.72 do 2 intro. intros zenon_H32 zenon_H33 zenon_H30 zenon_H19 zenon_H3c. % 102.51/102.72 generalize (zenon_H32 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H35. % 102.51/102.72 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 102.51/102.72 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_H25 ]. % 102.51/102.72 exact (zenon_H38 zenon_H33). % 102.51/102.72 exact (zenon_H25 zenon_H30). % 102.51/102.72 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H31 | zenon_intro zenon_H39 ]. % 102.51/102.72 apply (zenon_L5_ zenon_TA_y zenon_TL_x); trivial. % 102.51/102.72 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 102.51/102.72 exact (zenon_H3c zenon_H3a). % 102.51/102.72 (* end of lemma zenon_L8_ *) % 102.51/102.72 assert (zenon_L9_ : forall (zenon_TL_x : zenon_U) (zenon_TA_y : zenon_U), (forall L : zenon_U, (~(unorthogonal_lines (orthogonal_through_point L zenon_TA_y) L))) -> (~(unorthogonal_lines zenon_TL_x (orthogonal_through_point zenon_TL_x zenon_TA_y))) -> (unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (forall N : zenon_U, (((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x))->(((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N))\/((convergent_lines zenon_TL_x N)/\(unorthogonal_lines zenon_TL_x N))))) -> False). % 102.51/102.72 do 2 intro. intros zenon_H15 zenon_H3c zenon_H30 zenon_H33 zenon_H32. % 102.51/102.72 generalize (zenon_H15 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H19. % 102.51/102.72 apply (zenon_L8_ zenon_TA_y zenon_TL_x); trivial. % 102.51/102.72 (* end of lemma zenon_L9_ *) % 102.51/102.72 assert (zenon_L10_ : forall (zenon_TL_x : zenon_U), ((convergent_lines zenon_TL_x zenon_TL_x)/\(unorthogonal_lines zenon_TL_x zenon_TL_x)) -> (~(convergent_lines zenon_TL_x zenon_TL_x)) -> False). % 102.51/102.72 do 1 intro. intros zenon_H3d zenon_H3e. % 102.51/102.72 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 102.51/102.72 exact (zenon_H3e zenon_H40). % 102.51/102.72 (* end of lemma zenon_L10_ *) % 102.51/102.72 assert (zenon_L11_ : forall (zenon_TA_y : zenon_U) (zenon_TL_x : zenon_U), ((convergent_lines (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TL_x)/\(unorthogonal_lines (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TL_x)) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TL_x)) -> False). % 102.51/102.72 do 2 intro. intros zenon_H41 zenon_H26. % 102.51/102.72 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H42. zenon_intro zenon_H2f. % 102.51/102.72 exact (zenon_H26 zenon_H2f). % 102.51/102.72 (* end of lemma zenon_L11_ *) % 102.51/102.72 assert (zenon_L12_ : forall (zenon_TA_y : zenon_U) (zenon_TL_x : zenon_U), ((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)) -> (forall L : zenon_U, (~(unorthogonal_lines (orthogonal_through_point L zenon_TA_y) L))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x) -> (forall N : zenon_U, (((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) zenon_TL_x))->(((convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N)/\(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y) N))\/((convergent_lines zenon_TL_x N)/\(unorthogonal_lines zenon_TL_x N))))) -> (~(convergent_lines zenon_TL_x zenon_TL_x)) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TL_x)) -> (forall M : zenon_U, (forall N : zenon_U, (((convergent_lines zenon_TL_x M)/\(unorthogonal_lines zenon_TL_x M))->(((convergent_lines zenon_TL_x N)/\(unorthogonal_lines zenon_TL_x N))\/((convergent_lines M N)/\(unorthogonal_lines M N)))))) -> False). % 102.51/102.72 do 2 intro. intros zenon_H43 zenon_H15 zenon_H33 zenon_H32 zenon_H3e zenon_H26 zenon_H44. % 102.51/102.72 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H33. zenon_intro zenon_H30. % 102.51/102.72 generalize (zenon_H44 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H45. % 102.51/102.72 generalize (zenon_H45 zenon_TL_x). zenon_intro zenon_H46. % 102.51/102.72 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 102.51/102.72 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H34 | zenon_intro zenon_H3c ]. % 102.51/102.72 apply (zenon_L7_ zenon_TL_x zenon_TA_y); trivial. % 102.51/102.72 apply (zenon_L9_ zenon_TL_x zenon_TA_y); trivial. % 102.51/102.72 apply (zenon_or_s _ _ zenon_H47); [ zenon_intro zenon_H3d | zenon_intro zenon_H41 ]. % 102.51/102.72 apply (zenon_L10_ zenon_TL_x); trivial. % 102.51/102.72 apply (zenon_L11_ zenon_TA_y zenon_TL_x); trivial. % 102.51/102.72 (* end of lemma zenon_L12_ *) % 102.51/102.72 apply NNPP. intro zenon_G. % 102.51/102.72 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_H49; idtac ]. % 102.51/102.72 elim zenon_H49. zenon_intro zenon_TA_y. zenon_intro zenon_H4a. % 102.51/102.72 apply (zenon_notallex_s (fun L : zenon_U => (~(convergent_lines L (orthogonal_through_point (orthogonal_through_point L zenon_TA_y) zenon_TA_y)))) zenon_H4a); [ zenon_intro zenon_H4b; idtac ]. % 102.51/102.72 elim zenon_H4b. zenon_intro zenon_TL_x. zenon_intro zenon_H4c. % 102.51/102.72 apply zenon_H4c. zenon_intro zenon_H4d. % 102.51/102.72 generalize (apart6 zenon_TL_x). zenon_intro zenon_H4e. % 102.51/102.72 generalize (ceq3 (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y)). zenon_intro zenon_H1e. % 102.51/102.72 generalize (zenon_H4e (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y)). zenon_intro zenon_H4f. % 102.51/102.72 generalize (ooc2 zenon_TA_y). zenon_intro zenon_H50. % 102.51/102.73 generalize (zenon_H50 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H23. % 102.51/102.73 generalize (cup1 zenon_TA_y). zenon_intro zenon_H51. % 102.51/102.73 generalize (zenon_H51 (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y)). zenon_intro zenon_H52. % 102.51/102.73 generalize (apart3 zenon_TL_x). zenon_intro zenon_H3e. % 102.51/102.73 generalize (zenon_H4f zenon_TL_x). zenon_intro zenon_H53. % 102.51/102.73 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 102.51/102.73 exact (zenon_H55 zenon_H4d). % 102.51/102.73 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H40 | zenon_intro zenon_H33 ]. % 102.51/102.73 exact (zenon_H3e zenon_H40). % 102.51/102.73 generalize (oac1 zenon_TL_x). zenon_intro zenon_H44. % 102.51/102.73 generalize (oac1 (orthogonal_through_point (orthogonal_through_point zenon_TL_x zenon_TA_y) zenon_TA_y)). zenon_intro zenon_H56. % 102.51/102.73 generalize (ooc1 zenon_TA_y). zenon_intro zenon_H15. % 102.51/102.73 generalize (zenon_H15 zenon_TL_x). zenon_intro zenon_H26. % 102.51/102.73 generalize (zenon_H56 zenon_TL_x). zenon_intro zenon_H32. % 102.51/102.73 generalize (zenon_H32 zenon_TL_x). zenon_intro zenon_H57. % 102.51/102.73 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H37 | zenon_intro zenon_H58 ]. % 102.51/102.73 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_H25 ]. % 102.51/102.73 exact (zenon_H38 zenon_H33). % 102.51/102.73 generalize (zenon_H50 zenon_TL_x). zenon_intro zenon_H24. % 102.51/102.73 generalize (ouo1 zenon_TA_y). zenon_intro zenon_H22. % 102.51/102.73 generalize (zenon_H52 (orthogonal_through_point zenon_TL_x zenon_TA_y)). zenon_intro zenon_H59. % 102.51/102.73 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H1f | zenon_intro zenon_H5a ]. % 102.51/102.73 apply (zenon_L2_ zenon_TA_y zenon_TL_x); trivial. % 102.51/102.73 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H2c | zenon_intro zenon_H5b ]. % 102.51/102.73 exact (zenon_H23 zenon_H2c). % 102.51/102.73 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H2e | zenon_intro zenon_H1d ]. % 102.51/102.73 exact (zenon_H24 zenon_H2e). % 102.51/102.73 apply (zenon_L4_ zenon_TA_y zenon_TL_x); trivial. % 102.51/102.73 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H43 | zenon_intro zenon_H3d ]. % 102.51/102.73 apply (zenon_L12_ zenon_TA_y zenon_TL_x); trivial. % 102.51/102.73 apply (zenon_L10_ zenon_TL_x); trivial. % 102.51/102.73 Qed. % 102.51/102.73 % SZS output end Proof % 102.51/102.73 (* END-PROOF *) % 102.51/102.73 nodes searched: 13168368 % 102.51/102.73 max branch formulas: 53811 % 102.51/102.73 proof nodes created: 167524 % 102.51/102.73 formulas created: 16323189 % 102.51/102.73 %------------------------------------------------------------------------------