%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------