%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO212+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 07:00:53 EDT 2022 % Result : Theorem 0.22s 0.61s % Output : Proof 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO212+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.14 % Command : run_zenon %s %d % 0.14/0.36 % Computer : n015.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Sat Jun 18 00:11:58 EDT 2022 % 0.14/0.36 % CPUTime : % 0.22/0.61 (* PROOF-FOUND *) % 0.22/0.61 % SZS status Theorem % 0.22/0.61 (* BEGIN-PROOF *) % 0.22/0.61 % SZS output start Proof % 0.22/0.61 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((convergent_lines L N)\/(unorthogonal_lines M N)))))). % 0.22/0.61 Proof. % 0.22/0.61 assert (zenon_L1_ : forall (zenon_TM_y : zenon_U), (convergent_lines zenon_TM_y zenon_TM_y) -> False). % 0.22/0.61 do 1 intro. intros zenon_H17. % 0.22/0.61 generalize (apart3 zenon_TM_y). zenon_intro zenon_H19. % 0.22/0.61 exact (zenon_H19 zenon_H17). % 0.22/0.61 (* end of lemma zenon_L1_ *) % 0.22/0.61 assert (zenon_L2_ : forall (zenon_TN_bd : zenon_U) (zenon_TM_y : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TM_y zenon_TN_bd)->((convergent_lines zenon_TM_y Z)\/(convergent_lines zenon_TN_bd Z)))) -> (convergent_lines zenon_TM_y zenon_TN_bd) -> (~(convergent_lines zenon_TM_y zenon_TM_y)) -> (~(convergent_lines zenon_TN_bd zenon_TM_y)) -> False). % 0.22/0.61 do 2 intro. intros zenon_H1a zenon_H1b zenon_H19 zenon_H1c. % 0.22/0.61 generalize (zenon_H1a zenon_TM_y). zenon_intro zenon_H1e. % 0.22/0.61 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 0.22/0.61 exact (zenon_H20 zenon_H1b). % 0.22/0.61 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H17 | zenon_intro zenon_H21 ]. % 0.22/0.61 exact (zenon_H19 zenon_H17). % 0.22/0.61 exact (zenon_H1c zenon_H21). % 0.22/0.61 (* end of lemma zenon_L2_ *) % 0.22/0.61 assert (zenon_L3_ : forall (zenon_TL_bm : zenon_U) (zenon_TN_bd : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TN_bd Y)->((convergent_lines zenon_TN_bd Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (convergent_lines zenon_TN_bd zenon_TL_bm) -> False). % 0.22/0.61 do 2 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25. % 0.22/0.61 generalize (zenon_H22 zenon_TL_bm). zenon_intro zenon_H27. % 0.22/0.61 generalize (zenon_H27 zenon_TN_bd). zenon_intro zenon_H28. % 0.22/0.61 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.22/0.61 exact (zenon_H2a zenon_H25). % 0.22/0.61 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.22/0.61 exact (zenon_H24 zenon_H2c). % 0.22/0.61 exact (zenon_H23 zenon_H2b). % 0.22/0.61 (* end of lemma zenon_L3_ *) % 0.22/0.61 assert (zenon_L4_ : forall (zenon_TL_bm : zenon_U) (zenon_TM_y : zenon_U) (zenon_TN_bd : zenon_U), (convergent_lines zenon_TN_bd zenon_TM_y) -> (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TM_y Y)->((convergent_lines zenon_TM_y Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TL_bm zenon_TM_y)) -> (~(convergent_lines zenon_TM_y zenon_TM_y)) -> False). % 0.22/0.61 do 3 intro. intros zenon_H21 zenon_H23 zenon_H24 zenon_H2d zenon_H2e zenon_H19. % 0.22/0.61 generalize (ax6 zenon_TN_bd). zenon_intro zenon_H22. % 0.22/0.61 generalize (zenon_H22 zenon_TM_y). zenon_intro zenon_H2f. % 0.22/0.61 generalize (zenon_H2f zenon_TL_bm). zenon_intro zenon_H30. % 0.22/0.61 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ]. % 0.22/0.61 exact (zenon_H1c zenon_H21). % 0.22/0.61 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H25 | zenon_intro zenon_H32 ]. % 0.22/0.61 apply (zenon_L3_ zenon_TL_bm zenon_TN_bd); trivial. % 0.22/0.61 generalize (zenon_H2d zenon_TL_bm). zenon_intro zenon_H33. % 0.22/0.61 generalize (zenon_H33 zenon_TM_y). zenon_intro zenon_H34. % 0.22/0.61 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.22/0.61 exact (zenon_H36 zenon_H32). % 0.22/0.61 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H17 | zenon_intro zenon_H37 ]. % 0.22/0.61 exact (zenon_H19 zenon_H17). % 0.22/0.61 exact (zenon_H2e zenon_H37). % 0.22/0.61 (* end of lemma zenon_L4_ *) % 0.22/0.61 assert (zenon_L5_ : forall (zenon_TL_bm : zenon_U) (zenon_TM_y : zenon_U) (zenon_TN_bd : zenon_U), (~(unorthogonal_lines zenon_TN_bd zenon_TM_y)) -> (~(convergent_lines zenon_TM_y zenon_TM_y)) -> (~(convergent_lines zenon_TL_bm zenon_TM_y)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TM_y Y)->((convergent_lines zenon_TM_y Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> False). % 0.22/0.61 do 3 intro. intros zenon_H38 zenon_H19 zenon_H2e zenon_H2d zenon_H24 zenon_H23. % 0.22/0.61 generalize (occu1 zenon_TN_bd). zenon_intro zenon_H39. % 0.22/0.61 generalize (zenon_H39 zenon_TM_y). zenon_intro zenon_H3a. % 0.22/0.61 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H21 | zenon_intro zenon_H3b ]. % 0.22/0.61 apply (zenon_L4_ zenon_TL_bm zenon_TM_y zenon_TN_bd); trivial. % 0.22/0.61 exact (zenon_H38 zenon_H3b). % 0.22/0.61 (* end of lemma zenon_L5_ *) % 0.22/0.61 assert (zenon_L6_ : forall (zenon_TM_y : zenon_U) (zenon_TN_bd : zenon_U) (zenon_TL_bm : zenon_U), (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TM_y Y)->((convergent_lines zenon_TM_y Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TL_bm zenon_TM_y)) -> (~(convergent_lines zenon_TM_y zenon_TM_y)) -> (convergent_lines zenon_TM_y zenon_TN_bd) -> False). % 0.22/0.61 do 3 intro. intros zenon_H23 zenon_H24 zenon_H2d zenon_H2e zenon_H19 zenon_H1b. % 0.22/0.61 generalize (zenon_H2d zenon_TN_bd). zenon_intro zenon_H1a. % 0.22/0.61 generalize (oac1 zenon_TN_bd). zenon_intro zenon_H3c. % 0.22/0.61 generalize (zenon_H3c zenon_TM_y). zenon_intro zenon_H3d. % 0.22/0.61 generalize (zenon_H3d zenon_TM_y). zenon_intro zenon_H3e. % 0.22/0.61 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.22/0.61 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H1c | zenon_intro zenon_H38 ]. % 0.22/0.61 apply (zenon_L2_ zenon_TN_bd zenon_TM_y); trivial. % 0.22/0.61 apply (zenon_L5_ zenon_TL_bm zenon_TM_y zenon_TN_bd); trivial. % 0.22/0.61 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.22/0.61 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H21. zenon_intro zenon_H3b. % 0.22/0.61 apply (zenon_L4_ zenon_TL_bm zenon_TM_y zenon_TN_bd); trivial. % 0.22/0.61 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H17. zenon_intro zenon_H43. % 0.22/0.61 exact (zenon_H19 zenon_H17). % 0.22/0.61 (* end of lemma zenon_L6_ *) % 0.22/0.61 assert (zenon_L7_ : forall (zenon_TN_bd : zenon_U) (zenon_TM_y : zenon_U), ((convergent_lines zenon_TM_y zenon_TN_bd)/\(unorthogonal_lines zenon_TM_y zenon_TN_bd)) -> (~(unorthogonal_lines zenon_TM_y zenon_TN_bd)) -> False). % 0.22/0.61 do 2 intro. intros zenon_H44 zenon_H45. % 0.22/0.61 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H1b. zenon_intro zenon_H46. % 0.22/0.61 exact (zenon_H45 zenon_H46). % 0.22/0.61 (* end of lemma zenon_L7_ *) % 0.22/0.61 assert (zenon_L8_ : forall (zenon_TL_bm : zenon_U) (zenon_TN_bd : zenon_U) (zenon_TM_y : zenon_U), (forall M : zenon_U, ((convergent_lines zenon_TM_y M)\/(unorthogonal_lines zenon_TM_y M))) -> (~(unorthogonal_lines zenon_TM_y zenon_TN_bd)) -> (~(convergent_lines zenon_TL_bm zenon_TM_y)) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> False). % 0.22/0.61 do 3 intro. intros zenon_H47 zenon_H45 zenon_H2e zenon_H24 zenon_H23. % 0.22/0.61 generalize (zenon_H47 zenon_TN_bd). zenon_intro zenon_H48. % 0.22/0.61 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H1b | zenon_intro zenon_H46 ]. % 0.22/0.61 generalize (zenon_H47 zenon_TM_y). zenon_intro zenon_H49. % 0.22/0.61 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H17 | zenon_intro zenon_H43 ]. % 0.22/0.61 apply (zenon_L1_ zenon_TM_y); trivial. % 0.22/0.61 generalize (oac1 zenon_TM_y). zenon_intro zenon_H4a. % 0.22/0.61 generalize (zenon_H4a zenon_TM_y). zenon_intro zenon_H4b. % 0.22/0.61 generalize (ax6 zenon_TM_y). zenon_intro zenon_H2d. % 0.22/0.61 generalize (zenon_H4b zenon_TN_bd). zenon_intro zenon_H4c. % 0.22/0.61 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.22/0.61 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H19 | zenon_intro zenon_H4f ]. % 0.22/0.61 apply (zenon_L6_ zenon_TM_y zenon_TN_bd zenon_TL_bm); trivial. % 0.22/0.61 exact (zenon_H4f zenon_H43). % 0.22/0.61 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H44 | zenon_intro zenon_H44 ]. % 0.22/0.61 apply (zenon_L7_ zenon_TN_bd zenon_TM_y); trivial. % 0.22/0.61 apply (zenon_L7_ zenon_TN_bd zenon_TM_y); trivial. % 0.22/0.61 exact (zenon_H45 zenon_H46). % 0.22/0.61 (* end of lemma zenon_L8_ *) % 0.22/0.61 apply NNPP. intro zenon_G. % 0.22/0.61 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((convergent_lines L N)\/(unorthogonal_lines M N)))))) zenon_G); [ zenon_intro zenon_H50; idtac ]. % 0.22/0.61 elim zenon_H50. zenon_intro zenon_TL_bm. zenon_intro zenon_H51. % 0.22/0.61 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, ((unorthogonal_lines zenon_TL_bm M)->((convergent_lines zenon_TL_bm N)\/(unorthogonal_lines M N))))) zenon_H51); [ zenon_intro zenon_H52; idtac ]. % 0.22/0.61 elim zenon_H52. zenon_intro zenon_TM_y. zenon_intro zenon_H53. % 0.22/0.61 apply (zenon_notallex_s (fun N : zenon_U => ((unorthogonal_lines zenon_TL_bm zenon_TM_y)->((convergent_lines zenon_TL_bm N)\/(unorthogonal_lines zenon_TM_y N)))) zenon_H53); [ zenon_intro zenon_H54; idtac ]. % 0.22/0.61 elim zenon_H54. zenon_intro zenon_TN_bd. zenon_intro zenon_H55. % 0.22/0.61 apply (zenon_notimply_s _ _ zenon_H55). zenon_intro zenon_H57. zenon_intro zenon_H56. % 0.22/0.61 apply (zenon_notor_s _ _ zenon_H56). zenon_intro zenon_H23. zenon_intro zenon_H45. % 0.22/0.61 generalize (oac1 zenon_TL_bm). zenon_intro zenon_H58. % 0.22/0.61 generalize (apart3 zenon_TN_bd). zenon_intro zenon_H24. % 0.22/0.61 generalize (zenon_H58 zenon_TM_y). zenon_intro zenon_H59. % 0.22/0.61 generalize (occu1 zenon_TM_y). zenon_intro zenon_H47. % 0.22/0.61 generalize (zenon_H59 zenon_TM_y). zenon_intro zenon_H5a. % 0.22/0.61 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ]. % 0.22/0.61 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H2e | zenon_intro zenon_H5d ]. % 0.22/0.61 apply (zenon_L8_ zenon_TL_bm zenon_TN_bd zenon_TM_y); trivial. % 0.22/0.61 exact (zenon_H5d zenon_H57). % 0.22/0.61 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H5e | zenon_intro zenon_H41 ]. % 0.22/0.61 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H37. zenon_intro zenon_H57. % 0.22/0.61 generalize (zenon_H59 zenon_TN_bd). zenon_intro zenon_H5f. % 0.22/0.61 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H5c | zenon_intro zenon_H60 ]. % 0.22/0.61 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H2e | zenon_intro zenon_H5d ]. % 0.22/0.61 exact (zenon_H2e zenon_H37). % 0.22/0.61 exact (zenon_H5d zenon_H57). % 0.22/0.61 apply (zenon_or_s _ _ zenon_H60); [ zenon_intro zenon_H61 | zenon_intro zenon_H44 ]. % 0.22/0.61 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H2b. zenon_intro zenon_H62. % 0.22/0.61 exact (zenon_H23 zenon_H2b). % 0.22/0.61 apply (zenon_L7_ zenon_TN_bd zenon_TM_y); trivial. % 0.22/0.61 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H17. zenon_intro zenon_H43. % 0.22/0.61 apply (zenon_L1_ zenon_TM_y); trivial. % 0.22/0.61 Qed. % 0.22/0.61 % SZS output end Proof % 0.22/0.61 (* END-PROOF *) % 0.22/0.61 nodes searched: 3505 % 0.22/0.61 max branch formulas: 1198 % 0.22/0.61 proof nodes created: 263 % 0.22/0.61 formulas created: 12268 % 0.22/0.61 %------------------------------------------------------------------------------