%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO237+1 : TPTP v8.1.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 07:01:12 EDT 2022 % Result : Theorem 0.22s 0.55s % Output : Proof 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : GEO237+1 : TPTP v8.1.0. Bugfixed v6.4.0. % 0.09/0.15 % Command : run_zenon %s %d % 0.14/0.36 % Computer : n020.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 17:18:18 EDT 2022 % 0.14/0.37 % CPUTime : % 0.22/0.55 (* PROOF-FOUND *) % 0.22/0.55 % SZS status Theorem % 0.22/0.55 (* BEGIN-PROOF *) % 0.22/0.55 % SZS output start Proof % 0.22/0.55 Theorem con : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall L : zenon_U, ((apart_point_and_line C L)->((divides_points L A B)->((divides_points L A C)\/(divides_points L B C)))))))). % 0.22/0.55 Proof. % 0.22/0.55 assert (zenon_L1_ : forall (zenon_TB_bj : zenon_U) (zenon_TL_bk : zenon_U) (zenon_TA_bl : zenon_U), (((left_apart_point zenon_TA_bl zenon_TL_bk)/\(left_apart_point zenon_TB_bj (reverse_line zenon_TL_bk)))\/((left_apart_point zenon_TA_bl (reverse_line zenon_TL_bk))/\(left_apart_point zenon_TB_bj zenon_TL_bk))) -> (~(left_apart_point zenon_TB_bj zenon_TL_bk)) -> (~(left_apart_point zenon_TA_bl zenon_TL_bk)) -> False). % 0.22/0.55 do 3 intro. intros zenon_H20 zenon_H21 zenon_H22. % 0.22/0.55 apply (zenon_or_s _ _ zenon_H20); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.22/0.55 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.22/0.55 exact (zenon_H22 zenon_H29). % 0.22/0.55 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.22/0.55 exact (zenon_H21 zenon_H2a). % 0.22/0.55 (* end of lemma zenon_L1_ *) % 0.22/0.55 assert (zenon_L2_ : forall (zenon_TL_bk : zenon_U) (zenon_TC_bv : zenon_U), ((left_apart_point zenon_TC_bv zenon_TL_bk)\/(left_apart_point zenon_TC_bv (reverse_line zenon_TL_bk))) -> (~(left_apart_point zenon_TC_bv (reverse_line zenon_TL_bk))) -> (~(left_apart_point zenon_TC_bv zenon_TL_bk)) -> False). % 0.22/0.55 do 2 intro. intros zenon_H2c zenon_H2d zenon_H2e. % 0.22/0.55 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.22/0.55 exact (zenon_H2e zenon_H31). % 0.22/0.55 exact (zenon_H2d zenon_H30). % 0.22/0.55 (* end of lemma zenon_L2_ *) % 0.22/0.55 assert (zenon_L3_ : forall (zenon_TB_bj : zenon_U) (zenon_TC_bv : zenon_U) (zenon_TL_bk : zenon_U) (zenon_TA_bl : zenon_U), (~((left_apart_point zenon_TA_bl (reverse_line zenon_TL_bk))/\(left_apart_point zenon_TC_bv zenon_TL_bk))) -> (~(left_apart_point zenon_TC_bv (reverse_line zenon_TL_bk))) -> ((left_apart_point zenon_TC_bv zenon_TL_bk)\/(left_apart_point zenon_TC_bv (reverse_line zenon_TL_bk))) -> (~(left_apart_point zenon_TB_bj (reverse_line zenon_TL_bk))) -> (((left_apart_point zenon_TA_bl zenon_TL_bk)/\(left_apart_point zenon_TB_bj (reverse_line zenon_TL_bk)))\/((left_apart_point zenon_TA_bl (reverse_line zenon_TL_bk))/\(left_apart_point zenon_TB_bj zenon_TL_bk))) -> False). % 0.22/0.55 do 4 intro. intros zenon_H32 zenon_H2d zenon_H2c zenon_H33 zenon_H20. % 0.22/0.55 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H2e ]. % 0.22/0.55 apply (zenon_or_s _ _ zenon_H20); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.22/0.55 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.22/0.55 exact (zenon_H33 zenon_H28). % 0.22/0.55 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.22/0.55 exact (zenon_H34 zenon_H2b). % 0.22/0.55 apply (zenon_L2_ zenon_TL_bk zenon_TC_bv); trivial. % 0.22/0.55 (* end of lemma zenon_L3_ *) % 0.22/0.55 apply NNPP. intro zenon_G. % 0.22/0.55 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (forall L : zenon_U, ((apart_point_and_line C L)->((divides_points L A B)->((divides_points L A C)\/(divides_points L B C)))))))) zenon_G); [ zenon_intro zenon_H35; idtac ]. % 0.22/0.55 elim zenon_H35. zenon_intro zenon_TA_bl. zenon_intro zenon_H36. % 0.22/0.55 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall L : zenon_U, ((apart_point_and_line C L)->((divides_points L zenon_TA_bl B)->((divides_points L zenon_TA_bl C)\/(divides_points L B C))))))) zenon_H36); [ zenon_intro zenon_H37; idtac ]. % 0.22/0.55 elim zenon_H37. zenon_intro zenon_TB_bj. zenon_intro zenon_H38. % 0.22/0.55 apply (zenon_notallex_s (fun C : zenon_U => (forall L : zenon_U, ((apart_point_and_line C L)->((divides_points L zenon_TA_bl zenon_TB_bj)->((divides_points L zenon_TA_bl C)\/(divides_points L zenon_TB_bj C)))))) zenon_H38); [ zenon_intro zenon_H39; idtac ]. % 0.22/0.55 elim zenon_H39. zenon_intro zenon_TC_bv. zenon_intro zenon_H3a. % 0.22/0.55 apply (zenon_notallex_s (fun L : zenon_U => ((apart_point_and_line zenon_TC_bv L)->((divides_points L zenon_TA_bl zenon_TB_bj)->((divides_points L zenon_TA_bl zenon_TC_bv)\/(divides_points L zenon_TB_bj zenon_TC_bv))))) zenon_H3a); [ zenon_intro zenon_H3b; idtac ]. % 0.22/0.55 elim zenon_H3b. zenon_intro zenon_TL_bk. zenon_intro zenon_H3c. % 0.22/0.55 apply (zenon_notimply_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 0.22/0.55 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 0.22/0.55 apply (zenon_notor_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.22/0.55 generalize (apt_def zenon_TC_bv). zenon_intro zenon_H43. % 0.22/0.55 generalize (zenon_H43 zenon_TL_bk). zenon_intro zenon_H44. % 0.22/0.55 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H46; zenon_intro zenon_H45 | zenon_intro zenon_H3e; zenon_intro zenon_H2c ]. % 0.22/0.55 exact (zenon_H46 zenon_H3e). % 0.22/0.55 generalize (div_def zenon_TA_bl). zenon_intro zenon_H47. % 0.22/0.55 generalize (zenon_H47 zenon_TB_bj). zenon_intro zenon_H48. % 0.22/0.55 generalize (zenon_H48 zenon_TL_bk). zenon_intro zenon_H49. % 0.22/0.55 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H4b; zenon_intro zenon_H4a | zenon_intro zenon_H40; zenon_intro zenon_H20 ]. % 0.22/0.55 exact (zenon_H4b zenon_H40). % 0.22/0.55 generalize (div_def zenon_TA_bl). zenon_intro zenon_H47. % 0.22/0.55 generalize (zenon_H47 zenon_TC_bv). zenon_intro zenon_H4c. % 0.22/0.55 generalize (zenon_H4c zenon_TL_bk). zenon_intro zenon_H4d. % 0.22/0.55 apply (zenon_equiv_s _ _ zenon_H4d); [ zenon_intro zenon_H42; zenon_intro zenon_H50 | zenon_intro zenon_H4f; zenon_intro zenon_H4e ]. % 0.22/0.55 apply (zenon_notor_s _ _ zenon_H50). zenon_intro zenon_H51. zenon_intro zenon_H32. % 0.22/0.55 generalize (div_def zenon_TB_bj). zenon_intro zenon_H52. % 0.22/0.55 generalize (zenon_H52 zenon_TC_bv). zenon_intro zenon_H53. % 0.22/0.55 generalize (zenon_H53 zenon_TL_bk). zenon_intro zenon_H54. % 0.22/0.55 apply (zenon_equiv_s _ _ zenon_H54); [ zenon_intro zenon_H41; zenon_intro zenon_H57 | zenon_intro zenon_H56; zenon_intro zenon_H55 ]. % 0.22/0.55 apply (zenon_notor_s _ _ zenon_H57). zenon_intro zenon_H59. zenon_intro zenon_H58. % 0.22/0.55 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H21 | zenon_intro zenon_H2d ]. % 0.22/0.55 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e ]. % 0.22/0.55 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H22 | zenon_intro zenon_H2d ]. % 0.22/0.55 apply (zenon_L1_ zenon_TB_bj zenon_TL_bk zenon_TA_bl); trivial. % 0.22/0.55 apply (zenon_L3_ zenon_TB_bj zenon_TC_bv zenon_TL_bk zenon_TA_bl); trivial. % 0.22/0.55 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H22 | zenon_intro zenon_H2d ]. % 0.22/0.55 apply (zenon_L1_ zenon_TB_bj zenon_TL_bk zenon_TA_bl); trivial. % 0.22/0.55 apply (zenon_L2_ zenon_TL_bk zenon_TC_bv); trivial. % 0.22/0.55 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e ]. % 0.22/0.55 apply (zenon_L3_ zenon_TB_bj zenon_TC_bv zenon_TL_bk zenon_TA_bl); trivial. % 0.22/0.55 apply (zenon_L2_ zenon_TL_bk zenon_TC_bv); trivial. % 0.22/0.55 exact (zenon_H41 zenon_H56). % 0.22/0.55 exact (zenon_H42 zenon_H4f). % 0.22/0.55 Qed. % 0.22/0.55 % SZS output end Proof % 0.22/0.55 (* END-PROOF *) % 0.22/0.55 nodes searched: 40 % 0.22/0.55 max branch formulas: 53 % 0.22/0.55 proof nodes created: 30 % 0.22/0.55 formulas created: 702 % 0.22/0.55 %------------------------------------------------------------------------------