%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO185+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 07:00:31 EDT 2022 % Result : Theorem 1.89s 2.05s % Output : Proof 1.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO185+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n016.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 17:35:37 EDT 2022 % 0.13/0.34 % CPUTime : % 1.89/2.05 (* PROOF-FOUND *) % 1.89/2.05 % SZS status Theorem % 1.89/2.05 (* BEGIN-PROOF *) % 1.89/2.05 % SZS output start Proof % 1.89/2.05 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\(equal_points X (intersection_point U V))))->((incident_point_and_line X U)/\(incident_point_and_line X V))))))). % 1.89/2.05 Proof. % 1.89/2.05 assert (zenon_L1_ : forall (zenon_TV_bo : zenon_U) (zenon_TU_bp : zenon_U) (zenon_TX_bq : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line zenon_TX_bq Y)->((distinct_points zenon_TX_bq Z)\/(apart_point_and_line Z Y))))) -> (convergent_lines zenon_TU_bp zenon_TV_bo) -> (apart_point_and_line zenon_TX_bq zenon_TV_bo) -> (~(distinct_points zenon_TX_bq (intersection_point zenon_TU_bp zenon_TV_bo))) -> False). % 1.89/2.05 do 3 intro. intros zenon_H24 zenon_H25 zenon_H26 zenon_H27. % 1.89/2.05 generalize (zenon_H24 zenon_TV_bo). zenon_intro zenon_H2b. % 1.89/2.05 generalize (ci4 zenon_TU_bp). zenon_intro zenon_H2c. % 1.89/2.05 generalize (zenon_H2c zenon_TV_bo). zenon_intro zenon_H2d. % 1.89/2.05 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 1.89/2.05 exact (zenon_H2f zenon_H25). % 1.89/2.05 generalize (zenon_H2b (intersection_point zenon_TU_bp zenon_TV_bo)). zenon_intro zenon_H30. % 1.89/2.05 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 1.89/2.05 exact (zenon_H32 zenon_H26). % 1.89/2.05 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 1.89/2.05 exact (zenon_H27 zenon_H34). % 1.89/2.05 exact (zenon_H2e zenon_H33). % 1.89/2.05 (* end of lemma zenon_L1_ *) % 1.89/2.05 apply NNPP. intro zenon_G. % 1.89/2.05 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\(equal_points X (intersection_point U V))))->((incident_point_and_line X U)/\(incident_point_and_line X V))))))) zenon_G); [ zenon_intro zenon_H35; idtac ]. % 1.89/2.05 elim zenon_H35. zenon_intro zenon_TX_bq. zenon_intro zenon_H36. % 1.89/2.05 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bq Y)/\((convergent_lines U V)/\(equal_points zenon_TX_bq (intersection_point U V))))->((incident_point_and_line zenon_TX_bq U)/\(incident_point_and_line zenon_TX_bq V)))))) zenon_H36); [ zenon_intro zenon_H37; idtac ]. % 1.89/2.05 elim zenon_H37. zenon_intro zenon_TY_ce. zenon_intro zenon_H39. % 1.89/2.05 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bq zenon_TY_ce)/\((convergent_lines U V)/\(equal_points zenon_TX_bq (intersection_point U V))))->((incident_point_and_line zenon_TX_bq U)/\(incident_point_and_line zenon_TX_bq V))))) zenon_H39); [ zenon_intro zenon_H3a; idtac ]. % 1.89/2.05 elim zenon_H3a. zenon_intro zenon_TU_bp. zenon_intro zenon_H3b. % 1.89/2.05 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bq zenon_TY_ce)/\((convergent_lines zenon_TU_bp V)/\(equal_points zenon_TX_bq (intersection_point zenon_TU_bp V))))->((incident_point_and_line zenon_TX_bq zenon_TU_bp)/\(incident_point_and_line zenon_TX_bq V)))) zenon_H3b); [ zenon_intro zenon_H3c; idtac ]. % 1.89/2.05 elim zenon_H3c. zenon_intro zenon_TV_bo. zenon_intro zenon_H3d. % 1.89/2.05 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 1.89/2.05 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 1.89/2.05 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H25. zenon_intro zenon_H42. % 1.89/2.05 generalize (ax1 zenon_TX_bq). zenon_intro zenon_H43. % 1.89/2.05 generalize (zenon_H43 (intersection_point zenon_TU_bp zenon_TV_bo)). zenon_intro zenon_H44. % 1.89/2.05 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H46; zenon_intro zenon_H45 | zenon_intro zenon_H42; zenon_intro zenon_H27 ]. % 1.89/2.05 exact (zenon_H46 zenon_H42). % 1.89/2.05 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 1.89/2.05 generalize (a4 zenon_TX_bq). zenon_intro zenon_H49. % 1.89/2.05 generalize (zenon_H49 zenon_TU_bp). zenon_intro zenon_H4a. % 1.89/2.05 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H48; zenon_intro zenon_H4d | zenon_intro zenon_H4c; zenon_intro zenon_H4b ]. % 1.89/2.05 apply zenon_H4d. zenon_intro zenon_H4e. % 1.89/2.05 generalize (ci3 zenon_TU_bp). zenon_intro zenon_H4f. % 1.89/2.05 generalize (ceq1 zenon_TX_bq). zenon_intro zenon_H24. % 1.89/2.05 generalize (zenon_H24 zenon_TU_bp). zenon_intro zenon_H50. % 1.89/2.05 generalize (zenon_H4f zenon_TV_bo). zenon_intro zenon_H51. % 1.89/2.05 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H2f | zenon_intro zenon_H52 ]. % 1.89/2.05 exact (zenon_H2f zenon_H25). % 1.89/2.05 generalize (zenon_H50 (intersection_point zenon_TU_bp zenon_TV_bo)). zenon_intro zenon_H53. % 1.89/2.05 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H4b | zenon_intro zenon_H54 ]. % 1.89/2.05 exact (zenon_H4b zenon_H4e). % 1.89/2.05 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H34 | zenon_intro zenon_H55 ]. % 1.89/2.05 exact (zenon_H27 zenon_H34). % 1.89/2.05 exact (zenon_H52 zenon_H55). % 1.89/2.05 exact (zenon_H48 zenon_H4c). % 1.89/2.05 generalize (a4 zenon_TX_bq). zenon_intro zenon_H49. % 1.89/2.05 generalize (zenon_H49 zenon_TV_bo). zenon_intro zenon_H56. % 1.89/2.05 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H47; zenon_intro zenon_H58 | zenon_intro zenon_H57; zenon_intro zenon_H32 ]. % 1.89/2.05 apply zenon_H58. zenon_intro zenon_H26. % 1.89/2.05 generalize (ceq1 zenon_TX_bq). zenon_intro zenon_H24. % 1.89/2.05 apply (zenon_L1_ zenon_TV_bo zenon_TU_bp zenon_TX_bq); trivial. % 1.89/2.05 exact (zenon_H47 zenon_H57). % 1.89/2.05 Qed. % 1.89/2.05 % SZS output end Proof % 1.89/2.05 (* END-PROOF *) % 1.89/2.05 nodes searched: 164075 % 1.89/2.05 max branch formulas: 7397 % 1.89/2.05 proof nodes created: 5064 % 1.89/2.05 formulas created: 339780 % 1.89/2.05 %------------------------------------------------------------------------------