%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 07:00:25 EDT 2022 % Result : Theorem 0.37s 0.55s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 03:23:01 EDT 2022 % 0.12/0.33 % CPUTime : % 0.37/0.55 (* PROOF-FOUND *) % 0.37/0.55 % SZS status Theorem % 0.37/0.55 (* BEGIN-PROOF *) % 0.37/0.55 % SZS output start Proof % 0.37/0.55 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\(distinct_points U V))->(((apart_point_and_line X (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting X Y))\/(apart_point_and_line V (line_connecting X Y))))))))). % 0.37/0.55 Proof. % 0.37/0.55 assert (zenon_L1_ : forall (zenon_TY_br : zenon_U) (zenon_TX_bs : zenon_U) (zenon_TV_bt : zenon_U) (zenon_TU_bu : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TU_bu zenon_TV_bt)/\(distinct_lines U V))->((apart_point_and_line zenon_TU_bu U)\/((apart_point_and_line zenon_TU_bu V)\/((apart_point_and_line zenon_TV_bt U)\/(apart_point_and_line zenon_TV_bt V))))))) -> (~(apart_point_and_line zenon_TV_bt (line_connecting zenon_TX_bs zenon_TY_br))) -> (~(apart_point_and_line zenon_TV_bt (line_connecting zenon_TU_bu zenon_TV_bt))) -> (~(apart_point_and_line zenon_TU_bu (line_connecting zenon_TX_bs zenon_TY_br))) -> (~(apart_point_and_line zenon_TU_bu (line_connecting zenon_TU_bu zenon_TV_bt))) -> (distinct_lines (line_connecting zenon_TU_bu zenon_TV_bt) (line_connecting zenon_TX_bs zenon_TY_br)) -> (distinct_points zenon_TU_bu zenon_TV_bt) -> False). % 0.37/0.55 do 4 intro. intros zenon_H24 zenon_H25 zenon_H26 zenon_H27 zenon_H28 zenon_H29 zenon_H2a. % 0.37/0.55 generalize (zenon_H24 (line_connecting zenon_TU_bu zenon_TV_bt)). zenon_intro zenon_H2f. % 0.37/0.55 generalize (zenon_H2f (line_connecting zenon_TX_bs zenon_TY_br)). zenon_intro zenon_H30. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.37/0.55 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.37/0.55 exact (zenon_H34 zenon_H2a). % 0.37/0.55 exact (zenon_H33 zenon_H29). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.37/0.55 exact (zenon_H28 zenon_H36). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.37/0.55 exact (zenon_H27 zenon_H38). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.37/0.55 exact (zenon_H26 zenon_H3a). % 0.37/0.55 exact (zenon_H25 zenon_H39). % 0.37/0.55 (* end of lemma zenon_L1_ *) % 0.37/0.55 apply NNPP. intro zenon_G. % 0.37/0.55 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\(distinct_points U V))->(((apart_point_and_line X (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting X Y))\/(apart_point_and_line V (line_connecting X Y))))))))) zenon_G); [ zenon_intro zenon_H3b; idtac ]. % 0.37/0.55 elim zenon_H3b. zenon_intro zenon_TX_bs. zenon_intro zenon_H3c. % 0.37/0.55 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bs Y)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_bs (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_bs Y))\/(apart_point_and_line V (line_connecting zenon_TX_bs Y)))))))) zenon_H3c); [ zenon_intro zenon_H3d; idtac ]. % 0.37/0.55 elim zenon_H3d. zenon_intro zenon_TY_br. zenon_intro zenon_H3e. % 0.37/0.55 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bs zenon_TY_br)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_bs (line_connecting U V))\/(apart_point_and_line zenon_TY_br (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_bs zenon_TY_br))\/(apart_point_and_line V (line_connecting zenon_TX_bs zenon_TY_br))))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ]. % 0.37/0.55 elim zenon_H3f. zenon_intro zenon_TU_bu. zenon_intro zenon_H40. % 0.37/0.55 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bs zenon_TY_br)/\(distinct_points zenon_TU_bu V))->(((apart_point_and_line zenon_TX_bs (line_connecting zenon_TU_bu V))\/(apart_point_and_line zenon_TY_br (line_connecting zenon_TU_bu V)))->((apart_point_and_line zenon_TU_bu (line_connecting zenon_TX_bs zenon_TY_br))\/(apart_point_and_line V (line_connecting zenon_TX_bs zenon_TY_br)))))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 0.37/0.55 elim zenon_H41. zenon_intro zenon_TV_bt. zenon_intro zenon_H42. % 0.37/0.55 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.37/0.55 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 0.37/0.55 apply (zenon_notor_s _ _ zenon_H45). zenon_intro zenon_H27. zenon_intro zenon_H25. % 0.37/0.55 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H47. zenon_intro zenon_H2a. % 0.37/0.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.37/0.55 generalize (cu1 zenon_TU_bu). zenon_intro zenon_H4a. % 0.37/0.55 generalize (ci1 zenon_TU_bu). zenon_intro zenon_H4b. % 0.37/0.55 generalize (zenon_H4a zenon_TV_bt). zenon_intro zenon_H24. % 0.37/0.55 generalize (ci2 zenon_TU_bu). zenon_intro zenon_H4c. % 0.37/0.55 generalize (zenon_H4b zenon_TV_bt). zenon_intro zenon_H4d. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H34 | zenon_intro zenon_H28 ]. % 0.37/0.55 exact (zenon_H34 zenon_H2a). % 0.37/0.55 generalize (zenon_H4c zenon_TV_bt). zenon_intro zenon_H4e. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H34 | zenon_intro zenon_H26 ]. % 0.37/0.55 exact (zenon_H34 zenon_H2a). % 0.37/0.55 generalize (ceq2 zenon_TX_bs). zenon_intro zenon_H4f. % 0.37/0.55 generalize (zenon_H4f (line_connecting zenon_TU_bu zenon_TV_bt)). zenon_intro zenon_H50. % 0.37/0.55 generalize (ci1 zenon_TX_bs). zenon_intro zenon_H51. % 0.37/0.55 generalize (zenon_H51 zenon_TY_br). zenon_intro zenon_H52. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 0.37/0.55 exact (zenon_H54 zenon_H47). % 0.37/0.55 generalize (zenon_H50 (line_connecting zenon_TX_bs zenon_TY_br)). zenon_intro zenon_H55. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 0.37/0.55 exact (zenon_H57 zenon_H49). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H29 | zenon_intro zenon_H58 ]. % 0.37/0.55 apply (zenon_L1_ zenon_TY_br zenon_TX_bs zenon_TV_bt zenon_TU_bu); trivial. % 0.37/0.55 exact (zenon_H53 zenon_H58). % 0.37/0.55 generalize (cu1 zenon_TU_bu). zenon_intro zenon_H4a. % 0.37/0.55 generalize (ci1 zenon_TU_bu). zenon_intro zenon_H4b. % 0.37/0.55 generalize (zenon_H4a zenon_TV_bt). zenon_intro zenon_H24. % 0.37/0.55 generalize (ci2 zenon_TU_bu). zenon_intro zenon_H4c. % 0.37/0.55 generalize (zenon_H4b zenon_TV_bt). zenon_intro zenon_H4d. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H34 | zenon_intro zenon_H28 ]. % 0.37/0.55 exact (zenon_H34 zenon_H2a). % 0.37/0.55 generalize (zenon_H4c zenon_TV_bt). zenon_intro zenon_H4e. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H34 | zenon_intro zenon_H26 ]. % 0.37/0.55 exact (zenon_H34 zenon_H2a). % 0.37/0.55 generalize (ceq2 zenon_TY_br). zenon_intro zenon_H59. % 0.37/0.55 generalize (zenon_H59 (line_connecting zenon_TU_bu zenon_TV_bt)). zenon_intro zenon_H5a. % 0.37/0.55 generalize (ci2 zenon_TX_bs). zenon_intro zenon_H5b. % 0.37/0.55 generalize (zenon_H5b zenon_TY_br). zenon_intro zenon_H5c. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H54 | zenon_intro zenon_H5d ]. % 0.37/0.55 exact (zenon_H54 zenon_H47). % 0.37/0.55 generalize (zenon_H5a (line_connecting zenon_TX_bs zenon_TY_br)). zenon_intro zenon_H5e. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 0.37/0.55 exact (zenon_H60 zenon_H48). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H29 | zenon_intro zenon_H61 ]. % 0.37/0.55 apply (zenon_L1_ zenon_TY_br zenon_TX_bs zenon_TV_bt zenon_TU_bu); trivial. % 0.37/0.55 exact (zenon_H5d zenon_H61). % 0.37/0.55 Qed. % 0.37/0.55 % SZS output end Proof % 0.37/0.55 (* END-PROOF *) % 0.37/0.55 nodes searched: 3941 % 0.37/0.55 max branch formulas: 1303 % 0.37/0.55 proof nodes created: 311 % 0.37/0.55 formulas created: 13324 % 0.37/0.55 %------------------------------------------------------------------------------