%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.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 07:00:48 EDT 2022 % Result : Theorem 0.39s 0.61s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n027.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 16:17:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.39/0.61 (* PROOF-FOUND *) % 0.39/0.61 % SZS status Theorem % 0.39/0.61 (* BEGIN-PROOF *) % 0.39/0.61 % SZS output start Proof % 0.39/0.61 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\(~(distinct_lines Y Z)))->((convergent_lines X Z)/\(~(distinct_points (intersection_point X Y) (intersection_point X Z)))))))). % 0.39/0.61 Proof. % 0.39/0.61 assert (zenon_L1_ : forall (zenon_TZ_s : zenon_U) (zenon_TY_t : zenon_U) (zenon_TX_u : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TX_u zenon_TY_t)->((convergent_lines zenon_TX_u Z)\/(convergent_lines zenon_TY_t Z)))) -> (convergent_lines zenon_TX_u zenon_TY_t) -> (~(convergent_lines zenon_TX_u zenon_TZ_s)) -> (forall Y : zenon_U, ((convergent_lines zenon_TY_t Y)->(distinct_lines zenon_TY_t Y))) -> (~(distinct_lines zenon_TY_t zenon_TZ_s)) -> False). % 0.39/0.61 do 3 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11. % 0.39/0.61 generalize (zenon_Hd zenon_TZ_s). zenon_intro zenon_H15. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.39/0.61 exact (zenon_H17 zenon_He). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.39/0.61 exact (zenon_Hf zenon_H19). % 0.39/0.61 generalize (zenon_H10 zenon_TZ_s). zenon_intro zenon_H1a. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.39/0.61 exact (zenon_H1c zenon_H18). % 0.39/0.61 exact (zenon_H11 zenon_H1b). % 0.39/0.61 (* end of lemma zenon_L1_ *) % 0.39/0.61 assert (zenon_L2_ : forall (zenon_TY_t : zenon_U) (zenon_TZ_s : zenon_U), (distinct_lines zenon_TZ_s zenon_TY_t) -> (~(distinct_lines zenon_TY_t zenon_TZ_s)) -> False). % 0.39/0.61 do 2 intro. intros zenon_H1d zenon_H11. % 0.39/0.61 generalize (apart5 zenon_TZ_s). zenon_intro zenon_H1e. % 0.39/0.61 generalize (zenon_H1e zenon_TY_t). zenon_intro zenon_H1f. % 0.39/0.61 generalize (zenon_H1f zenon_TZ_s). zenon_intro zenon_H20. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.39/0.61 exact (zenon_H22 zenon_H1d). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H1b ]. % 0.39/0.61 generalize (apart2 zenon_TZ_s). zenon_intro zenon_H24. % 0.39/0.61 exact (zenon_H24 zenon_H23). % 0.39/0.61 exact (zenon_H11 zenon_H1b). % 0.39/0.61 (* end of lemma zenon_L2_ *) % 0.39/0.61 assert (zenon_L3_ : forall (zenon_TZ_s : zenon_U) (zenon_TY_t : zenon_U) (zenon_TX_u : zenon_U), (apart_point_and_line (intersection_point zenon_TX_u zenon_TY_t) zenon_TZ_s) -> (~(distinct_lines zenon_TY_t zenon_TZ_s)) -> (~(apart_point_and_line (intersection_point zenon_TX_u zenon_TY_t) zenon_TY_t)) -> False). % 0.39/0.61 do 3 intro. intros zenon_H25 zenon_H11 zenon_H26. % 0.39/0.61 generalize (ceq2 (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H27. % 0.39/0.61 generalize (zenon_H27 zenon_TZ_s). zenon_intro zenon_H28. % 0.39/0.61 generalize (zenon_H28 zenon_TY_t). zenon_intro zenon_H29. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.39/0.61 exact (zenon_H2b zenon_H25). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H1d | zenon_intro zenon_H2c ]. % 0.39/0.61 apply (zenon_L2_ zenon_TY_t zenon_TZ_s); trivial. % 0.39/0.61 exact (zenon_H26 zenon_H2c). % 0.39/0.61 (* end of lemma zenon_L3_ *) % 0.39/0.61 apply NNPP. intro zenon_G. % 0.39/0.61 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\(~(distinct_lines Y Z)))->((convergent_lines X Z)/\(~(distinct_points (intersection_point X Y) (intersection_point X Z)))))))) zenon_G); [ zenon_intro zenon_H2d; idtac ]. % 0.39/0.61 elim zenon_H2d. zenon_intro zenon_TX_u. zenon_intro zenon_H2e. % 0.39/0.61 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_u Y)/\(~(distinct_lines Y Z)))->((convergent_lines zenon_TX_u Z)/\(~(distinct_points (intersection_point zenon_TX_u Y) (intersection_point zenon_TX_u Z))))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ]. % 0.39/0.61 elim zenon_H2f. zenon_intro zenon_TY_t. zenon_intro zenon_H30. % 0.39/0.61 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_u zenon_TY_t)/\(~(distinct_lines zenon_TY_t Z)))->((convergent_lines zenon_TX_u Z)/\(~(distinct_points (intersection_point zenon_TX_u zenon_TY_t) (intersection_point zenon_TX_u Z)))))) zenon_H30); [ zenon_intro zenon_H31; idtac ]. % 0.39/0.61 elim zenon_H31. zenon_intro zenon_TZ_s. zenon_intro zenon_H32. % 0.39/0.61 apply (zenon_notimply_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33. % 0.39/0.61 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_He. zenon_intro zenon_H11. % 0.39/0.61 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_Hf | zenon_intro zenon_H35 ]. % 0.39/0.61 generalize (apart6 zenon_TX_u). zenon_intro zenon_H36. % 0.39/0.61 generalize (ceq3 zenon_TY_t). zenon_intro zenon_H10. % 0.39/0.61 generalize (zenon_H36 zenon_TY_t). zenon_intro zenon_Hd. % 0.39/0.61 apply (zenon_L1_ zenon_TZ_s zenon_TY_t zenon_TX_u); trivial. % 0.39/0.61 apply zenon_H35. zenon_intro zenon_H37. % 0.39/0.61 generalize (apart2 zenon_TY_t). zenon_intro zenon_H38. % 0.39/0.61 generalize (ceq3 zenon_TY_t). zenon_intro zenon_H10. % 0.39/0.61 generalize (apart6 zenon_TX_u). zenon_intro zenon_H36. % 0.39/0.61 generalize (zenon_H36 zenon_TY_t). zenon_intro zenon_Hd. % 0.39/0.61 generalize (con2 zenon_TX_u). zenon_intro zenon_H39. % 0.39/0.61 generalize (zenon_H39 zenon_TZ_s). zenon_intro zenon_H3a. % 0.39/0.61 generalize (apart4 (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H3b. % 0.39/0.61 generalize (apart1 (intersection_point zenon_TX_u zenon_TZ_s)). zenon_intro zenon_H3c. % 0.39/0.61 generalize (zenon_H3b (intersection_point zenon_TX_u zenon_TZ_s)). zenon_intro zenon_H3d. % 0.39/0.61 generalize (zenon_H3a (intersection_point zenon_TX_u zenon_TZ_s)). zenon_intro zenon_H3e. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_Hf | zenon_intro zenon_H3f ]. % 0.39/0.61 apply (zenon_L1_ zenon_TZ_s zenon_TY_t zenon_TX_u); trivial. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 0.39/0.61 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 0.39/0.61 generalize (apart1 (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H44. % 0.39/0.61 generalize (zenon_H39 zenon_TY_t). zenon_intro zenon_H45. % 0.39/0.61 generalize (zenon_H3d (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H46. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 0.39/0.61 exact (zenon_H48 zenon_H37). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H47); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.39/0.61 exact (zenon_H44 zenon_H4a). % 0.39/0.61 generalize (cu1 (intersection_point zenon_TX_u zenon_TZ_s)). zenon_intro zenon_H4b. % 0.39/0.61 generalize (zenon_H45 (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H4c. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H17 | zenon_intro zenon_H4d ]. % 0.39/0.61 exact (zenon_H17 zenon_He). % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4e | zenon_intro zenon_H4a ]. % 0.39/0.61 apply (zenon_notor_s _ _ zenon_H4e). zenon_intro zenon_H4f. zenon_intro zenon_H26. % 0.39/0.61 generalize (zenon_H4b (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H50. % 0.39/0.61 generalize (apart5 zenon_TX_u). zenon_intro zenon_H51. % 0.39/0.61 generalize (zenon_H51 zenon_TY_t). zenon_intro zenon_H52. % 0.39/0.61 generalize (zenon_H52 zenon_TY_t). zenon_intro zenon_H53. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.39/0.61 generalize (ceq3 zenon_TX_u). zenon_intro zenon_H56. % 0.39/0.61 generalize (zenon_H56 zenon_TY_t). zenon_intro zenon_H57. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H17 | zenon_intro zenon_H58 ]. % 0.39/0.61 exact (zenon_H17 zenon_He). % 0.39/0.61 exact (zenon_H55 zenon_H58). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ]. % 0.39/0.61 generalize (zenon_H52 zenon_TZ_s). zenon_intro zenon_H5a. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H55 | zenon_intro zenon_H5b ]. % 0.39/0.61 exact (zenon_H55 zenon_H58). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H5c | zenon_intro zenon_H1b ]. % 0.39/0.61 generalize (zenon_H50 zenon_TX_u). zenon_intro zenon_H5d. % 0.39/0.61 generalize (zenon_H5d zenon_TZ_s). zenon_intro zenon_H5e. % 0.39/0.61 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 0.39/0.61 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H62 | zenon_intro zenon_H61 ]. % 0.39/0.61 exact (zenon_H62 zenon_H49). % 0.39/0.61 exact (zenon_H61 zenon_H5c). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.39/0.61 exact (zenon_H43 zenon_H64). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 0.39/0.61 exact (zenon_H42 zenon_H66). % 0.39/0.61 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H67 | zenon_intro zenon_H25 ]. % 0.39/0.61 exact (zenon_H4f zenon_H67). % 0.39/0.61 apply (zenon_L3_ zenon_TZ_s zenon_TY_t zenon_TX_u); trivial. % 0.39/0.61 exact (zenon_H11 zenon_H1b). % 0.39/0.61 exact (zenon_H38 zenon_H59). % 0.39/0.61 exact (zenon_H44 zenon_H4a). % 0.39/0.61 exact (zenon_H3c zenon_H40). % 0.39/0.61 Qed. % 0.39/0.61 % SZS output end Proof % 0.39/0.61 (* END-PROOF *) % 0.39/0.61 nodes searched: 8917 % 0.39/0.61 max branch formulas: 1527 % 0.39/0.61 proof nodes created: 831 % 0.39/0.61 formulas created: 24286 % 0.39/0.61 %------------------------------------------------------------------------------