%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO197+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 07:00:41 EDT 2022 % Result : Theorem 1.61s 1.82s % Output : Proof 1.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO197+2 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n006.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sat Jun 18 09:58:25 EDT 2022 % 0.14/0.36 % CPUTime : % 1.61/1.82 (* PROOF-FOUND *) % 1.61/1.82 % SZS status Theorem % 1.61/1.82 (* BEGIN-PROOF *) % 1.61/1.82 % SZS output start Proof % 1.61/1.82 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\((convergent_lines X Z)/\(~(apart_point_and_line (intersection_point X Y) Z)))))->(~(apart_point_and_line (intersection_point Z Y) X)))))). % 1.61/1.82 Proof. % 1.61/1.82 assert (zenon_L1_ : forall (zenon_TX_r : zenon_U) (zenon_TY_s : zenon_U) (zenon_TZ_t : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TZ_t zenon_TY_s) zenon_TX_r)->((distinct_points (intersection_point zenon_TZ_t zenon_TY_s) Z)\/(apart_point_and_line Z zenon_TX_r)))) -> (apart_point_and_line (intersection_point zenon_TZ_t zenon_TY_s) zenon_TX_r) -> (~(distinct_points (intersection_point zenon_TZ_t zenon_TY_s) (intersection_point zenon_TX_r zenon_TY_s))) -> (~(apart_point_and_line (intersection_point zenon_TX_r zenon_TY_s) zenon_TX_r)) -> False). % 1.61/1.82 do 3 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10. % 1.61/1.82 generalize (zenon_Hd (intersection_point zenon_TX_r zenon_TY_s)). zenon_intro zenon_H14. % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 1.61/1.82 exact (zenon_H16 zenon_He). % 1.61/1.82 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 1.61/1.82 exact (zenon_Hf zenon_H18). % 1.61/1.82 exact (zenon_H10 zenon_H17). % 1.61/1.82 (* end of lemma zenon_L1_ *) % 1.61/1.82 assert (zenon_L2_ : forall (zenon_TY_s : zenon_U) (zenon_TZ_t : zenon_U), (apart_point_and_line (intersection_point zenon_TZ_t zenon_TY_s) zenon_TZ_t) -> (convergent_lines zenon_TZ_t zenon_TY_s) -> False). % 1.61/1.82 do 2 intro. intros zenon_H19 zenon_H1a. % 1.61/1.82 generalize (con2 zenon_TZ_t). zenon_intro zenon_H1b. % 1.61/1.82 generalize (zenon_H1b zenon_TY_s). zenon_intro zenon_H1c. % 1.61/1.82 generalize (apart1 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H1d. % 1.61/1.82 generalize (zenon_H1c (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H1e. % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 1.61/1.82 exact (zenon_H20 zenon_H1a). % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 1.61/1.82 apply (zenon_notor_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23. % 1.61/1.82 exact (zenon_H24 zenon_H19). % 1.61/1.82 exact (zenon_H1d zenon_H21). % 1.61/1.82 (* end of lemma zenon_L2_ *) % 1.61/1.82 assert (zenon_L3_ : forall (zenon_TZ_t : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_r : zenon_U), (convergent_lines zenon_TX_r zenon_TY_s) -> (~(apart_point_and_line (intersection_point zenon_TX_r zenon_TY_s) zenon_TZ_t)) -> (distinct_lines zenon_TY_s zenon_TZ_t) -> (apart_point_and_line (intersection_point zenon_TZ_t zenon_TY_s) zenon_TX_r) -> (convergent_lines zenon_TZ_t zenon_TY_s) -> (~(distinct_lines zenon_TZ_t zenon_TZ_t)) -> False). % 1.61/1.82 do 3 intro. intros zenon_H25 zenon_H26 zenon_H27 zenon_He zenon_H1a zenon_H28. % 1.61/1.82 generalize (ceq2 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H29. % 1.61/1.82 generalize (ceq1 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H2a. % 1.61/1.82 generalize (zenon_H2a zenon_TX_r). zenon_intro zenon_Hd. % 1.61/1.82 generalize (zenon_H29 zenon_TZ_t). zenon_intro zenon_H2b. % 1.61/1.82 generalize (zenon_H2b zenon_TZ_t). zenon_intro zenon_H2c. % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H24 | zenon_intro zenon_H2d ]. % 1.61/1.82 generalize (con2 zenon_TZ_t). zenon_intro zenon_H1b. % 1.61/1.82 generalize (zenon_H1b zenon_TY_s). zenon_intro zenon_H1c. % 1.61/1.82 generalize (apart1 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H1d. % 1.61/1.82 generalize (zenon_H1c (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H1e. % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 1.61/1.82 exact (zenon_H20 zenon_H1a). % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 1.61/1.82 apply (zenon_notor_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23. % 1.61/1.82 generalize (cu1 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H2e. % 1.61/1.82 generalize (apart1 (intersection_point zenon_TX_r zenon_TY_s)). zenon_intro zenon_H2f. % 1.61/1.82 generalize (con2 zenon_TX_r). zenon_intro zenon_H30. % 1.61/1.82 generalize (zenon_H30 zenon_TY_s). zenon_intro zenon_H31. % 1.61/1.82 generalize (zenon_H31 (intersection_point zenon_TX_r zenon_TY_s)). zenon_intro zenon_H32. % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 1.61/1.82 exact (zenon_H34 zenon_H25). % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 1.61/1.82 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H10. zenon_intro zenon_H37. % 1.61/1.82 generalize (zenon_H2e (intersection_point zenon_TX_r zenon_TY_s)). zenon_intro zenon_H38. % 1.61/1.82 generalize (zenon_H38 zenon_TY_s). zenon_intro zenon_H39. % 1.61/1.82 generalize (zenon_H39 zenon_TZ_t). zenon_intro zenon_H3a. % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 1.61/1.82 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_Hf | zenon_intro zenon_H3d ]. % 1.61/1.82 apply (zenon_L1_ zenon_TX_r zenon_TY_s zenon_TZ_t); trivial. % 1.61/1.82 exact (zenon_H3d zenon_H27). % 1.61/1.82 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 1.61/1.82 exact (zenon_H23 zenon_H3f). % 1.61/1.82 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H19 | zenon_intro zenon_H40 ]. % 1.61/1.82 exact (zenon_H24 zenon_H19). % 1.61/1.82 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 1.61/1.82 exact (zenon_H37 zenon_H42). % 1.61/1.82 exact (zenon_H26 zenon_H41). % 1.61/1.82 exact (zenon_H2f zenon_H35). % 1.61/1.82 exact (zenon_H1d zenon_H21). % 1.61/1.82 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H43 | zenon_intro zenon_H19 ]. % 1.61/1.82 exact (zenon_H28 zenon_H43). % 1.61/1.82 apply (zenon_L2_ zenon_TY_s zenon_TZ_t); trivial. % 1.61/1.82 (* end of lemma zenon_L3_ *) % 1.61/1.82 apply NNPP. intro zenon_G. % 1.61/1.82 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\((convergent_lines X Z)/\(~(apart_point_and_line (intersection_point X Y) Z)))))->(~(apart_point_and_line (intersection_point Z Y) X)))))) zenon_G); [ zenon_intro zenon_H44; idtac ]. % 1.61/1.82 elim zenon_H44. zenon_intro zenon_TX_r. zenon_intro zenon_H45. % 1.61/1.82 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_r Y)/\((convergent_lines Z Y)/\((convergent_lines zenon_TX_r Z)/\(~(apart_point_and_line (intersection_point zenon_TX_r Y) Z)))))->(~(apart_point_and_line (intersection_point Z Y) zenon_TX_r))))) zenon_H45); [ zenon_intro zenon_H46; idtac ]. % 1.61/1.82 elim zenon_H46. zenon_intro zenon_TY_s. zenon_intro zenon_H47. % 1.61/1.82 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_r zenon_TY_s)/\((convergent_lines Z zenon_TY_s)/\((convergent_lines zenon_TX_r Z)/\(~(apart_point_and_line (intersection_point zenon_TX_r zenon_TY_s) Z)))))->(~(apart_point_and_line (intersection_point Z zenon_TY_s) zenon_TX_r)))) zenon_H47); [ zenon_intro zenon_H48; idtac ]. % 1.61/1.82 elim zenon_H48. zenon_intro zenon_TZ_t. zenon_intro zenon_H49. % 1.61/1.82 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 1.61/1.82 apply zenon_H4a. zenon_intro zenon_He. % 1.61/1.82 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H25. zenon_intro zenon_H4c. % 1.61/1.82 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H1a. zenon_intro zenon_H4d. % 1.61/1.82 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H4e. zenon_intro zenon_H26. % 1.61/1.82 generalize (apart3 zenon_TZ_t). zenon_intro zenon_H4f. % 1.61/1.82 generalize (apart2 zenon_TZ_t). zenon_intro zenon_H28. % 1.61/1.82 generalize (apart6 zenon_TZ_t). zenon_intro zenon_H50. % 1.61/1.82 generalize (ceq3 zenon_TY_s). zenon_intro zenon_H51. % 1.61/1.82 generalize (zenon_H50 zenon_TY_s). zenon_intro zenon_H52. % 1.61/1.82 generalize (zenon_H52 zenon_TZ_t). zenon_intro zenon_H53. % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H20 | zenon_intro zenon_H54 ]. % 1.61/1.82 exact (zenon_H20 zenon_H1a). % 1.61/1.82 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 1.61/1.82 exact (zenon_H4f zenon_H56). % 1.61/1.82 generalize (zenon_H51 zenon_TZ_t). zenon_intro zenon_H57. % 1.61/1.82 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H27 ]. % 1.61/1.82 exact (zenon_H58 zenon_H55). % 1.61/1.82 apply (zenon_L3_ zenon_TZ_t zenon_TY_s zenon_TX_r); trivial. % 1.61/1.82 Qed. % 1.61/1.82 % SZS output end Proof % 1.61/1.82 (* END-PROOF *) % 1.61/1.82 nodes searched: 138566 % 1.61/1.82 max branch formulas: 3265 % 1.61/1.82 proof nodes created: 3711 % 1.61/1.82 formulas created: 199469 % 1.61/1.82 %------------------------------------------------------------------------------