%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO203+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n029.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 07:00:46 EDT 2022 % Result : Theorem 0.60s 0.76s % Output : Proof 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO203+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n029.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 06:21:28 EDT 2022 % 0.13/0.34 % CPUTime : % 0.60/0.76 (* PROOF-FOUND *) % 0.60/0.76 % SZS status Theorem % 0.60/0.76 (* BEGIN-PROOF *) % 0.60/0.76 % SZS output start Proof % 0.60/0.76 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines X Z)/\(distinct_points (intersection_point X Y) (intersection_point X Z))))->(~(distinct_lines (line_connecting (intersection_point X Y) (intersection_point X Z)) X)))))). % 0.60/0.76 Proof. % 0.60/0.76 assert (zenon_L1_ : forall (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_t Y)->(~(apart_point_and_line (intersection_point zenon_TX_t Y) zenon_TX_t)))) -> (convergent_lines zenon_TX_t zenon_TY_s) -> (apart_point_and_line (intersection_point zenon_TX_t zenon_TY_s) zenon_TX_t) -> False). % 0.60/0.76 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11. % 0.60/0.76 generalize (zenon_Hf zenon_TY_s). zenon_intro zenon_H14. % 0.60/0.76 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.60/0.76 exact (zenon_H16 zenon_H10). % 0.60/0.76 exact (zenon_H15 zenon_H11). % 0.60/0.76 (* end of lemma zenon_L1_ *) % 0.60/0.76 assert (zenon_L2_ : forall (zenon_TZ_z : zenon_U) (zenon_TX_t : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_t Y)->(~(apart_point_and_line (intersection_point zenon_TX_t Y) zenon_TX_t)))) -> (convergent_lines zenon_TX_t zenon_TZ_z) -> (apart_point_and_line (intersection_point zenon_TX_t zenon_TZ_z) zenon_TX_t) -> False). % 0.60/0.76 do 2 intro. intros zenon_Hf zenon_H17 zenon_H18. % 0.60/0.76 generalize (zenon_Hf zenon_TZ_z). zenon_intro zenon_H1a. % 0.60/0.76 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.60/0.76 exact (zenon_H1c zenon_H17). % 0.60/0.76 exact (zenon_H1b zenon_H18). % 0.60/0.76 (* end of lemma zenon_L2_ *) % 0.60/0.76 apply NNPP. intro zenon_G. % 0.60/0.76 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines X Z)/\(distinct_points (intersection_point X Y) (intersection_point X Z))))->(~(distinct_lines (line_connecting (intersection_point X Y) (intersection_point X Z)) X)))))) zenon_G); [ zenon_intro zenon_H1d; idtac ]. % 0.60/0.76 elim zenon_H1d. zenon_intro zenon_TX_t. zenon_intro zenon_H1e. % 0.60/0.76 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_t Y)/\((convergent_lines zenon_TX_t Z)/\(distinct_points (intersection_point zenon_TX_t Y) (intersection_point zenon_TX_t Z))))->(~(distinct_lines (line_connecting (intersection_point zenon_TX_t Y) (intersection_point zenon_TX_t Z)) zenon_TX_t))))) zenon_H1e); [ zenon_intro zenon_H1f; idtac ]. % 0.60/0.76 elim zenon_H1f. zenon_intro zenon_TY_s. zenon_intro zenon_H20. % 0.60/0.76 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_t zenon_TY_s)/\((convergent_lines zenon_TX_t Z)/\(distinct_points (intersection_point zenon_TX_t zenon_TY_s) (intersection_point zenon_TX_t Z))))->(~(distinct_lines (line_connecting (intersection_point zenon_TX_t zenon_TY_s) (intersection_point zenon_TX_t Z)) zenon_TX_t)))) zenon_H20); [ zenon_intro zenon_H21; idtac ]. % 0.60/0.76 elim zenon_H21. zenon_intro zenon_TZ_z. zenon_intro zenon_H22. % 0.60/0.76 apply (zenon_notimply_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.60/0.76 apply zenon_H23. zenon_intro zenon_H25. % 0.60/0.76 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H10. zenon_intro zenon_H26. % 0.60/0.76 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H17. zenon_intro zenon_H27. % 0.60/0.76 generalize (apart2 zenon_TX_t). zenon_intro zenon_H28. % 0.60/0.76 generalize (cu1 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H29. % 0.60/0.76 generalize (zenon_H29 (intersection_point zenon_TX_t zenon_TZ_z)). zenon_intro zenon_H2a. % 0.60/0.76 generalize (ceq2 (intersection_point zenon_TX_t zenon_TZ_z)). zenon_intro zenon_H2b. % 0.60/0.76 generalize (ci3 zenon_TX_t). zenon_intro zenon_Hf. % 0.60/0.76 generalize (zenon_H2b zenon_TX_t). zenon_intro zenon_H2c. % 0.60/0.76 generalize (zenon_H2c zenon_TX_t). zenon_intro zenon_H2d. % 0.60/0.76 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H1b | zenon_intro zenon_H2e ]. % 0.60/0.76 generalize (ceq2 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H2f. % 0.60/0.76 generalize (zenon_H2f zenon_TX_t). zenon_intro zenon_H30. % 0.60/0.76 generalize (zenon_H30 zenon_TX_t). zenon_intro zenon_H31. % 0.60/0.76 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H15 | zenon_intro zenon_H32 ]. % 0.60/0.77 generalize (zenon_H2a (line_connecting (intersection_point zenon_TX_t zenon_TY_s) (intersection_point zenon_TX_t zenon_TZ_z))). zenon_intro zenon_H33. % 0.60/0.77 generalize (zenon_H33 zenon_TX_t). zenon_intro zenon_H34. % 0.60/0.77 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.60/0.77 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.60/0.77 exact (zenon_H38 zenon_H27). % 0.60/0.77 exact (zenon_H37 zenon_H25). % 0.60/0.77 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.60/0.77 generalize (ci1 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H3b. % 0.60/0.77 generalize (zenon_H3b (intersection_point zenon_TX_t zenon_TZ_z)). zenon_intro zenon_H3c. % 0.60/0.77 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H38 | zenon_intro zenon_H3d ]. % 0.60/0.77 exact (zenon_H38 zenon_H27). % 0.60/0.77 exact (zenon_H3d zenon_H3a). % 0.60/0.77 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H11 | zenon_intro zenon_H3e ]. % 0.60/0.77 exact (zenon_H15 zenon_H11). % 0.60/0.77 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H3f | zenon_intro zenon_H18 ]. % 0.60/0.77 generalize (ci2 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H40. % 0.60/0.77 generalize (zenon_H40 (intersection_point zenon_TX_t zenon_TZ_z)). zenon_intro zenon_H41. % 0.60/0.77 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H38 | zenon_intro zenon_H42 ]. % 0.60/0.77 exact (zenon_H38 zenon_H27). % 0.60/0.77 exact (zenon_H42 zenon_H3f). % 0.60/0.77 exact (zenon_H1b zenon_H18). % 0.60/0.77 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H43 | zenon_intro zenon_H11 ]. % 0.60/0.77 exact (zenon_H28 zenon_H43). % 0.60/0.77 apply (zenon_L1_ zenon_TY_s zenon_TX_t); trivial. % 0.60/0.77 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H43 | zenon_intro zenon_H18 ]. % 0.60/0.77 exact (zenon_H28 zenon_H43). % 0.60/0.77 apply (zenon_L2_ zenon_TZ_z zenon_TX_t); trivial. % 0.60/0.77 Qed. % 0.60/0.77 % SZS output end Proof % 0.60/0.77 (* END-PROOF *) % 0.60/0.77 nodes searched: 19207 % 0.60/0.77 max branch formulas: 3137 % 0.60/0.77 proof nodes created: 938 % 0.60/0.77 formulas created: 52907 % 0.60/0.77 %------------------------------------------------------------------------------