%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO193+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 07:00:37 EDT 2022 % Result : Theorem 0.77s 0.96s % Output : Proof 0.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO193+2 : TPTP v8.1.0. Released v3.3.0. % 0.00/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n018.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 : Fri Jun 17 17:55:47 EDT 2022 % 0.12/0.33 % CPUTime : % 0.77/0.96 (* PROOF-FOUND *) % 0.77/0.96 % SZS status Theorem % 0.77/0.96 (* BEGIN-PROOF *) % 0.77/0.96 % SZS output start Proof % 0.77/0.96 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)))))). % 0.77/0.96 Proof. % 0.77/0.96 assert (zenon_L1_ : forall (zenon_TY_p : zenon_U) (zenon_TX_q : zenon_U), (apart_point_and_line (intersection_point zenon_TX_q zenon_TY_p) zenon_TY_p) -> (convergent_lines zenon_TX_q zenon_TY_p) -> False). % 0.77/0.96 do 2 intro. intros zenon_Hd zenon_He. % 0.77/0.96 generalize (con2 zenon_TX_q). zenon_intro zenon_H11. % 0.77/0.96 generalize (zenon_H11 zenon_TY_p). zenon_intro zenon_H12. % 0.77/0.96 generalize (apart1 (intersection_point zenon_TX_q zenon_TY_p)). zenon_intro zenon_H13. % 0.77/0.96 generalize (zenon_H12 (intersection_point zenon_TX_q zenon_TY_p)). zenon_intro zenon_H14. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.77/0.96 exact (zenon_H16 zenon_He). % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.77/0.96 apply (zenon_notor_s _ _ zenon_H18). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.77/0.96 exact (zenon_H19 zenon_Hd). % 0.77/0.96 exact (zenon_H13 zenon_H17). % 0.77/0.96 (* end of lemma zenon_L1_ *) % 0.77/0.96 assert (zenon_L2_ : forall (zenon_TY_p : zenon_U) (zenon_TX_q : zenon_U), (apart_point_and_line (intersection_point zenon_TX_q zenon_TY_p) zenon_TX_q) -> (convergent_lines zenon_TX_q zenon_TY_p) -> False). % 0.77/0.96 do 2 intro. intros zenon_H1b zenon_He. % 0.77/0.96 generalize (con2 zenon_TX_q). zenon_intro zenon_H11. % 0.77/0.96 generalize (zenon_H11 zenon_TY_p). zenon_intro zenon_H12. % 0.77/0.96 generalize (apart1 (intersection_point zenon_TX_q zenon_TY_p)). zenon_intro zenon_H13. % 0.77/0.96 generalize (zenon_H12 (intersection_point zenon_TX_q zenon_TY_p)). zenon_intro zenon_H14. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.77/0.96 exact (zenon_H16 zenon_He). % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.77/0.96 apply (zenon_notor_s _ _ zenon_H18). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.77/0.96 exact (zenon_H1a zenon_H1b). % 0.77/0.96 exact (zenon_H13 zenon_H17). % 0.77/0.96 (* end of lemma zenon_L2_ *) % 0.77/0.96 apply NNPP. intro zenon_G. % 0.77/0.96 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_H1c; idtac ]. % 0.77/0.96 elim zenon_H1c. zenon_intro zenon_TX_q. zenon_intro zenon_H1d. % 0.77/0.96 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_q Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_q Z)))->((apart_point_and_line (intersection_point zenon_TX_q Y) Z)->(apart_point_and_line (intersection_point Z Y) zenon_TX_q))))) zenon_H1d); [ zenon_intro zenon_H1e; idtac ]. % 0.77/0.96 elim zenon_H1e. zenon_intro zenon_TY_p. zenon_intro zenon_H1f. % 0.77/0.96 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_q zenon_TY_p)/\((convergent_lines Z zenon_TY_p)/\(convergent_lines zenon_TX_q Z)))->((apart_point_and_line (intersection_point zenon_TX_q zenon_TY_p) Z)->(apart_point_and_line (intersection_point Z zenon_TY_p) zenon_TX_q)))) zenon_H1f); [ zenon_intro zenon_H20; idtac ]. % 0.77/0.96 elim zenon_H20. zenon_intro zenon_TZ_bh. zenon_intro zenon_H22. % 0.77/0.96 apply (zenon_notimply_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.77/0.96 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.77/0.96 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_He. zenon_intro zenon_H27. % 0.77/0.96 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.77/0.96 generalize (apart2 zenon_TY_p). zenon_intro zenon_H2a. % 0.77/0.96 generalize (ceq2 (intersection_point zenon_TX_q zenon_TY_p)). zenon_intro zenon_H2b. % 0.77/0.96 generalize (apart5 zenon_TX_q). zenon_intro zenon_H2c. % 0.77/0.96 generalize (zenon_H2c zenon_TY_p). zenon_intro zenon_H2d. % 0.77/0.96 generalize (zenon_H2d zenon_TY_p). zenon_intro zenon_H2e. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.77/0.96 generalize (ceq3 zenon_TX_q). zenon_intro zenon_H31. % 0.77/0.96 generalize (zenon_H31 zenon_TY_p). zenon_intro zenon_H32. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H16 | zenon_intro zenon_H33 ]. % 0.77/0.96 exact (zenon_H16 zenon_He). % 0.77/0.96 exact (zenon_H30 zenon_H33). % 0.77/0.96 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H33 | zenon_intro zenon_H34 ]. % 0.77/0.96 generalize (ceq1 (intersection_point zenon_TX_q zenon_TY_p)). zenon_intro zenon_H35. % 0.77/0.96 generalize (zenon_H35 zenon_TZ_bh). zenon_intro zenon_H36. % 0.77/0.96 generalize (zenon_H35 zenon_TX_q). zenon_intro zenon_H37. % 0.77/0.96 generalize (zenon_H37 (intersection_point zenon_TZ_bh zenon_TY_p)). zenon_intro zenon_H38. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H1a | zenon_intro zenon_H39 ]. % 0.77/0.96 generalize (zenon_H2b zenon_TY_p). zenon_intro zenon_H3a. % 0.77/0.96 generalize (zenon_H3a zenon_TY_p). zenon_intro zenon_H3b. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H19 | zenon_intro zenon_H3c ]. % 0.77/0.96 generalize (apart1 (intersection_point zenon_TZ_bh zenon_TY_p)). zenon_intro zenon_H3d. % 0.77/0.96 generalize (con2 zenon_TZ_bh). zenon_intro zenon_H3e. % 0.77/0.96 generalize (zenon_H3e zenon_TY_p). zenon_intro zenon_H3f. % 0.77/0.96 generalize (zenon_H3f (intersection_point zenon_TZ_bh zenon_TY_p)). zenon_intro zenon_H40. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.77/0.96 exact (zenon_H42 zenon_H29). % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.77/0.96 apply (zenon_notor_s _ _ zenon_H44). zenon_intro zenon_H46. zenon_intro zenon_H45. % 0.77/0.96 generalize (zenon_H36 (intersection_point zenon_TZ_bh zenon_TY_p)). zenon_intro zenon_H47. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.77/0.96 exact (zenon_H49 zenon_H26). % 0.77/0.96 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 0.77/0.96 generalize (cu1 (intersection_point zenon_TX_q zenon_TY_p)). zenon_intro zenon_H4c. % 0.77/0.96 generalize (zenon_H4c (intersection_point zenon_TZ_bh zenon_TY_p)). zenon_intro zenon_H4d. % 0.77/0.96 generalize (zenon_H4d zenon_TX_q). zenon_intro zenon_H4e. % 0.77/0.96 generalize (zenon_H4e zenon_TY_p). zenon_intro zenon_H4f. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.77/0.96 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H30 ]. % 0.77/0.96 exact (zenon_H52 zenon_H4b). % 0.77/0.96 exact (zenon_H30 zenon_H33). % 0.77/0.96 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H1b | zenon_intro zenon_H53 ]. % 0.77/0.96 exact (zenon_H1a zenon_H1b). % 0.77/0.96 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_Hd | zenon_intro zenon_H54 ]. % 0.77/0.96 exact (zenon_H19 zenon_Hd). % 0.77/0.96 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.77/0.96 exact (zenon_H25 zenon_H56). % 0.77/0.96 exact (zenon_H45 zenon_H55). % 0.77/0.96 exact (zenon_H46 zenon_H4a). % 0.77/0.96 exact (zenon_H3d zenon_H43). % 0.77/0.96 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H34 | zenon_intro zenon_Hd ]. % 0.77/0.96 exact (zenon_H2a zenon_H34). % 0.77/0.96 apply (zenon_L1_ zenon_TY_p zenon_TX_q); trivial. % 0.77/0.96 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H4b | zenon_intro zenon_H56 ]. % 0.77/0.96 generalize (con2 zenon_TZ_bh). zenon_intro zenon_H3e. % 0.77/0.96 generalize (zenon_H3e zenon_TY_p). zenon_intro zenon_H3f. % 0.77/0.96 generalize (apart1 (intersection_point zenon_TZ_bh zenon_TY_p)). zenon_intro zenon_H3d. % 0.77/0.96 generalize (zenon_H3f (intersection_point zenon_TZ_bh zenon_TY_p)). zenon_intro zenon_H40. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.77/0.96 exact (zenon_H42 zenon_H29). % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.77/0.96 apply (zenon_notor_s _ _ zenon_H44). zenon_intro zenon_H46. zenon_intro zenon_H45. % 0.77/0.96 generalize (cu1 (intersection_point zenon_TX_q zenon_TY_p)). zenon_intro zenon_H4c. % 0.77/0.96 generalize (zenon_H4c (intersection_point zenon_TZ_bh zenon_TY_p)). zenon_intro zenon_H4d. % 0.77/0.96 generalize (zenon_H4d zenon_TX_q). zenon_intro zenon_H4e. % 0.77/0.96 generalize (zenon_H4e zenon_TY_p). zenon_intro zenon_H4f. % 0.77/0.96 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.77/0.96 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H30 ]. % 0.77/0.96 exact (zenon_H52 zenon_H4b). % 0.77/0.96 exact (zenon_H30 zenon_H33). % 0.77/0.96 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H1b | zenon_intro zenon_H53 ]. % 0.77/0.96 apply (zenon_L2_ zenon_TY_p zenon_TX_q); trivial. % 0.77/0.96 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_Hd | zenon_intro zenon_H54 ]. % 0.77/0.96 apply (zenon_L1_ zenon_TY_p zenon_TX_q); trivial. % 0.77/0.96 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.77/0.96 exact (zenon_H25 zenon_H56). % 0.77/0.96 exact (zenon_H45 zenon_H55). % 0.77/0.96 exact (zenon_H3d zenon_H43). % 0.77/0.96 exact (zenon_H25 zenon_H56). % 0.77/0.96 exact (zenon_H2a zenon_H34). % 0.77/0.96 Qed. % 0.77/0.96 % SZS output end Proof % 0.77/0.96 (* END-PROOF *) % 0.77/0.96 nodes searched: 34958 % 0.77/0.96 max branch formulas: 2810 % 0.77/0.96 proof nodes created: 1369 % 0.77/0.96 formulas created: 70630 % 0.77/0.96 %------------------------------------------------------------------------------