%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO190+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 07:00:35 EDT 2022 % Result : Theorem 0.38s 0.56s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO190+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n018.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 06:54:18 EDT 2022 % 0.13/0.33 % CPUTime : % 0.38/0.56 (* PROOF-FOUND *) % 0.38/0.56 % SZS status Theorem % 0.38/0.56 (* BEGIN-PROOF *) % 0.38/0.56 % SZS output start Proof % 0.38/0.56 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting X Y))))))->(~(apart_point_and_line Z (line_connecting Y X))))))). % 0.38/0.56 Proof. % 0.38/0.56 assert (zenon_L1_ : forall (zenon_TX_p : zenon_U) (zenon_TY_q : zenon_U), ((distinct_points zenon_TY_q zenon_TX_p)/\(distinct_points zenon_TY_q zenon_TY_q)) -> (~(distinct_points zenon_TY_q zenon_TY_q)) -> False). % 0.38/0.56 do 2 intro. intros zenon_Hd zenon_He. % 0.38/0.56 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.38/0.56 exact (zenon_He zenon_H11). % 0.38/0.56 (* end of lemma zenon_L1_ *) % 0.38/0.56 assert (zenon_L2_ : forall (zenon_TY_q : zenon_U) (zenon_TX_p : zenon_U), ((distinct_points zenon_TX_p zenon_TX_p)/\(distinct_points zenon_TX_p zenon_TY_q)) -> (~(distinct_points zenon_TX_p zenon_TX_p)) -> False). % 0.38/0.56 do 2 intro. intros zenon_H13 zenon_H14. % 0.38/0.56 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.38/0.56 exact (zenon_H14 zenon_H16). % 0.38/0.56 (* end of lemma zenon_L2_ *) % 0.38/0.56 apply NNPP. intro zenon_G. % 0.38/0.56 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting X Y))))))->(~(apart_point_and_line Z (line_connecting Y X))))))) zenon_G); [ zenon_intro zenon_H17; idtac ]. % 0.38/0.56 elim zenon_H17. zenon_intro zenon_TX_p. zenon_intro zenon_H18. % 0.38/0.56 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_p Y)/\((distinct_points zenon_TX_p Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting zenon_TX_p Y))))))->(~(apart_point_and_line Z (line_connecting Y zenon_TX_p)))))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.38/0.56 elim zenon_H19. zenon_intro zenon_TY_q. zenon_intro zenon_H1a. % 0.38/0.56 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_p zenon_TY_q)/\((distinct_points zenon_TX_p Z)/\((distinct_points zenon_TY_q Z)/\(~(apart_point_and_line Z (line_connecting zenon_TX_p zenon_TY_q))))))->(~(apart_point_and_line Z (line_connecting zenon_TY_q zenon_TX_p))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.38/0.56 elim zenon_H1b. zenon_intro zenon_TZ_bc. zenon_intro zenon_H1d. % 0.38/0.56 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.38/0.56 apply zenon_H1e. zenon_intro zenon_H20. % 0.38/0.56 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H15. zenon_intro zenon_H21. % 0.38/0.56 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.38/0.56 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.38/0.56 generalize (apart4 zenon_TX_p). zenon_intro zenon_H26. % 0.38/0.56 generalize (cu1 zenon_TX_p). zenon_intro zenon_H27. % 0.38/0.56 generalize (apart1 zenon_TY_q). zenon_intro zenon_He. % 0.38/0.56 generalize (apart4 zenon_TY_q). zenon_intro zenon_H28. % 0.38/0.56 generalize (zenon_H27 zenon_TY_q). zenon_intro zenon_H29. % 0.38/0.56 generalize (con1 zenon_TY_q). zenon_intro zenon_H2a. % 0.38/0.56 generalize (ceq2 zenon_TZ_bc). zenon_intro zenon_H2b. % 0.38/0.56 generalize (zenon_H26 zenon_TY_q). zenon_intro zenon_H2c. % 0.38/0.56 generalize (con1 zenon_TX_p). zenon_intro zenon_H2d. % 0.38/0.56 generalize (apart1 zenon_TX_p). zenon_intro zenon_H14. % 0.38/0.56 generalize (zenon_H28 zenon_TX_p). zenon_intro zenon_H2e. % 0.38/0.56 generalize (zenon_H2d zenon_TY_q). zenon_intro zenon_H2f. % 0.38/0.56 generalize (zenon_H2a zenon_TX_p). zenon_intro zenon_H30. % 0.38/0.56 generalize (zenon_H2e zenon_TX_p). zenon_intro zenon_H31. % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.38/0.56 generalize (zenon_H2c zenon_TX_p). zenon_intro zenon_H34. % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.38/0.56 exact (zenon_H36 zenon_H15). % 0.38/0.56 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H16 | zenon_intro zenon_H12 ]. % 0.38/0.56 exact (zenon_H14 zenon_H16). % 0.38/0.56 exact (zenon_H33 zenon_H12). % 0.38/0.56 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H12 | zenon_intro zenon_H16 ]. % 0.38/0.56 generalize (zenon_H30 zenon_TY_q). zenon_intro zenon_H37. % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H33 | zenon_intro zenon_H38 ]. % 0.38/0.56 exact (zenon_H33 zenon_H12). % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.38/0.56 generalize (zenon_H2f zenon_TX_p). zenon_intro zenon_H3b. % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H36 | zenon_intro zenon_H3c ]. % 0.38/0.56 exact (zenon_H36 zenon_H15). % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3d | zenon_intro zenon_H13 ]. % 0.38/0.56 generalize (zenon_H30 zenon_TX_p). zenon_intro zenon_H3e. % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H33 | zenon_intro zenon_H3f ]. % 0.38/0.56 exact (zenon_H33 zenon_H12). % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 0.38/0.56 generalize (zenon_H2f zenon_TY_q). zenon_intro zenon_H42. % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H36 | zenon_intro zenon_H43 ]. % 0.38/0.56 exact (zenon_H36 zenon_H15). % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H44 | zenon_intro zenon_Hd ]. % 0.38/0.56 generalize (zenon_H2b (line_connecting zenon_TY_q zenon_TX_p)). zenon_intro zenon_H45. % 0.38/0.56 generalize (zenon_H45 (line_connecting zenon_TX_p zenon_TY_q)). zenon_intro zenon_H46. % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 0.38/0.56 exact (zenon_H48 zenon_H20). % 0.38/0.56 apply (zenon_or_s _ _ zenon_H47); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.38/0.56 generalize (zenon_H29 (line_connecting zenon_TY_q zenon_TX_p)). zenon_intro zenon_H4b. % 0.38/0.56 generalize (zenon_H4b (line_connecting zenon_TX_p zenon_TY_q)). zenon_intro zenon_H4c. % 0.38/0.56 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.38/0.56 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H36 | zenon_intro zenon_H4f ]. % 0.38/0.56 exact (zenon_H36 zenon_H15). % 0.38/0.56 exact (zenon_H4f zenon_H4a). % 0.38/0.56 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.38/0.56 exact (zenon_H41 zenon_H51). % 0.38/0.56 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.38/0.56 exact (zenon_H3d zenon_H53). % 0.38/0.56 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.38/0.56 exact (zenon_H3a zenon_H55). % 0.38/0.56 exact (zenon_H44 zenon_H54). % 0.38/0.56 exact (zenon_H24 zenon_H49). % 0.38/0.56 apply (zenon_L1_ zenon_TX_p zenon_TY_q); trivial. % 0.38/0.56 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H15. zenon_intro zenon_H16. % 0.38/0.56 exact (zenon_H14 zenon_H16). % 0.38/0.56 apply (zenon_L2_ zenon_TY_q zenon_TX_p); trivial. % 0.38/0.56 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H11. zenon_intro zenon_H12. % 0.38/0.56 exact (zenon_He zenon_H11). % 0.38/0.56 exact (zenon_H14 zenon_H16). % 0.38/0.56 Qed. % 0.38/0.56 % SZS output end Proof % 0.38/0.56 (* END-PROOF *) % 0.38/0.56 nodes searched: 2390 % 0.38/0.56 max branch formulas: 817 % 0.38/0.56 proof nodes created: 262 % 0.38/0.56 formulas created: 7654 % 0.38/0.56 %------------------------------------------------------------------------------