%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO188+2 : 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 07:00:33 EDT 2022 % Result : Theorem 0.21s 0.58s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n029.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 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Sat Jun 18 14:12:44 EDT 2022 % 0.14/0.36 % CPUTime : % 0.21/0.58 (* PROOF-FOUND *) % 0.21/0.58 % SZS status Theorem % 0.21/0.58 (* BEGIN-PROOF *) % 0.21/0.58 % SZS output start Proof % 0.21/0.58 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 X (line_connecting Z Y))))))). % 0.21/0.58 Proof. % 0.21/0.58 assert (zenon_L1_ : forall (zenon_TZ_r : zenon_U) (zenon_TY_s : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TY_s zenon_TZ_r)->((distinct_points zenon_TY_s Z)\/(distinct_points zenon_TZ_r Z)))) -> (distinct_points zenon_TY_s zenon_TZ_r) -> (~(distinct_points zenon_TY_s zenon_TY_s)) -> (~(distinct_points zenon_TZ_r zenon_TY_s)) -> False). % 0.21/0.58 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10. % 0.21/0.58 generalize (zenon_Hd zenon_TY_s). zenon_intro zenon_H13. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 0.21/0.58 exact (zenon_H15 zenon_He). % 0.21/0.58 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.21/0.58 exact (zenon_Hf zenon_H17). % 0.21/0.58 exact (zenon_H10 zenon_H16). % 0.21/0.58 (* end of lemma zenon_L1_ *) % 0.21/0.58 apply NNPP. intro zenon_G. % 0.21/0.58 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 X (line_connecting Z Y))))))) zenon_G); [ zenon_intro zenon_H18; idtac ]. % 0.21/0.58 elim zenon_H18. zenon_intro zenon_TX_z. zenon_intro zenon_H1a. % 0.21/0.58 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_z Y)/\((distinct_points zenon_TX_z Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting zenon_TX_z Y))))))->(~(apart_point_and_line zenon_TX_z (line_connecting Z Y)))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.21/0.58 elim zenon_H1b. zenon_intro zenon_TY_s. zenon_intro zenon_H1c. % 0.21/0.58 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_z zenon_TY_s)/\((distinct_points zenon_TX_z Z)/\((distinct_points zenon_TY_s Z)/\(~(apart_point_and_line Z (line_connecting zenon_TX_z zenon_TY_s))))))->(~(apart_point_and_line zenon_TX_z (line_connecting Z zenon_TY_s))))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ]. % 0.21/0.58 elim zenon_H1d. zenon_intro zenon_TZ_r. zenon_intro zenon_H1e. % 0.21/0.58 apply (zenon_notimply_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H1f. % 0.21/0.58 apply zenon_H1f. zenon_intro zenon_H21. % 0.21/0.58 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.21/0.58 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.21/0.58 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_He. zenon_intro zenon_H26. % 0.21/0.58 generalize (apart1 zenon_TZ_r). zenon_intro zenon_H27. % 0.21/0.58 generalize (apart1 zenon_TY_s). zenon_intro zenon_Hf. % 0.21/0.58 generalize (con1 zenon_TZ_r). zenon_intro zenon_H28. % 0.21/0.58 generalize (apart4 zenon_TY_s). zenon_intro zenon_H29. % 0.21/0.58 generalize (cu1 zenon_TY_s). zenon_intro zenon_H2a. % 0.21/0.58 generalize (ceq2 zenon_TX_z). zenon_intro zenon_H2b. % 0.21/0.58 generalize (zenon_H28 zenon_TY_s). zenon_intro zenon_H2c. % 0.21/0.58 generalize (zenon_H2a zenon_TZ_r). zenon_intro zenon_H2d. % 0.21/0.58 generalize (con1 zenon_TX_z). zenon_intro zenon_H2e. % 0.21/0.58 generalize (zenon_H29 zenon_TZ_r). zenon_intro zenon_Hd. % 0.21/0.58 generalize (zenon_H2c zenon_TY_s). zenon_intro zenon_H2f. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H10 | zenon_intro zenon_H30 ]. % 0.21/0.58 apply (zenon_L1_ zenon_TZ_r zenon_TY_s); trivial. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.21/0.58 generalize (apart1 zenon_TX_z). zenon_intro zenon_H33. % 0.21/0.58 generalize (zenon_H2c zenon_TZ_r). zenon_intro zenon_H34. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H10 | zenon_intro zenon_H35 ]. % 0.21/0.58 apply (zenon_L1_ zenon_TZ_r zenon_TY_s); trivial. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.21/0.58 generalize (zenon_H2e zenon_TY_s). zenon_intro zenon_H38. % 0.21/0.58 generalize (zenon_H38 zenon_TX_z). zenon_intro zenon_H39. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.21/0.58 exact (zenon_H3b zenon_H23). % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 0.21/0.58 generalize (zenon_H38 zenon_TY_s). zenon_intro zenon_H3e. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H3b | zenon_intro zenon_H3f ]. % 0.21/0.58 exact (zenon_H3b zenon_H23). % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 0.21/0.58 generalize (zenon_H2b (line_connecting zenon_TZ_r zenon_TY_s)). zenon_intro zenon_H42. % 0.21/0.58 generalize (zenon_H42 (line_connecting zenon_TX_z zenon_TY_s)). zenon_intro zenon_H43. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.21/0.58 exact (zenon_H45 zenon_H21). % 0.21/0.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.21/0.58 generalize (zenon_H2d (line_connecting zenon_TZ_r zenon_TY_s)). zenon_intro zenon_H48. % 0.21/0.58 generalize (zenon_H48 (line_connecting zenon_TX_z zenon_TY_s)). zenon_intro zenon_H49. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 0.21/0.58 apply (zenon_notand_s _ _ zenon_H4b); [ zenon_intro zenon_H15 | zenon_intro zenon_H4c ]. % 0.21/0.58 exact (zenon_H15 zenon_He). % 0.21/0.58 exact (zenon_H4c zenon_H47). % 0.21/0.58 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.21/0.58 exact (zenon_H32 zenon_H4e). % 0.21/0.58 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ]. % 0.21/0.58 exact (zenon_H41 zenon_H50). % 0.21/0.58 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 0.21/0.58 exact (zenon_H37 zenon_H52). % 0.21/0.58 exact (zenon_H26 zenon_H51). % 0.21/0.58 exact (zenon_H3d zenon_H46). % 0.21/0.58 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H53. zenon_intro zenon_H17. % 0.21/0.58 exact (zenon_Hf zenon_H17). % 0.21/0.58 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H54. zenon_intro zenon_H23. % 0.21/0.58 exact (zenon_H33 zenon_H54). % 0.21/0.58 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H55. zenon_intro zenon_H16. % 0.21/0.58 exact (zenon_H27 zenon_H55). % 0.21/0.58 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_He. zenon_intro zenon_H17. % 0.21/0.58 exact (zenon_Hf zenon_H17). % 0.21/0.58 Qed. % 0.21/0.58 % SZS output end Proof % 0.21/0.58 (* END-PROOF *) % 0.21/0.58 nodes searched: 2166 % 0.21/0.58 max branch formulas: 793 % 0.21/0.58 proof nodes created: 248 % 0.21/0.58 formulas created: 7130 % 0.21/0.58 %------------------------------------------------------------------------------