%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO204+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 07:00:47 EDT 2022 % Result : Theorem 0.37s 0.54s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO204+2 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n025.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 : Sat Jun 18 05:39:43 EDT 2022 % 0.12/0.34 % CPUTime : % 0.37/0.54 (* PROOF-FOUND *) % 0.37/0.54 % SZS status Theorem % 0.37/0.54 (* BEGIN-PROOF *) % 0.37/0.54 % SZS output start Proof % 0.37/0.54 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\(~(distinct_points Y Z)))->((distinct_points X Z)/\(~(distinct_lines (line_connecting X Y) (line_connecting X Z)))))))). % 0.37/0.54 Proof. % 0.37/0.54 assert (zenon_L1_ : forall (zenon_TZ_r : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TX_t zenon_TY_s)->((distinct_points zenon_TX_t Z)\/(distinct_points zenon_TY_s Z)))) -> (distinct_points zenon_TX_t zenon_TY_s) -> (~(distinct_points zenon_TX_t zenon_TZ_r)) -> (~(distinct_points zenon_TY_s zenon_TZ_r)) -> False). % 0.37/0.54 do 3 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10. % 0.37/0.54 generalize (zenon_Hd zenon_TZ_r). zenon_intro zenon_H14. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.37/0.54 exact (zenon_H16 zenon_He). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.37/0.54 exact (zenon_Hf zenon_H18). % 0.37/0.54 exact (zenon_H10 zenon_H17). % 0.37/0.54 (* end of lemma zenon_L1_ *) % 0.37/0.54 apply NNPP. intro zenon_G. % 0.37/0.54 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\(~(distinct_points Y Z)))->((distinct_points X Z)/\(~(distinct_lines (line_connecting X Y) (line_connecting X Z)))))))) zenon_G); [ zenon_intro zenon_H19; idtac ]. % 0.37/0.54 elim zenon_H19. zenon_intro zenon_TX_t. zenon_intro zenon_H1a. % 0.37/0.54 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_t Y)/\(~(distinct_points Y Z)))->((distinct_points zenon_TX_t Z)/\(~(distinct_lines (line_connecting zenon_TX_t Y) (line_connecting zenon_TX_t Z))))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.37/0.54 elim zenon_H1b. zenon_intro zenon_TY_s. zenon_intro zenon_H1c. % 0.37/0.54 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_t zenon_TY_s)/\(~(distinct_points zenon_TY_s Z)))->((distinct_points zenon_TX_t Z)/\(~(distinct_lines (line_connecting zenon_TX_t zenon_TY_s) (line_connecting zenon_TX_t Z)))))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ]. % 0.37/0.54 elim zenon_H1d. zenon_intro zenon_TZ_r. zenon_intro zenon_H1e. % 0.37/0.54 apply (zenon_notimply_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H1f. % 0.37/0.54 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_He. zenon_intro zenon_H10. % 0.37/0.54 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_Hf | zenon_intro zenon_H21 ]. % 0.37/0.54 generalize (apart4 zenon_TX_t). zenon_intro zenon_H22. % 0.37/0.54 generalize (zenon_H22 zenon_TY_s). zenon_intro zenon_Hd. % 0.37/0.54 apply (zenon_L1_ zenon_TZ_r zenon_TY_s zenon_TX_t); trivial. % 0.37/0.54 apply zenon_H21. zenon_intro zenon_H23. % 0.37/0.54 generalize (apart1 zenon_TY_s). zenon_intro zenon_H24. % 0.37/0.54 generalize (cu1 zenon_TX_t). zenon_intro zenon_H25. % 0.37/0.54 generalize (apart4 zenon_TX_t). zenon_intro zenon_H22. % 0.37/0.54 generalize (apart1 zenon_TZ_r). zenon_intro zenon_H26. % 0.37/0.54 generalize (zenon_H25 zenon_TY_s). zenon_intro zenon_H27. % 0.37/0.54 generalize (zenon_H22 zenon_TZ_r). zenon_intro zenon_H28. % 0.37/0.54 generalize (zenon_H22 zenon_TY_s). zenon_intro zenon_Hd. % 0.37/0.54 generalize (zenon_H28 zenon_TZ_r). zenon_intro zenon_H29. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_Hf | zenon_intro zenon_H2a ]. % 0.37/0.54 apply (zenon_L1_ zenon_TZ_r zenon_TY_s zenon_TX_t); trivial. % 0.37/0.54 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H18 | zenon_intro zenon_H2b ]. % 0.37/0.54 generalize (con1 zenon_TX_t). zenon_intro zenon_H2c. % 0.37/0.54 generalize (apart1 zenon_TX_t). zenon_intro zenon_H2d. % 0.37/0.54 generalize (zenon_H2c zenon_TY_s). zenon_intro zenon_H2e. % 0.37/0.54 generalize (zenon_H2c zenon_TZ_r). zenon_intro zenon_H2f. % 0.37/0.54 generalize (zenon_H2e zenon_TX_t). zenon_intro zenon_H30. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H16 | zenon_intro zenon_H31 ]. % 0.37/0.54 exact (zenon_H16 zenon_He). % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.37/0.54 generalize (zenon_H2e zenon_TY_s). zenon_intro zenon_H34. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H16 | zenon_intro zenon_H35 ]. % 0.37/0.54 exact (zenon_H16 zenon_He). % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.37/0.54 generalize (zenon_H2f zenon_TY_s). zenon_intro zenon_H38. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_Hf | zenon_intro zenon_H39 ]. % 0.37/0.54 exact (zenon_Hf zenon_H18). % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.37/0.54 generalize (zenon_H2f zenon_TX_t). zenon_intro zenon_H3c. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_Hf | zenon_intro zenon_H3d ]. % 0.37/0.54 exact (zenon_Hf zenon_H18). % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 0.37/0.54 generalize (zenon_H27 (line_connecting zenon_TX_t zenon_TY_s)). zenon_intro zenon_H40. % 0.37/0.54 generalize (zenon_H40 (line_connecting zenon_TX_t zenon_TZ_r)). zenon_intro zenon_H41. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.37/0.54 apply (zenon_notand_s _ _ zenon_H43); [ zenon_intro zenon_H16 | zenon_intro zenon_H44 ]. % 0.37/0.54 exact (zenon_H16 zenon_He). % 0.37/0.54 exact (zenon_H44 zenon_H23). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.37/0.54 exact (zenon_H33 zenon_H46). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 0.37/0.54 exact (zenon_H3f zenon_H48). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H47); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.37/0.54 exact (zenon_H37 zenon_H4a). % 0.37/0.54 exact (zenon_H3b zenon_H49). % 0.37/0.54 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H4b. zenon_intro zenon_H18. % 0.37/0.54 exact (zenon_H2d zenon_H4b). % 0.37/0.54 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H4c. zenon_intro zenon_H17. % 0.37/0.54 exact (zenon_H10 zenon_H17). % 0.37/0.54 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H4c. zenon_intro zenon_H4d. % 0.37/0.54 exact (zenon_H24 zenon_H4d). % 0.37/0.54 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H4b. zenon_intro zenon_He. % 0.37/0.54 exact (zenon_H2d zenon_H4b). % 0.37/0.54 exact (zenon_H26 zenon_H2b). % 0.37/0.54 Qed. % 0.37/0.54 % SZS output end Proof % 0.37/0.54 (* END-PROOF *) % 0.37/0.54 nodes searched: 1562 % 0.37/0.54 max branch formulas: 497 % 0.37/0.54 proof nodes created: 216 % 0.37/0.54 formulas created: 4826 % 0.37/0.54 %------------------------------------------------------------------------------