%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 0.89s 1.06s % Output : Proof 0.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n022.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 16:02:17 EDT 2022 % 0.12/0.33 % CPUTime : % 0.89/1.06 (* PROOF-FOUND *) % 0.89/1.06 % SZS status Theorem % 0.89/1.06 (* BEGIN-PROOF *) % 0.89/1.06 % SZS output start Proof % 0.89/1.06 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines X Y)->((apart_point_and_line (intersection_point X Y) Z)->((distinct_lines X Z)/\(distinct_lines Y Z))))))). % 0.89/1.06 Proof. % 0.89/1.06 assert (zenon_L1_ : forall (zenon_TZ_o : zenon_U), (distinct_lines zenon_TZ_o zenon_TZ_o) -> False). % 0.89/1.06 do 1 intro. intros zenon_Hd. % 0.89/1.06 generalize (apart2 zenon_TZ_o). zenon_intro zenon_Hf. % 0.89/1.06 exact (zenon_Hf zenon_Hd). % 0.89/1.06 (* end of lemma zenon_L1_ *) % 0.89/1.06 assert (zenon_L2_ : forall (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (apart_point_and_line (intersection_point zenon_TX_t zenon_TY_s) zenon_TY_s) -> (convergent_lines zenon_TX_t zenon_TY_s) -> False). % 0.89/1.06 do 2 intro. intros zenon_H10 zenon_H11. % 0.89/1.06 generalize (con2 zenon_TX_t). zenon_intro zenon_H14. % 0.89/1.06 generalize (zenon_H14 zenon_TY_s). zenon_intro zenon_H15. % 0.89/1.06 generalize (apart1 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H16. % 0.89/1.06 generalize (zenon_H15 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H17. % 0.89/1.06 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.89/1.06 exact (zenon_H19 zenon_H11). % 0.89/1.06 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.89/1.06 apply (zenon_notor_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.89/1.06 exact (zenon_H1c zenon_H10). % 0.89/1.06 exact (zenon_H16 zenon_H1a). % 0.89/1.06 (* end of lemma zenon_L2_ *) % 0.89/1.06 apply NNPP. intro zenon_G. % 0.89/1.06 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines X Y)->((apart_point_and_line (intersection_point X Y) Z)->((distinct_lines X Z)/\(distinct_lines Y Z))))))) zenon_G); [ zenon_intro zenon_H1e; idtac ]. % 0.89/1.06 elim zenon_H1e. zenon_intro zenon_TX_t. zenon_intro zenon_H1f. % 0.89/1.06 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((convergent_lines zenon_TX_t Y)->((apart_point_and_line (intersection_point zenon_TX_t Y) Z)->((distinct_lines zenon_TX_t Z)/\(distinct_lines Y Z)))))) zenon_H1f); [ zenon_intro zenon_H20; idtac ]. % 0.89/1.06 elim zenon_H20. zenon_intro zenon_TY_s. zenon_intro zenon_H21. % 0.89/1.06 apply (zenon_notallex_s (fun Z : zenon_U => ((convergent_lines zenon_TX_t zenon_TY_s)->((apart_point_and_line (intersection_point zenon_TX_t zenon_TY_s) Z)->((distinct_lines zenon_TX_t Z)/\(distinct_lines zenon_TY_s Z))))) zenon_H21); [ zenon_intro zenon_H22; idtac ]. % 0.89/1.06 elim zenon_H22. zenon_intro zenon_TZ_o. zenon_intro zenon_H23. % 0.89/1.06 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H11. zenon_intro zenon_H24. % 0.89/1.06 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.89/1.06 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.89/1.06 generalize (ceq2 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H29. % 0.89/1.06 generalize (zenon_H29 zenon_TZ_o). zenon_intro zenon_H2a. % 0.89/1.06 generalize (apart5 zenon_TZ_o). zenon_intro zenon_H2b. % 0.89/1.06 generalize (zenon_H2a zenon_TX_t). zenon_intro zenon_H2c. % 0.89/1.06 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.89/1.06 exact (zenon_H2e zenon_H26). % 0.89/1.06 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.89/1.06 generalize (zenon_H2b zenon_TX_t). zenon_intro zenon_H31. % 0.89/1.06 generalize (zenon_H31 zenon_TZ_o). zenon_intro zenon_H32. % 0.89/1.06 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.89/1.06 exact (zenon_H34 zenon_H30). % 0.89/1.06 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_Hd | zenon_intro zenon_H35 ]. % 0.89/1.06 apply (zenon_L1_ zenon_TZ_o); trivial. % 0.89/1.06 exact (zenon_H28 zenon_H35). % 0.89/1.06 generalize (con2 zenon_TX_t). zenon_intro zenon_H14. % 0.89/1.06 generalize (zenon_H14 zenon_TY_s). zenon_intro zenon_H15. % 0.89/1.06 generalize (apart1 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H16. % 0.89/1.06 generalize (zenon_H15 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H17. % 0.89/1.06 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.89/1.06 exact (zenon_H19 zenon_H11). % 0.89/1.06 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.89/1.06 apply (zenon_notor_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.89/1.06 exact (zenon_H1d zenon_H2f). % 0.89/1.06 exact (zenon_H16 zenon_H1a). % 0.89/1.06 generalize (ceq2 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H29. % 0.89/1.06 generalize (zenon_H29 zenon_TZ_o). zenon_intro zenon_H2a. % 0.89/1.06 generalize (zenon_H2a zenon_TY_s). zenon_intro zenon_H36. % 0.89/1.06 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H2e | zenon_intro zenon_H37 ]. % 0.89/1.06 exact (zenon_H2e zenon_H26). % 0.89/1.06 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_H10 ]. % 0.89/1.06 generalize (apart5 zenon_TZ_o). zenon_intro zenon_H2b. % 0.89/1.06 generalize (zenon_H2b zenon_TY_s). zenon_intro zenon_H39. % 0.89/1.06 generalize (zenon_H39 zenon_TZ_o). zenon_intro zenon_H3a. % 0.89/1.06 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.89/1.06 exact (zenon_H3c zenon_H38). % 0.89/1.06 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_Hd | zenon_intro zenon_H3d ]. % 0.89/1.06 apply (zenon_L1_ zenon_TZ_o); trivial. % 0.89/1.06 exact (zenon_H27 zenon_H3d). % 0.89/1.06 apply (zenon_L2_ zenon_TY_s zenon_TX_t); trivial. % 0.89/1.06 Qed. % 0.89/1.06 % SZS output end Proof % 0.89/1.06 (* END-PROOF *) % 0.89/1.06 nodes searched: 76102 % 0.89/1.06 max branch formulas: 3644 % 0.89/1.06 proof nodes created: 1200 % 0.89/1.06 formulas created: 89240 % 0.89/1.06 %------------------------------------------------------------------------------