%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO175+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 07:00:23 EDT 2022 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO175+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n006.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 01:23:55 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.50 (* PROOF-FOUND *) % 0.19/0.50 % SZS status Theorem % 0.19/0.50 (* BEGIN-PROOF *) % 0.19/0.50 % SZS output start Proof % 0.19/0.50 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\(distinct_points X (intersection_point U V))))->((apart_point_and_line X U)\/(apart_point_and_line X V))))))). % 0.19/0.50 Proof. % 0.19/0.50 assert (zenon_L1_ : forall (zenon_TV_s : zenon_U) (zenon_TU_t : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TU_t Y)->(~(apart_point_and_line (intersection_point zenon_TU_t Y) zenon_TU_t)))) -> (convergent_lines zenon_TU_t zenon_TV_s) -> (apart_point_and_line (intersection_point zenon_TU_t zenon_TV_s) zenon_TU_t) -> False). % 0.19/0.50 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11. % 0.19/0.50 generalize (zenon_Hf zenon_TV_s). zenon_intro zenon_H14. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.19/0.50 exact (zenon_H16 zenon_H10). % 0.19/0.50 exact (zenon_H15 zenon_H11). % 0.19/0.50 (* end of lemma zenon_L1_ *) % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\(distinct_points X (intersection_point U V))))->((apart_point_and_line X U)\/(apart_point_and_line X V))))))) zenon_G); [ zenon_intro zenon_H17; idtac ]. % 0.19/0.50 elim zenon_H17. zenon_intro zenon_TX_y. zenon_intro zenon_H19. % 0.19/0.50 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_y Y)/\((convergent_lines U V)/\(distinct_points zenon_TX_y (intersection_point U V))))->((apart_point_and_line zenon_TX_y U)\/(apart_point_and_line zenon_TX_y V)))))) zenon_H19); [ zenon_intro zenon_H1a; idtac ]. % 0.19/0.50 elim zenon_H1a. zenon_intro zenon_TY_bb. zenon_intro zenon_H1c. % 0.19/0.50 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_y zenon_TY_bb)/\((convergent_lines U V)/\(distinct_points zenon_TX_y (intersection_point U V))))->((apart_point_and_line zenon_TX_y U)\/(apart_point_and_line zenon_TX_y V))))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ]. % 0.19/0.50 elim zenon_H1d. zenon_intro zenon_TU_t. zenon_intro zenon_H1e. % 0.19/0.50 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_y zenon_TY_bb)/\((convergent_lines zenon_TU_t V)/\(distinct_points zenon_TX_y (intersection_point zenon_TU_t V))))->((apart_point_and_line zenon_TX_y zenon_TU_t)\/(apart_point_and_line zenon_TX_y V)))) zenon_H1e); [ zenon_intro zenon_H1f; idtac ]. % 0.19/0.50 elim zenon_H1f. zenon_intro zenon_TV_s. zenon_intro zenon_H20. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.19/0.50 apply (zenon_notor_s _ _ zenon_H21). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H10. zenon_intro zenon_H27. % 0.19/0.50 generalize (ceq3 zenon_TU_t). zenon_intro zenon_H28. % 0.19/0.50 generalize (zenon_H28 zenon_TV_s). zenon_intro zenon_H29. % 0.19/0.50 generalize (cu1 zenon_TX_y). zenon_intro zenon_H2a. % 0.19/0.50 generalize (zenon_H2a (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H2b. % 0.19/0.50 generalize (zenon_H29 zenon_TU_t). zenon_intro zenon_H2c. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H16 | zenon_intro zenon_H2d ]. % 0.19/0.50 exact (zenon_H16 zenon_H10). % 0.19/0.50 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.19/0.50 generalize (ci3 zenon_TU_t). zenon_intro zenon_Hf. % 0.19/0.50 generalize (zenon_H2b zenon_TV_s). zenon_intro zenon_H30. % 0.19/0.50 generalize (zenon_H30 zenon_TU_t). zenon_intro zenon_H31. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.19/0.50 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.19/0.50 exact (zenon_H35 zenon_H27). % 0.19/0.50 exact (zenon_H34 zenon_H2f). % 0.19/0.50 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.19/0.50 exact (zenon_H23 zenon_H37). % 0.19/0.50 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 0.19/0.50 exact (zenon_H24 zenon_H39). % 0.19/0.50 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H11 ]. % 0.19/0.50 generalize (ci4 zenon_TU_t). zenon_intro zenon_H3b. % 0.19/0.50 generalize (zenon_H3b zenon_TV_s). zenon_intro zenon_H3c. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H16 | zenon_intro zenon_H3d ]. % 0.19/0.50 exact (zenon_H16 zenon_H10). % 0.19/0.50 exact (zenon_H3d zenon_H3a). % 0.19/0.50 apply (zenon_L1_ zenon_TV_s zenon_TU_t); trivial. % 0.19/0.50 generalize (apart3 zenon_TU_t). zenon_intro zenon_H3e. % 0.19/0.50 exact (zenon_H3e zenon_H2e). % 0.19/0.50 Qed. % 0.19/0.50 % SZS output end Proof % 0.19/0.50 (* END-PROOF *) % 0.19/0.50 nodes searched: 479 % 0.19/0.50 max branch formulas: 340 % 0.19/0.50 proof nodes created: 67 % 0.19/0.50 formulas created: 2594 % 0.19/0.50 %------------------------------------------------------------------------------