%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO173+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 07:00:22 EDT 2022 % Result : Theorem 0.20s 0.51s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : GEO173+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n012.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 01:48:23 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.51 (* PROOF-FOUND *) % 0.20/0.51 % SZS status Theorem % 0.20/0.51 (* BEGIN-PROOF *) % 0.20/0.51 % SZS output start Proof % 0.20/0.51 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_lines U (line_connecting X Y))))->((apart_point_and_line X U)\/(apart_point_and_line Y U))))))). % 0.20/0.51 Proof. % 0.20/0.51 assert (zenon_L1_ : forall (zenon_TX_r : zenon_U) (zenon_TY_s : zenon_U), (apart_point_and_line zenon_TY_s (line_connecting zenon_TX_r zenon_TY_s)) -> (distinct_points zenon_TX_r zenon_TY_s) -> False). % 0.20/0.51 do 2 intro. intros zenon_Hf zenon_H10. % 0.20/0.51 generalize (ci2 zenon_TX_r). zenon_intro zenon_H13. % 0.20/0.51 generalize (zenon_H13 zenon_TY_s). zenon_intro zenon_H14. % 0.20/0.51 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.20/0.51 exact (zenon_H16 zenon_H10). % 0.20/0.51 exact (zenon_H15 zenon_Hf). % 0.20/0.51 (* end of lemma zenon_L1_ *) % 0.20/0.51 apply NNPP. intro zenon_G. % 0.20/0.51 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_lines U (line_connecting X Y))))->((apart_point_and_line X U)\/(apart_point_and_line Y U))))))) zenon_G); [ zenon_intro zenon_H17; idtac ]. % 0.20/0.51 elim zenon_H17. zenon_intro zenon_TX_r. zenon_intro zenon_H18. % 0.20/0.51 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_r Y)/\((convergent_lines U V)/\(distinct_lines U (line_connecting zenon_TX_r Y))))->((apart_point_and_line zenon_TX_r U)\/(apart_point_and_line Y U)))))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.20/0.51 elim zenon_H19. zenon_intro zenon_TY_s. zenon_intro zenon_H1a. % 0.20/0.51 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_r zenon_TY_s)/\((convergent_lines U V)/\(distinct_lines U (line_connecting zenon_TX_r zenon_TY_s))))->((apart_point_and_line zenon_TX_r U)\/(apart_point_and_line zenon_TY_s U))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.20/0.51 elim zenon_H1b. zenon_intro zenon_TU_bc. zenon_intro zenon_H1d. % 0.20/0.51 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_r zenon_TY_s)/\((convergent_lines zenon_TU_bc V)/\(distinct_lines zenon_TU_bc (line_connecting zenon_TX_r zenon_TY_s))))->((apart_point_and_line zenon_TX_r zenon_TU_bc)\/(apart_point_and_line zenon_TY_s zenon_TU_bc)))) zenon_H1d); [ zenon_intro zenon_H1e; idtac ]. % 0.20/0.51 elim zenon_H1e. zenon_intro zenon_TV_bf. zenon_intro zenon_H20. % 0.20/0.51 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.20/0.51 apply (zenon_notor_s _ _ zenon_H21). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.20/0.51 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H10. zenon_intro zenon_H25. % 0.20/0.51 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.20/0.51 generalize (cu1 zenon_TX_r). zenon_intro zenon_H28. % 0.20/0.51 generalize (zenon_H28 zenon_TY_s). zenon_intro zenon_H29. % 0.20/0.51 generalize (zenon_H29 zenon_TU_bc). zenon_intro zenon_H2a. % 0.20/0.51 generalize (zenon_H2a (line_connecting zenon_TX_r zenon_TY_s)). zenon_intro zenon_H2b. % 0.20/0.51 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.20/0.51 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H16 | zenon_intro zenon_H2e ]. % 0.20/0.51 exact (zenon_H16 zenon_H10). % 0.20/0.51 exact (zenon_H2e zenon_H26). % 0.20/0.51 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.20/0.51 exact (zenon_H24 zenon_H30). % 0.20/0.51 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.20/0.51 generalize (ci1 zenon_TX_r). zenon_intro zenon_H33. % 0.20/0.51 generalize (zenon_H33 zenon_TY_s). zenon_intro zenon_H34. % 0.20/0.51 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H16 | zenon_intro zenon_H35 ]. % 0.20/0.51 exact (zenon_H16 zenon_H10). % 0.20/0.51 exact (zenon_H35 zenon_H32). % 0.20/0.51 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H36 | zenon_intro zenon_Hf ]. % 0.20/0.51 exact (zenon_H23 zenon_H36). % 0.20/0.51 apply (zenon_L1_ zenon_TX_r zenon_TY_s); trivial. % 0.20/0.51 Qed. % 0.20/0.51 % SZS output end Proof % 0.20/0.51 (* END-PROOF *) % 0.20/0.51 nodes searched: 219 % 0.20/0.51 max branch formulas: 183 % 0.20/0.51 proof nodes created: 33 % 0.20/0.51 formulas created: 1317 % 0.20/0.51 %------------------------------------------------------------------------------