%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO186+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 07:00:32 EDT 2022 % Result : Theorem 0.19s 0.56s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO186+2 : TPTP v8.1.0. Released v3.3.0. % 0.00/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n004.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 13:04:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.56 (* PROOF-FOUND *) % 0.19/0.56 % SZS status Theorem % 0.19/0.56 (* BEGIN-PROOF *) % 0.19/0.56 % SZS output start Proof % 0.19/0.56 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)/\((~(apart_point_and_line X U))/\(~(apart_point_and_line X V)))))->(~(distinct_points X (intersection_point U V)))))))). % 0.19/0.56 Proof. % 0.19/0.56 apply NNPP. intro zenon_G. % 0.19/0.56 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)/\((~(apart_point_and_line X U))/\(~(apart_point_and_line X V)))))->(~(distinct_points X (intersection_point U V)))))))) zenon_G); [ zenon_intro zenon_Hd; idtac ]. % 0.19/0.56 elim zenon_Hd. zenon_intro zenon_TX_o. zenon_intro zenon_Hf. % 0.19/0.56 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_o Y)/\((convergent_lines U V)/\((~(apart_point_and_line zenon_TX_o U))/\(~(apart_point_and_line zenon_TX_o V)))))->(~(distinct_points zenon_TX_o (intersection_point U V))))))) zenon_Hf); [ zenon_intro zenon_H10; idtac ]. % 0.19/0.56 elim zenon_H10. zenon_intro zenon_TY_r. zenon_intro zenon_H12. % 0.19/0.56 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_o zenon_TY_r)/\((convergent_lines U V)/\((~(apart_point_and_line zenon_TX_o U))/\(~(apart_point_and_line zenon_TX_o V)))))->(~(distinct_points zenon_TX_o (intersection_point U V)))))) zenon_H12); [ zenon_intro zenon_H13; idtac ]. % 0.19/0.56 elim zenon_H13. zenon_intro zenon_TU_u. zenon_intro zenon_H15. % 0.19/0.56 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_o zenon_TY_r)/\((convergent_lines zenon_TU_u V)/\((~(apart_point_and_line zenon_TX_o zenon_TU_u))/\(~(apart_point_and_line zenon_TX_o V)))))->(~(distinct_points zenon_TX_o (intersection_point zenon_TU_u V))))) zenon_H15); [ zenon_intro zenon_H16; idtac ]. % 0.19/0.56 elim zenon_H16. zenon_intro zenon_TV_x. zenon_intro zenon_H18. % 0.19/0.56 apply (zenon_notimply_s _ _ zenon_H18). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.19/0.56 apply zenon_H19. zenon_intro zenon_H1b. % 0.19/0.56 apply (zenon_and_s _ _ zenon_H1a). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.19/0.56 apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.19/0.56 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.19/0.56 generalize (cu1 zenon_TX_o). zenon_intro zenon_H22. % 0.19/0.56 generalize (apart2 zenon_TV_x). zenon_intro zenon_H23. % 0.19/0.56 generalize (con2 zenon_TU_u). zenon_intro zenon_H24. % 0.19/0.56 generalize (zenon_H24 zenon_TV_x). zenon_intro zenon_H25. % 0.19/0.56 generalize (zenon_H22 (intersection_point zenon_TU_u zenon_TV_x)). zenon_intro zenon_H26. % 0.19/0.56 generalize (apart1 (intersection_point zenon_TU_u zenon_TV_x)). zenon_intro zenon_H27. % 0.19/0.56 generalize (zenon_H25 (intersection_point zenon_TU_u zenon_TV_x)). zenon_intro zenon_H28. % 0.19/0.56 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.19/0.56 exact (zenon_H2a zenon_H1f). % 0.19/0.56 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.19/0.56 apply (zenon_notor_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.19/0.56 generalize (apart5 zenon_TU_u). zenon_intro zenon_H2f. % 0.19/0.56 generalize (zenon_H2f zenon_TV_x). zenon_intro zenon_H30. % 0.19/0.56 generalize (zenon_H30 zenon_TV_x). zenon_intro zenon_H31. % 0.19/0.56 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.19/0.56 generalize (ceq3 zenon_TU_u). zenon_intro zenon_H34. % 0.19/0.56 generalize (zenon_H34 zenon_TV_x). zenon_intro zenon_H35. % 0.19/0.56 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H2a | zenon_intro zenon_H36 ]. % 0.19/0.56 exact (zenon_H2a zenon_H1f). % 0.19/0.56 exact (zenon_H33 zenon_H36). % 0.19/0.56 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 0.19/0.56 generalize (zenon_H26 zenon_TU_u). zenon_intro zenon_H38. % 0.19/0.56 generalize (zenon_H38 zenon_TV_x). zenon_intro zenon_H39. % 0.19/0.56 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.19/0.56 apply (zenon_notand_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H33 ]. % 0.19/0.56 exact (zenon_H3c zenon_H1b). % 0.19/0.56 exact (zenon_H33 zenon_H36). % 0.19/0.56 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 0.19/0.56 exact (zenon_H21 zenon_H3e). % 0.19/0.56 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.19/0.56 exact (zenon_H20 zenon_H40). % 0.19/0.56 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.19/0.56 exact (zenon_H2e zenon_H42). % 0.19/0.56 exact (zenon_H2d zenon_H41). % 0.19/0.56 exact (zenon_H23 zenon_H37). % 0.19/0.56 exact (zenon_H27 zenon_H2b). % 0.19/0.56 Qed. % 0.19/0.56 % SZS output end Proof % 0.19/0.56 (* END-PROOF *) % 0.19/0.56 nodes searched: 3474 % 0.19/0.56 max branch formulas: 948 % 0.19/0.56 proof nodes created: 371 % 0.19/0.56 formulas created: 10586 % 0.19/0.56 %------------------------------------------------------------------------------