%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO185+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n009.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 07:00:31 EDT 2022 % Result : Theorem 0.19s 0.51s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO185+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n009.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 18:05:07 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.51 (* PROOF-FOUND *) % 0.19/0.51 % SZS status Theorem % 0.19/0.51 (* BEGIN-PROOF *) % 0.19/0.51 % SZS output start Proof % 0.19/0.51 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_points X (intersection_point U V)))))->((~(apart_point_and_line X U))/\(~(apart_point_and_line X V)))))))). % 0.19/0.51 Proof. % 0.19/0.51 apply NNPP. intro zenon_G. % 0.19/0.51 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_points X (intersection_point U V)))))->((~(apart_point_and_line X U))/\(~(apart_point_and_line X V)))))))) zenon_G); [ zenon_intro zenon_Hd; idtac ]. % 0.19/0.51 elim zenon_Hd. zenon_intro zenon_TX_o. zenon_intro zenon_Hf. % 0.19/0.51 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)/\(~(distinct_points zenon_TX_o (intersection_point U V)))))->((~(apart_point_and_line zenon_TX_o U))/\(~(apart_point_and_line zenon_TX_o V))))))) zenon_Hf); [ zenon_intro zenon_H10; idtac ]. % 0.19/0.51 elim zenon_H10. zenon_intro zenon_TY_r. zenon_intro zenon_H12. % 0.19/0.51 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_o zenon_TY_r)/\((convergent_lines U V)/\(~(distinct_points zenon_TX_o (intersection_point U V)))))->((~(apart_point_and_line zenon_TX_o U))/\(~(apart_point_and_line zenon_TX_o V)))))) zenon_H12); [ zenon_intro zenon_H13; idtac ]. % 0.19/0.51 elim zenon_H13. zenon_intro zenon_TU_u. zenon_intro zenon_H15. % 0.19/0.51 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_o zenon_TY_r)/\((convergent_lines zenon_TU_u V)/\(~(distinct_points zenon_TX_o (intersection_point zenon_TU_u V)))))->((~(apart_point_and_line zenon_TX_o zenon_TU_u))/\(~(apart_point_and_line zenon_TX_o V))))) zenon_H15); [ zenon_intro zenon_H16; idtac ]. % 0.19/0.51 elim zenon_H16. zenon_intro zenon_TV_x. zenon_intro zenon_H18. % 0.19/0.51 apply (zenon_notimply_s _ _ zenon_H18). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.19/0.51 apply (zenon_and_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.19/0.51 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 0.19/0.51 apply (zenon_notand_s _ _ zenon_H19); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 0.19/0.51 apply zenon_H20. zenon_intro zenon_H21. % 0.19/0.51 generalize (con2 zenon_TU_u). zenon_intro zenon_H22. % 0.19/0.51 generalize (zenon_H22 zenon_TV_x). zenon_intro zenon_H23. % 0.19/0.51 generalize (zenon_H23 zenon_TX_o). zenon_intro zenon_H24. % 0.19/0.51 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.19/0.51 exact (zenon_H26 zenon_H1e). % 0.19/0.51 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.19/0.51 apply (zenon_notor_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.19/0.51 exact (zenon_H2a zenon_H21). % 0.19/0.51 exact (zenon_H1d zenon_H27). % 0.19/0.51 apply zenon_H1f. zenon_intro zenon_H2b. % 0.19/0.51 generalize (con2 zenon_TU_u). zenon_intro zenon_H22. % 0.19/0.51 generalize (zenon_H22 zenon_TV_x). zenon_intro zenon_H23. % 0.19/0.51 generalize (zenon_H23 zenon_TX_o). zenon_intro zenon_H24. % 0.19/0.51 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.19/0.51 exact (zenon_H26 zenon_H1e). % 0.19/0.51 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.19/0.51 apply (zenon_notor_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.19/0.51 exact (zenon_H29 zenon_H2b). % 0.19/0.51 exact (zenon_H1d zenon_H27). % 0.19/0.51 Qed. % 0.19/0.51 % SZS output end Proof % 0.19/0.51 (* END-PROOF *) % 0.19/0.51 nodes searched: 559 % 0.19/0.51 max branch formulas: 243 % 0.19/0.51 proof nodes created: 64 % 0.19/0.51 formulas created: 2137 % 0.19/0.51 %------------------------------------------------------------------------------