%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 07:00:46 EDT 2022 % Result : Theorem 1.62s 1.80s % Output : Proof 1.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n010.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 15:26:08 EDT 2022 % 0.12/0.33 % CPUTime : % 1.62/1.80 (* PROOF-FOUND *) % 1.62/1.80 % SZS status Theorem % 1.62/1.80 (* BEGIN-PROOF *) % 1.62/1.80 % SZS output start Proof % 1.62/1.80 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines X Z)/\(distinct_points (intersection_point X Y) (intersection_point X Z))))->(~(distinct_lines (line_connecting (intersection_point X Y) (intersection_point X Z)) X)))))). % 1.62/1.80 Proof. % 1.62/1.80 assert (zenon_L1_ : forall (zenon_TY_p : zenon_U) (zenon_TZ_q : zenon_U) (zenon_TX_r : zenon_U), ((distinct_points (intersection_point zenon_TX_r zenon_TZ_q) (intersection_point zenon_TX_r zenon_TY_p))/\(distinct_points (intersection_point zenon_TX_r zenon_TZ_q) (intersection_point zenon_TX_r zenon_TZ_q))) -> (~(distinct_points (intersection_point zenon_TX_r zenon_TZ_q) (intersection_point zenon_TX_r zenon_TZ_q))) -> False). % 1.62/1.80 do 3 intro. intros zenon_Hd zenon_He. % 1.62/1.80 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H13. zenon_intro zenon_H12. % 1.62/1.80 exact (zenon_He zenon_H12). % 1.62/1.80 (* end of lemma zenon_L1_ *) % 1.62/1.80 assert (zenon_L2_ : forall (zenon_TZ_q : zenon_U) (zenon_TY_p : zenon_U) (zenon_TX_r : zenon_U), ((distinct_points (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r zenon_TY_p))/\(distinct_points (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r zenon_TZ_q))) -> (~(distinct_points (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r zenon_TY_p))) -> False). % 1.62/1.80 do 3 intro. intros zenon_H14 zenon_H15. % 1.62/1.80 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H17. zenon_intro zenon_H16. % 1.62/1.80 exact (zenon_H15 zenon_H17). % 1.62/1.80 (* end of lemma zenon_L2_ *) % 1.62/1.80 apply NNPP. intro zenon_G. % 1.62/1.80 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines X Z)/\(distinct_points (intersection_point X Y) (intersection_point X Z))))->(~(distinct_lines (line_connecting (intersection_point X Y) (intersection_point X Z)) X)))))) zenon_G); [ zenon_intro zenon_H18; idtac ]. % 1.62/1.80 elim zenon_H18. zenon_intro zenon_TX_r. zenon_intro zenon_H19. % 1.62/1.80 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_r Y)/\((convergent_lines zenon_TX_r Z)/\(distinct_points (intersection_point zenon_TX_r Y) (intersection_point zenon_TX_r Z))))->(~(distinct_lines (line_connecting (intersection_point zenon_TX_r Y) (intersection_point zenon_TX_r Z)) zenon_TX_r))))) zenon_H19); [ zenon_intro zenon_H1a; idtac ]. % 1.62/1.80 elim zenon_H1a. zenon_intro zenon_TY_p. zenon_intro zenon_H1b. % 1.62/1.80 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_r zenon_TY_p)/\((convergent_lines zenon_TX_r Z)/\(distinct_points (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r Z))))->(~(distinct_lines (line_connecting (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r Z)) zenon_TX_r)))) zenon_H1b); [ zenon_intro zenon_H1c; idtac ]. % 1.62/1.80 elim zenon_H1c. zenon_intro zenon_TZ_q. zenon_intro zenon_H1d. % 1.62/1.80 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 1.62/1.80 apply zenon_H1e. zenon_intro zenon_H20. % 1.62/1.80 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21. % 1.62/1.80 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H16. % 1.62/1.80 generalize (con2 zenon_TX_r). zenon_intro zenon_H24. % 1.62/1.80 generalize (zenon_H24 zenon_TZ_q). zenon_intro zenon_H25. % 1.62/1.80 generalize (cu1 (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H26. % 1.62/1.80 generalize (zenon_H26 (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_H27. % 1.62/1.80 generalize (apart1 (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_He. % 1.62/1.80 generalize (zenon_H25 (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_H28. % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 1.62/1.80 exact (zenon_H2a zenon_H23). % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H12 ]. % 1.62/1.80 apply (zenon_notor_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 1.62/1.80 generalize (con1 (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H2e. % 1.62/1.80 generalize (zenon_H24 zenon_TY_p). zenon_intro zenon_H2f. % 1.62/1.80 generalize (apart1 (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H15. % 1.62/1.80 generalize (zenon_H2e (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_H30. % 1.62/1.80 generalize (zenon_H2f (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H31. % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 1.62/1.80 exact (zenon_H33 zenon_H22). % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H17 ]. % 1.62/1.80 apply (zenon_notor_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 1.62/1.80 generalize (zenon_H30 (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H37. % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 1.62/1.80 exact (zenon_H39 zenon_H16). % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H14 ]. % 1.62/1.80 generalize (zenon_H30 (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_H3b. % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H39 | zenon_intro zenon_H3c ]. % 1.62/1.80 exact (zenon_H39 zenon_H16). % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3d | zenon_intro zenon_Hd ]. % 1.62/1.80 generalize (zenon_H27 (line_connecting (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r zenon_TZ_q))). zenon_intro zenon_H3e. % 1.62/1.80 generalize (zenon_H3e zenon_TX_r). zenon_intro zenon_H3f. % 1.62/1.80 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 1.62/1.80 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H39 | zenon_intro zenon_H42 ]. % 1.62/1.80 exact (zenon_H39 zenon_H16). % 1.62/1.80 exact (zenon_H42 zenon_H20). % 1.62/1.80 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 1.62/1.80 exact (zenon_H3a zenon_H44). % 1.62/1.80 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 1.62/1.80 exact (zenon_H36 zenon_H46). % 1.62/1.80 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 1.62/1.80 exact (zenon_H3d zenon_H48). % 1.62/1.80 exact (zenon_H2d zenon_H47). % 1.62/1.80 apply (zenon_L1_ zenon_TY_p zenon_TZ_q zenon_TX_r); trivial. % 1.62/1.80 apply (zenon_L2_ zenon_TZ_q zenon_TY_p zenon_TX_r); trivial. % 1.62/1.80 exact (zenon_H15 zenon_H17). % 1.62/1.80 exact (zenon_He zenon_H12). % 1.62/1.80 Qed. % 1.62/1.80 % SZS output end Proof % 1.62/1.80 (* END-PROOF *) % 1.62/1.80 nodes searched: 162760 % 1.62/1.80 max branch formulas: 7649 % 1.62/1.80 proof nodes created: 7388 % 1.62/1.80 formulas created: 294905 % 1.62/1.80 %------------------------------------------------------------------------------