%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n007.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 0.48s 0.73s % Output : Proof 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.13 % Command : run_zenon %s %d % 0.15/0.35 % Computer : n007.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 600 % 0.15/0.35 % DateTime : Sat Jun 18 16:38:43 EDT 2022 % 0.15/0.35 % CPUTime : % 0.48/0.73 (* PROOF-FOUND *) % 0.48/0.73 % SZS status Theorem % 0.48/0.73 (* BEGIN-PROOF *) % 0.48/0.73 % SZS output start Proof % 0.48/0.73 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((distinct_points U V)/\((~(apart_point_and_line X (line_connecting U V)))/\(~(apart_point_and_line Y (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting X Y)))/\(~(apart_point_and_line V (line_connecting X Y))))))))). % 0.48/0.73 Proof. % 0.48/0.73 assert (zenon_L1_ : forall (zenon_TV_u : zenon_U) (zenon_TU_v : zenon_U) (zenon_TY_w : zenon_U) (zenon_TX_x : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_x zenon_TY_w)/\(distinct_lines U V))->((apart_point_and_line zenon_TX_x U)\/((apart_point_and_line zenon_TX_x V)\/((apart_point_and_line zenon_TY_w U)\/(apart_point_and_line zenon_TY_w V))))))) -> (~(apart_point_and_line zenon_TY_w (line_connecting zenon_TU_v zenon_TV_u))) -> (~(apart_point_and_line zenon_TY_w (line_connecting zenon_TX_x zenon_TY_w))) -> (~(apart_point_and_line zenon_TX_x (line_connecting zenon_TU_v zenon_TV_u))) -> (~(apart_point_and_line zenon_TX_x (line_connecting zenon_TX_x zenon_TY_w))) -> (distinct_lines (line_connecting zenon_TX_x zenon_TY_w) (line_connecting zenon_TU_v zenon_TV_u)) -> (distinct_points zenon_TX_x zenon_TY_w) -> False). % 0.48/0.73 do 4 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13. % 0.48/0.73 generalize (zenon_Hd (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H18. % 0.48/0.73 generalize (zenon_H18 (line_connecting zenon_TU_v zenon_TV_u)). zenon_intro zenon_H19. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.48/0.73 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.48/0.73 exact (zenon_H1d zenon_H13). % 0.48/0.73 exact (zenon_H1c zenon_H12). % 0.48/0.73 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.48/0.73 exact (zenon_H11 zenon_H1f). % 0.48/0.73 apply (zenon_or_s _ _ zenon_H1e); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.48/0.73 exact (zenon_H10 zenon_H21). % 0.48/0.73 apply (zenon_or_s _ _ zenon_H20); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.48/0.73 exact (zenon_Hf zenon_H23). % 0.48/0.73 exact (zenon_He zenon_H22). % 0.48/0.73 (* end of lemma zenon_L1_ *) % 0.48/0.73 assert (zenon_L2_ : forall (zenon_TY_w : zenon_U) (zenon_TX_x : zenon_U), ((distinct_points zenon_TX_x zenon_TX_x)/\(distinct_points zenon_TX_x zenon_TY_w)) -> (~(distinct_points zenon_TX_x zenon_TX_x)) -> False). % 0.48/0.73 do 2 intro. intros zenon_H24 zenon_H25. % 0.48/0.73 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H13. % 0.48/0.73 exact (zenon_H25 zenon_H26). % 0.48/0.73 (* end of lemma zenon_L2_ *) % 0.48/0.73 assert (zenon_L3_ : forall (zenon_TX_x : zenon_U) (zenon_TY_w : zenon_U), ((distinct_points zenon_TY_w zenon_TX_x)/\(distinct_points zenon_TY_w zenon_TY_w)) -> (~(distinct_points zenon_TY_w zenon_TY_w)) -> False). % 0.48/0.73 do 2 intro. intros zenon_H27 zenon_H28. % 0.48/0.73 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.48/0.73 exact (zenon_H28 zenon_H29). % 0.48/0.73 (* end of lemma zenon_L3_ *) % 0.48/0.73 assert (zenon_L4_ : forall (zenon_TV_u : zenon_U) (zenon_TU_v : zenon_U), ((distinct_points zenon_TU_v zenon_TU_v)/\(distinct_points zenon_TU_v zenon_TV_u)) -> (~(distinct_points zenon_TU_v zenon_TU_v)) -> False). % 0.48/0.73 do 2 intro. intros zenon_H2b zenon_H2c. % 0.48/0.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.48/0.73 exact (zenon_H2c zenon_H2e). % 0.48/0.73 (* end of lemma zenon_L4_ *) % 0.48/0.73 assert (zenon_L5_ : forall (zenon_TU_v : zenon_U) (zenon_TV_u : zenon_U), ((distinct_points zenon_TV_u zenon_TU_v)/\(distinct_points zenon_TV_u zenon_TV_u)) -> (~(distinct_points zenon_TV_u zenon_TV_u)) -> False). % 0.48/0.73 do 2 intro. intros zenon_H2f zenon_H30. % 0.48/0.73 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.48/0.73 exact (zenon_H30 zenon_H31). % 0.48/0.73 (* end of lemma zenon_L5_ *) % 0.48/0.73 apply NNPP. intro zenon_G. % 0.48/0.73 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((distinct_points U V)/\((~(apart_point_and_line X (line_connecting U V)))/\(~(apart_point_and_line Y (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting X Y)))/\(~(apart_point_and_line V (line_connecting X Y))))))))) zenon_G); [ zenon_intro zenon_H33; idtac ]. % 0.48/0.73 elim zenon_H33. zenon_intro zenon_TX_x. zenon_intro zenon_H34. % 0.48/0.73 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_x Y)/\((distinct_points U V)/\((~(apart_point_and_line zenon_TX_x (line_connecting U V)))/\(~(apart_point_and_line Y (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting zenon_TX_x Y)))/\(~(apart_point_and_line V (line_connecting zenon_TX_x Y)))))))) zenon_H34); [ zenon_intro zenon_H35; idtac ]. % 0.48/0.73 elim zenon_H35. zenon_intro zenon_TY_w. zenon_intro zenon_H36. % 0.48/0.73 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_x zenon_TY_w)/\((distinct_points U V)/\((~(apart_point_and_line zenon_TX_x (line_connecting U V)))/\(~(apart_point_and_line zenon_TY_w (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting zenon_TX_x zenon_TY_w)))/\(~(apart_point_and_line V (line_connecting zenon_TX_x zenon_TY_w))))))) zenon_H36); [ zenon_intro zenon_H37; idtac ]. % 0.48/0.73 elim zenon_H37. zenon_intro zenon_TU_v. zenon_intro zenon_H38. % 0.48/0.73 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_x zenon_TY_w)/\((distinct_points zenon_TU_v V)/\((~(apart_point_and_line zenon_TX_x (line_connecting zenon_TU_v V)))/\(~(apart_point_and_line zenon_TY_w (line_connecting zenon_TU_v V))))))->((~(apart_point_and_line zenon_TU_v (line_connecting zenon_TX_x zenon_TY_w)))/\(~(apart_point_and_line V (line_connecting zenon_TX_x zenon_TY_w)))))) zenon_H38); [ zenon_intro zenon_H39; idtac ]. % 0.48/0.73 elim zenon_H39. zenon_intro zenon_TV_u. zenon_intro zenon_H3a. % 0.48/0.73 apply (zenon_notimply_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 0.48/0.73 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H13. zenon_intro zenon_H3d. % 0.48/0.73 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H2d. zenon_intro zenon_H3e. % 0.48/0.73 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H10. zenon_intro zenon_He. % 0.48/0.73 apply (zenon_notand_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.48/0.73 apply zenon_H40. zenon_intro zenon_H41. % 0.48/0.73 generalize (apart1 zenon_TY_w). zenon_intro zenon_H28. % 0.48/0.73 generalize (cu1 zenon_TX_x). zenon_intro zenon_H42. % 0.48/0.73 generalize (con1 zenon_TU_v). zenon_intro zenon_H43. % 0.48/0.73 generalize (con1 zenon_TX_x). zenon_intro zenon_H44. % 0.48/0.73 generalize (zenon_H42 zenon_TY_w). zenon_intro zenon_Hd. % 0.48/0.73 generalize (zenon_H43 zenon_TV_u). zenon_intro zenon_H45. % 0.48/0.73 generalize (zenon_H44 zenon_TY_w). zenon_intro zenon_H46. % 0.48/0.73 generalize (apart1 zenon_TU_v). zenon_intro zenon_H2c. % 0.48/0.73 generalize (apart1 zenon_TX_x). zenon_intro zenon_H25. % 0.48/0.73 generalize (ceq2 zenon_TU_v). zenon_intro zenon_H47. % 0.48/0.73 generalize (zenon_H45 zenon_TU_v). zenon_intro zenon_H48. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.48/0.73 exact (zenon_H4a zenon_H2d). % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H2b ]. % 0.48/0.73 generalize (zenon_H46 zenon_TY_w). zenon_intro zenon_H4c. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H1d | zenon_intro zenon_H4d ]. % 0.48/0.73 exact (zenon_H1d zenon_H13). % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_Hf | zenon_intro zenon_H27 ]. % 0.48/0.73 generalize (zenon_H46 zenon_TX_x). zenon_intro zenon_H4e. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H1d | zenon_intro zenon_H4f ]. % 0.48/0.73 exact (zenon_H1d zenon_H13). % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H11 | zenon_intro zenon_H24 ]. % 0.48/0.73 generalize (zenon_H47 (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H50. % 0.48/0.73 generalize (zenon_H50 (line_connecting zenon_TU_v zenon_TV_u)). zenon_intro zenon_H51. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.48/0.73 exact (zenon_H53 zenon_H41). % 0.48/0.73 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H54 ]. % 0.48/0.73 apply (zenon_L1_ zenon_TV_u zenon_TU_v zenon_TY_w zenon_TX_x); trivial. % 0.48/0.73 exact (zenon_H4b zenon_H54). % 0.48/0.73 apply (zenon_L2_ zenon_TY_w zenon_TX_x); trivial. % 0.48/0.73 apply (zenon_L3_ zenon_TX_x zenon_TY_w); trivial. % 0.48/0.73 apply (zenon_L4_ zenon_TV_u zenon_TU_v); trivial. % 0.48/0.73 apply zenon_H3f. zenon_intro zenon_H55. % 0.48/0.73 generalize (apart1 zenon_TV_u). zenon_intro zenon_H30. % 0.48/0.73 generalize (apart1 zenon_TY_w). zenon_intro zenon_H28. % 0.48/0.73 generalize (cu1 zenon_TX_x). zenon_intro zenon_H42. % 0.48/0.73 generalize (con1 zenon_TU_v). zenon_intro zenon_H43. % 0.48/0.73 generalize (con1 zenon_TX_x). zenon_intro zenon_H44. % 0.48/0.73 generalize (zenon_H42 zenon_TY_w). zenon_intro zenon_Hd. % 0.48/0.73 generalize (zenon_H43 zenon_TV_u). zenon_intro zenon_H45. % 0.48/0.73 generalize (zenon_H45 zenon_TV_u). zenon_intro zenon_H56. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H4a | zenon_intro zenon_H57 ]. % 0.48/0.73 exact (zenon_H4a zenon_H2d). % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H2f ]. % 0.48/0.73 generalize (zenon_H44 zenon_TY_w). zenon_intro zenon_H46. % 0.48/0.73 generalize (apart1 zenon_TX_x). zenon_intro zenon_H25. % 0.48/0.73 generalize (ceq2 zenon_TV_u). zenon_intro zenon_H59. % 0.48/0.73 generalize (zenon_H46 zenon_TY_w). zenon_intro zenon_H4c. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H1d | zenon_intro zenon_H4d ]. % 0.48/0.73 exact (zenon_H1d zenon_H13). % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_Hf | zenon_intro zenon_H27 ]. % 0.48/0.73 generalize (zenon_H46 zenon_TX_x). zenon_intro zenon_H4e. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H1d | zenon_intro zenon_H4f ]. % 0.48/0.73 exact (zenon_H1d zenon_H13). % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H11 | zenon_intro zenon_H24 ]. % 0.48/0.73 generalize (zenon_H59 (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H5a. % 0.48/0.73 generalize (zenon_H5a (line_connecting zenon_TU_v zenon_TV_u)). zenon_intro zenon_H5b. % 0.48/0.73 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 0.48/0.73 exact (zenon_H5d zenon_H55). % 0.48/0.73 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H12 | zenon_intro zenon_H5e ]. % 0.48/0.73 apply (zenon_L1_ zenon_TV_u zenon_TU_v zenon_TY_w zenon_TX_x); trivial. % 0.48/0.73 exact (zenon_H58 zenon_H5e). % 0.48/0.73 apply (zenon_L2_ zenon_TY_w zenon_TX_x); trivial. % 0.48/0.73 apply (zenon_L3_ zenon_TX_x zenon_TY_w); trivial. % 0.48/0.73 apply (zenon_L5_ zenon_TU_v zenon_TV_u); trivial. % 0.48/0.73 Qed. % 0.48/0.73 % SZS output end Proof % 0.48/0.73 (* END-PROOF *) % 0.48/0.73 nodes searched: 13014 % 0.48/0.73 max branch formulas: 1682 % 0.48/0.73 proof nodes created: 1239 % 0.48/0.73 formulas created: 25564 % 0.48/0.73 %------------------------------------------------------------------------------