%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n014.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 0.44s 0.63s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.14 % Command : run_zenon %s %d % 0.14/0.36 % Computer : n014.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Fri Jun 17 20:47:04 EDT 2022 % 0.14/0.36 % CPUTime : % 0.44/0.63 (* PROOF-FOUND *) % 0.44/0.63 % SZS status Theorem % 0.44/0.63 (* BEGIN-PROOF *) % 0.44/0.63 % SZS output start Proof % 0.44/0.63 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))))))))). % 0.44/0.63 Proof. % 0.44/0.63 assert (zenon_L1_ : forall (zenon_TY_t : zenon_U) (zenon_TX_u : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TX_u zenon_TY_t)->((distinct_points zenon_TX_u Z)\/(distinct_points zenon_TY_t Z)))) -> (distinct_points zenon_TX_u zenon_TY_t) -> (~(distinct_points zenon_TX_u zenon_TX_u)) -> (~(distinct_points zenon_TY_t zenon_TX_u)) -> False). % 0.44/0.63 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H12. % 0.44/0.63 generalize (zenon_Hf zenon_TX_u). zenon_intro zenon_H15. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.44/0.63 exact (zenon_H17 zenon_H10). % 0.44/0.63 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.44/0.63 exact (zenon_H11 zenon_H19). % 0.44/0.63 exact (zenon_H12 zenon_H18). % 0.44/0.63 (* end of lemma zenon_L1_ *) % 0.44/0.63 assert (zenon_L2_ : forall (zenon_TV_bg : zenon_U) (zenon_TU_bh : zenon_U) (zenon_TX_u : zenon_U) (zenon_TY_t : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TY_t zenon_TX_u)/\(distinct_lines U V))->((apart_point_and_line zenon_TY_t U)\/((apart_point_and_line zenon_TY_t V)\/((apart_point_and_line zenon_TX_u U)\/(apart_point_and_line zenon_TX_u V))))))) -> (~(apart_point_and_line zenon_TX_u (line_connecting zenon_TU_bh zenon_TV_bg))) -> (~(apart_point_and_line zenon_TX_u (line_connecting zenon_TX_u zenon_TY_t))) -> (~(apart_point_and_line zenon_TY_t (line_connecting zenon_TU_bh zenon_TV_bg))) -> (~(apart_point_and_line zenon_TY_t (line_connecting zenon_TX_u zenon_TY_t))) -> (distinct_lines (line_connecting zenon_TX_u zenon_TY_t) (line_connecting zenon_TU_bh zenon_TV_bg)) -> (distinct_points zenon_TY_t zenon_TX_u) -> False). % 0.44/0.63 do 4 intro. intros zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_H1e zenon_H1f zenon_H18. % 0.44/0.63 generalize (zenon_H1a (line_connecting zenon_TX_u zenon_TY_t)). zenon_intro zenon_H22. % 0.44/0.63 generalize (zenon_H22 (line_connecting zenon_TU_bh zenon_TV_bg)). zenon_intro zenon_H23. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.44/0.63 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H12 | zenon_intro zenon_H26 ]. % 0.44/0.63 exact (zenon_H12 zenon_H18). % 0.44/0.63 exact (zenon_H26 zenon_H1f). % 0.44/0.63 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.44/0.63 exact (zenon_H1e zenon_H28). % 0.44/0.63 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.44/0.63 exact (zenon_H1d zenon_H2a). % 0.44/0.63 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.44/0.63 exact (zenon_H1c zenon_H2c). % 0.44/0.63 exact (zenon_H1b zenon_H2b). % 0.44/0.63 (* end of lemma zenon_L2_ *) % 0.44/0.63 apply NNPP. intro zenon_G. % 0.44/0.63 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_H2d; idtac ]. % 0.44/0.63 elim zenon_H2d. zenon_intro zenon_TX_u. zenon_intro zenon_H2e. % 0.44/0.63 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_u Y)/\((distinct_points U V)/\((~(apart_point_and_line zenon_TX_u (line_connecting U V)))/\(~(apart_point_and_line Y (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting zenon_TX_u Y)))/\(~(apart_point_and_line V (line_connecting zenon_TX_u Y)))))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ]. % 0.44/0.63 elim zenon_H2f. zenon_intro zenon_TY_t. zenon_intro zenon_H30. % 0.44/0.63 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_u zenon_TY_t)/\((distinct_points U V)/\((~(apart_point_and_line zenon_TX_u (line_connecting U V)))/\(~(apart_point_and_line zenon_TY_t (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting zenon_TX_u zenon_TY_t)))/\(~(apart_point_and_line V (line_connecting zenon_TX_u zenon_TY_t))))))) zenon_H30); [ zenon_intro zenon_H31; idtac ]. % 0.44/0.63 elim zenon_H31. zenon_intro zenon_TU_bh. zenon_intro zenon_H32. % 0.44/0.63 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_u zenon_TY_t)/\((distinct_points zenon_TU_bh V)/\((~(apart_point_and_line zenon_TX_u (line_connecting zenon_TU_bh V)))/\(~(apart_point_and_line zenon_TY_t (line_connecting zenon_TU_bh V))))))->((~(apart_point_and_line zenon_TU_bh (line_connecting zenon_TX_u zenon_TY_t)))/\(~(apart_point_and_line V (line_connecting zenon_TX_u zenon_TY_t)))))) zenon_H32); [ zenon_intro zenon_H33; idtac ]. % 0.44/0.63 elim zenon_H33. zenon_intro zenon_TV_bg. zenon_intro zenon_H34. % 0.44/0.63 apply (zenon_notimply_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.44/0.63 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H10. zenon_intro zenon_H37. % 0.44/0.63 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 0.44/0.63 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H1b. zenon_intro zenon_H1d. % 0.44/0.63 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.44/0.63 apply zenon_H3b. zenon_intro zenon_H3c. % 0.44/0.63 generalize (apart4 zenon_TX_u). zenon_intro zenon_H3d. % 0.44/0.63 generalize (ci1 zenon_TX_u). zenon_intro zenon_H3e. % 0.44/0.63 generalize (zenon_H3d zenon_TY_t). zenon_intro zenon_Hf. % 0.44/0.63 generalize (cu1 zenon_TY_t). zenon_intro zenon_H3f. % 0.44/0.63 generalize (apart4 zenon_TY_t). zenon_intro zenon_H40. % 0.44/0.63 generalize (ci2 zenon_TX_u). zenon_intro zenon_H41. % 0.44/0.63 generalize (zenon_H3e zenon_TY_t). zenon_intro zenon_H42. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H17 | zenon_intro zenon_H1c ]. % 0.44/0.63 exact (zenon_H17 zenon_H10). % 0.44/0.63 generalize (zenon_H41 zenon_TY_t). zenon_intro zenon_H43. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H17 | zenon_intro zenon_H1e ]. % 0.44/0.63 exact (zenon_H17 zenon_H10). % 0.44/0.63 generalize (apart1 zenon_TX_u). zenon_intro zenon_H11. % 0.44/0.63 generalize (zenon_H3f zenon_TX_u). zenon_intro zenon_H1a. % 0.44/0.63 generalize (zenon_H40 zenon_TX_u). zenon_intro zenon_H44. % 0.44/0.63 generalize (zenon_H44 zenon_TX_u). zenon_intro zenon_H45. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H12 | zenon_intro zenon_H46 ]. % 0.44/0.63 apply (zenon_L1_ zenon_TY_t zenon_TX_u); trivial. % 0.44/0.63 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H18 | zenon_intro zenon_H19 ]. % 0.44/0.63 generalize (ceq2 zenon_TU_bh). zenon_intro zenon_H47. % 0.44/0.63 generalize (zenon_H47 (line_connecting zenon_TX_u zenon_TY_t)). zenon_intro zenon_H48. % 0.44/0.63 generalize (ci1 zenon_TU_bh). zenon_intro zenon_H49. % 0.44/0.63 generalize (zenon_H49 zenon_TV_bg). zenon_intro zenon_H4a. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.44/0.63 exact (zenon_H4c zenon_H39). % 0.44/0.63 generalize (zenon_H48 (line_connecting zenon_TU_bh zenon_TV_bg)). zenon_intro zenon_H4d. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 0.44/0.63 exact (zenon_H4f zenon_H3c). % 0.44/0.63 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H1f | zenon_intro zenon_H50 ]. % 0.44/0.63 apply (zenon_L2_ zenon_TV_bg zenon_TU_bh zenon_TX_u zenon_TY_t); trivial. % 0.44/0.63 exact (zenon_H4b zenon_H50). % 0.44/0.63 exact (zenon_H11 zenon_H19). % 0.44/0.63 apply zenon_H3a. zenon_intro zenon_H51. % 0.44/0.63 generalize (apart4 zenon_TX_u). zenon_intro zenon_H3d. % 0.44/0.63 generalize (ci1 zenon_TX_u). zenon_intro zenon_H3e. % 0.44/0.63 generalize (zenon_H3d zenon_TY_t). zenon_intro zenon_Hf. % 0.44/0.63 generalize (cu1 zenon_TY_t). zenon_intro zenon_H3f. % 0.44/0.63 generalize (apart4 zenon_TY_t). zenon_intro zenon_H40. % 0.44/0.63 generalize (ci2 zenon_TX_u). zenon_intro zenon_H41. % 0.44/0.63 generalize (zenon_H3e zenon_TY_t). zenon_intro zenon_H42. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H17 | zenon_intro zenon_H1c ]. % 0.44/0.63 exact (zenon_H17 zenon_H10). % 0.44/0.63 generalize (zenon_H41 zenon_TY_t). zenon_intro zenon_H43. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H17 | zenon_intro zenon_H1e ]. % 0.44/0.63 exact (zenon_H17 zenon_H10). % 0.44/0.63 generalize (apart1 zenon_TX_u). zenon_intro zenon_H11. % 0.44/0.63 generalize (zenon_H3f zenon_TX_u). zenon_intro zenon_H1a. % 0.44/0.63 generalize (zenon_H40 zenon_TX_u). zenon_intro zenon_H44. % 0.44/0.63 generalize (zenon_H44 zenon_TX_u). zenon_intro zenon_H45. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H12 | zenon_intro zenon_H46 ]. % 0.44/0.63 apply (zenon_L1_ zenon_TY_t zenon_TX_u); trivial. % 0.44/0.63 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H18 | zenon_intro zenon_H19 ]. % 0.44/0.63 generalize (ceq2 zenon_TV_bg). zenon_intro zenon_H52. % 0.44/0.63 generalize (zenon_H52 (line_connecting zenon_TX_u zenon_TY_t)). zenon_intro zenon_H53. % 0.44/0.63 generalize (ci2 zenon_TU_bh). zenon_intro zenon_H54. % 0.44/0.63 generalize (zenon_H54 zenon_TV_bg). zenon_intro zenon_H55. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H4c | zenon_intro zenon_H56 ]. % 0.44/0.63 exact (zenon_H4c zenon_H39). % 0.44/0.63 generalize (zenon_H53 (line_connecting zenon_TU_bh zenon_TV_bg)). zenon_intro zenon_H57. % 0.44/0.63 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 0.44/0.63 exact (zenon_H59 zenon_H51). % 0.44/0.63 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H1f | zenon_intro zenon_H5a ]. % 0.44/0.63 apply (zenon_L2_ zenon_TV_bg zenon_TU_bh zenon_TX_u zenon_TY_t); trivial. % 0.44/0.63 exact (zenon_H56 zenon_H5a). % 0.44/0.63 exact (zenon_H11 zenon_H19). % 0.44/0.63 Qed. % 0.44/0.63 % SZS output end Proof % 0.44/0.63 (* END-PROOF *) % 0.44/0.63 nodes searched: 3524 % 0.44/0.63 max branch formulas: 1045 % 0.44/0.63 proof nodes created: 303 % 0.44/0.63 formulas created: 10995 % 0.44/0.63 %------------------------------------------------------------------------------