%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.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 07:00:25 EDT 2022 % Result : Theorem 0.53s 0.76s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n026.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 17:55:24 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.76 (* PROOF-FOUND *) % 0.53/0.76 % SZS status Theorem % 0.53/0.76 (* BEGIN-PROOF *) % 0.53/0.76 % SZS output start Proof % 0.53/0.76 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))))))))). % 0.53/0.76 Proof. % 0.53/0.76 assert (zenon_L1_ : forall (zenon_TV_r : zenon_U) (zenon_TU_s : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TU_s zenon_TV_r)->((distinct_points zenon_TU_s Z)\/(distinct_points zenon_TV_r Z)))) -> (distinct_points zenon_TU_s zenon_TV_r) -> (~(distinct_points zenon_TU_s zenon_TU_s)) -> (~(distinct_points zenon_TV_r zenon_TU_s)) -> False). % 0.53/0.76 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10. % 0.53/0.76 generalize (zenon_Hd zenon_TU_s). zenon_intro zenon_H13. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 0.53/0.76 exact (zenon_H15 zenon_He). % 0.53/0.76 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.53/0.76 exact (zenon_Hf zenon_H17). % 0.53/0.76 exact (zenon_H10 zenon_H16). % 0.53/0.76 (* end of lemma zenon_L1_ *) % 0.53/0.76 assert (zenon_L2_ : forall (zenon_TU_s : zenon_U) (zenon_TV_r : zenon_U), (~(distinct_points zenon_TV_r zenon_TU_s)) -> (distinct_points zenon_TU_s zenon_TV_r) -> (forall Z : zenon_U, ((distinct_points zenon_TU_s zenon_TV_r)->((distinct_points zenon_TU_s Z)\/(distinct_points zenon_TV_r Z)))) -> False). % 0.53/0.76 do 2 intro. intros zenon_H10 zenon_He zenon_Hd. % 0.53/0.76 generalize (apart1 zenon_TU_s). zenon_intro zenon_Hf. % 0.53/0.76 apply (zenon_L1_ zenon_TV_r zenon_TU_s); trivial. % 0.53/0.76 (* end of lemma zenon_L2_ *) % 0.53/0.76 assert (zenon_L3_ : forall (zenon_TY_be : zenon_U) (zenon_TX_bf : zenon_U) (zenon_TU_s : zenon_U) (zenon_TV_r : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TV_r zenon_TU_s)/\(distinct_lines U V))->((apart_point_and_line zenon_TV_r U)\/((apart_point_and_line zenon_TV_r V)\/((apart_point_and_line zenon_TU_s U)\/(apart_point_and_line zenon_TU_s V))))))) -> (~(apart_point_and_line zenon_TU_s (line_connecting zenon_TX_bf zenon_TY_be))) -> (~(apart_point_and_line zenon_TU_s (line_connecting zenon_TU_s zenon_TV_r))) -> (~(apart_point_and_line zenon_TV_r (line_connecting zenon_TX_bf zenon_TY_be))) -> (~(apart_point_and_line zenon_TV_r (line_connecting zenon_TU_s zenon_TV_r))) -> (distinct_lines (line_connecting zenon_TU_s zenon_TV_r) (line_connecting zenon_TX_bf zenon_TY_be)) -> (distinct_points zenon_TV_r zenon_TU_s) -> False). % 0.53/0.76 do 4 intro. intros zenon_H18 zenon_H19 zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_H16. % 0.53/0.76 generalize (zenon_H18 (line_connecting zenon_TU_s zenon_TV_r)). zenon_intro zenon_H20. % 0.53/0.76 generalize (zenon_H20 (line_connecting zenon_TX_bf zenon_TY_be)). zenon_intro zenon_H21. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.53/0.76 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H10 | zenon_intro zenon_H24 ]. % 0.53/0.76 exact (zenon_H10 zenon_H16). % 0.53/0.76 exact (zenon_H24 zenon_H1d). % 0.53/0.76 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.53/0.76 exact (zenon_H1c zenon_H26). % 0.53/0.76 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.53/0.76 exact (zenon_H1b zenon_H28). % 0.53/0.76 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.53/0.76 exact (zenon_H1a zenon_H2a). % 0.53/0.76 exact (zenon_H19 zenon_H29). % 0.53/0.76 (* end of lemma zenon_L3_ *) % 0.53/0.76 assert (zenon_L4_ : forall (zenon_TU_s : zenon_U) (zenon_TV_r : zenon_U) (zenon_TY_be : zenon_U) (zenon_TX_bf : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line zenon_TX_bf Y)->((distinct_lines Y Z)\/(apart_point_and_line zenon_TX_bf Z))))) -> (~(apart_point_and_line zenon_TX_bf (line_connecting zenon_TX_bf zenon_TY_be))) -> (distinct_points zenon_TV_r zenon_TU_s) -> (~(apart_point_and_line zenon_TV_r (line_connecting zenon_TU_s zenon_TV_r))) -> (~(apart_point_and_line zenon_TV_r (line_connecting zenon_TX_bf zenon_TY_be))) -> (~(apart_point_and_line zenon_TU_s (line_connecting zenon_TU_s zenon_TV_r))) -> (~(apart_point_and_line zenon_TU_s (line_connecting zenon_TX_bf zenon_TY_be))) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TV_r zenon_TU_s)/\(distinct_lines U V))->((apart_point_and_line zenon_TV_r U)\/((apart_point_and_line zenon_TV_r V)\/((apart_point_and_line zenon_TU_s U)\/(apart_point_and_line zenon_TU_s V))))))) -> (apart_point_and_line zenon_TX_bf (line_connecting zenon_TU_s zenon_TV_r)) -> False). % 0.53/0.76 do 4 intro. intros zenon_H2b zenon_H2c zenon_H16 zenon_H1c zenon_H1b zenon_H1a zenon_H19 zenon_H18 zenon_H2d. % 0.53/0.76 generalize (zenon_H2b (line_connecting zenon_TU_s zenon_TV_r)). zenon_intro zenon_H2e. % 0.53/0.76 generalize (zenon_H2e (line_connecting zenon_TX_bf zenon_TY_be)). zenon_intro zenon_H2f. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.53/0.76 exact (zenon_H31 zenon_H2d). % 0.53/0.76 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H1d | zenon_intro zenon_H32 ]. % 0.53/0.76 apply (zenon_L3_ zenon_TY_be zenon_TX_bf zenon_TU_s zenon_TV_r); trivial. % 0.53/0.76 exact (zenon_H2c zenon_H32). % 0.53/0.76 (* end of lemma zenon_L4_ *) % 0.53/0.76 assert (zenon_L5_ : forall (zenon_TY_be : zenon_U) (zenon_TX_bf : zenon_U), ((distinct_points zenon_TX_bf zenon_TX_bf)/\(distinct_points zenon_TX_bf zenon_TY_be)) -> (~(distinct_points zenon_TX_bf zenon_TX_bf)) -> False). % 0.53/0.76 do 2 intro. intros zenon_H33 zenon_H34. % 0.53/0.76 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.53/0.76 exact (zenon_H34 zenon_H36). % 0.53/0.76 (* end of lemma zenon_L5_ *) % 0.53/0.76 assert (zenon_L6_ : forall (zenon_TV_r : zenon_U) (zenon_TU_s : zenon_U), ((distinct_points zenon_TU_s zenon_TU_s)/\(distinct_points zenon_TU_s zenon_TV_r)) -> (~(distinct_points zenon_TU_s zenon_TU_s)) -> False). % 0.53/0.76 do 2 intro. intros zenon_H37 zenon_Hf. % 0.53/0.76 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H17. zenon_intro zenon_He. % 0.53/0.76 exact (zenon_Hf zenon_H17). % 0.53/0.76 (* end of lemma zenon_L6_ *) % 0.53/0.76 assert (zenon_L7_ : forall (zenon_TU_s : zenon_U) (zenon_TV_r : zenon_U), ((distinct_points zenon_TV_r zenon_TU_s)/\(distinct_points zenon_TV_r zenon_TV_r)) -> (~(distinct_points zenon_TV_r zenon_TV_r)) -> False). % 0.53/0.76 do 2 intro. intros zenon_H38 zenon_H39. % 0.53/0.76 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H16. zenon_intro zenon_H3a. % 0.53/0.76 exact (zenon_H39 zenon_H3a). % 0.53/0.76 (* end of lemma zenon_L7_ *) % 0.53/0.76 assert (zenon_L8_ : forall (zenon_TX_bf : zenon_U) (zenon_TY_be : zenon_U), ((distinct_points zenon_TY_be zenon_TX_bf)/\(distinct_points zenon_TY_be zenon_TY_be)) -> (~(distinct_points zenon_TY_be zenon_TY_be)) -> False). % 0.53/0.76 do 2 intro. intros zenon_H3b zenon_H3c. % 0.53/0.76 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 0.53/0.76 exact (zenon_H3c zenon_H3d). % 0.53/0.76 (* end of lemma zenon_L8_ *) % 0.53/0.76 apply NNPP. intro zenon_G. % 0.53/0.76 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_H3f; idtac ]. % 0.53/0.76 elim zenon_H3f. zenon_intro zenon_TX_bf. zenon_intro zenon_H40. % 0.53/0.76 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bf Y)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_bf (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_bf Y))\/(apart_point_and_line V (line_connecting zenon_TX_bf Y)))))))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 0.53/0.76 elim zenon_H41. zenon_intro zenon_TY_be. zenon_intro zenon_H42. % 0.53/0.76 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bf zenon_TY_be)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_bf (line_connecting U V))\/(apart_point_and_line zenon_TY_be (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_bf zenon_TY_be))\/(apart_point_and_line V (line_connecting zenon_TX_bf zenon_TY_be))))))) zenon_H42); [ zenon_intro zenon_H43; idtac ]. % 0.53/0.76 elim zenon_H43. zenon_intro zenon_TU_s. zenon_intro zenon_H44. % 0.53/0.76 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bf zenon_TY_be)/\(distinct_points zenon_TU_s V))->(((apart_point_and_line zenon_TX_bf (line_connecting zenon_TU_s V))\/(apart_point_and_line zenon_TY_be (line_connecting zenon_TU_s V)))->((apart_point_and_line zenon_TU_s (line_connecting zenon_TX_bf zenon_TY_be))\/(apart_point_and_line V (line_connecting zenon_TX_bf zenon_TY_be)))))) zenon_H44); [ zenon_intro zenon_H45; idtac ]. % 0.53/0.76 elim zenon_H45. zenon_intro zenon_TV_r. zenon_intro zenon_H46. % 0.53/0.76 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47. % 0.53/0.76 apply (zenon_notimply_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.53/0.76 apply (zenon_notor_s _ _ zenon_H49). zenon_intro zenon_H19. zenon_intro zenon_H1b. % 0.53/0.76 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H35. zenon_intro zenon_He. % 0.53/0.76 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H2d | zenon_intro zenon_H4b ]. % 0.53/0.76 generalize (apart1 zenon_TV_r). zenon_intro zenon_H39. % 0.53/0.76 generalize (apart4 zenon_TU_s). zenon_intro zenon_H4c. % 0.53/0.76 generalize (zenon_H4c zenon_TV_r). zenon_intro zenon_Hd. % 0.53/0.76 generalize (con1 zenon_TU_s). zenon_intro zenon_H4d. % 0.53/0.76 generalize (con1 zenon_TX_bf). zenon_intro zenon_H4e. % 0.53/0.76 generalize (zenon_H4d zenon_TV_r). zenon_intro zenon_H4f. % 0.53/0.76 generalize (apart4 zenon_TV_r). zenon_intro zenon_H50. % 0.53/0.76 generalize (cu1 zenon_TV_r). zenon_intro zenon_H51. % 0.53/0.76 generalize (zenon_H4f zenon_TV_r). zenon_intro zenon_H52. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H15 | zenon_intro zenon_H53 ]. % 0.53/0.76 exact (zenon_H15 zenon_He). % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H1c | zenon_intro zenon_H38 ]. % 0.53/0.76 generalize (zenon_H4e zenon_TY_be). zenon_intro zenon_H54. % 0.53/0.76 generalize (apart1 zenon_TU_s). zenon_intro zenon_Hf. % 0.53/0.76 generalize (apart1 zenon_TX_bf). zenon_intro zenon_H34. % 0.53/0.76 generalize (ceq2 zenon_TX_bf). zenon_intro zenon_H2b. % 0.53/0.76 generalize (zenon_H50 zenon_TU_s). zenon_intro zenon_H55. % 0.53/0.76 generalize (zenon_H51 zenon_TU_s). zenon_intro zenon_H18. % 0.53/0.76 generalize (zenon_H4f zenon_TU_s). zenon_intro zenon_H56. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H15 | zenon_intro zenon_H57 ]. % 0.53/0.76 exact (zenon_H15 zenon_He). % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H1a | zenon_intro zenon_H37 ]. % 0.53/0.76 generalize (zenon_H55 zenon_TU_s). zenon_intro zenon_H58. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H10 | zenon_intro zenon_H59 ]. % 0.53/0.76 apply (zenon_L2_ zenon_TU_s zenon_TV_r); trivial. % 0.53/0.76 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H16 | zenon_intro zenon_H17 ]. % 0.53/0.76 generalize (zenon_H54 zenon_TX_bf). zenon_intro zenon_H5a. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ]. % 0.53/0.76 exact (zenon_H5c zenon_H35). % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H2c | zenon_intro zenon_H33 ]. % 0.53/0.76 apply (zenon_L4_ zenon_TU_s zenon_TV_r zenon_TY_be zenon_TX_bf); trivial. % 0.53/0.76 apply (zenon_L5_ zenon_TY_be zenon_TX_bf); trivial. % 0.53/0.76 exact (zenon_Hf zenon_H17). % 0.53/0.76 apply (zenon_L6_ zenon_TV_r zenon_TU_s); trivial. % 0.53/0.76 apply (zenon_L7_ zenon_TU_s zenon_TV_r); trivial. % 0.53/0.76 generalize (apart1 zenon_TV_r). zenon_intro zenon_H39. % 0.53/0.76 generalize (apart1 zenon_TY_be). zenon_intro zenon_H3c. % 0.53/0.76 generalize (apart4 zenon_TU_s). zenon_intro zenon_H4c. % 0.53/0.76 generalize (zenon_H4c zenon_TV_r). zenon_intro zenon_Hd. % 0.53/0.76 generalize (con1 zenon_TU_s). zenon_intro zenon_H4d. % 0.53/0.76 generalize (con1 zenon_TX_bf). zenon_intro zenon_H4e. % 0.53/0.76 generalize (zenon_H4d zenon_TV_r). zenon_intro zenon_H4f. % 0.53/0.76 generalize (apart4 zenon_TV_r). zenon_intro zenon_H50. % 0.53/0.76 generalize (cu1 zenon_TV_r). zenon_intro zenon_H51. % 0.53/0.76 generalize (zenon_H4f zenon_TV_r). zenon_intro zenon_H52. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H15 | zenon_intro zenon_H53 ]. % 0.53/0.76 exact (zenon_H15 zenon_He). % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H1c | zenon_intro zenon_H38 ]. % 0.53/0.76 generalize (zenon_H4e zenon_TY_be). zenon_intro zenon_H54. % 0.53/0.76 generalize (apart1 zenon_TU_s). zenon_intro zenon_Hf. % 0.53/0.76 generalize (ceq2 zenon_TY_be). zenon_intro zenon_H5d. % 0.53/0.76 generalize (zenon_H50 zenon_TU_s). zenon_intro zenon_H55. % 0.53/0.76 generalize (zenon_H51 zenon_TU_s). zenon_intro zenon_H18. % 0.53/0.76 generalize (zenon_H54 zenon_TY_be). zenon_intro zenon_H5e. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5c | zenon_intro zenon_H5f ]. % 0.53/0.76 exact (zenon_H5c zenon_H35). % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H60 | zenon_intro zenon_H3b ]. % 0.53/0.76 generalize (zenon_H4f zenon_TU_s). zenon_intro zenon_H56. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H15 | zenon_intro zenon_H57 ]. % 0.53/0.76 exact (zenon_H15 zenon_He). % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H1a | zenon_intro zenon_H37 ]. % 0.53/0.76 generalize (zenon_H55 zenon_TU_s). zenon_intro zenon_H58. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H10 | zenon_intro zenon_H59 ]. % 0.53/0.76 apply (zenon_L2_ zenon_TU_s zenon_TV_r); trivial. % 0.53/0.76 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H16 | zenon_intro zenon_H17 ]. % 0.53/0.76 generalize (zenon_H5d (line_connecting zenon_TU_s zenon_TV_r)). zenon_intro zenon_H61. % 0.53/0.76 generalize (zenon_H61 (line_connecting zenon_TX_bf zenon_TY_be)). zenon_intro zenon_H62. % 0.53/0.76 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.53/0.76 exact (zenon_H64 zenon_H4b). % 0.53/0.76 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H1d | zenon_intro zenon_H65 ]. % 0.53/0.76 apply (zenon_L3_ zenon_TY_be zenon_TX_bf zenon_TU_s zenon_TV_r); trivial. % 0.53/0.76 exact (zenon_H60 zenon_H65). % 0.53/0.76 exact (zenon_Hf zenon_H17). % 0.53/0.76 apply (zenon_L6_ zenon_TV_r zenon_TU_s); trivial. % 0.53/0.76 apply (zenon_L8_ zenon_TX_bf zenon_TY_be); trivial. % 0.53/0.76 apply (zenon_L7_ zenon_TU_s zenon_TV_r); trivial. % 0.53/0.76 Qed. % 0.53/0.76 % SZS output end Proof % 0.53/0.76 (* END-PROOF *) % 0.53/0.76 nodes searched: 19769 % 0.53/0.76 max branch formulas: 2779 % 0.53/0.76 proof nodes created: 1586 % 0.53/0.76 formulas created: 39938 % 0.53/0.76 %------------------------------------------------------------------------------