%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : PRO009+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 : Mon Jul 18 17:56:22 EDT 2022 % Result : Theorem 13.89s 14.12s % Output : Proof 13.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : PRO009+2 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n016.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jun 13 03:40:58 EDT 2022 % 0.13/0.33 % CPUTime : % 13.89/14.12 (* PROOF-FOUND *) % 13.89/14.12 % SZS status Theorem % 13.89/14.12 (* BEGIN-PROOF *) % 13.89/14.12 % SZS output start Proof % 13.89/14.12 Theorem goals : (forall X99 : zenon_U, ((occurrence_of X99 (tptp0))->(exists X100 : zenon_U, (exists X101 : zenon_U, ((occurrence_of X100 (tptp3))/\((root_occ X100 X99)/\(((occurrence_of X101 (tptp2))\/(occurrence_of X101 (tptp1)))/\((min_precedes X100 X101 (tptp0))/\(leaf_occ X101 X99))))))))). % 13.89/14.12 Proof. % 13.89/14.12 assert (zenon_L1_ : forall (zenon_TX96_bv : zenon_U) (zenon_TX99_bw : zenon_U), (exists X34 : zenon_U, ((occurrence_of zenon_TX99_bw X34)/\((subactivity_occurrence zenon_TX96_bv zenon_TX99_bw)/\(root zenon_TX96_bv X34)))) -> (~(root_occ zenon_TX96_bv zenon_TX99_bw)) -> False). % 13.89/14.12 do 2 intro. intros zenon_H2d zenon_H2e. % 13.89/14.12 generalize (sos_10 zenon_TX96_bv). zenon_intro zenon_H31. % 13.89/14.12 generalize (zenon_H31 zenon_TX99_bw). zenon_intro zenon_H32. % 13.89/14.12 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H2e; zenon_intro zenon_H34 | zenon_intro zenon_H33; zenon_intro zenon_H2d ]. % 13.89/14.12 exact (zenon_H34 zenon_H2d). % 13.89/14.12 exact (zenon_H2e zenon_H33). % 13.89/14.12 (* end of lemma zenon_L1_ *) % 13.89/14.12 assert (zenon_L2_ : forall (zenon_TX97_ce : zenon_U) (zenon_TX98_cf : zenon_U) (zenon_TX96_bv : zenon_U), (~(min_precedes zenon_TX96_bv zenon_TX98_cf (tptp0))) -> (min_precedes zenon_TX97_ce zenon_TX98_cf (tptp0)) -> (min_precedes zenon_TX96_bv zenon_TX97_ce (tptp0)) -> False). % 13.89/14.12 do 3 intro. intros zenon_H35 zenon_H36 zenon_H37. % 13.89/14.12 generalize (sos zenon_TX96_bv). zenon_intro zenon_H3a. % 13.89/14.12 generalize (zenon_H3a zenon_TX97_ce). zenon_intro zenon_H3b. % 13.89/14.12 generalize (zenon_H3b zenon_TX98_cf). zenon_intro zenon_H3c. % 13.89/14.12 generalize (zenon_H3c (tptp0)). zenon_intro zenon_H3d. % 13.89/14.12 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 13.89/14.12 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 13.89/14.12 exact (zenon_H41 zenon_H37). % 13.89/14.12 exact (zenon_H40 zenon_H36). % 13.89/14.12 exact (zenon_H35 zenon_H3e). % 13.89/14.12 (* end of lemma zenon_L2_ *) % 13.89/14.12 assert (zenon_L3_ : forall (zenon_TX98_cf : zenon_U) (zenon_TX99_bw : zenon_U), (exists X37 : zenon_U, ((occurrence_of zenon_TX99_bw X37)/\((subactivity_occurrence zenon_TX98_cf zenon_TX99_bw)/\(leaf zenon_TX98_cf X37)))) -> (~(leaf_occ zenon_TX98_cf zenon_TX99_bw)) -> False). % 13.89/14.13 do 2 intro. intros zenon_H42 zenon_H43. % 13.89/14.13 generalize (sos_11 zenon_TX98_cf). zenon_intro zenon_H44. % 13.89/14.13 generalize (zenon_H44 zenon_TX99_bw). zenon_intro zenon_H45. % 13.89/14.13 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H43; zenon_intro zenon_H47 | zenon_intro zenon_H46; zenon_intro zenon_H42 ]. % 13.89/14.13 exact (zenon_H47 zenon_H42). % 13.89/14.13 exact (zenon_H43 zenon_H46). % 13.89/14.13 (* end of lemma zenon_L3_ *) % 13.89/14.13 apply NNPP. intro zenon_G. % 13.89/14.13 apply (zenon_notallex_s (fun X99 : zenon_U => ((occurrence_of X99 (tptp0))->(exists X100 : zenon_U, (exists X101 : zenon_U, ((occurrence_of X100 (tptp3))/\((root_occ X100 X99)/\(((occurrence_of X101 (tptp2))\/(occurrence_of X101 (tptp1)))/\((min_precedes X100 X101 (tptp0))/\(leaf_occ X101 X99))))))))) zenon_G); [ zenon_intro zenon_H48; idtac ]. % 13.89/14.13 elim zenon_H48. zenon_intro zenon_TX99_bw. zenon_intro zenon_H49. % 13.89/14.13 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 13.89/14.13 generalize (sos_32 zenon_TX99_bw). zenon_intro zenon_H4c. % 13.89/14.13 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 13.89/14.13 exact (zenon_H4e zenon_H4b). % 13.89/14.13 elim zenon_H4d. zenon_intro zenon_TX96_bv. zenon_intro zenon_H4f. % 13.89/14.13 elim zenon_H4f. zenon_intro zenon_TX97_ce. zenon_intro zenon_H50. % 13.89/14.13 elim zenon_H50. zenon_intro zenon_TX98_cf. zenon_intro zenon_H51. % 13.89/14.13 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52. % 13.89/14.13 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H33. zenon_intro zenon_H54. % 13.89/14.13 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H55. % 13.89/14.13 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57. % 13.89/14.13 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 13.89/14.13 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5b. zenon_intro zenon_H46. % 13.89/14.13 generalize (sos_10 zenon_TX96_bv). zenon_intro zenon_H31. % 13.89/14.13 generalize (zenon_H31 zenon_TX99_bw). zenon_intro zenon_H32. % 13.89/14.13 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H2e; zenon_intro zenon_H34 | zenon_intro zenon_H33; zenon_intro zenon_H2d ]. % 13.89/14.13 exact (zenon_H2e zenon_H33). % 13.89/14.13 generalize (sos_04 zenon_TX96_bv). zenon_intro zenon_H5c. % 13.89/14.13 generalize (zenon_H5c zenon_TX97_ce). zenon_intro zenon_H5d. % 13.89/14.13 generalize (zenon_H5d (tptp0)). zenon_intro zenon_H5e. % 13.89/14.13 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H61; zenon_intro zenon_H60 | zenon_intro zenon_H58; zenon_intro zenon_H5f ]. % 13.89/14.13 exact (zenon_H61 zenon_H58). % 13.89/14.13 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H37. zenon_intro zenon_H62. % 13.89/14.13 generalize (sos_04 zenon_TX97_ce). zenon_intro zenon_H63. % 13.89/14.13 generalize (zenon_H63 zenon_TX98_cf). zenon_intro zenon_H64. % 13.89/14.13 generalize (zenon_H64 (tptp0)). zenon_intro zenon_H65. % 13.89/14.13 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H68; zenon_intro zenon_H67 | zenon_intro zenon_H5b; zenon_intro zenon_H66 ]. % 13.89/14.13 exact (zenon_H68 zenon_H5b). % 13.89/14.13 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H36. zenon_intro zenon_H69. % 13.89/14.13 generalize (sos_11 zenon_TX98_cf). zenon_intro zenon_H44. % 13.89/14.13 generalize (zenon_H44 zenon_TX99_bw). zenon_intro zenon_H45. % 13.89/14.13 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H43; zenon_intro zenon_H47 | zenon_intro zenon_H46; zenon_intro zenon_H42 ]. % 13.89/14.13 exact (zenon_H43 zenon_H46). % 13.89/14.13 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ]. % 13.89/14.13 apply zenon_H4a. exists zenon_TX96_bv. apply NNPP. zenon_intro zenon_H6c. % 13.89/14.13 apply zenon_H6c. exists zenon_TX98_cf. apply NNPP. zenon_intro zenon_H6d. % 13.89/14.13 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 13.89/14.13 exact (zenon_H6f zenon_H53). % 13.89/14.13 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H2e | zenon_intro zenon_H70 ]. % 13.89/14.13 apply (zenon_L1_ zenon_TX96_bv zenon_TX99_bw); trivial. % 13.89/14.13 apply (zenon_notand_s _ _ zenon_H70); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ]. % 13.89/14.13 apply (zenon_notor_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73. % 13.89/14.13 exact (zenon_H74 zenon_H6b). % 13.89/14.13 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H35 | zenon_intro zenon_H43 ]. % 13.89/14.13 apply (zenon_L2_ zenon_TX97_ce zenon_TX98_cf zenon_TX96_bv); trivial. % 13.89/14.13 apply (zenon_L3_ zenon_TX98_cf zenon_TX99_bw); trivial. % 13.89/14.13 apply zenon_H4a. exists zenon_TX96_bv. apply NNPP. zenon_intro zenon_H6c. % 13.89/14.13 apply zenon_H6c. exists zenon_TX98_cf. apply NNPP. zenon_intro zenon_H6d. % 13.89/14.13 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 13.89/14.13 exact (zenon_H6f zenon_H53). % 13.89/14.13 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H2e | zenon_intro zenon_H70 ]. % 13.89/14.13 apply (zenon_L1_ zenon_TX96_bv zenon_TX99_bw); trivial. % 13.89/14.13 apply (zenon_notand_s _ _ zenon_H70); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ]. % 13.89/14.13 apply (zenon_notor_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73. % 13.89/14.13 exact (zenon_H73 zenon_H6a). % 13.89/14.13 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H35 | zenon_intro zenon_H43 ]. % 13.89/14.13 apply (zenon_L2_ zenon_TX97_ce zenon_TX98_cf zenon_TX96_bv); trivial. % 13.89/14.13 apply (zenon_L3_ zenon_TX98_cf zenon_TX99_bw); trivial. % 13.89/14.13 Qed. % 13.89/14.13 % SZS output end Proof % 13.89/14.13 (* END-PROOF *) % 13.89/14.13 nodes searched: 488076 % 13.89/14.13 max branch formulas: 7639 % 13.89/14.13 proof nodes created: 23110 % 13.89/14.13 formulas created: 1313300 % 13.89/14.13 %------------------------------------------------------------------------------