%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV138+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 : Wed Jul 20 23:03:04 EDT 2022 % Result : Theorem 0.48s 0.66s % Output : Proof 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWV138+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.07/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n013.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Tue Jun 14 18:56:44 EDT 2022 % 0.14/0.35 % CPUTime : % 0.48/0.66 (* PROOF-FOUND *) % 0.48/0.66 % SZS status Theorem % 0.48/0.66 (* BEGIN-PROOF *) % 0.48/0.66 % SZS output start Proof % 0.48/0.66 Theorem gauss_array_0008 : (((leq (n0) (s_best7))/\((leq (n0) (s_sworst7))/\((leq (n0) (s_worst7))/\((leq (n2) (pv1325))/\((leq (s_best7) (n3))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv1325) (n3))/\(gt (a_select2 (s_values7) (pv1325)) (a_select2 (s_values7) (s_best7)))))))))))->(leq (n0) (pv1325))). % 0.48/0.66 Proof. % 0.48/0.66 assert (zenon_L1_ : (~((n0) = (n0))) -> False). % 0.48/0.66 do 0 intro. intros zenon_H55. % 0.48/0.66 apply zenon_H55. apply refl_equal. % 0.48/0.66 (* end of lemma zenon_L1_ *) % 0.48/0.66 apply NNPP. intro zenon_G. % 0.48/0.66 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z))))))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 0.48/0.66 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H59. zenon_intro zenon_H58. % 0.48/0.66 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5b. zenon_intro zenon_H5a. % 0.48/0.66 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 0.48/0.66 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e. % 0.48/0.66 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H61. zenon_intro zenon_H60. % 0.48/0.66 generalize (leq_succ_gt_equiv (n2)). zenon_intro zenon_H62. % 0.48/0.66 generalize (zenon_H62 (pv1325)). zenon_intro zenon_H63. % 0.48/0.66 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H66; zenon_intro zenon_H65 | zenon_intro zenon_H61; zenon_intro zenon_H64 ]. % 0.48/0.66 exact (zenon_H66 zenon_H61). % 0.48/0.66 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.48/0.66 generalize (zenon_H67 (pv1325)). zenon_intro zenon_H68. % 0.48/0.66 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H58; zenon_intro zenon_H6b | zenon_intro zenon_H6a; zenon_intro zenon_H69 ]. % 0.48/0.66 elim (classic ((~((succ (pv1325)) = (n2)))/\(~(gt (succ (pv1325)) (n2))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 0.48/0.66 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H65. % 0.48/0.66 exact (zenon_H65 zenon_H64). % 0.48/0.66 cut ((gt (n2) (n0)) = (gt (succ (pv1325)) (n0))). % 0.48/0.66 intro zenon_D_pnotp. % 0.48/0.66 apply zenon_H6b. % 0.48/0.66 rewrite <- zenon_D_pnotp. % 0.48/0.66 exact gt_2_0. % 0.48/0.66 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 0.48/0.66 cut (((n2) = (succ (pv1325)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 0.48/0.66 congruence. % 0.48/0.66 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H71 | zenon_intro zenon_H70 ]. % 0.48/0.66 apply zenon_H71. zenon_intro zenon_H72. % 0.48/0.66 elim (classic ((succ (pv1325)) = (succ (pv1325)))); [ zenon_intro zenon_H73 | zenon_intro zenon_H74 ]. % 0.48/0.66 cut (((succ (pv1325)) = (succ (pv1325))) = ((n2) = (succ (pv1325)))). % 0.48/0.66 intro zenon_D_pnotp. % 0.48/0.66 apply zenon_H6f. % 0.48/0.66 rewrite <- zenon_D_pnotp. % 0.48/0.66 exact zenon_H73. % 0.48/0.66 cut (((succ (pv1325)) = (succ (pv1325)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 0.48/0.66 cut (((succ (pv1325)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 0.48/0.66 congruence. % 0.48/0.66 exact (zenon_H6e zenon_H72). % 0.48/0.66 apply zenon_H74. apply refl_equal. % 0.48/0.66 apply zenon_H74. apply refl_equal. % 0.48/0.66 apply zenon_H70. zenon_intro zenon_H64. % 0.48/0.66 generalize (zenon_H56 (succ (pv1325))). zenon_intro zenon_H75. % 0.48/0.66 generalize (zenon_H75 (n2)). zenon_intro zenon_H76. % 0.48/0.66 generalize (zenon_H76 (n0)). zenon_intro zenon_H77. % 0.48/0.66 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H65 | zenon_intro zenon_H78 ]. % 0.48/0.66 exact (zenon_H65 zenon_H64). % 0.48/0.66 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H69 ]. % 0.48/0.66 exact (zenon_H79 gt_2_0). % 0.48/0.66 exact (zenon_H6b zenon_H69). % 0.48/0.66 apply zenon_H55. apply refl_equal. % 0.48/0.66 exact (zenon_H58 zenon_H6a). % 0.48/0.66 apply zenon_H57. zenon_intro zenon_Tx_es. apply NNPP. zenon_intro zenon_H7b. % 0.48/0.66 apply zenon_H7b. zenon_intro zenon_Ty_eu. apply NNPP. zenon_intro zenon_H7d. % 0.48/0.66 apply zenon_H7d. zenon_intro zenon_Tz_ew. apply NNPP. zenon_intro zenon_H7f. % 0.48/0.66 apply (zenon_notimply_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 0.48/0.66 apply (zenon_notimply_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 0.48/0.66 generalize (transitivity_gt zenon_Tx_es). zenon_intro zenon_H84. % 0.48/0.66 generalize (zenon_H84 zenon_Ty_eu). zenon_intro zenon_H85. % 0.48/0.66 generalize (zenon_H85 zenon_Tz_ew). zenon_intro zenon_H86. % 0.48/0.66 apply (zenon_imply_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 0.48/0.66 apply (zenon_notand_s _ _ zenon_H88); [ zenon_intro zenon_H8a | zenon_intro zenon_H89 ]. % 0.48/0.66 exact (zenon_H8a zenon_H81). % 0.48/0.66 exact (zenon_H89 zenon_H83). % 0.48/0.66 exact (zenon_H82 zenon_H87). % 0.48/0.66 Qed. % 0.48/0.66 % SZS output end Proof % 0.48/0.66 (* END-PROOF *) % 0.48/0.66 nodes searched: 4187 % 0.48/0.66 max branch formulas: 984 % 0.48/0.66 proof nodes created: 8 % 0.48/0.66 formulas created: 15114 % 0.48/0.66 %------------------------------------------------------------------------------