%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV141+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 23:03:05 EDT 2022 % Result : Theorem 51.96s 52.15s % Output : Proof 51.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV141+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.14/0.34 % Computer : n020.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Tue Jun 14 23:53:49 EDT 2022 % 0.14/0.35 % CPUTime : % 51.96/52.15 (* PROOF-FOUND *) % 51.96/52.15 % SZS status Theorem % 51.96/52.15 (* BEGIN-PROOF *) % 51.96/52.15 % SZS output start Proof % 51.96/52.15 Theorem gauss_array_0011 : (((leq (tptp_float_0_001) (pv1341))/\((leq (n1) (loopcounter))/\(((~(leq (tptp_float_0_001) (pv1341)))->(leq (n0) (s_best7)))/\(((~(leq (tptp_float_0_001) (pv1341)))->(leq (n0) (s_sworst7)))/\(((~(leq (tptp_float_0_001) (pv1341)))->(leq (n0) (s_worst7)))/\(((~(leq (tptp_float_0_001) (pv1341)))->(leq (s_best7) (n3)))/\(((~(leq (tptp_float_0_001) (pv1341)))->(leq (s_sworst7) (n3)))/\(((~(leq (tptp_float_0_001) (pv1341)))->(leq (s_worst7) (n3)))/\(((gt (loopcounter) (n0))->(leq (n0) (s_best7)))/\(((gt (loopcounter) (n0))->(leq (n0) (s_sworst7)))/\(((gt (loopcounter) (n0))->(leq (n0) (s_worst7)))/\(((gt (loopcounter) (n0))->(leq (s_best7) (n3)))/\(((gt (loopcounter) (n0))->(leq (s_sworst7) (n3)))/\((gt (loopcounter) (n0))->(leq (s_worst7) (n3))))))))))))))))->(leq (n0) (s_worst7))). % 51.96/52.15 Proof. % 51.96/52.15 assert (zenon_L1_ : (~((n0) = (n0))) -> False). % 51.96/52.15 do 0 intro. intros zenon_H55. % 51.96/52.15 apply zenon_H55. apply refl_equal. % 51.96/52.15 (* end of lemma zenon_L1_ *) % 51.96/52.15 assert (zenon_L2_ : (leq (n0) (s_worst7)) -> (~(gt (succ (s_worst7)) (n0))) -> False). % 51.96/52.15 do 0 intro. intros zenon_H56 zenon_H57. % 51.96/52.15 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 51.96/52.15 generalize (zenon_H58 (s_worst7)). zenon_intro zenon_H59. % 51.96/52.15 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H5b; zenon_intro zenon_H57 | zenon_intro zenon_H56; zenon_intro zenon_H5a ]. % 51.96/52.15 exact (zenon_H5b zenon_H56). % 51.96/52.15 exact (zenon_H57 zenon_H5a). % 51.96/52.15 (* end of lemma zenon_L2_ *) % 51.96/52.15 apply NNPP. intro zenon_G. % 51.96/52.15 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_H5c | zenon_intro zenon_H5d ]. % 51.96/52.15 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H5e. zenon_intro zenon_H5b. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H62. zenon_intro zenon_H61. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 51.96/52.15 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H75. % 51.96/52.15 generalize (zenon_H75 (loopcounter)). zenon_intro zenon_H76. % 51.96/52.15 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H79; zenon_intro zenon_H78 | zenon_intro zenon_H62; zenon_intro zenon_H77 ]. % 51.96/52.15 exact (zenon_H79 zenon_H62). % 51.96/52.15 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58. % 51.96/52.15 generalize (zenon_H58 (s_worst7)). zenon_intro zenon_H59. % 51.96/52.15 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H5b; zenon_intro zenon_H57 | zenon_intro zenon_H56; zenon_intro zenon_H5a ]. % 51.96/52.15 apply (zenon_imply_s _ _ zenon_H74); [ zenon_intro zenon_H7a | zenon_intro zenon_H56 ]. % 51.96/52.15 elim (classic ((~((loopcounter) = (n1)))/\(~(gt (loopcounter) (n1))))); [ zenon_intro zenon_H7b | zenon_intro zenon_H7c ]. % 51.96/52.15 apply (zenon_and_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H7d. % 51.96/52.15 generalize (leq_gt2 (n1)). zenon_intro zenon_H7f. % 51.96/52.15 generalize (zenon_H7f (loopcounter)). zenon_intro zenon_H80. % 51.96/52.15 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H82 | zenon_intro zenon_H81 ]. % 51.96/52.15 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H79 | zenon_intro zenon_H83 ]. % 51.96/52.15 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H75. % 51.96/52.15 generalize (zenon_H75 (loopcounter)). zenon_intro zenon_H76. % 51.96/52.15 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H79; zenon_intro zenon_H78 | zenon_intro zenon_H62; zenon_intro zenon_H77 ]. % 51.96/52.15 exact (zenon_H78 zenon_H77). % 51.96/52.15 exact (zenon_H79 zenon_H62). % 51.96/52.18 apply zenon_H83. zenon_intro zenon_H84. % 51.96/52.18 apply zenon_H7e. apply sym_equal. exact zenon_H84. % 51.96/52.18 exact (zenon_H7d zenon_H81). % 51.96/52.18 cut ((gt (n1) (n0)) = (gt (loopcounter) (n0))). % 51.96/52.18 intro zenon_D_pnotp. % 51.96/52.18 apply zenon_H7a. % 51.96/52.18 rewrite <- zenon_D_pnotp. % 51.96/52.18 exact gt_1_0. % 51.96/52.18 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 51.96/52.18 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 51.96/52.18 congruence. % 51.96/52.18 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ]. % 51.96/52.18 apply zenon_H87. zenon_intro zenon_H88. % 51.96/52.18 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_H89 | zenon_intro zenon_H8a ]. % 51.96/52.18 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))). % 51.96/52.18 intro zenon_D_pnotp. % 51.96/52.18 apply zenon_H85. % 51.96/52.18 rewrite <- zenon_D_pnotp. % 51.96/52.18 exact zenon_H89. % 51.96/52.18 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 51.96/52.18 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 51.96/52.18 congruence. % 51.96/52.18 exact (zenon_H7e zenon_H88). % 51.96/52.18 apply zenon_H8a. apply refl_equal. % 51.96/52.18 apply zenon_H8a. apply refl_equal. % 51.96/52.18 apply zenon_H86. zenon_intro zenon_H81. % 51.96/52.18 generalize (zenon_H5c (loopcounter)). zenon_intro zenon_H8b. % 51.96/52.18 generalize (zenon_H8b (n1)). zenon_intro zenon_H8c. % 51.96/52.18 generalize (zenon_H8c (n0)). zenon_intro zenon_H8d. % 51.96/52.18 apply (zenon_imply_s _ _ zenon_H8d); [ zenon_intro zenon_H7d | zenon_intro zenon_H8e ]. % 51.96/52.18 exact (zenon_H7d zenon_H81). % 51.96/52.18 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H90 | zenon_intro zenon_H8f ]. % 51.96/52.18 exact (zenon_H90 gt_1_0). % 51.96/52.18 exact (zenon_H7a zenon_H8f). % 51.96/52.18 apply zenon_H55. apply refl_equal. % 51.96/52.18 apply (zenon_L2_); trivial. % 51.96/52.18 exact (zenon_H5b zenon_H56). % 51.96/52.18 apply zenon_H5d. zenon_intro zenon_Tx_fp. apply NNPP. zenon_intro zenon_H92. % 51.96/52.18 apply zenon_H92. zenon_intro zenon_Ty_fr. apply NNPP. zenon_intro zenon_H94. % 51.96/52.18 apply zenon_H94. zenon_intro zenon_Tz_ft. apply NNPP. zenon_intro zenon_H96. % 51.96/52.18 apply (zenon_notimply_s _ _ zenon_H96). zenon_intro zenon_H98. zenon_intro zenon_H97. % 51.96/52.18 apply (zenon_notimply_s _ _ zenon_H97). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 51.96/52.18 generalize (transitivity_gt zenon_Tx_fp). zenon_intro zenon_H9b. % 51.96/52.18 generalize (zenon_H9b zenon_Ty_fr). zenon_intro zenon_H9c. % 51.96/52.18 generalize (zenon_H9c zenon_Tz_ft). zenon_intro zenon_H9d. % 51.96/52.18 apply (zenon_imply_s _ _ zenon_H9d); [ zenon_intro zenon_H9f | zenon_intro zenon_H9e ]. % 51.96/52.18 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0 ]. % 51.96/52.18 exact (zenon_Ha1 zenon_H98). % 51.96/52.18 exact (zenon_Ha0 zenon_H9a). % 51.96/52.18 exact (zenon_H99 zenon_H9e). % 51.96/52.18 Qed. % 51.96/52.18 % SZS output end Proof % 51.96/52.18 (* END-PROOF *) % 51.96/52.18 nodes searched: 3455787 % 51.96/52.18 max branch formulas: 44107 % 51.96/52.18 proof nodes created: 5118 % 51.96/52.18 formulas created: 692262 % 51.96/52.18 %------------------------------------------------------------------------------