%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV140+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 25.13s 25.34s % Output : Proof 25.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SWV140+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.08/0.15 % Command : run_zenon %s %d % 0.14/0.37 % Computer : n025.cluster.edu % 0.14/0.37 % Model : x86_64 x86_64 % 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.37 % Memory : 8042.1875MB % 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.37 % CPULimit : 300 % 0.14/0.37 % WCLimit : 600 % 0.14/0.37 % DateTime : Thu Jun 16 06:57:41 EDT 2022 % 0.14/0.37 % CPUTime : % 25.13/25.34 (* PROOF-FOUND *) % 25.13/25.34 % SZS status Theorem % 25.13/25.34 (* BEGIN-PROOF *) % 25.13/25.34 % SZS output start Proof % 25.13/25.34 Theorem gauss_array_0010 : (((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_sworst7))). % 25.13/25.34 Proof. % 25.13/25.34 assert (zenon_L1_ : (~(gt (succ (loopcounter)) (succ (n0)))) -> (gt (succ (loopcounter)) (n1)) -> False). % 25.13/25.34 do 0 intro. intros zenon_H55 zenon_H56. % 25.13/25.34 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ]. % 25.13/25.34 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (loopcounter)) (succ (n0)))). % 25.13/25.34 intro zenon_D_pnotp. % 25.13/25.34 apply zenon_H55. % 25.13/25.34 rewrite <- zenon_D_pnotp. % 25.13/25.34 exact zenon_H56. % 25.13/25.34 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 25.13/25.34 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 25.13/25.34 congruence. % 25.13/25.34 apply zenon_H59. apply refl_equal. % 25.13/25.34 exact (zenon_H58 zenon_H57). % 25.13/25.34 apply zenon_H58. apply sym_equal. exact successor_1. % 25.13/25.34 (* end of lemma zenon_L1_ *) % 25.13/25.34 assert (zenon_L2_ : (leq (n0) (s_sworst7)) -> (~(gt (succ (s_sworst7)) (n0))) -> False). % 25.13/25.34 do 0 intro. intros zenon_H5a zenon_H5b. % 25.13/25.34 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5c. % 25.13/25.34 generalize (zenon_H5c (s_sworst7)). zenon_intro zenon_H5d. % 25.13/25.34 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ]. % 25.13/25.34 exact (zenon_H5f zenon_H5a). % 25.13/25.34 exact (zenon_H5b zenon_H5e). % 25.13/25.34 (* end of lemma zenon_L2_ *) % 25.13/25.34 apply NNPP. intro zenon_G. % 25.13/25.34 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71. % 25.13/25.34 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 25.13/25.34 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H75. % 25.13/25.34 generalize (zenon_H75 (loopcounter)). zenon_intro zenon_H76. % 25.13/25.34 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H78; zenon_intro zenon_H77 | zenon_intro zenon_H64; zenon_intro zenon_H56 ]. % 25.13/25.34 exact (zenon_H78 zenon_H64). % 25.13/25.34 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5c. % 25.13/25.34 generalize (zenon_H5c (s_sworst7)). zenon_intro zenon_H5d. % 25.13/25.34 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ]. % 25.13/25.34 apply (zenon_imply_s _ _ zenon_H74); [ zenon_intro zenon_H79 | zenon_intro zenon_H5a ]. % 25.13/25.34 generalize (leq_succ_gt (n0)). zenon_intro zenon_H7a. % 25.13/25.34 generalize (zenon_H7a (loopcounter)). zenon_intro zenon_H7b. % 25.13/25.34 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 25.13/25.34 generalize (leq_succ_gt_equiv (succ (n0))). zenon_intro zenon_H7e. % 25.13/25.34 generalize (zenon_H7e (loopcounter)). zenon_intro zenon_H7f. % 25.13/25.34 apply (zenon_equiv_s _ _ zenon_H7f); [ zenon_intro zenon_H7d; zenon_intro zenon_H55 | zenon_intro zenon_H81; zenon_intro zenon_H80 ]. % 25.13/25.36 apply (zenon_L1_); trivial. % 25.13/25.36 exact (zenon_H7d zenon_H81). % 25.13/25.36 exact (zenon_H79 zenon_H7c). % 25.13/25.36 apply (zenon_L2_); trivial. % 25.13/25.36 exact (zenon_H5f zenon_H5a). % 25.13/25.36 Qed. % 25.13/25.36 % SZS output end Proof % 25.13/25.36 (* END-PROOF *) % 25.13/25.36 nodes searched: 1557500 % 25.13/25.36 max branch formulas: 29169 % 25.13/25.36 proof nodes created: 2540 % 25.13/25.36 formulas created: 382414 % 25.13/25.36 %------------------------------------------------------------------------------