%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV144+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.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 23:03:06 EDT 2022 % Result : Theorem 267.24s 267.46s % Output : Proof 267.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWV144+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.12/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n005.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 : Thu Jun 16 00:05:08 EDT 2022 % 0.12/0.33 % CPUTime : % 267.24/267.46 (* PROOF-FOUND *) % 267.24/267.46 % SZS status Theorem % 267.24/267.46 (* BEGIN-PROOF *) % 267.24/267.46 % SZS output start Proof % 267.24/267.46 Theorem gauss_array_0014 : (((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 (s_worst7) (n3))). % 267.24/267.46 Proof. % 267.24/267.46 assert (zenon_L1_ : (~(gt (succ (loopcounter)) (succ (n0)))) -> (gt (succ (loopcounter)) (n1)) -> False). % 267.24/267.46 do 0 intro. intros zenon_H55 zenon_H56. % 267.24/267.46 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ]. % 267.24/267.46 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (loopcounter)) (succ (n0)))). % 267.24/267.46 intro zenon_D_pnotp. % 267.24/267.46 apply zenon_H55. % 267.24/267.46 rewrite <- zenon_D_pnotp. % 267.24/267.46 exact zenon_H56. % 267.24/267.46 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 267.24/267.46 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 267.24/267.46 congruence. % 267.24/267.46 apply zenon_H59. apply refl_equal. % 267.24/267.46 exact (zenon_H58 zenon_H57). % 267.24/267.46 apply zenon_H58. apply sym_equal. exact successor_1. % 267.24/267.46 (* end of lemma zenon_L1_ *) % 267.24/267.46 assert (zenon_L2_ : (leq (s_worst7) (n3)) -> (~(gt (succ (n3)) (s_worst7))) -> False). % 267.24/267.46 do 0 intro. intros zenon_H5a zenon_H5b. % 267.24/267.46 generalize (leq_succ_gt_equiv (s_worst7)). zenon_intro zenon_H5c. % 267.24/267.46 generalize (zenon_H5c (n3)). zenon_intro zenon_H5d. % 267.24/267.46 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ]. % 267.24/267.46 exact (zenon_H5f zenon_H5a). % 267.24/267.46 exact (zenon_H5b zenon_H5e). % 267.24/267.46 (* end of lemma zenon_L2_ *) % 267.24/267.46 apply NNPP. intro zenon_G. % 267.24/267.46 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 267.24/267.46 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H7a. zenon_intro zenon_H79. % 267.24/267.46 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H7b. % 267.24/267.46 generalize (zenon_H7b (loopcounter)). zenon_intro zenon_H7c. % 267.24/267.46 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7e; zenon_intro zenon_H7d | zenon_intro zenon_H64; zenon_intro zenon_H56 ]. % 267.24/267.46 exact (zenon_H7e zenon_H64). % 267.24/267.46 generalize (leq_succ_gt_equiv (s_worst7)). zenon_intro zenon_H5c. % 267.24/267.46 generalize (zenon_H5c (n3)). zenon_intro zenon_H5d. % 267.24/267.46 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ]. % 267.24/267.46 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H7f | zenon_intro zenon_H5a ]. % 267.24/267.46 generalize (leq_succ_gt (n0)). zenon_intro zenon_H80. % 267.24/267.46 generalize (zenon_H80 (loopcounter)). zenon_intro zenon_H81. % 267.24/267.46 apply (zenon_imply_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 267.24/267.46 generalize (leq_succ_gt_equiv (succ (n0))). zenon_intro zenon_H84. % 267.24/267.48 generalize (zenon_H84 (loopcounter)). zenon_intro zenon_H85. % 267.24/267.48 apply (zenon_equiv_s _ _ zenon_H85); [ zenon_intro zenon_H83; zenon_intro zenon_H55 | zenon_intro zenon_H87; zenon_intro zenon_H86 ]. % 267.24/267.48 apply (zenon_L1_); trivial. % 267.24/267.48 exact (zenon_H83 zenon_H87). % 267.24/267.48 exact (zenon_H7f zenon_H82). % 267.24/267.48 apply (zenon_L2_); trivial. % 267.24/267.48 exact (zenon_H5f zenon_H5a). % 267.24/267.48 Qed. % 267.24/267.48 % SZS output end Proof % 267.24/267.48 (* END-PROOF *) % 267.24/267.48 nodes searched: 20815743 % 267.24/267.48 max branch formulas: 45753 % 267.24/267.48 proof nodes created: 40650 % 267.24/267.48 formulas created: 5250570 % 267.24/267.48 %------------------------------------------------------------------------------