%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV142+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 86.82s 87.03s % Output : Proof 86.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV142+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n010.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 : Tue Jun 14 14:18:24 EDT 2022 % 0.12/0.34 % CPUTime : % 86.82/87.03 (* PROOF-FOUND *) % 86.82/87.03 % SZS status Theorem % 86.82/87.03 (* BEGIN-PROOF *) % 86.82/87.03 % SZS output start Proof % 86.82/87.03 Theorem gauss_array_0012 : (((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_best7) (n3))). % 86.82/87.03 Proof. % 86.82/87.03 assert (zenon_L1_ : (~(gt (succ (loopcounter)) (succ (n0)))) -> (gt (succ (loopcounter)) (n1)) -> False). % 86.82/87.03 do 0 intro. intros zenon_H55 zenon_H56. % 86.82/87.03 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ]. % 86.82/87.03 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (loopcounter)) (succ (n0)))). % 86.82/87.03 intro zenon_D_pnotp. % 86.82/87.03 apply zenon_H55. % 86.82/87.03 rewrite <- zenon_D_pnotp. % 86.82/87.03 exact zenon_H56. % 86.82/87.03 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 86.82/87.03 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 86.82/87.03 congruence. % 86.82/87.03 apply zenon_H59. apply refl_equal. % 86.82/87.03 exact (zenon_H58 zenon_H57). % 86.82/87.03 apply zenon_H58. apply sym_equal. exact successor_1. % 86.82/87.03 (* end of lemma zenon_L1_ *) % 86.82/87.03 assert (zenon_L2_ : (leq (s_best7) (n3)) -> (~(gt (succ (n3)) (s_best7))) -> False). % 86.82/87.03 do 0 intro. intros zenon_H5a zenon_H5b. % 86.82/87.03 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H5c. % 86.82/87.03 generalize (zenon_H5c (n3)). zenon_intro zenon_H5d. % 86.82/87.03 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ]. % 86.82/87.03 exact (zenon_H5f zenon_H5a). % 86.82/87.03 exact (zenon_H5b zenon_H5e). % 86.82/87.03 (* end of lemma zenon_L2_ *) % 86.82/87.03 apply NNPP. intro zenon_G. % 86.82/87.03 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 86.82/87.03 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 86.82/87.03 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H79. % 86.82/87.03 generalize (zenon_H79 (loopcounter)). zenon_intro zenon_H7a. % 86.82/87.03 apply (zenon_equiv_s _ _ zenon_H7a); [ zenon_intro zenon_H7c; zenon_intro zenon_H7b | zenon_intro zenon_H64; zenon_intro zenon_H56 ]. % 86.82/87.03 exact (zenon_H7c zenon_H64). % 86.82/87.03 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H5c. % 86.82/87.03 generalize (zenon_H5c (n3)). zenon_intro zenon_H5d. % 86.82/87.03 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ]. % 86.82/87.03 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7d | zenon_intro zenon_H5a ]. % 86.82/87.03 generalize (leq_succ_gt (n0)). zenon_intro zenon_H7e. % 86.82/87.03 generalize (zenon_H7e (loopcounter)). zenon_intro zenon_H7f. % 86.82/87.03 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H81 | zenon_intro zenon_H80 ]. % 86.82/87.03 generalize (leq_succ_gt_equiv (succ (n0))). zenon_intro zenon_H82. % 86.82/87.03 generalize (zenon_H82 (loopcounter)). zenon_intro zenon_H83. % 86.82/87.06 apply (zenon_equiv_s _ _ zenon_H83); [ zenon_intro zenon_H81; zenon_intro zenon_H55 | zenon_intro zenon_H85; zenon_intro zenon_H84 ]. % 86.82/87.06 apply (zenon_L1_); trivial. % 86.82/87.06 exact (zenon_H81 zenon_H85). % 86.82/87.06 exact (zenon_H7d zenon_H80). % 86.82/87.06 apply (zenon_L2_); trivial. % 86.82/87.06 exact (zenon_H5f zenon_H5a). % 86.82/87.06 Qed. % 86.82/87.06 % SZS output end Proof % 86.82/87.06 (* END-PROOF *) % 86.82/87.06 nodes searched: 6056427 % 86.82/87.06 max branch formulas: 44098 % 86.82/87.06 proof nodes created: 12099 % 86.82/87.06 formulas created: 1637727 % 86.82/87.06 %------------------------------------------------------------------------------