%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV155+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 23:03:08 EDT 2022 % Result : Theorem 73.31s 73.47s % Output : Proof 73.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV155+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n018.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 00:09:30 EDT 2022 % 0.12/0.33 % CPUTime : % 73.31/73.47 (* PROOF-FOUND *) % 73.31/73.47 % SZS status Theorem % 73.31/73.47 (* BEGIN-PROOF *) % 73.31/73.47 % SZS output start Proof % 73.31/73.47 Theorem cl5_nebula_norm_0005 : ((((pv70) = (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))/\((leq (n0) (pv10))/\((leq (n0) (pv12))/\((leq (pv10) (n135299))/\((leq (pv12) (n4))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (pred (pv12))))->((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))))))))))/\(forall B : zenon_U, (((leq (n0) B)/\(leq B (pred (pv10))))->((sum (n0) (n4) (a_select3 (q) B (tptp_sum_index))) = (n1))))))))))->(forall C : zenon_U, (((leq (n0) C)/\(leq C (pred (pv10))))->((~((pv10) = C))->((sum (n0) (n4) (a_select3 (q) C (tptp_sum_index))) = (n1)))))). % 73.31/73.47 Proof. % 73.31/73.47 apply NNPP. intro zenon_G. % 73.31/73.47 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 73.31/73.47 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H5f. zenon_intro zenon_H5e. % 73.31/73.47 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H61. zenon_intro zenon_H60. % 73.31/73.47 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62. % 73.31/73.47 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H65. zenon_intro zenon_H64. % 73.31/73.47 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H67. zenon_intro zenon_H66. % 73.31/73.47 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68. % 73.31/73.47 apply (zenon_notallex_s (fun C : zenon_U => (((leq (n0) C)/\(leq C (pred (pv10))))->((~((pv10) = C))->((sum (n0) (n4) (a_select3 (q) C (tptp_sum_index))) = (n1))))) zenon_H5c); [ zenon_intro zenon_H6a; idtac ]. % 73.31/73.47 elim zenon_H6a. zenon_intro zenon_TC_ed. zenon_intro zenon_H6c. % 73.31/73.47 apply (zenon_notimply_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 73.31/73.47 apply (zenon_notimply_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 73.31/73.47 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H72. zenon_intro zenon_H71. % 73.31/73.47 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H73. % 73.31/73.47 generalize (zenon_H73 zenon_TC_ed). zenon_intro zenon_H74. % 73.31/73.47 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H77; zenon_intro zenon_H76 | zenon_intro zenon_H72; zenon_intro zenon_H75 ]. % 73.31/73.47 exact (zenon_H77 zenon_H72). % 73.31/73.47 generalize (leq_succ_gt_equiv zenon_TC_ed). zenon_intro zenon_H78. % 73.31/73.47 generalize (zenon_H78 (pred (pv10))). zenon_intro zenon_H79. % 73.31/73.47 apply (zenon_equiv_s _ _ zenon_H79); [ zenon_intro zenon_H7c; zenon_intro zenon_H7b | zenon_intro zenon_H71; zenon_intro zenon_H7a ]. % 73.31/73.47 exact (zenon_H7c zenon_H71). % 73.31/73.47 generalize (zenon_H68 zenon_TC_ed). zenon_intro zenon_H7d. % 73.31/73.47 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 73.31/73.47 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H77 | zenon_intro zenon_H7c ]. % 73.31/73.47 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H73. % 73.31/73.47 generalize (zenon_H73 zenon_TC_ed). zenon_intro zenon_H74. % 73.31/73.47 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H77; zenon_intro zenon_H76 | zenon_intro zenon_H72; zenon_intro zenon_H75 ]. % 73.31/73.47 exact (zenon_H76 zenon_H75). % 73.31/73.47 exact (zenon_H77 zenon_H72). % 73.31/73.47 generalize (leq_succ_gt_equiv zenon_TC_ed). zenon_intro zenon_H78. % 73.31/73.47 generalize (zenon_H78 (pred (pv10))). zenon_intro zenon_H79. % 73.31/73.47 apply (zenon_equiv_s _ _ zenon_H79); [ zenon_intro zenon_H7c; zenon_intro zenon_H7b | zenon_intro zenon_H71; zenon_intro zenon_H7a ]. % 73.31/73.47 exact (zenon_H7b zenon_H7a). % 73.31/73.47 exact (zenon_H7c zenon_H71). % 73.31/73.47 exact (zenon_H6f zenon_H7e). % 73.31/73.47 Qed. % 73.31/73.47 % SZS output end Proof % 73.31/73.47 (* END-PROOF *) % 73.31/73.47 nodes searched: 6114855 % 73.31/73.47 max branch formulas: 31360 % 73.31/73.47 proof nodes created: 16839 % 73.31/73.47 formulas created: 1657002 % 73.31/73.47 %------------------------------------------------------------------------------