%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV159+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 23:03:09 EDT 2022 % Result : Theorem 39.35s 39.55s % Output : Proof 39.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV159+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n008.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 04:10:37 EDT 2022 % 0.12/0.33 % CPUTime : % 39.35/39.55 (* PROOF-FOUND *) % 39.35/39.55 % SZS status Theorem % 39.35/39.55 (* BEGIN-PROOF *) % 39.35/39.55 % SZS output start Proof % 39.35/39.55 Theorem cl5_nebula_norm_0009 : ((((pv84) = (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index))))))/\((leq (n0) (pv10))/\((leq (n0) (pv47))/\((leq (pv10) (n135299))/\((leq (pv47) (n4))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (pred (pv47))))->((a_select3 (q) (pv10) A) = (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) A)) (minus (a_select2 (x) (pv10)) (a_select2 (mu) A))) (tptp_minus_2)) (times (a_select2 (sigma) A) (a_select2 (sigma) A)))) (a_select2 (rho) A)) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) A))) (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index)))))))))/\(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)))))). % 39.35/39.55 Proof. % 39.35/39.55 apply NNPP. intro zenon_G. % 39.35/39.55 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H65. zenon_intro zenon_H64. % 39.35/39.55 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 39.35/39.55 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68. % 39.35/39.55 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 39.35/39.55 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c. % 39.35/39.55 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 39.35/39.55 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70. % 39.35/39.55 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_H64); [ zenon_intro zenon_H72; idtac ]. % 39.35/39.55 elim zenon_H72. zenon_intro zenon_TC_el. zenon_intro zenon_H74. % 39.35/39.55 apply (zenon_notimply_s _ _ zenon_H74). zenon_intro zenon_H76. zenon_intro zenon_H75. % 39.35/39.55 apply (zenon_notimply_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 39.35/39.55 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H7a. zenon_intro zenon_H79. % 39.35/39.55 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H7b. % 39.35/39.55 generalize (zenon_H7b zenon_TC_el). zenon_intro zenon_H7c. % 39.35/39.55 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7f; zenon_intro zenon_H7e | zenon_intro zenon_H7a; zenon_intro zenon_H7d ]. % 39.35/39.55 exact (zenon_H7f zenon_H7a). % 39.35/39.55 generalize (leq_succ_gt_equiv zenon_TC_el). zenon_intro zenon_H80. % 39.35/39.55 generalize (zenon_H80 (pred (pv10))). zenon_intro zenon_H81. % 39.35/39.55 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H84; zenon_intro zenon_H83 | zenon_intro zenon_H79; zenon_intro zenon_H82 ]. % 39.35/39.55 exact (zenon_H84 zenon_H79). % 39.35/39.55 generalize (zenon_H70 zenon_TC_el). zenon_intro zenon_H85. % 39.35/39.55 apply (zenon_imply_s _ _ zenon_H85); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ]. % 39.35/39.55 apply (zenon_notand_s _ _ zenon_H87); [ zenon_intro zenon_H7f | zenon_intro zenon_H84 ]. % 39.35/39.55 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H7b. % 39.35/39.55 generalize (zenon_H7b zenon_TC_el). zenon_intro zenon_H7c. % 39.35/39.55 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7f; zenon_intro zenon_H7e | zenon_intro zenon_H7a; zenon_intro zenon_H7d ]. % 39.35/39.55 exact (zenon_H7e zenon_H7d). % 39.35/39.55 exact (zenon_H7f zenon_H7a). % 39.35/39.55 generalize (leq_succ_gt_equiv zenon_TC_el). zenon_intro zenon_H80. % 39.35/39.55 generalize (zenon_H80 (pred (pv10))). zenon_intro zenon_H81. % 39.35/39.55 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H84; zenon_intro zenon_H83 | zenon_intro zenon_H79; zenon_intro zenon_H82 ]. % 39.35/39.56 exact (zenon_H83 zenon_H82). % 39.35/39.56 exact (zenon_H84 zenon_H79). % 39.35/39.56 exact (zenon_H77 zenon_H86). % 39.35/39.56 Qed. % 39.35/39.56 % SZS output end Proof % 39.35/39.56 (* END-PROOF *) % 39.35/39.56 nodes searched: 2883627 % 39.35/39.56 max branch formulas: 24646 % 39.35/39.56 proof nodes created: 8616 % 39.35/39.56 formulas created: 864272 % 39.35/39.56 %------------------------------------------------------------------------------