TSTP Solution File: SWV159+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% 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 :
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%----WARNING: Could not form TPTP format derivation
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%----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
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