TSTP Solution File: SWV135+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV135+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n023.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 23:03:04 EDT 2022
% Result : Theorem 0.44s 0.62s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV135+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.10/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n023.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 17:40:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.44/0.62 (* PROOF-FOUND *)
% 0.44/0.62 % SZS status Theorem
% 0.44/0.62 (* BEGIN-PROOF *)
% 0.44/0.62 % SZS output start Proof
% 0.44/0.62 Theorem gauss_array_0005 : (((leq (n0) (s_best7))/\((leq (n0) (s_sworst7))/\((leq (n0) (s_worst7))/\((leq (n2) (pv1325))/\((leq (s_best7) (n3))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\(leq (pv1325) (n3)))))))))->(leq (n0) (pv1325))).
% 0.44/0.62 Proof.
% 0.44/0.62 assert (zenon_L1_ : (~((n0) = (n0))) -> False).
% 0.44/0.62 do 0 intro. intros zenon_H55.
% 0.44/0.62 apply zenon_H55. apply refl_equal.
% 0.44/0.62 (* end of lemma zenon_L1_ *)
% 0.44/0.62 apply NNPP. intro zenon_G.
% 0.44/0.62 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z))))))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ].
% 0.44/0.62 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H59. zenon_intro zenon_H58.
% 0.44/0.62 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5b. zenon_intro zenon_H5a.
% 0.44/0.62 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 0.44/0.62 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 0.44/0.62 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H61. zenon_intro zenon_H60.
% 0.44/0.62 generalize (leq_succ_gt_equiv (n2)). zenon_intro zenon_H62.
% 0.44/0.62 generalize (zenon_H62 (pv1325)). zenon_intro zenon_H63.
% 0.44/0.62 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H66; zenon_intro zenon_H65 | zenon_intro zenon_H61; zenon_intro zenon_H64 ].
% 0.44/0.62 exact (zenon_H66 zenon_H61).
% 0.44/0.62 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67.
% 0.44/0.62 generalize (zenon_H67 (pv1325)). zenon_intro zenon_H68.
% 0.44/0.62 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H58; zenon_intro zenon_H6b | zenon_intro zenon_H6a; zenon_intro zenon_H69 ].
% 0.44/0.62 elim (classic ((~((succ (pv1325)) = (n2)))/\(~(gt (succ (pv1325)) (n2))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ].
% 0.44/0.62 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H65.
% 0.44/0.62 exact (zenon_H65 zenon_H64).
% 0.44/0.62 cut ((gt (n2) (n0)) = (gt (succ (pv1325)) (n0))).
% 0.44/0.62 intro zenon_D_pnotp.
% 0.44/0.62 apply zenon_H6b.
% 0.44/0.62 rewrite <- zenon_D_pnotp.
% 0.44/0.62 exact gt_2_0.
% 0.44/0.62 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H55].
% 0.44/0.62 cut (((n2) = (succ (pv1325)))); [idtac | apply NNPP; zenon_intro zenon_H6f].
% 0.44/0.62 congruence.
% 0.44/0.62 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H71 | zenon_intro zenon_H70 ].
% 0.44/0.62 apply zenon_H71. zenon_intro zenon_H72.
% 0.44/0.62 elim (classic ((succ (pv1325)) = (succ (pv1325)))); [ zenon_intro zenon_H73 | zenon_intro zenon_H74 ].
% 0.44/0.62 cut (((succ (pv1325)) = (succ (pv1325))) = ((n2) = (succ (pv1325)))).
% 0.44/0.62 intro zenon_D_pnotp.
% 0.44/0.62 apply zenon_H6f.
% 0.44/0.62 rewrite <- zenon_D_pnotp.
% 0.44/0.62 exact zenon_H73.
% 0.44/0.62 cut (((succ (pv1325)) = (succ (pv1325)))); [idtac | apply NNPP; zenon_intro zenon_H74].
% 0.44/0.62 cut (((succ (pv1325)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H6e].
% 0.44/0.62 congruence.
% 0.44/0.62 exact (zenon_H6e zenon_H72).
% 0.44/0.62 apply zenon_H74. apply refl_equal.
% 0.44/0.62 apply zenon_H74. apply refl_equal.
% 0.44/0.62 apply zenon_H70. zenon_intro zenon_H64.
% 0.44/0.62 generalize (zenon_H56 (succ (pv1325))). zenon_intro zenon_H75.
% 0.44/0.62 generalize (zenon_H75 (n2)). zenon_intro zenon_H76.
% 0.44/0.62 generalize (zenon_H76 (n0)). zenon_intro zenon_H77.
% 0.44/0.62 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H65 | zenon_intro zenon_H78 ].
% 0.44/0.62 exact (zenon_H65 zenon_H64).
% 0.44/0.62 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H69 ].
% 0.44/0.62 exact (zenon_H79 gt_2_0).
% 0.44/0.62 exact (zenon_H6b zenon_H69).
% 0.44/0.62 apply zenon_H55. apply refl_equal.
% 0.44/0.62 exact (zenon_H58 zenon_H6a).
% 0.44/0.62 apply zenon_H57. zenon_intro zenon_Tx_es. apply NNPP. zenon_intro zenon_H7b.
% 0.44/0.62 apply zenon_H7b. zenon_intro zenon_Ty_eu. apply NNPP. zenon_intro zenon_H7d.
% 0.44/0.62 apply zenon_H7d. zenon_intro zenon_Tz_ew. apply NNPP. zenon_intro zenon_H7f.
% 0.44/0.62 apply (zenon_notimply_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80.
% 0.44/0.62 apply (zenon_notimply_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82.
% 0.44/0.62 generalize (transitivity_gt zenon_Tx_es). zenon_intro zenon_H84.
% 0.44/0.62 generalize (zenon_H84 zenon_Ty_eu). zenon_intro zenon_H85.
% 0.44/0.62 generalize (zenon_H85 zenon_Tz_ew). zenon_intro zenon_H86.
% 0.44/0.62 apply (zenon_imply_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ].
% 0.44/0.62 apply (zenon_notand_s _ _ zenon_H88); [ zenon_intro zenon_H8a | zenon_intro zenon_H89 ].
% 0.44/0.62 exact (zenon_H8a zenon_H81).
% 0.44/0.62 exact (zenon_H89 zenon_H83).
% 0.44/0.62 exact (zenon_H82 zenon_H87).
% 0.44/0.62 Qed.
% 0.44/0.62 % SZS output end Proof
% 0.44/0.62 (* END-PROOF *)
% 0.44/0.62 nodes searched: 4141
% 0.44/0.62 max branch formulas: 970
% 0.44/0.62 proof nodes created: 8
% 0.44/0.62 formulas created: 14796
% 0.44/0.62
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