TSTP Solution File: SWV139+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV139+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n006.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 81.62s 81.85s
% Output : Proof 81.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV139+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n006.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 : Wed Jun 15 20:12:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 81.62/81.85 (* PROOF-FOUND *)
% 81.62/81.85 % SZS status Theorem
% 81.62/81.85 (* BEGIN-PROOF *)
% 81.62/81.85 % SZS output start Proof
% 81.62/81.85 Theorem gauss_array_0009 : (((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 (n0) (s_best7))).
% 81.62/81.85 Proof.
% 81.62/81.85 assert (zenon_L1_ : (~((n0) = (n0))) -> False).
% 81.62/81.85 do 0 intro. intros zenon_H55.
% 81.62/81.85 apply zenon_H55. apply refl_equal.
% 81.62/81.85 (* end of lemma zenon_L1_ *)
% 81.62/81.85 assert (zenon_L2_ : (leq (n0) (s_best7)) -> (~(gt (succ (s_best7)) (n0))) -> False).
% 81.62/81.85 do 0 intro. intros zenon_H56 zenon_H57.
% 81.62/81.85 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58.
% 81.62/81.85 generalize (zenon_H58 (s_best7)). zenon_intro zenon_H59.
% 81.62/81.85 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H5b; zenon_intro zenon_H57 | zenon_intro zenon_H56; zenon_intro zenon_H5a ].
% 81.62/81.85 exact (zenon_H5b zenon_H56).
% 81.62/81.85 exact (zenon_H57 zenon_H5a).
% 81.62/81.85 (* end of lemma zenon_L2_ *)
% 81.62/81.85 apply NNPP. intro zenon_G.
% 81.62/81.85 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_H5c | zenon_intro zenon_H5d ].
% 81.62/81.85 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H5e. zenon_intro zenon_H5b.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H60. zenon_intro zenon_H5f.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H62. zenon_intro zenon_H61.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 81.62/81.85 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H71.
% 81.62/81.85 generalize (zenon_H71 (loopcounter)). zenon_intro zenon_H72.
% 81.62/81.85 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H75; zenon_intro zenon_H74 | zenon_intro zenon_H62; zenon_intro zenon_H73 ].
% 81.62/81.85 exact (zenon_H75 zenon_H62).
% 81.62/81.85 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H58.
% 81.62/81.85 generalize (zenon_H58 (s_best7)). zenon_intro zenon_H59.
% 81.62/81.85 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H5b; zenon_intro zenon_H57 | zenon_intro zenon_H56; zenon_intro zenon_H5a ].
% 81.62/81.85 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H56 ].
% 81.62/81.85 elim (classic ((~((loopcounter) = (n1)))/\(~(gt (loopcounter) (n1))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ].
% 81.62/81.85 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H7a. zenon_intro zenon_H79.
% 81.62/81.85 generalize (leq_gt2 (n1)). zenon_intro zenon_H7b.
% 81.62/81.85 generalize (zenon_H7b (loopcounter)). zenon_intro zenon_H7c.
% 81.62/81.85 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ].
% 81.62/81.85 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H75 | zenon_intro zenon_H7f ].
% 81.62/81.85 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H71.
% 81.62/81.85 generalize (zenon_H71 (loopcounter)). zenon_intro zenon_H72.
% 81.62/81.85 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H75; zenon_intro zenon_H74 | zenon_intro zenon_H62; zenon_intro zenon_H73 ].
% 81.62/81.85 exact (zenon_H74 zenon_H73).
% 81.62/81.85 exact (zenon_H75 zenon_H62).
% 81.62/81.85 apply zenon_H7f. zenon_intro zenon_H80.
% 81.62/81.85 apply zenon_H7a. apply sym_equal. exact zenon_H80.
% 81.62/81.85 exact (zenon_H79 zenon_H7d).
% 81.62/81.85 cut ((gt (n1) (n0)) = (gt (loopcounter) (n0))).
% 81.70/81.88 intro zenon_D_pnotp.
% 81.70/81.88 apply zenon_H76.
% 81.70/81.88 rewrite <- zenon_D_pnotp.
% 81.70/81.88 exact gt_1_0.
% 81.70/81.88 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H55].
% 81.70/81.88 cut (((n1) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 81.70/81.88 congruence.
% 81.70/81.88 apply (zenon_notand_s _ _ zenon_H78); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ].
% 81.70/81.88 apply zenon_H83. zenon_intro zenon_H84.
% 81.70/81.88 elim (classic ((loopcounter) = (loopcounter))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ].
% 81.70/81.88 cut (((loopcounter) = (loopcounter)) = ((n1) = (loopcounter))).
% 81.70/81.88 intro zenon_D_pnotp.
% 81.70/81.88 apply zenon_H81.
% 81.70/81.88 rewrite <- zenon_D_pnotp.
% 81.70/81.88 exact zenon_H85.
% 81.70/81.88 cut (((loopcounter) = (loopcounter))); [idtac | apply NNPP; zenon_intro zenon_H86].
% 81.70/81.88 cut (((loopcounter) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H7a].
% 81.70/81.88 congruence.
% 81.70/81.88 exact (zenon_H7a zenon_H84).
% 81.70/81.88 apply zenon_H86. apply refl_equal.
% 81.70/81.88 apply zenon_H86. apply refl_equal.
% 81.70/81.88 apply zenon_H82. zenon_intro zenon_H7d.
% 81.70/81.88 generalize (zenon_H5c (loopcounter)). zenon_intro zenon_H87.
% 81.70/81.88 generalize (zenon_H87 (n1)). zenon_intro zenon_H88.
% 81.70/81.88 generalize (zenon_H88 (n0)). zenon_intro zenon_H89.
% 81.70/81.88 apply (zenon_imply_s _ _ zenon_H89); [ zenon_intro zenon_H79 | zenon_intro zenon_H8a ].
% 81.70/81.88 exact (zenon_H79 zenon_H7d).
% 81.70/81.88 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ].
% 81.70/81.88 exact (zenon_H8c gt_1_0).
% 81.70/81.88 exact (zenon_H76 zenon_H8b).
% 81.70/81.88 apply zenon_H55. apply refl_equal.
% 81.70/81.88 apply (zenon_L2_); trivial.
% 81.70/81.88 exact (zenon_H5b zenon_H56).
% 81.70/81.88 apply zenon_H5d. zenon_intro zenon_Tx_fl. apply NNPP. zenon_intro zenon_H8e.
% 81.70/81.88 apply zenon_H8e. zenon_intro zenon_Ty_fn. apply NNPP. zenon_intro zenon_H90.
% 81.70/81.88 apply zenon_H90. zenon_intro zenon_Tz_fp. apply NNPP. zenon_intro zenon_H92.
% 81.70/81.88 apply (zenon_notimply_s _ _ zenon_H92). zenon_intro zenon_H94. zenon_intro zenon_H93.
% 81.70/81.88 apply (zenon_notimply_s _ _ zenon_H93). zenon_intro zenon_H96. zenon_intro zenon_H95.
% 81.70/81.88 generalize (transitivity_gt zenon_Tx_fl). zenon_intro zenon_H97.
% 81.70/81.88 generalize (zenon_H97 zenon_Ty_fn). zenon_intro zenon_H98.
% 81.70/81.88 generalize (zenon_H98 zenon_Tz_fp). zenon_intro zenon_H99.
% 81.70/81.88 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H9b | zenon_intro zenon_H9a ].
% 81.70/81.88 apply (zenon_notand_s _ _ zenon_H9b); [ zenon_intro zenon_H9d | zenon_intro zenon_H9c ].
% 81.70/81.88 exact (zenon_H9d zenon_H94).
% 81.70/81.88 exact (zenon_H9c zenon_H96).
% 81.70/81.88 exact (zenon_H95 zenon_H9a).
% 81.70/81.88 Qed.
% 81.70/81.88 % SZS output end Proof
% 81.70/81.88 (* END-PROOF *)
% 81.70/81.88 nodes searched: 6231101
% 81.70/81.88 max branch formulas: 33772
% 81.70/81.88 proof nodes created: 8440
% 81.70/81.88 formulas created: 1040635
% 81.70/81.88
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