TSTP Solution File: SWV140+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV140+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n025.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 25.13s 25.34s
% Output : Proof 25.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV140+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.08/0.15 % Command : run_zenon %s %d
% 0.14/0.37 % Computer : n025.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Thu Jun 16 06:57:41 EDT 2022
% 0.14/0.37 % CPUTime :
% 25.13/25.34 (* PROOF-FOUND *)
% 25.13/25.34 % SZS status Theorem
% 25.13/25.34 (* BEGIN-PROOF *)
% 25.13/25.34 % SZS output start Proof
% 25.13/25.34 Theorem gauss_array_0010 : (((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_sworst7))).
% 25.13/25.34 Proof.
% 25.13/25.34 assert (zenon_L1_ : (~(gt (succ (loopcounter)) (succ (n0)))) -> (gt (succ (loopcounter)) (n1)) -> False).
% 25.13/25.34 do 0 intro. intros zenon_H55 zenon_H56.
% 25.13/25.34 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 25.13/25.34 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (loopcounter)) (succ (n0)))).
% 25.13/25.34 intro zenon_D_pnotp.
% 25.13/25.34 apply zenon_H55.
% 25.13/25.34 rewrite <- zenon_D_pnotp.
% 25.13/25.34 exact zenon_H56.
% 25.13/25.34 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 25.13/25.34 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 25.13/25.34 congruence.
% 25.13/25.34 apply zenon_H59. apply refl_equal.
% 25.13/25.34 exact (zenon_H58 zenon_H57).
% 25.13/25.34 apply zenon_H58. apply sym_equal. exact successor_1.
% 25.13/25.34 (* end of lemma zenon_L1_ *)
% 25.13/25.34 assert (zenon_L2_ : (leq (n0) (s_sworst7)) -> (~(gt (succ (s_sworst7)) (n0))) -> False).
% 25.13/25.34 do 0 intro. intros zenon_H5a zenon_H5b.
% 25.13/25.34 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5c.
% 25.13/25.34 generalize (zenon_H5c (s_sworst7)). zenon_intro zenon_H5d.
% 25.13/25.34 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ].
% 25.13/25.34 exact (zenon_H5f zenon_H5a).
% 25.13/25.34 exact (zenon_H5b zenon_H5e).
% 25.13/25.34 (* end of lemma zenon_L2_ *)
% 25.13/25.34 apply NNPP. intro zenon_G.
% 25.13/25.34 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H60. zenon_intro zenon_H5f.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71.
% 25.13/25.34 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 25.13/25.34 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H75.
% 25.13/25.34 generalize (zenon_H75 (loopcounter)). zenon_intro zenon_H76.
% 25.13/25.34 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H78; zenon_intro zenon_H77 | zenon_intro zenon_H64; zenon_intro zenon_H56 ].
% 25.13/25.34 exact (zenon_H78 zenon_H64).
% 25.13/25.34 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5c.
% 25.13/25.34 generalize (zenon_H5c (s_sworst7)). zenon_intro zenon_H5d.
% 25.13/25.34 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ].
% 25.13/25.34 apply (zenon_imply_s _ _ zenon_H74); [ zenon_intro zenon_H79 | zenon_intro zenon_H5a ].
% 25.13/25.34 generalize (leq_succ_gt (n0)). zenon_intro zenon_H7a.
% 25.13/25.34 generalize (zenon_H7a (loopcounter)). zenon_intro zenon_H7b.
% 25.13/25.34 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ].
% 25.13/25.34 generalize (leq_succ_gt_equiv (succ (n0))). zenon_intro zenon_H7e.
% 25.13/25.34 generalize (zenon_H7e (loopcounter)). zenon_intro zenon_H7f.
% 25.13/25.34 apply (zenon_equiv_s _ _ zenon_H7f); [ zenon_intro zenon_H7d; zenon_intro zenon_H55 | zenon_intro zenon_H81; zenon_intro zenon_H80 ].
% 25.13/25.36 apply (zenon_L1_); trivial.
% 25.13/25.36 exact (zenon_H7d zenon_H81).
% 25.13/25.36 exact (zenon_H79 zenon_H7c).
% 25.13/25.36 apply (zenon_L2_); trivial.
% 25.13/25.36 exact (zenon_H5f zenon_H5a).
% 25.13/25.36 Qed.
% 25.13/25.36 % SZS output end Proof
% 25.13/25.36 (* END-PROOF *)
% 25.13/25.36 nodes searched: 1557500
% 25.13/25.36 max branch formulas: 29169
% 25.13/25.36 proof nodes created: 2540
% 25.13/25.36 formulas created: 382414
% 25.13/25.36
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