TSTP Solution File: SWV142+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV142+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n010.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 86.82s 87.03s
% Output : Proof 86.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV142+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n010.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 14:18:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 86.82/87.03 (* PROOF-FOUND *)
% 86.82/87.03 % SZS status Theorem
% 86.82/87.03 (* BEGIN-PROOF *)
% 86.82/87.03 % SZS output start Proof
% 86.82/87.03 Theorem gauss_array_0012 : (((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 (s_best7) (n3))).
% 86.82/87.03 Proof.
% 86.82/87.03 assert (zenon_L1_ : (~(gt (succ (loopcounter)) (succ (n0)))) -> (gt (succ (loopcounter)) (n1)) -> False).
% 86.82/87.03 do 0 intro. intros zenon_H55 zenon_H56.
% 86.82/87.03 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 86.82/87.03 cut ((gt (succ (loopcounter)) (n1)) = (gt (succ (loopcounter)) (succ (n0)))).
% 86.82/87.03 intro zenon_D_pnotp.
% 86.82/87.03 apply zenon_H55.
% 86.82/87.03 rewrite <- zenon_D_pnotp.
% 86.82/87.03 exact zenon_H56.
% 86.82/87.03 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 86.82/87.03 cut (((succ (loopcounter)) = (succ (loopcounter)))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 86.82/87.03 congruence.
% 86.82/87.03 apply zenon_H59. apply refl_equal.
% 86.82/87.03 exact (zenon_H58 zenon_H57).
% 86.82/87.03 apply zenon_H58. apply sym_equal. exact successor_1.
% 86.82/87.03 (* end of lemma zenon_L1_ *)
% 86.82/87.03 assert (zenon_L2_ : (leq (s_best7) (n3)) -> (~(gt (succ (n3)) (s_best7))) -> False).
% 86.82/87.03 do 0 intro. intros zenon_H5a zenon_H5b.
% 86.82/87.03 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H5c.
% 86.82/87.03 generalize (zenon_H5c (n3)). zenon_intro zenon_H5d.
% 86.82/87.03 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ].
% 86.82/87.03 exact (zenon_H5f zenon_H5a).
% 86.82/87.03 exact (zenon_H5b zenon_H5e).
% 86.82/87.03 (* end of lemma zenon_L2_ *)
% 86.82/87.03 apply NNPP. intro zenon_G.
% 86.82/87.03 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H60. zenon_intro zenon_H5f.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 86.82/87.03 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77.
% 86.82/87.03 generalize (leq_succ_gt_equiv (n1)). zenon_intro zenon_H79.
% 86.82/87.03 generalize (zenon_H79 (loopcounter)). zenon_intro zenon_H7a.
% 86.82/87.03 apply (zenon_equiv_s _ _ zenon_H7a); [ zenon_intro zenon_H7c; zenon_intro zenon_H7b | zenon_intro zenon_H64; zenon_intro zenon_H56 ].
% 86.82/87.03 exact (zenon_H7c zenon_H64).
% 86.82/87.03 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H5c.
% 86.82/87.03 generalize (zenon_H5c (n3)). zenon_intro zenon_H5d.
% 86.82/87.03 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5f; zenon_intro zenon_H5b | zenon_intro zenon_H5a; zenon_intro zenon_H5e ].
% 86.82/87.03 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7d | zenon_intro zenon_H5a ].
% 86.82/87.03 generalize (leq_succ_gt (n0)). zenon_intro zenon_H7e.
% 86.82/87.03 generalize (zenon_H7e (loopcounter)). zenon_intro zenon_H7f.
% 86.82/87.03 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H81 | zenon_intro zenon_H80 ].
% 86.82/87.03 generalize (leq_succ_gt_equiv (succ (n0))). zenon_intro zenon_H82.
% 86.82/87.03 generalize (zenon_H82 (loopcounter)). zenon_intro zenon_H83.
% 86.82/87.06 apply (zenon_equiv_s _ _ zenon_H83); [ zenon_intro zenon_H81; zenon_intro zenon_H55 | zenon_intro zenon_H85; zenon_intro zenon_H84 ].
% 86.82/87.06 apply (zenon_L1_); trivial.
% 86.82/87.06 exact (zenon_H81 zenon_H85).
% 86.82/87.06 exact (zenon_H7d zenon_H80).
% 86.82/87.06 apply (zenon_L2_); trivial.
% 86.82/87.06 exact (zenon_H5f zenon_H5a).
% 86.82/87.06 Qed.
% 86.82/87.06 % SZS output end Proof
% 86.82/87.06 (* END-PROOF *)
% 86.82/87.06 nodes searched: 6056427
% 86.82/87.06 max branch formulas: 44098
% 86.82/87.06 proof nodes created: 12099
% 86.82/87.06 formulas created: 1637727
% 86.82/87.06
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