TSTP Solution File: SWV163+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV163+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n016.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 23:03:10 EDT 2022
% Result : Theorem 48.68s 48.85s
% Output : Proof 48.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV163+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 18:57:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 48.68/48.85 (* PROOF-FOUND *)
% 48.68/48.85 % SZS status Theorem
% 48.68/48.85 (* BEGIN-PROOF *)
% 48.68/48.85 % SZS output start Proof
% 48.68/48.85 Theorem cl5_nebula_norm_0013 : (((leq (n0) (pv10))/\((leq (pv10) (n135299))/\(forall A : zenon_U, (((leq (n0) A)/\(leq A (pred (pv10))))->((sum (n0) (n4) (a_select3 (q) A (tptp_sum_index))) = (n1))))))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (tptp_minus_1)))->((a_select3 (q) (pv10) B) = (divide (sqrt (times (minus (a_select3 (center) B (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) B (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))))))))))).
% 48.68/48.85 Proof.
% 48.68/48.85 assert (zenon_L1_ : forall (zenon_TB_dq : zenon_U), (gt (succ zenon_TB_dq) (n0)) -> (~(leq (n0) zenon_TB_dq)) -> False).
% 48.68/48.85 do 1 intro. intros zenon_H5c zenon_H5d.
% 48.68/48.85 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 48.68/48.85 generalize (zenon_H5f zenon_TB_dq). zenon_intro zenon_H60.
% 48.68/48.85 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H5d; zenon_intro zenon_H62 | zenon_intro zenon_H61; zenon_intro zenon_H5c ].
% 48.68/48.85 exact (zenon_H62 zenon_H5c).
% 48.68/48.85 exact (zenon_H5d zenon_H61).
% 48.68/48.85 (* end of lemma zenon_L1_ *)
% 48.68/48.85 assert (zenon_L2_ : (~((n1) = (n1))) -> False).
% 48.68/48.85 do 0 intro. intros zenon_H63.
% 48.68/48.85 apply zenon_H63. apply refl_equal.
% 48.68/48.85 (* end of lemma zenon_L2_ *)
% 48.68/48.85 assert (zenon_L3_ : (~(gt (n1) (succ (tptp_minus_1)))) -> False).
% 48.68/48.85 do 0 intro. intros zenon_H64.
% 48.68/48.85 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ].
% 48.68/48.85 cut ((gt (n1) (n0)) = (gt (n1) (succ (tptp_minus_1)))).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H64.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact gt_1_0.
% 48.68/48.85 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 48.68/48.85 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 48.68/48.85 congruence.
% 48.68/48.85 apply zenon_H63. apply refl_equal.
% 48.68/48.85 exact (zenon_H66 zenon_H65).
% 48.68/48.85 apply zenon_H66. apply sym_equal. exact succ_tptp_minus_1.
% 48.68/48.85 (* end of lemma zenon_L3_ *)
% 48.68/48.85 assert (zenon_L4_ : (~(gt (succ (n0)) (succ (tptp_minus_1)))) -> False).
% 48.68/48.85 do 0 intro. intros zenon_H67.
% 48.68/48.85 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H68 | zenon_intro zenon_H64 ].
% 48.68/48.85 cut ((gt (n1) (succ (tptp_minus_1))) = (gt (succ (n0)) (succ (tptp_minus_1)))).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H67.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact zenon_H68.
% 48.68/48.85 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H69].
% 48.68/48.85 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 48.68/48.85 congruence.
% 48.68/48.85 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ].
% 48.68/48.85 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H6a.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact zenon_H6b.
% 48.68/48.85 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H6c].
% 48.68/48.85 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H6d].
% 48.68/48.85 congruence.
% 48.68/48.85 exact (zenon_H6d successor_1).
% 48.68/48.85 apply zenon_H6c. apply refl_equal.
% 48.68/48.85 apply zenon_H6c. apply refl_equal.
% 48.68/48.85 apply zenon_H69. apply refl_equal.
% 48.68/48.85 apply (zenon_L3_); trivial.
% 48.68/48.85 (* end of lemma zenon_L4_ *)
% 48.68/48.85 assert (zenon_L5_ : forall (zenon_TB_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (tptp_minus_1)) zenon_TB_dq) -> (~(leq zenon_TB_dq (n0))) -> False).
% 48.68/48.85 do 1 intro. intros zenon_H6e zenon_H6f zenon_H70.
% 48.68/48.85 generalize (leq_succ_gt_equiv zenon_TB_dq). zenon_intro zenon_H71.
% 48.68/48.85 generalize (zenon_H71 (n0)). zenon_intro zenon_H72.
% 48.68/48.85 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H70; zenon_intro zenon_H75 | zenon_intro zenon_H74; zenon_intro zenon_H73 ].
% 48.68/48.85 elim (classic ((~((succ (n0)) = (succ (tptp_minus_1))))/\(~(gt (succ (n0)) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H76 | zenon_intro zenon_H77 ].
% 48.68/48.85 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H78. zenon_intro zenon_H67.
% 48.68/48.85 apply (zenon_L4_); trivial.
% 48.68/48.85 cut ((gt (succ (tptp_minus_1)) zenon_TB_dq) = (gt (succ (n0)) zenon_TB_dq)).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H75.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact zenon_H6f.
% 48.68/48.85 cut ((zenon_TB_dq = zenon_TB_dq)); [idtac | apply NNPP; zenon_intro zenon_H79].
% 48.68/48.85 cut (((succ (tptp_minus_1)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H7a].
% 48.68/48.85 congruence.
% 48.68/48.85 apply (zenon_notand_s _ _ zenon_H77); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ].
% 48.68/48.85 apply zenon_H7c. zenon_intro zenon_H7d.
% 48.68/48.85 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ].
% 48.68/48.85 cut (((succ (n0)) = (succ (n0))) = ((succ (tptp_minus_1)) = (succ (n0)))).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H7a.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact zenon_H6b.
% 48.68/48.85 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H6c].
% 48.68/48.85 cut (((succ (n0)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H78].
% 48.68/48.85 congruence.
% 48.68/48.85 exact (zenon_H78 zenon_H7d).
% 48.68/48.85 apply zenon_H6c. apply refl_equal.
% 48.68/48.85 apply zenon_H6c. apply refl_equal.
% 48.68/48.85 apply zenon_H7b. zenon_intro zenon_H7e.
% 48.68/48.85 generalize (zenon_H6e (succ (n0))). zenon_intro zenon_H7f.
% 48.68/48.85 generalize (zenon_H7f (succ (tptp_minus_1))). zenon_intro zenon_H80.
% 48.68/48.85 generalize (zenon_H80 zenon_TB_dq). zenon_intro zenon_H81.
% 48.68/48.85 apply (zenon_imply_s _ _ zenon_H81); [ zenon_intro zenon_H67 | zenon_intro zenon_H82 ].
% 48.68/48.85 exact (zenon_H67 zenon_H7e).
% 48.68/48.85 apply (zenon_imply_s _ _ zenon_H82); [ zenon_intro zenon_H83 | zenon_intro zenon_H73 ].
% 48.68/48.85 exact (zenon_H83 zenon_H6f).
% 48.68/48.85 exact (zenon_H75 zenon_H73).
% 48.68/48.85 apply zenon_H79. apply refl_equal.
% 48.68/48.85 exact (zenon_H70 zenon_H74).
% 48.68/48.85 (* end of lemma zenon_L5_ *)
% 48.68/48.85 assert (zenon_L6_ : forall (zenon_TB_dq : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (zenon_TB_dq = (n0)) -> (~(gt zenon_TB_dq zenon_TB_dq)) -> (gt (succ (tptp_minus_1)) zenon_TB_dq) -> False).
% 48.68/48.85 do 1 intro. intros zenon_H6e zenon_H84 zenon_H85 zenon_H6f.
% 48.68/48.85 elim (classic (gt (n0) zenon_TB_dq)); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ].
% 48.68/48.85 cut ((gt (n0) zenon_TB_dq) = (gt zenon_TB_dq zenon_TB_dq)).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H85.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact zenon_H86.
% 48.68/48.85 cut ((zenon_TB_dq = zenon_TB_dq)); [idtac | apply NNPP; zenon_intro zenon_H79].
% 48.68/48.85 cut (((n0) = zenon_TB_dq)); [idtac | apply NNPP; zenon_intro zenon_H88].
% 48.68/48.85 congruence.
% 48.68/48.85 elim (classic (zenon_TB_dq = zenon_TB_dq)); [ zenon_intro zenon_H89 | zenon_intro zenon_H79 ].
% 48.68/48.85 cut ((zenon_TB_dq = zenon_TB_dq) = ((n0) = zenon_TB_dq)).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H88.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact zenon_H89.
% 48.68/48.85 cut ((zenon_TB_dq = zenon_TB_dq)); [idtac | apply NNPP; zenon_intro zenon_H79].
% 48.68/48.85 cut ((zenon_TB_dq = (n0))); [idtac | apply NNPP; zenon_intro zenon_H8a].
% 48.68/48.85 congruence.
% 48.68/48.85 exact (zenon_H8a zenon_H84).
% 48.68/48.85 apply zenon_H79. apply refl_equal.
% 48.68/48.85 apply zenon_H79. apply refl_equal.
% 48.68/48.85 apply zenon_H79. apply refl_equal.
% 48.68/48.85 elim (classic ((~((n0) = (succ (tptp_minus_1))))/\(~(gt (n0) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ].
% 48.68/48.85 apply (zenon_and_s _ _ zenon_H8b). zenon_intro zenon_H66. zenon_intro zenon_H8d.
% 48.68/48.85 apply zenon_H66. apply sym_equal. exact succ_tptp_minus_1.
% 48.68/48.85 cut ((gt (succ (tptp_minus_1)) zenon_TB_dq) = (gt (n0) zenon_TB_dq)).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H87.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact zenon_H6f.
% 48.68/48.85 cut ((zenon_TB_dq = zenon_TB_dq)); [idtac | apply NNPP; zenon_intro zenon_H79].
% 48.68/48.85 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H8e].
% 48.68/48.85 congruence.
% 48.68/48.85 apply (zenon_notand_s _ _ zenon_H8c); [ zenon_intro zenon_H90 | zenon_intro zenon_H8f ].
% 48.68/48.85 apply zenon_H90. zenon_intro zenon_H65.
% 48.68/48.85 elim (classic ((n0) = (n0))); [ zenon_intro zenon_H91 | zenon_intro zenon_H92 ].
% 48.68/48.85 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))).
% 48.68/48.85 intro zenon_D_pnotp.
% 48.68/48.85 apply zenon_H8e.
% 48.68/48.85 rewrite <- zenon_D_pnotp.
% 48.68/48.85 exact zenon_H91.
% 48.68/48.85 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H92].
% 48.68/48.85 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 48.68/48.85 congruence.
% 48.68/48.85 exact (zenon_H66 zenon_H65).
% 48.68/48.85 apply zenon_H92. apply refl_equal.
% 48.68/48.85 apply zenon_H92. apply refl_equal.
% 48.68/48.85 apply zenon_H8f. zenon_intro zenon_H93.
% 48.68/48.85 generalize (zenon_H6e (n0)). zenon_intro zenon_H94.
% 48.68/48.85 generalize (zenon_H94 (succ (tptp_minus_1))). zenon_intro zenon_H95.
% 48.68/48.85 generalize (zenon_H95 zenon_TB_dq). zenon_intro zenon_H96.
% 48.68/48.86 apply (zenon_imply_s _ _ zenon_H96); [ zenon_intro zenon_H8d | zenon_intro zenon_H97 ].
% 48.68/48.86 exact (zenon_H8d zenon_H93).
% 48.68/48.86 apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H83 | zenon_intro zenon_H86 ].
% 48.68/48.86 exact (zenon_H83 zenon_H6f).
% 48.68/48.86 exact (zenon_H87 zenon_H86).
% 48.68/48.86 apply zenon_H79. apply refl_equal.
% 48.68/48.86 (* end of lemma zenon_L6_ *)
% 48.68/48.86 apply NNPP. intro zenon_G.
% 48.68/48.86 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_H6e | zenon_intro zenon_H98 ].
% 48.68/48.86 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H9a. zenon_intro zenon_H99.
% 48.68/48.86 apply (zenon_notallex_s (fun B : zenon_U => (((leq (n0) B)/\(leq B (tptp_minus_1)))->((a_select3 (q) (pv10) B) = (divide (sqrt (times (minus (a_select3 (center) B (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) B (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))) zenon_H99); [ zenon_intro zenon_H9b; idtac ].
% 48.68/48.86 elim zenon_H9b. zenon_intro zenon_TB_dq. zenon_intro zenon_H9c.
% 48.68/48.86 apply (zenon_notimply_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H9d.
% 48.68/48.86 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_H61. zenon_intro zenon_H9f.
% 48.68/48.86 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H5f.
% 48.68/48.86 generalize (zenon_H5f zenon_TB_dq). zenon_intro zenon_H60.
% 48.68/48.86 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H5d; zenon_intro zenon_H62 | zenon_intro zenon_H61; zenon_intro zenon_H5c ].
% 48.68/48.86 exact (zenon_H5d zenon_H61).
% 48.68/48.86 generalize (leq_succ_gt_equiv zenon_TB_dq). zenon_intro zenon_H71.
% 48.68/48.86 generalize (zenon_H71 (tptp_minus_1)). zenon_intro zenon_Ha0.
% 48.68/48.86 apply (zenon_equiv_s _ _ zenon_Ha0); [ zenon_intro zenon_Ha1; zenon_intro zenon_H83 | zenon_intro zenon_H9f; zenon_intro zenon_H6f ].
% 48.68/48.86 exact (zenon_Ha1 zenon_H9f).
% 48.68/48.86 generalize (finite_domain_0 zenon_TB_dq). zenon_intro zenon_Ha2.
% 48.68/48.86 apply (zenon_imply_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H84 ].
% 48.68/48.86 apply (zenon_notand_s _ _ zenon_Ha3); [ zenon_intro zenon_H5d | zenon_intro zenon_H70 ].
% 48.68/48.86 apply (zenon_L1_ zenon_TB_dq); trivial.
% 48.68/48.86 apply (zenon_L5_ zenon_TB_dq); trivial.
% 48.68/48.86 generalize (irreflexivity_gt zenon_TB_dq). zenon_intro zenon_H85.
% 48.68/48.86 apply (zenon_L6_ zenon_TB_dq); trivial.
% 48.68/48.86 apply zenon_H98. zenon_intro zenon_Tx_gi. apply NNPP. zenon_intro zenon_Ha5.
% 48.68/48.86 apply zenon_Ha5. zenon_intro zenon_Ty_gk. apply NNPP. zenon_intro zenon_Ha7.
% 48.68/48.86 apply zenon_Ha7. zenon_intro zenon_Tz_gm. apply NNPP. zenon_intro zenon_Ha9.
% 48.68/48.86 apply (zenon_notimply_s _ _ zenon_Ha9). zenon_intro zenon_Hab. zenon_intro zenon_Haa.
% 48.68/48.86 apply (zenon_notimply_s _ _ zenon_Haa). zenon_intro zenon_Had. zenon_intro zenon_Hac.
% 48.68/48.86 generalize (transitivity_gt zenon_Tx_gi). zenon_intro zenon_Hae.
% 48.68/48.86 generalize (zenon_Hae zenon_Ty_gk). zenon_intro zenon_Haf.
% 48.68/48.86 generalize (zenon_Haf zenon_Tz_gm). zenon_intro zenon_Hb0.
% 48.68/48.86 apply (zenon_imply_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb1 ].
% 48.68/48.86 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ].
% 48.68/48.86 exact (zenon_Hb4 zenon_Hab).
% 48.68/48.86 exact (zenon_Hb3 zenon_Had).
% 48.68/48.86 exact (zenon_Hac zenon_Hb1).
% 48.68/48.86 Qed.
% 48.68/48.86 % SZS output end Proof
% 48.68/48.86 (* END-PROOF *)
% 48.68/48.86 nodes searched: 3463873
% 48.68/48.86 max branch formulas: 8069
% 48.68/48.86 proof nodes created: 6195
% 48.68/48.86 formulas created: 1154979
% 48.68/48.86
%------------------------------------------------------------------------------