%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------