%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV160+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 23:03:09 EDT 2022 % Result : Theorem 16.98s 17.23s % Output : Proof 16.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SWV160+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n024.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Wed Jun 15 09:45:48 EDT 2022 % 0.14/0.35 % CPUTime : % 16.98/17.23 (* PROOF-FOUND *) % 16.98/17.23 % SZS status Theorem % 16.98/17.23 (* BEGIN-PROOF *) % 16.98/17.23 % SZS output start Proof % 16.98/17.23 Theorem cl5_nebula_norm_0010 : ((((pv84) = (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index))))))/\((leq (n0) (pv10))/\((leq (n0) (pv47))/\((leq (pv10) (n135299))/\((leq (pv47) (n4))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (pred (pv47))))->((a_select3 (q) (pv10) A) = (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) A)) (minus (a_select2 (x) (pv10)) (a_select2 (mu) A))) (tptp_minus_2)) (times (a_select2 (sigma) A) (a_select2 (sigma) A)))) (a_select2 (rho) A)) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) A))) (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index)))))))))/\(forall B : zenon_U, (((leq (n0) B)/\(leq B (pred (pv10))))->((sum (n0) (n4) (a_select3 (q) B (tptp_sum_index))) = (n1))))))))))->(forall C : zenon_U, (((leq (n0) C)/\(leq C (pred (pv10))))->(((pv10) = C)->((sum (n0) (n4) (cond (tptp_term_equals (pv47) (tptp_sum_index)) (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (pv47))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (pv47)))) (tptp_minus_2)) (times (a_select2 (sigma) (pv47)) (a_select2 (sigma) (pv47))))) (a_select2 (rho) (pv47))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (pv47)))) (pv84)) (a_select3 (q) C (tptp_sum_index)))) = (n1)))))). % 16.98/17.23 Proof. % 16.98/17.23 assert (zenon_L1_ : (~((pv10) = (pv10))) -> False). % 16.98/17.23 do 0 intro. intros zenon_H64. % 16.98/17.23 apply zenon_H64. apply refl_equal. % 16.98/17.23 (* end of lemma zenon_L1_ *) % 16.98/17.23 assert (zenon_L2_ : forall (zenon_TC_eb : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((pv10) = zenon_TC_eb) -> (gt (succ (pred (pv10))) zenon_TC_eb) -> (~(gt zenon_TC_eb zenon_TC_eb)) -> False). % 16.98/17.23 do 1 intro. intros zenon_H65 zenon_H66 zenon_H67 zenon_H68. % 16.98/17.23 generalize (succ_pred zenon_TC_eb). zenon_intro zenon_H6a. % 16.98/17.23 elim (classic (gt zenon_TC_eb (succ (pred zenon_TC_eb)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 16.98/17.23 cut ((gt zenon_TC_eb (succ (pred zenon_TC_eb))) = (gt zenon_TC_eb zenon_TC_eb)). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H68. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H6b. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = zenon_TC_eb)); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 16.98/17.23 cut ((zenon_TC_eb = zenon_TC_eb)); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 16.98/17.23 congruence. % 16.98/17.23 apply zenon_H6e. apply refl_equal. % 16.98/17.23 exact (zenon_H6d zenon_H6a). % 16.98/17.23 elim (classic (zenon_TC_eb = (succ (pred zenon_TC_eb)))); [ zenon_intro zenon_H6f | zenon_intro zenon_H70 ]. % 16.98/17.23 elim (classic (gt (succ (pred zenon_TC_eb)) (succ (pred zenon_TC_eb)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 16.98/17.23 cut ((gt (succ (pred zenon_TC_eb)) (succ (pred zenon_TC_eb))) = (gt zenon_TC_eb (succ (pred zenon_TC_eb)))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H6c. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H71. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = (succ (pred zenon_TC_eb)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = zenon_TC_eb)); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 16.98/17.23 congruence. % 16.98/17.23 elim (classic (zenon_TC_eb = zenon_TC_eb)); [ zenon_intro zenon_H74 | zenon_intro zenon_H6e ]. % 16.98/17.23 cut ((zenon_TC_eb = zenon_TC_eb) = ((succ (pred zenon_TC_eb)) = zenon_TC_eb)). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H6d. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H74. % 16.98/17.23 cut ((zenon_TC_eb = zenon_TC_eb)); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 16.98/17.23 cut ((zenon_TC_eb = (succ (pred zenon_TC_eb)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 16.98/17.23 congruence. % 16.98/17.23 exact (zenon_H70 zenon_H6f). % 16.98/17.23 apply zenon_H6e. apply refl_equal. % 16.98/17.23 apply zenon_H6e. apply refl_equal. % 16.98/17.23 apply zenon_H73. apply refl_equal. % 16.98/17.23 elim (classic ((~((succ (pred zenon_TC_eb)) = (succ (pred (pv10)))))/\(~(gt (succ (pred zenon_TC_eb)) (succ (pred (pv10))))))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ]. % 16.98/17.23 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 16.98/17.23 cut (((pred zenon_TC_eb) = (pred (pv10)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 16.98/17.23 congruence. % 16.98/17.23 cut ((zenon_TC_eb = (pv10))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 16.98/17.23 congruence. % 16.98/17.23 apply zenon_H7a. apply sym_equal. exact zenon_H66. % 16.98/17.23 elim (classic (zenon_TC_eb = (succ (pred zenon_TC_eb)))); [ zenon_intro zenon_H6f | zenon_intro zenon_H70 ]. % 16.98/17.23 cut ((gt (succ (pred (pv10))) zenon_TC_eb) = (gt (succ (pred zenon_TC_eb)) (succ (pred zenon_TC_eb)))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H72. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H67. % 16.98/17.23 cut ((zenon_TC_eb = (succ (pred zenon_TC_eb)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 16.98/17.23 cut (((succ (pred (pv10))) = (succ (pred zenon_TC_eb)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 16.98/17.23 congruence. % 16.98/17.23 apply (zenon_notand_s _ _ zenon_H76); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 16.98/17.23 apply zenon_H7d. zenon_intro zenon_H7e. % 16.98/17.23 elim (classic ((succ (pred zenon_TC_eb)) = (succ (pred zenon_TC_eb)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H73 ]. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = (succ (pred zenon_TC_eb))) = ((succ (pred (pv10))) = (succ (pred zenon_TC_eb)))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H7b. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H7f. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = (succ (pred zenon_TC_eb)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = (succ (pred (pv10))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 16.98/17.23 congruence. % 16.98/17.23 exact (zenon_H78 zenon_H7e). % 16.98/17.23 apply zenon_H73. apply refl_equal. % 16.98/17.23 apply zenon_H73. apply refl_equal. % 16.98/17.23 apply zenon_H7c. zenon_intro zenon_H80. % 16.98/17.23 generalize (zenon_H65 (succ (pred zenon_TC_eb))). zenon_intro zenon_H81. % 16.98/17.23 generalize (zenon_H81 (succ (pred (pv10)))). zenon_intro zenon_H82. % 16.98/17.23 generalize (zenon_H82 zenon_TC_eb). zenon_intro zenon_H83. % 16.98/17.23 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H77 | zenon_intro zenon_H84 ]. % 16.98/17.23 exact (zenon_H77 zenon_H80). % 16.98/17.23 apply (zenon_imply_s _ _ zenon_H84); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 16.98/17.23 exact (zenon_H86 zenon_H67). % 16.98/17.23 cut ((gt (succ (pred zenon_TC_eb)) zenon_TC_eb) = (gt (succ (pred zenon_TC_eb)) (succ (pred zenon_TC_eb)))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H72. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H85. % 16.98/17.23 cut ((zenon_TC_eb = (succ (pred zenon_TC_eb)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = (succ (pred zenon_TC_eb)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 16.98/17.23 congruence. % 16.98/17.23 apply zenon_H73. apply refl_equal. % 16.98/17.23 exact (zenon_H70 zenon_H6f). % 16.98/17.23 exact (zenon_H70 zenon_H6f). % 16.98/17.23 apply zenon_H70. apply sym_equal. exact zenon_H6a. % 16.98/17.23 elim (classic ((succ (pred zenon_TC_eb)) = (succ (pred zenon_TC_eb)))); [ zenon_intro zenon_H7f | zenon_intro zenon_H73 ]. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = (succ (pred zenon_TC_eb))) = (zenon_TC_eb = (succ (pred zenon_TC_eb)))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H70. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H7f. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = (succ (pred zenon_TC_eb)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 16.98/17.23 cut (((succ (pred zenon_TC_eb)) = zenon_TC_eb)); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 16.98/17.23 congruence. % 16.98/17.23 exact (zenon_H6d zenon_H6a). % 16.98/17.23 apply zenon_H73. apply refl_equal. % 16.98/17.23 apply zenon_H73. apply refl_equal. % 16.98/17.23 (* end of lemma zenon_L2_ *) % 16.98/17.23 assert (zenon_L3_ : forall (zenon_TC_eb : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (pv10) (pv10))) -> (gt (succ (pred (pv10))) zenon_TC_eb) -> ((pv10) = zenon_TC_eb) -> False). % 16.98/17.23 do 1 intro. intros zenon_H65 zenon_H87 zenon_H67 zenon_H66. % 16.98/17.23 elim (classic (gt zenon_TC_eb (pv10))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 16.98/17.23 cut ((gt zenon_TC_eb (pv10)) = (gt (pv10) (pv10))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H87. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H88. % 16.98/17.23 cut (((pv10) = (pv10))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 16.98/17.23 cut ((zenon_TC_eb = (pv10))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 16.98/17.23 congruence. % 16.98/17.23 elim (classic ((pv10) = (pv10))); [ zenon_intro zenon_H8a | zenon_intro zenon_H64 ]. % 16.98/17.23 cut (((pv10) = (pv10)) = (zenon_TC_eb = (pv10))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H7a. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H8a. % 16.98/17.23 cut (((pv10) = (pv10))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 16.98/17.23 cut (((pv10) = zenon_TC_eb)); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 16.98/17.23 congruence. % 16.98/17.23 exact (zenon_H8b zenon_H66). % 16.98/17.23 apply zenon_H64. apply refl_equal. % 16.98/17.23 apply zenon_H64. apply refl_equal. % 16.98/17.23 apply zenon_H64. apply refl_equal. % 16.98/17.23 elim (classic (zenon_TC_eb = (pv10))); [ zenon_intro zenon_H8c | zenon_intro zenon_H7a ]. % 16.98/17.23 elim (classic (gt zenon_TC_eb zenon_TC_eb)); [ zenon_intro zenon_H8d | zenon_intro zenon_H68 ]. % 16.98/17.23 cut ((gt zenon_TC_eb zenon_TC_eb) = (gt zenon_TC_eb (pv10))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H89. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H8d. % 16.98/17.23 cut ((zenon_TC_eb = (pv10))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 16.98/17.23 cut ((zenon_TC_eb = zenon_TC_eb)); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 16.98/17.23 congruence. % 16.98/17.23 apply zenon_H6e. apply refl_equal. % 16.98/17.23 exact (zenon_H7a zenon_H8c). % 16.98/17.23 apply (zenon_L2_ zenon_TC_eb); trivial. % 16.98/17.23 elim (classic ((pv10) = (pv10))); [ zenon_intro zenon_H8a | zenon_intro zenon_H64 ]. % 16.98/17.23 cut (((pv10) = (pv10)) = (zenon_TC_eb = (pv10))). % 16.98/17.23 intro zenon_D_pnotp. % 16.98/17.23 apply zenon_H7a. % 16.98/17.23 rewrite <- zenon_D_pnotp. % 16.98/17.23 exact zenon_H8a. % 16.98/17.23 cut (((pv10) = (pv10))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 16.98/17.23 cut (((pv10) = zenon_TC_eb)); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 16.98/17.23 congruence. % 16.98/17.23 exact (zenon_H8b zenon_H66). % 16.98/17.23 apply zenon_H64. apply refl_equal. % 16.98/17.23 apply zenon_H64. apply refl_equal. % 16.98/17.23 (* end of lemma zenon_L3_ *) % 16.98/17.23 apply NNPP. intro zenon_G. % 16.98/17.23 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_H65 | zenon_intro zenon_H8e ]. % 16.98/17.23 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 16.98/17.23 apply (zenon_notallex_s (fun C : zenon_U => (((leq (n0) C)/\(leq C (pred (pv10))))->(((pv10) = C)->((sum (n0) (n4) (cond (tptp_term_equals (pv47) (tptp_sum_index)) (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (pv47))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (pv47)))) (tptp_minus_2)) (times (a_select2 (sigma) (pv47)) (a_select2 (sigma) (pv47))))) (a_select2 (rho) (pv47))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (pv47)))) (pv84)) (a_select3 (q) C (tptp_sum_index)))) = (n1))))) zenon_H8f); [ zenon_intro zenon_H91; idtac ]. % 16.98/17.23 elim zenon_H91. zenon_intro zenon_TC_eb. zenon_intro zenon_H92. % 16.98/17.23 apply (zenon_notimply_s _ _ zenon_H92). zenon_intro zenon_H94. zenon_intro zenon_H93. % 16.98/17.23 apply (zenon_notimply_s _ _ zenon_H93). zenon_intro zenon_H66. zenon_intro zenon_H95. % 16.98/17.23 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H97. zenon_intro zenon_H96. % 16.98/17.23 generalize (leq_succ_gt_equiv zenon_TC_eb). zenon_intro zenon_H98. % 16.98/17.23 generalize (zenon_H98 (pred (pv10))). zenon_intro zenon_H99. % 16.98/17.23 apply (zenon_equiv_s _ _ zenon_H99); [ zenon_intro zenon_H9a; zenon_intro zenon_H86 | zenon_intro zenon_H96; zenon_intro zenon_H67 ]. % 16.98/17.23 exact (zenon_H9a zenon_H96). % 16.98/17.23 generalize (irreflexivity_gt (pv10)). zenon_intro zenon_H87. % 16.98/17.23 apply (zenon_L3_ zenon_TC_eb); trivial. % 16.98/17.23 apply zenon_H8e. zenon_intro zenon_Tx_fz. apply NNPP. zenon_intro zenon_H9c. % 16.98/17.23 apply zenon_H9c. zenon_intro zenon_Ty_gb. apply NNPP. zenon_intro zenon_H9e. % 16.98/17.23 apply zenon_H9e. zenon_intro zenon_Tz_gd. apply NNPP. zenon_intro zenon_Ha0. % 16.98/17.23 apply (zenon_notimply_s _ _ zenon_Ha0). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1. % 16.98/17.23 apply (zenon_notimply_s _ _ zenon_Ha1). zenon_intro zenon_Ha4. zenon_intro zenon_Ha3. % 16.98/17.23 generalize (transitivity_gt zenon_Tx_fz). zenon_intro zenon_Ha5. % 16.98/17.23 generalize (zenon_Ha5 zenon_Ty_gb). zenon_intro zenon_Ha6. % 16.98/17.23 generalize (zenon_Ha6 zenon_Tz_gd). zenon_intro zenon_Ha7. % 16.98/17.23 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8 ]. % 16.98/17.24 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 16.98/17.24 exact (zenon_Hab zenon_Ha2). % 16.98/17.24 exact (zenon_Haa zenon_Ha4). % 16.98/17.24 exact (zenon_Ha3 zenon_Ha8). % 16.98/17.24 Qed. % 16.98/17.24 % SZS output end Proof % 16.98/17.24 (* END-PROOF *) % 16.98/17.24 nodes searched: 1270751 % 16.98/17.24 max branch formulas: 18097 % 16.98/17.24 proof nodes created: 3846 % 16.98/17.24 formulas created: 426029 % 16.98/17.24 %------------------------------------------------------------------------------