%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV154+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 23:03:08 EDT 2022 % Result : Theorem 0.47s 0.65s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SWV154+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.03/0.14 % Command : run_zenon %s %d % 0.14/0.36 % Computer : n018.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Wed Jun 15 12:19:14 EDT 2022 % 0.14/0.36 % CPUTime : % 0.47/0.65 (* PROOF-FOUND *) % 0.47/0.65 % SZS status Theorem % 0.47/0.65 (* BEGIN-PROOF *) % 0.47/0.65 % SZS output start Proof % 0.47/0.65 Theorem cl5_nebula_norm_0004 : ((((pv70) = (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)))))))/\((leq (n0) (pv10))/\((leq (n0) (pv12))/\((leq (pv10) (n135299))/\((leq (pv12) (n4))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (pred (pv12))))->((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (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))))))))))/\(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 (pv12)))->(((pv12) = C)->((divide (sqrt (times (minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))))) (pv70)) = (divide (sqrt (times (minus (a_select3 (center) C (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) C (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)))))))))))). % 0.47/0.65 Proof. % 0.47/0.65 assert (zenon_L1_ : (~((n0) = (n0))) -> False). % 0.47/0.65 do 0 intro. intros zenon_H5c. % 0.47/0.65 apply zenon_H5c. apply refl_equal. % 0.47/0.65 (* end of lemma zenon_L1_ *) % 0.47/0.65 assert (zenon_L2_ : forall (zenon_TC_dr : zenon_U), (~((minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))) = (minus (a_select3 (center) zenon_TC_dr (n0)) (a_select2 (x) (pv10))))) -> ((pv12) = zenon_TC_dr) -> False). % 0.47/0.65 do 1 intro. intros zenon_H5d zenon_H5e. % 0.47/0.65 cut (((a_select2 (x) (pv10)) = (a_select2 (x) (pv10)))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 0.47/0.65 cut (((a_select3 (center) (pv12) (n0)) = (a_select3 (center) zenon_TC_dr (n0)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 0.47/0.65 congruence. % 0.47/0.65 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 0.47/0.65 cut (((pv12) = zenon_TC_dr)); [idtac | apply NNPP; zenon_intro zenon_H62]. % 0.47/0.65 cut (((center) = (center))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 0.47/0.65 congruence. % 0.47/0.65 apply zenon_H63. apply refl_equal. % 0.47/0.65 exact (zenon_H62 zenon_H5e). % 0.47/0.65 apply zenon_H5c. apply refl_equal. % 0.47/0.65 apply zenon_H60. apply refl_equal. % 0.47/0.65 (* end of lemma zenon_L2_ *) % 0.47/0.65 apply NNPP. intro zenon_G. % 0.47/0.65 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H65. zenon_intro zenon_H64. % 0.47/0.65 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 0.47/0.65 apply (zenon_notallex_s (fun C : zenon_U => (((leq (n0) C)/\(leq C (pv12)))->(((pv12) = C)->((divide (sqrt (times (minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))))) (pv70)) = (divide (sqrt (times (minus (a_select3 (center) C (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) C (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_H64); [ zenon_intro zenon_H68; idtac ]. % 0.47/0.65 elim zenon_H68. zenon_intro zenon_TC_dr. zenon_intro zenon_H69. % 0.47/0.65 apply (zenon_notimply_s _ _ zenon_H69). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 0.47/0.65 apply (zenon_notimply_s _ _ zenon_H6a). zenon_intro zenon_H5e. zenon_intro zenon_H6c. % 0.47/0.65 cut (((pv70) = (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)))))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 0.47/0.65 cut (((sqrt (times (minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))))) = (sqrt (times (minus (a_select3 (center) zenon_TC_dr (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) zenon_TC_dr (n0)) (a_select2 (x) (pv10))))))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 0.47/0.65 congruence. % 0.47/0.65 cut (((times (minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10)))) = (times (minus (a_select3 (center) zenon_TC_dr (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) zenon_TC_dr (n0)) (a_select2 (x) (pv10)))))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 0.47/0.65 congruence. % 0.47/0.65 cut (((minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))) = (minus (a_select3 (center) zenon_TC_dr (n0)) (a_select2 (x) (pv10))))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 0.47/0.65 cut (((minus (a_select3 (center) (pv12) (n0)) (a_select2 (x) (pv10))) = (minus (a_select3 (center) zenon_TC_dr (n0)) (a_select2 (x) (pv10))))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 0.47/0.65 congruence. % 0.47/0.65 apply (zenon_L2_ zenon_TC_dr); trivial. % 0.47/0.65 apply (zenon_L2_ zenon_TC_dr); trivial. % 0.47/0.65 exact (zenon_H6d zenon_H67). % 0.47/0.65 Qed. % 0.47/0.65 % SZS output end Proof % 0.47/0.65 (* END-PROOF *) % 0.47/0.65 nodes searched: 3942 % 0.47/0.65 max branch formulas: 876 % 0.47/0.65 proof nodes created: 14 % 0.47/0.65 formulas created: 14068 % 0.47/0.65 %------------------------------------------------------------------------------