%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU401+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 : Tue Jul 19 16:01:49 EDT 2022 % Result : Theorem 1.09s 1.31s % Output : Proof 1.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU401+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n004.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 : Mon Jun 20 09:41:08 EDT 2022 % 0.12/0.33 % CPUTime : % 1.09/1.31 Zenon warning: unused variable (C : zenon_U) in zenon_G % 1.09/1.31 (* PROOF-FOUND *) % 1.09/1.31 % SZS status Theorem % 1.09/1.31 (* BEGIN-PROOF *) % 1.09/1.31 % SZS output start Proof % 1.09/1.31 Theorem s2_xboole_0__e6_39_3__yellow19__1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((~(empty_carrier A))/\((topological_space A)/\((top_str A)/\((~(empty_carrier B))/\((transitive_relstr B)/\((directed_relstr B)/\(net_str B A)))))))->(forall D : zenon_U, (forall E : zenon_U, (forall F : zenon_U, (((forall G : zenon_U, ((in G E)<->((in G (the_carrier B))/\(exists H : zenon_U, ((netstr_induced_subset H A B)/\(exists I : zenon_U, ((element I (the_carrier B))/\((D = (topstr_closure A H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element A B I)) (the_carrier A) (the_mapping A (subnetstr_of_element A B I)))))))))))))/\(forall G : zenon_U, ((in G F)<->((in G (the_carrier B))/\(exists H : zenon_U, ((netstr_induced_subset H A B)/\(exists I : zenon_U, ((element I (the_carrier B))/\((D = (topstr_closure A H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element A B I)) (the_carrier A) (the_mapping A (subnetstr_of_element A B I))))))))))))))->(E = F))))))))). % 1.09/1.31 Proof. % 1.09/1.31 assert (zenon_L1_ : forall (zenon_TD_cm : zenon_U) (zenon_TA_cn : zenon_U) (zenon_TB_co : zenon_U) (zenon_TC_cp : zenon_U), ((in zenon_TC_cp (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((zenon_TD_cm = (topstr_closure zenon_TA_cn H))/\((zenon_TC_cp = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I))))))))))) -> (~(in zenon_TC_cp (the_carrier zenon_TB_co))) -> False). % 1.09/1.31 do 4 intro. intros zenon_H3e zenon_H3f. % 1.09/1.31 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H45. zenon_intro zenon_H44. % 1.09/1.31 exact (zenon_H3f zenon_H45). % 1.09/1.31 (* end of lemma zenon_L1_ *) % 1.09/1.31 assert (zenon_L2_ : forall (zenon_TD_cm : zenon_U) (zenon_TA_cn : zenon_U) (zenon_TB_co : zenon_U) (zenon_TC_cp : zenon_U), ((in zenon_TC_cp (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((zenon_TD_cm = (topstr_closure zenon_TA_cn H))/\((zenon_TC_cp = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I))))))))))) -> (~(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((zenon_TD_cm = (topstr_closure zenon_TA_cn H))/\((zenon_TC_cp = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I))))))))))) -> False). % 1.09/1.31 do 4 intro. intros zenon_H3e zenon_H46. % 1.09/1.31 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H45. zenon_intro zenon_H44. % 1.09/1.31 exact (zenon_H46 zenon_H44). % 1.09/1.31 (* end of lemma zenon_L2_ *) % 1.09/1.31 apply NNPP. intro zenon_G. % 1.09/1.31 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((~(empty_carrier A))/\((topological_space A)/\((top_str A)/\((~(empty_carrier B))/\((transitive_relstr B)/\((directed_relstr B)/\(net_str B A)))))))->(forall D : zenon_U, (forall E : zenon_U, (forall F : zenon_U, (((forall G : zenon_U, ((in G E)<->((in G (the_carrier B))/\(exists H : zenon_U, ((netstr_induced_subset H A B)/\(exists I : zenon_U, ((element I (the_carrier B))/\((D = (topstr_closure A H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element A B I)) (the_carrier A) (the_mapping A (subnetstr_of_element A B I)))))))))))))/\(forall G : zenon_U, ((in G F)<->((in G (the_carrier B))/\(exists H : zenon_U, ((netstr_induced_subset H A B)/\(exists I : zenon_U, ((element I (the_carrier B))/\((D = (topstr_closure A H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element A B I)) (the_carrier A) (the_mapping A (subnetstr_of_element A B I))))))))))))))->(E = F))))))))) zenon_G); [ zenon_intro zenon_H47; idtac ]. % 1.09/1.31 elim zenon_H47. zenon_intro zenon_TA_cn. zenon_intro zenon_H48. % 1.09/1.31 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((~(empty_carrier zenon_TA_cn))/\((topological_space zenon_TA_cn)/\((top_str zenon_TA_cn)/\((~(empty_carrier B))/\((transitive_relstr B)/\((directed_relstr B)/\(net_str B zenon_TA_cn)))))))->(forall D : zenon_U, (forall E : zenon_U, (forall F : zenon_U, (((forall G : zenon_U, ((in G E)<->((in G (the_carrier B))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn B)/\(exists I : zenon_U, ((element I (the_carrier B))/\((D = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn B I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn B I)))))))))))))/\(forall G : zenon_U, ((in G F)<->((in G (the_carrier B))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn B)/\(exists I : zenon_U, ((element I (the_carrier B))/\((D = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn B I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn B I))))))))))))))->(E = F)))))))) zenon_H48); [ zenon_intro zenon_H49; idtac ]. % 1.09/1.31 elim zenon_H49. zenon_intro zenon_TB_co. zenon_intro zenon_H4a. % 1.09/1.31 apply (zenon_notallex_s (fun C : zenon_U => (((~(empty_carrier zenon_TA_cn))/\((topological_space zenon_TA_cn)/\((top_str zenon_TA_cn)/\((~(empty_carrier zenon_TB_co))/\((transitive_relstr zenon_TB_co)/\((directed_relstr zenon_TB_co)/\(net_str zenon_TB_co zenon_TA_cn)))))))->(forall D : zenon_U, (forall E : zenon_U, (forall F : zenon_U, (((forall G : zenon_U, ((in G E)<->((in G (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((D = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I)))))))))))))/\(forall G : zenon_U, ((in G F)<->((in G (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((D = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I))))))))))))))->(E = F))))))) zenon_H4a); [ zenon_intro zenon_H4b; idtac ]. % 1.09/1.31 elim zenon_H4b. zenon_intro zenon_TC_cy. zenon_intro zenon_H4d. % 1.09/1.31 apply (zenon_notimply_s _ _ zenon_H4d). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 1.09/1.31 apply (zenon_notallex_s (fun D : zenon_U => (forall E : zenon_U, (forall F : zenon_U, (((forall G : zenon_U, ((in G E)<->((in G (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((D = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I)))))))))))))/\(forall G : zenon_U, ((in G F)<->((in G (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((D = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I))))))))))))))->(E = F))))) zenon_H4e); [ zenon_intro zenon_H50; idtac ]. % 1.09/1.31 elim zenon_H50. zenon_intro zenon_TD_cm. zenon_intro zenon_H51. % 1.09/1.31 apply (zenon_notallex_s (fun E : zenon_U => (forall F : zenon_U, (((forall G : zenon_U, ((in G E)<->((in G (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((zenon_TD_cm = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I)))))))))))))/\(forall G : zenon_U, ((in G F)<->((in G (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((zenon_TD_cm = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I))))))))))))))->(E = F)))) zenon_H51); [ zenon_intro zenon_H52; idtac ]. % 1.09/1.31 elim zenon_H52. zenon_intro zenon_TE_df. zenon_intro zenon_H54. % 1.09/1.31 apply (zenon_notallex_s (fun F : zenon_U => (((forall G : zenon_U, ((in G zenon_TE_df)<->((in G (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((zenon_TD_cm = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I)))))))))))))/\(forall G : zenon_U, ((in G F)<->((in G (the_carrier zenon_TB_co))/\(exists H : zenon_U, ((netstr_induced_subset H zenon_TA_cn zenon_TB_co)/\(exists I : zenon_U, ((element I (the_carrier zenon_TB_co))/\((zenon_TD_cm = (topstr_closure zenon_TA_cn H))/\((G = I)/\(H = (relation_rng_as_subset (the_carrier (subnetstr_of_element zenon_TA_cn zenon_TB_co I)) (the_carrier zenon_TA_cn) (the_mapping zenon_TA_cn (subnetstr_of_element zenon_TA_cn zenon_TB_co I))))))))))))))->(zenon_TE_df = F))) zenon_H54); [ zenon_intro zenon_H55; idtac ]. % 1.09/1.31 elim zenon_H55. zenon_intro zenon_TF_di. zenon_intro zenon_H57. % 1.09/1.31 apply (zenon_notimply_s _ _ zenon_H57). zenon_intro zenon_H59. zenon_intro zenon_H58. % 1.09/1.31 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5b. zenon_intro zenon_H5a. % 1.09/1.31 generalize (t2_tarski zenon_TF_di). zenon_intro zenon_H5c. % 1.09/1.31 generalize (zenon_H5c zenon_TE_df). zenon_intro zenon_H5d. % 1.09/1.31 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 1.09/1.31 apply (zenon_notallex_s (fun C : zenon_U => ((in C zenon_TF_di)<->(in C zenon_TE_df))) zenon_H5f); [ zenon_intro zenon_H60; idtac ]. % 1.09/1.31 elim zenon_H60. zenon_intro zenon_TC_cp. zenon_intro zenon_H61. % 1.09/1.31 apply (zenon_notequiv_s _ _ zenon_H61); [ zenon_intro zenon_H65; zenon_intro zenon_H64 | zenon_intro zenon_H63; zenon_intro zenon_H62 ]. % 1.09/1.31 generalize (zenon_H5a zenon_TC_cp). zenon_intro zenon_H66. % 1.09/1.31 apply (zenon_equiv_s _ _ zenon_H66); [ zenon_intro zenon_H65; zenon_intro zenon_H67 | zenon_intro zenon_H63; zenon_intro zenon_H3e ]. % 1.09/1.31 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H3f | zenon_intro zenon_H46 ]. % 1.09/1.31 generalize (zenon_H5b zenon_TC_cp). zenon_intro zenon_H68. % 1.09/1.31 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H62; zenon_intro zenon_H67 | zenon_intro zenon_H64; zenon_intro zenon_H3e ]. % 1.09/1.31 exact (zenon_H62 zenon_H64). % 1.09/1.31 apply (zenon_L1_ zenon_TD_cm zenon_TA_cn zenon_TB_co zenon_TC_cp); trivial. % 1.09/1.31 generalize (zenon_H5b zenon_TC_cp). zenon_intro zenon_H68. % 1.09/1.31 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H62; zenon_intro zenon_H67 | zenon_intro zenon_H64; zenon_intro zenon_H3e ]. % 1.09/1.31 exact (zenon_H62 zenon_H64). % 1.09/1.31 apply (zenon_L2_ zenon_TD_cm zenon_TA_cn zenon_TB_co zenon_TC_cp); trivial. % 1.09/1.31 exact (zenon_H65 zenon_H63). % 1.09/1.31 generalize (zenon_H5b zenon_TC_cp). zenon_intro zenon_H68. % 1.09/1.31 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H62; zenon_intro zenon_H67 | zenon_intro zenon_H64; zenon_intro zenon_H3e ]. % 1.09/1.31 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H3f | zenon_intro zenon_H46 ]. % 1.09/1.31 generalize (zenon_H5a zenon_TC_cp). zenon_intro zenon_H66. % 1.09/1.31 apply (zenon_equiv_s _ _ zenon_H66); [ zenon_intro zenon_H65; zenon_intro zenon_H67 | zenon_intro zenon_H63; zenon_intro zenon_H3e ]. % 1.09/1.31 exact (zenon_H65 zenon_H63). % 1.09/1.31 apply (zenon_L1_ zenon_TD_cm zenon_TA_cn zenon_TB_co zenon_TC_cp); trivial. % 1.09/1.31 generalize (zenon_H5a zenon_TC_cp). zenon_intro zenon_H66. % 1.09/1.31 apply (zenon_equiv_s _ _ zenon_H66); [ zenon_intro zenon_H65; zenon_intro zenon_H67 | zenon_intro zenon_H63; zenon_intro zenon_H3e ]. % 1.09/1.31 exact (zenon_H65 zenon_H63). % 1.09/1.31 apply (zenon_L2_ zenon_TD_cm zenon_TA_cn zenon_TB_co zenon_TC_cp); trivial. % 1.09/1.31 exact (zenon_H62 zenon_H64). % 1.09/1.31 apply zenon_H58. apply sym_equal. exact zenon_H5e. % 1.09/1.31 Qed. % 1.09/1.31 % SZS output end Proof % 1.09/1.31 (* END-PROOF *) % 1.09/1.31 nodes searched: 6522 % 1.09/1.31 max branch formulas: 1969 % 1.09/1.31 proof nodes created: 704 % 1.09/1.31 formulas created: 32233 % 1.09/1.31 %------------------------------------------------------------------------------