%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU341+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 16:01:21 EDT 2022 % Result : Theorem 2.05s 2.27s % Output : Proof 2.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU341+1 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n008.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 : Sun Jun 19 10:44:22 EDT 2022 % 0.12/0.34 % CPUTime : % 2.05/2.27 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 2.05/2.27 (* PROOF-FOUND *) % 2.05/2.27 % SZS status Theorem % 2.05/2.27 (* BEGIN-PROOF *) % 2.05/2.27 % SZS output start Proof % 2.05/2.27 Theorem t5_connsp_2 : (forall A : zenon_U, (((~(empty_carrier A))/\((topological_space A)/\(top_str A)))->(forall B : zenon_U, ((element B (powerset (the_carrier A)))->(forall C : zenon_U, ((element C (the_carrier A))->(((open_subset B A)/\(in C B))->(point_neighbourhood B A C)))))))). % 2.05/2.27 Proof. % 2.05/2.27 assert (zenon_L1_ : forall (zenon_TC_by : zenon_U) (zenon_TA_bz : zenon_U) (zenon_TB_ca : zenon_U), ((open_subset zenon_TB_ca zenon_TA_bz)->((interior zenon_TA_bz zenon_TB_ca) = zenon_TB_ca)) -> (in zenon_TC_by zenon_TB_ca) -> (~(point_neighbourhood zenon_TB_ca zenon_TA_bz zenon_TC_by)) -> (element zenon_TB_ca (powerset (the_carrier zenon_TA_bz))) -> (element zenon_TC_by (the_carrier zenon_TA_bz)) -> (top_str zenon_TA_bz) -> (topological_space zenon_TA_bz) -> (~(empty_carrier zenon_TA_bz)) -> (open_subset zenon_TB_ca zenon_TA_bz) -> False). % 2.05/2.27 do 3 intro. intros zenon_H29 zenon_H2a zenon_H2b zenon_H2c zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H31. % 2.05/2.27 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 2.05/2.27 exact (zenon_H36 zenon_H31). % 2.05/2.27 generalize (d1_connsp_2 zenon_TA_bz). zenon_intro zenon_H37. % 2.05/2.27 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 2.05/2.27 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 2.05/2.27 exact (zenon_H3b zenon_H30). % 2.05/2.27 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 2.05/2.27 exact (zenon_H3d zenon_H2f). % 2.05/2.27 exact (zenon_H3c zenon_H2e). % 2.05/2.27 generalize (zenon_H38 zenon_TC_by). zenon_intro zenon_H3e. % 2.05/2.27 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 2.05/2.27 exact (zenon_H40 zenon_H2d). % 2.05/2.27 generalize (zenon_H3f zenon_TB_ca). zenon_intro zenon_H41. % 2.05/2.27 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 2.05/2.27 exact (zenon_H43 zenon_H2c). % 2.05/2.27 apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H2b; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H44 ]. % 2.05/2.27 cut ((in zenon_TC_by zenon_TB_ca) = (in zenon_TC_by (interior zenon_TA_bz zenon_TB_ca))). % 2.05/2.27 intro zenon_D_pnotp. % 2.05/2.27 apply zenon_H46. % 2.05/2.27 rewrite <- zenon_D_pnotp. % 2.05/2.27 exact zenon_H2a. % 2.05/2.27 cut ((zenon_TB_ca = (interior zenon_TA_bz zenon_TB_ca))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 2.05/2.27 cut ((zenon_TC_by = zenon_TC_by)); [idtac | apply NNPP; zenon_intro zenon_H48]. % 2.05/2.27 congruence. % 2.05/2.27 apply zenon_H48. apply refl_equal. % 2.05/2.27 apply zenon_H47. apply sym_equal. exact zenon_H35. % 2.05/2.27 exact (zenon_H2b zenon_H45). % 2.05/2.27 (* end of lemma zenon_L1_ *) % 2.05/2.27 apply NNPP. intro zenon_G. % 2.05/2.27 apply (zenon_notallex_s (fun A : zenon_U => (((~(empty_carrier A))/\((topological_space A)/\(top_str A)))->(forall B : zenon_U, ((element B (powerset (the_carrier A)))->(forall C : zenon_U, ((element C (the_carrier A))->(((open_subset B A)/\(in C B))->(point_neighbourhood B A C)))))))) zenon_G); [ zenon_intro zenon_H49; idtac ]. % 2.05/2.27 elim zenon_H49. zenon_intro zenon_TA_bz. zenon_intro zenon_H4a. % 2.05/2.27 apply (zenon_notimply_s _ _ zenon_H4a). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 2.05/2.27 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H30. zenon_intro zenon_H4d. % 2.05/2.27 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H2f. zenon_intro zenon_H2e. % 2.05/2.27 apply (zenon_notallex_s (fun B : zenon_U => ((element B (powerset (the_carrier zenon_TA_bz)))->(forall C : zenon_U, ((element C (the_carrier zenon_TA_bz))->(((open_subset B zenon_TA_bz)/\(in C B))->(point_neighbourhood B zenon_TA_bz C)))))) zenon_H4b); [ zenon_intro zenon_H4e; idtac ]. % 2.05/2.27 elim zenon_H4e. zenon_intro zenon_TB_ca. zenon_intro zenon_H4f. % 2.05/2.27 apply (zenon_notimply_s _ _ zenon_H4f). zenon_intro zenon_H2c. zenon_intro zenon_H50. % 2.05/2.27 apply (zenon_notallex_s (fun C : zenon_U => ((element C (the_carrier zenon_TA_bz))->(((open_subset zenon_TB_ca zenon_TA_bz)/\(in C zenon_TB_ca))->(point_neighbourhood zenon_TB_ca zenon_TA_bz C)))) zenon_H50); [ zenon_intro zenon_H51; idtac ]. % 2.05/2.27 elim zenon_H51. zenon_intro zenon_TC_by. zenon_intro zenon_H52. % 2.05/2.27 apply (zenon_notimply_s _ _ zenon_H52). zenon_intro zenon_H2d. zenon_intro zenon_H53. % 2.05/2.27 apply (zenon_notimply_s _ _ zenon_H53). zenon_intro zenon_H54. zenon_intro zenon_H2b. % 2.05/2.27 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H31. zenon_intro zenon_H2a. % 2.05/2.27 generalize (t55_tops_1 zenon_TA_bz). zenon_intro zenon_H55. % 2.05/2.27 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H3a | zenon_intro zenon_H56 ]. % 2.05/2.27 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 2.05/2.27 exact (zenon_H3d zenon_H2f). % 2.05/2.27 exact (zenon_H3c zenon_H2e). % 2.05/2.27 generalize (zenon_H56 zenon_TA_bz). zenon_intro zenon_H57. % 2.05/2.27 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H3c | zenon_intro zenon_H58 ]. % 2.05/2.27 exact (zenon_H3c zenon_H2e). % 2.05/2.27 generalize (zenon_H58 zenon_TB_ca). zenon_intro zenon_H59. % 2.05/2.27 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H43 | zenon_intro zenon_H5a ]. % 2.05/2.27 exact (zenon_H43 zenon_H2c). % 2.05/2.27 generalize (zenon_H5a zenon_TB_ca). zenon_intro zenon_H5b. % 2.05/2.27 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H43 | zenon_intro zenon_H5c ]. % 2.05/2.27 exact (zenon_H43 zenon_H2c). % 2.05/2.27 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H29. zenon_intro zenon_H5d. % 2.05/2.27 apply (zenon_L1_ zenon_TC_by zenon_TA_bz zenon_TB_ca); trivial. % 2.05/2.27 Qed. % 2.05/2.27 % SZS output end Proof % 2.05/2.27 (* END-PROOF *) % 2.05/2.27 nodes searched: 73429 % 2.05/2.27 max branch formulas: 5863 % 2.05/2.27 proof nodes created: 5479 % 2.05/2.27 formulas created: 147356 % 2.05/2.27 %------------------------------------------------------------------------------