TSTP Solution File: SEU341+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% 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
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%----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
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