TSTP Solution File: SEU394+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU394+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n009.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 16:01:46 EDT 2022
% Result : Theorem 0.59s 0.73s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU394+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : run_zenon %s %d
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 18:42:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.59/0.73 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.59/0.73 (* PROOF-FOUND *)
% 0.59/0.73 % SZS status Theorem
% 0.59/0.73 (* BEGIN-PROOF *)
% 0.59/0.73 % SZS output start Proof
% 0.59/0.73 Theorem t15_yellow19 : (forall A : zenon_U, (((~(empty_carrier A))/\(one_sorted_str A))->(forall B : zenon_U, (((~(empty B))/\((filtered_subset B (boole_POSet (cast_as_carrier_subset A)))/\((upper_relstr_subset B (boole_POSet (cast_as_carrier_subset A)))/\((proper_element B (powerset (the_carrier (boole_POSet (cast_as_carrier_subset A)))))/\(element B (powerset (the_carrier (boole_POSet (cast_as_carrier_subset A)))))))))->(B = (filter_of_net_str A (net_of_bool_filter A (cast_as_carrier_subset A) B))))))).
% 0.59/0.73 Proof.
% 0.59/0.73 assert (zenon_L1_ : forall (zenon_TB_er : zenon_U), (forall C : zenon_U, (~((in C zenon_TB_er)/\(empty C)))) -> (in (empty_set) zenon_TB_er) -> (empty (empty_set)) -> False).
% 0.59/0.73 do 1 intro. intros zenon_H76 zenon_H77 zenon_H78.
% 0.59/0.73 generalize (zenon_H76 (empty_set)). zenon_intro zenon_H7a.
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_H7a); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ].
% 0.59/0.73 exact (zenon_H7c zenon_H77).
% 0.59/0.73 exact (zenon_H7b zenon_H78).
% 0.59/0.73 (* end of lemma zenon_L1_ *)
% 0.59/0.73 assert (zenon_L2_ : forall (zenon_TA_fd : zenon_U) (zenon_TB_er : zenon_U), (~(zenon_TB_er = (set_difference zenon_TB_er (singleton (empty_set))))) -> (one_sorted_str zenon_TA_fd) -> (~(empty_carrier zenon_TA_fd)) -> (~(empty zenon_TB_er)) -> (filtered_subset zenon_TB_er (boole_POSet (cast_as_carrier_subset zenon_TA_fd))) -> (upper_relstr_subset zenon_TB_er (boole_POSet (cast_as_carrier_subset zenon_TA_fd))) -> (proper_element zenon_TB_er (powerset (the_carrier (boole_POSet (cast_as_carrier_subset zenon_TA_fd))))) -> (element zenon_TB_er (powerset (the_carrier (boole_POSet (cast_as_carrier_subset zenon_TA_fd))))) -> (empty (empty_set)) -> False).
% 0.59/0.73 do 2 intro. intros zenon_H7d zenon_H7e zenon_H7f zenon_H80 zenon_H81 zenon_H82 zenon_H83 zenon_H84 zenon_H78.
% 0.59/0.73 generalize (t65_zfmisc_1 zenon_TB_er). zenon_intro zenon_H86.
% 0.59/0.73 generalize (zenon_H86 (empty_set)). zenon_intro zenon_H87.
% 0.59/0.73 apply (zenon_equiv_s _ _ zenon_H87); [ zenon_intro zenon_H8a; zenon_intro zenon_H89 | zenon_intro zenon_H88; zenon_intro zenon_H7c ].
% 0.59/0.73 apply zenon_H89. zenon_intro zenon_H77.
% 0.59/0.73 generalize (t2_yellow19 (cast_as_carrier_subset zenon_TA_fd)). zenon_intro zenon_H8b.
% 0.59/0.73 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H8d | zenon_intro zenon_H8c ].
% 0.59/0.73 apply zenon_H8d. zenon_intro zenon_H8e.
% 0.59/0.73 generalize (fc2_pre_topc zenon_TA_fd). zenon_intro zenon_H8f.
% 0.59/0.73 apply (zenon_imply_s _ _ zenon_H8f); [ zenon_intro zenon_H91 | zenon_intro zenon_H90 ].
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 0.59/0.73 exact (zenon_H93 zenon_H7f).
% 0.59/0.73 exact (zenon_H92 zenon_H7e).
% 0.59/0.73 exact (zenon_H90 zenon_H8e).
% 0.59/0.73 generalize (zenon_H8c zenon_TB_er). zenon_intro zenon_H94.
% 0.59/0.73 apply (zenon_imply_s _ _ zenon_H94); [ zenon_intro zenon_H95 | zenon_intro zenon_H76 ].
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ].
% 0.59/0.73 exact (zenon_H97 zenon_H80).
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_H96); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ].
% 0.59/0.73 exact (zenon_H99 zenon_H81).
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H9b | zenon_intro zenon_H9a ].
% 0.59/0.73 exact (zenon_H9b zenon_H82).
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_H9a); [ zenon_intro zenon_H9d | zenon_intro zenon_H9c ].
% 0.59/0.73 exact (zenon_H9d zenon_H83).
% 0.59/0.73 exact (zenon_H9c zenon_H84).
% 0.59/0.73 apply (zenon_L1_ zenon_TB_er); trivial.
% 0.59/0.73 apply zenon_H7d. apply sym_equal. exact zenon_H88.
% 0.59/0.73 (* end of lemma zenon_L2_ *)
% 0.59/0.73 apply NNPP. intro zenon_G.
% 0.59/0.73 apply (zenon_and_s _ _ fc12_relat_1). zenon_intro zenon_H78. zenon_intro zenon_H9e.
% 0.59/0.73 apply (zenon_notallex_s (fun A : zenon_U => (((~(empty_carrier A))/\(one_sorted_str A))->(forall B : zenon_U, (((~(empty B))/\((filtered_subset B (boole_POSet (cast_as_carrier_subset A)))/\((upper_relstr_subset B (boole_POSet (cast_as_carrier_subset A)))/\((proper_element B (powerset (the_carrier (boole_POSet (cast_as_carrier_subset A)))))/\(element B (powerset (the_carrier (boole_POSet (cast_as_carrier_subset A)))))))))->(B = (filter_of_net_str A (net_of_bool_filter A (cast_as_carrier_subset A) B))))))) zenon_G); [ zenon_intro zenon_H9f; idtac ].
% 0.59/0.73 elim zenon_H9f. zenon_intro zenon_TA_fd. zenon_intro zenon_Ha0.
% 0.59/0.73 apply (zenon_notimply_s _ _ zenon_Ha0). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1.
% 0.59/0.73 apply (zenon_and_s _ _ zenon_Ha2). zenon_intro zenon_H7f. zenon_intro zenon_H7e.
% 0.59/0.73 apply (zenon_notallex_s (fun B : zenon_U => (((~(empty B))/\((filtered_subset B (boole_POSet (cast_as_carrier_subset zenon_TA_fd)))/\((upper_relstr_subset B (boole_POSet (cast_as_carrier_subset zenon_TA_fd)))/\((proper_element B (powerset (the_carrier (boole_POSet (cast_as_carrier_subset zenon_TA_fd)))))/\(element B (powerset (the_carrier (boole_POSet (cast_as_carrier_subset zenon_TA_fd)))))))))->(B = (filter_of_net_str zenon_TA_fd (net_of_bool_filter zenon_TA_fd (cast_as_carrier_subset zenon_TA_fd) B))))) zenon_Ha1); [ zenon_intro zenon_Ha3; idtac ].
% 0.59/0.73 elim zenon_Ha3. zenon_intro zenon_TB_er. zenon_intro zenon_Ha4.
% 0.59/0.73 apply (zenon_notimply_s _ _ zenon_Ha4). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5.
% 0.59/0.73 apply (zenon_and_s _ _ zenon_Ha6). zenon_intro zenon_H80. zenon_intro zenon_Ha7.
% 0.59/0.73 apply (zenon_and_s _ _ zenon_Ha7). zenon_intro zenon_H81. zenon_intro zenon_Ha8.
% 0.59/0.73 apply (zenon_and_s _ _ zenon_Ha8). zenon_intro zenon_H82. zenon_intro zenon_Ha9.
% 0.59/0.73 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_H83. zenon_intro zenon_H84.
% 0.59/0.73 generalize (t14_yellow19 zenon_TA_fd). zenon_intro zenon_Haa.
% 0.59/0.73 apply (zenon_imply_s _ _ zenon_Haa); [ zenon_intro zenon_H91 | zenon_intro zenon_Hab ].
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 0.59/0.73 exact (zenon_H93 zenon_H7f).
% 0.59/0.73 exact (zenon_H92 zenon_H7e).
% 0.59/0.73 generalize (zenon_Hab zenon_TB_er). zenon_intro zenon_Hac.
% 0.59/0.73 apply (zenon_imply_s _ _ zenon_Hac); [ zenon_intro zenon_Hae | zenon_intro zenon_Had ].
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_Hae); [ zenon_intro zenon_H97 | zenon_intro zenon_Haf ].
% 0.59/0.73 exact (zenon_H97 zenon_H80).
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_Haf); [ zenon_intro zenon_H99 | zenon_intro zenon_Hb0 ].
% 0.59/0.73 exact (zenon_H99 zenon_H81).
% 0.59/0.73 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ].
% 0.59/0.73 exact (zenon_H9b zenon_H82).
% 0.59/0.73 exact (zenon_H9c zenon_H84).
% 0.59/0.73 cut (((set_difference zenon_TB_er (singleton (empty_set))) = (filter_of_net_str zenon_TA_fd (net_of_bool_filter zenon_TA_fd (cast_as_carrier_subset zenon_TA_fd) zenon_TB_er))) = (zenon_TB_er = (filter_of_net_str zenon_TA_fd (net_of_bool_filter zenon_TA_fd (cast_as_carrier_subset zenon_TA_fd) zenon_TB_er)))).
% 0.59/0.73 intro zenon_D_pnotp.
% 0.59/0.73 apply zenon_Ha5.
% 0.59/0.73 rewrite <- zenon_D_pnotp.
% 0.59/0.73 exact zenon_Had.
% 0.59/0.73 cut (((filter_of_net_str zenon_TA_fd (net_of_bool_filter zenon_TA_fd (cast_as_carrier_subset zenon_TA_fd) zenon_TB_er)) = (filter_of_net_str zenon_TA_fd (net_of_bool_filter zenon_TA_fd (cast_as_carrier_subset zenon_TA_fd) zenon_TB_er)))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 0.59/0.73 cut (((set_difference zenon_TB_er (singleton (empty_set))) = zenon_TB_er)); [idtac | apply NNPP; zenon_intro zenon_H8a].
% 0.59/0.73 congruence.
% 0.59/0.73 elim (classic (zenon_TB_er = zenon_TB_er)); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 0.59/0.73 cut ((zenon_TB_er = zenon_TB_er) = ((set_difference zenon_TB_er (singleton (empty_set))) = zenon_TB_er)).
% 0.59/0.73 intro zenon_D_pnotp.
% 0.59/0.73 apply zenon_H8a.
% 0.59/0.73 rewrite <- zenon_D_pnotp.
% 0.59/0.73 exact zenon_Hb2.
% 0.59/0.73 cut ((zenon_TB_er = zenon_TB_er)); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 0.59/0.73 cut ((zenon_TB_er = (set_difference zenon_TB_er (singleton (empty_set))))); [idtac | apply NNPP; zenon_intro zenon_H7d].
% 0.59/0.73 congruence.
% 0.59/0.73 apply (zenon_L2_ zenon_TA_fd zenon_TB_er); trivial.
% 0.59/0.73 apply zenon_Hb3. apply refl_equal.
% 0.59/0.73 apply zenon_Hb3. apply refl_equal.
% 0.59/0.73 apply zenon_Hb1. apply refl_equal.
% 0.59/0.73 Qed.
% 0.59/0.73 % SZS output end Proof
% 0.59/0.73 (* END-PROOF *)
% 0.59/0.73 nodes searched: 5871
% 0.59/0.73 max branch formulas: 1907
% 0.59/0.73 proof nodes created: 567
% 0.59/0.73 formulas created: 25797
% 0.59/0.73
%------------------------------------------------------------------------------