%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n020.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  : 300s
% DateTime : Thu Aug 31 16:31:22 EDT 2023

% Result   : Theorem 0.21s 0.75s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Wed Aug 23 20:50:00 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.75  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.yTJwlZgFsc/cvc5---1.0.5_12119.p...
% 0.21/0.75  ------- get file name : TPTP file name is SEU395+1
% 0.21/0.75  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12119.smt2...
% 0.21/0.75  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.75  % SZS status Theorem for SEU395+1
% 0.21/0.75  % SZS output start Proof for SEU395+1
% 0.21/0.75  (
% 0.21/0.75  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.boole_POSet (tptp.cast_as_carrier_subset A)))) (let ((_let_2 (tptp.powerset (tptp.the_carrier _let_1)))) (=> (and (not (tptp.empty B)) (tptp.filtered_subset B _let_1) (tptp.upper_relstr_subset B _let_1) (tptp.proper_element B _let_2) (tptp.element B _let_2)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.in C (tptp.lim_points_of_net A (tptp.net_of_bool_filter A (tptp.cast_as_carrier_subset A) B))) (tptp.is_a_convergence_point_of_set A B C))))))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (let ((_let_2 (tptp.boole_POSet _let_1))) (let ((_let_3 (tptp.powerset (tptp.the_carrier _let_2)))) (=> (and (not (tptp.empty B)) (tptp.filtered_subset B _let_2) (tptp.upper_relstr_subset B _let_2) (tptp.proper_element B _let_3) (tptp.element B _let_3)) (= B (tptp.filter_of_net_str A (tptp.net_of_bool_filter A _let_1 B)))))))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.in C (tptp.lim_points_of_net A B)) (tptp.is_a_convergence_point_of_set A (tptp.filter_of_net_str A B) C)))))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.net_of_bool_filter A B C))) (let ((_let_2 (tptp.boole_POSet B))) (let ((_let_3 (tptp.powerset (tptp.the_carrier _let_2)))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty B)) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty C)) (tptp.filtered_subset C _let_2) (tptp.upper_relstr_subset C _let_2) (tptp.proper_element C _let_3) (tptp.element C _let_3)) (and (not (tptp.empty_carrier _let_1)) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.strict_net_str _let_1 A) (tptp.directed_relstr _let_1))))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.net_of_bool_filter A B C))) (let ((_let_2 (tptp.boole_POSet B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty B)) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty C)) (tptp.filtered_subset C _let_2) (tptp.upper_relstr_subset C _let_2) (tptp.element C (tptp.powerset (tptp.the_carrier _let_2)))) (and (not (tptp.empty_carrier _let_1)) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.strict_net_str _let_1 A)))))))) (let ((_let_6 (tptp.relation tptp.empty_set))) (let ((_let_7 (tptp.empty tptp.empty_set))) (let ((_let_8 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.cast_as_carrier_subset A))))))) (let ((_let_9 (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.net_of_bool_filter A B C))) (let ((_let_2 (tptp.boole_POSet B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty B)) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty C)) (tptp.filtered_subset C _let_2) (tptp.upper_relstr_subset C _let_2) (tptp.element C (tptp.powerset (tptp.the_carrier _let_2)))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A)))))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (tptp.element (tptp.cast_as_carrier_subset A) (tptp.powerset (tptp.the_carrier A))))))) (let ((_let_12 (tptp.cast_as_carrier_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_13 (tptp.net_of_bool_filter SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_14 (tptp.filter_of_net_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_13))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_14))) (let ((_let_16 (tptp.is_a_convergence_point_of_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_17 (tptp.is_a_convergence_point_of_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_18 (tptp.boole_POSet _let_12))) (let ((_let_19 (tptp.powerset (tptp.the_carrier _let_18)))) (let ((_let_20 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_19))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.proper_element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_19))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.upper_relstr_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_18))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.filtered_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_18))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_29 (tptp.one_sorted_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_32 (or _let_31 _let_30 _let_28 _let_27 _let_25 _let_23 _let_21 _let_15))) (let ((_let_33 (forall ((A $$unsorted) (BOUND_VARIABLE_4201 $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (let ((_let_2 (tptp.boole_POSet _let_1))) (let ((_let_3 (tptp.powerset (tptp.the_carrier _let_2)))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty BOUND_VARIABLE_4201) (not (tptp.filtered_subset BOUND_VARIABLE_4201 _let_2)) (not (tptp.upper_relstr_subset BOUND_VARIABLE_4201 _let_2)) (not (tptp.proper_element BOUND_VARIABLE_4201 _let_3)) (not (tptp.element BOUND_VARIABLE_4201 _let_3)) (= BOUND_VARIABLE_4201 (tptp.filter_of_net_str A (tptp.net_of_bool_filter A _let_1 BOUND_VARIABLE_4201)))))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (tptp.top_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_29))) (let ((_let_38 (forall ((A $$unsorted)) (or (not (tptp.top_str A)) (tptp.one_sorted_str A))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 (tptp.lim_points_of_net SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_13)))) (let ((_let_41 (= _let_40 _let_16))) (let ((_let_42 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_43 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_42))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.topological_space SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_31 _let_46 _let_36 _let_28 _let_27 _let_25 _let_23 _let_21 _let_44 _let_41))) (let ((_let_48 (forall ((A $$unsorted) (BOUND_VARIABLE_4258 $$unsorted) (BOUND_VARIABLE_4256 $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (let ((_let_2 (tptp.boole_POSet _let_1))) (let ((_let_3 (tptp.powerset (tptp.the_carrier _let_2)))) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (tptp.empty BOUND_VARIABLE_4256) (not (tptp.filtered_subset BOUND_VARIABLE_4256 _let_2)) (not (tptp.upper_relstr_subset BOUND_VARIABLE_4256 _let_2)) (not (tptp.proper_element BOUND_VARIABLE_4256 _let_3)) (not (tptp.element BOUND_VARIABLE_4256 _let_3)) (not (tptp.element BOUND_VARIABLE_4258 (tptp.the_carrier A))) (= (tptp.in BOUND_VARIABLE_4258 (tptp.lim_points_of_net A (tptp.net_of_bool_filter A _let_1 BOUND_VARIABLE_4256))) (tptp.is_a_convergence_point_of_set A BOUND_VARIABLE_4256 BOUND_VARIABLE_4258))))))))) (let ((_let_49 (not _let_47))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (or))) (let ((_let_52 (not _let_48))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_50) :args (_let_52))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_48))) (REFL :args (_let_49)) :args _let_51)) _let_50 :args (_let_49 true _let_48)))) (let ((_let_54 (REFL :args (_let_47)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 2)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_51)) :args ((or _let_35 _let_47))) _let_53 :args (_let_35 true _let_47)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_29 (not _let_37)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.top_str A) false))))) :args (_let_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_29 false _let_35 false _let_37)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 7)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_51)) :args ((or _let_20 _let_47))) _let_53 :args (_let_20 true _let_47)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 6)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_51)) :args ((or _let_22 _let_47))) _let_53 :args (_let_22 true _let_47)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 5)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_51)) :args ((or _let_24 _let_47))) _let_53 :args (_let_24 true _let_47)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 4)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_51)) :args ((or _let_26 _let_47))) _let_53 :args (_let_26 true _let_47)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_47 3)) _let_53 :args ((not _let_28) true _let_47)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_47 0)) _let_53 :args ((not _let_31) true _let_47)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_28 _let_27 _let_25 _let_23 _let_21 _let_30 _let_15 (not _let_32)))) _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.filtered_subset BOUND_VARIABLE_4201 (tptp.boole_POSet (tptp.cast_as_carrier_subset A))) false))))) :args (_let_33))) _let_34 :args (_let_32 false _let_33)) :args (_let_15 true _let_31 true _let_28 false _let_26 false _let_24 false _let_22 false _let_20 false _let_29 false _let_32)))) (let ((_let_64 (not _let_16))) (let ((_let_65 (= _let_40 _let_17))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_47 9)) _let_53 :args ((not _let_41) true _let_47)))) (let ((_let_67 (_let_41))) (let ((_let_68 (tptp.net_str _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.directed_relstr _let_13))) (let ((_let_71 (not _let_70))) (let ((_let_72 (tptp.transitive_relstr _let_13))) (let ((_let_73 (not _let_72))) (let ((_let_74 (tptp.empty_carrier _let_13))) (let ((_let_75 (or _let_31 _let_46 _let_36 _let_74 _let_73 _let_71 _let_69 _let_44 _let_65))) (let ((_let_76 (forall ((A $$unsorted) (BOUND_VARIABLE_4163 $$unsorted) (BOUND_VARIABLE_4161 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (tptp.empty_carrier BOUND_VARIABLE_4161) (not (tptp.transitive_relstr BOUND_VARIABLE_4161)) (not (tptp.directed_relstr BOUND_VARIABLE_4161)) (not (tptp.net_str BOUND_VARIABLE_4161 A)) (not (tptp.element BOUND_VARIABLE_4163 (tptp.the_carrier A))) (= (tptp.in BOUND_VARIABLE_4163 (tptp.lim_points_of_net A BOUND_VARIABLE_4161)) (tptp.is_a_convergence_point_of_set A (tptp.filter_of_net_str A BOUND_VARIABLE_4161) BOUND_VARIABLE_4163)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (tptp.strict_net_str _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_79 (not _let_74))) (let ((_let_80 (and _let_79 _let_78 _let_68))) (let ((_let_81 (tptp.element _let_12 (tptp.powerset _let_42)))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.empty _let_12))) (let ((_let_84 (or _let_31 _let_30 _let_83 _let_82 _let_28 _let_27 _let_25 _let_21 _let_80))) (let ((_let_85 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.net_of_bool_filter A B C))) (let ((_let_2 (tptp.boole_POSet B))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty B) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.empty C) (not (tptp.filtered_subset C _let_2)) (not (tptp.upper_relstr_subset C _let_2)) (not (tptp.element C (tptp.powerset (tptp.the_carrier _let_2)))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A)))))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (or _let_30 _let_81))) (let ((_let_88 (forall ((A $$unsorted)) (or (not (tptp.one_sorted_str A)) (tptp.element (tptp.cast_as_carrier_subset A) (tptp.powerset (tptp.the_carrier A))))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_30 _let_81 (not _let_87)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cast_as_carrier_subset A)))) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_81 false _let_29 false _let_87)))) (let ((_let_91 (not _let_83))) (let ((_let_92 (or _let_31 _let_30 _let_91))) (let ((_let_93 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (not (tptp.empty (tptp.cast_as_carrier_subset A))))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_31 _let_30 _let_91 (not _let_92)))) _let_62 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.empty_carrier A) true))))) :args (_let_93))) _let_94 :args (_let_92 false _let_93)) :args (_let_91 true _let_31 false _let_29 false _let_92)))) (let ((_let_96 (tptp.reflexive_relstr _let_13))) (let ((_let_97 (and _let_79 _let_96 _let_72 _let_78 _let_70))) (let ((_let_98 (or _let_31 _let_30 _let_83 _let_82 _let_28 _let_27 _let_25 _let_23 _let_21 _let_97))) (let ((_let_99 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.net_of_bool_filter A B C))) (let ((_let_2 (tptp.boole_POSet B))) (let ((_let_3 (tptp.powerset (tptp.the_carrier _let_2)))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty B) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.empty C) (not (tptp.filtered_subset C _let_2)) (not (tptp.upper_relstr_subset C _let_2)) (not (tptp.proper_element C _let_3)) (not (tptp.element C _let_3)) (and (not (tptp.empty_carrier _let_1)) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.strict_net_str _let_1 A) (tptp.directed_relstr _let_1))))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (and _let_79 _let_96 _let_72 _let_78))) (let ((_let_102 (or _let_31 _let_30 _let_83 _let_82 _let_28 _let_27 _let_25 _let_21 _let_101))) (let ((_let_103 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.net_of_bool_filter A B C))) (let ((_let_2 (tptp.boole_POSet B))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty B) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.empty C) (not (tptp.filtered_subset C _let_2)) (not (tptp.upper_relstr_subset C _let_2)) (not (tptp.element C (tptp.powerset (tptp.the_carrier _let_2)))) (and (not (tptp.empty_carrier _let_1)) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.strict_net_str _let_1 A)))))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_31 _let_28 _let_27 _let_25 _let_21 _let_30 _let_83 _let_82 _let_101 (not _let_102)))) _let_62 _let_61 _let_60 _let_59 _let_57 _let_56 _let_95 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.net_of_bool_filter A B C)))) :args (_let_103))) _let_104 :args (_let_102 false _let_103)) :args (_let_101 true _let_31 true _let_28 false _let_26 false _let_24 false _let_20 false _let_29 true _let_83 false _let_81 false _let_102)))) (let ((_let_106 (not _let_101))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_31 _let_46 _let_36 _let_44 _let_74 _let_73 _let_71 _let_69 _let_65 (not _let_75)))) _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 1)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_51)) :args ((or _let_45 _let_47))) _let_53 :args (_let_45 true _let_47)) _let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 8)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_51)) :args ((or _let_43 _let_47))) _let_53 :args (_let_43 true _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 0)) :args ((or _let_79 _let_106))) _let_105 :args (_let_79 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 2)) :args ((or _let_72 _let_106))) _let_105 :args (_let_72 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 4)) :args ((or _let_70 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_31 _let_28 _let_27 _let_25 _let_23 _let_21 _let_30 _let_83 _let_82 _let_97 (not _let_98)))) _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_95 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.net_of_bool_filter A B C)))) :args (_let_99))) _let_100 :args (_let_98 false _let_99)) :args (_let_97 true _let_31 true _let_28 false _let_26 false _let_24 false _let_22 false _let_20 false _let_29 true _let_83 false _let_81 false _let_98)) :args (_let_70 false _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_80 2)) :args ((or _let_68 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_31 _let_28 _let_27 _let_25 _let_21 _let_30 _let_83 _let_82 _let_80 (not _let_84)))) _let_62 _let_61 _let_60 _let_59 _let_57 _let_56 _let_95 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.net_of_bool_filter A B C)))) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_80 true _let_31 true _let_28 false _let_26 false _let_24 false _let_20 false _let_29 true _let_83 false _let_81 false _let_84)) :args (_let_68 false _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_13 QUANTIFIERS_INST_E_MATCHING ((tptp.in BOUND_VARIABLE_4163 (tptp.lim_points_of_net A BOUND_VARIABLE_4161))))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_65 true _let_31 false _let_45 false _let_35 false _let_43 true _let_74 false _let_72 false _let_70 false _let_68 false _let_75)))) (let ((_let_108 (not _let_65))) (let ((_let_109 (not _let_17))) (let ((_let_110 (_let_65))) (let ((_let_111 (not _let_15))) (let ((_let_112 (and _let_16 _let_15))) (let ((_let_113 (_let_16 _let_15))) (let ((_let_114 (ASSUME :args (_let_16)))) (let ((_let_115 (ASSUME :args (_let_15)))) (let ((_let_116 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) (SYMM _let_115) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)) :args (APPLY_UF tptp.is_a_convergence_point_of_set)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_112)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_114 _let_115) (SCOPE (TRUE_ELIM (TRANS _let_116 (TRUE_INTRO _let_114))) :args _let_113)) :args _let_113)) :args (true _let_112)) :args ((or _let_64 _let_17 _let_111))) _let_63 (REORDERING (CNF_EQUIV_POS2 :args _let_110) :args ((or _let_40 _let_109 _let_108))) _let_107 (REORDERING (CNF_EQUIV_NEG1 :args _let_67) :args ((or _let_40 _let_16 _let_41))) _let_66 :args (_let_40 false _let_15 true _let_17 false _let_65 false _let_16 true _let_41)))) (let ((_let_118 (and _let_64 _let_15))) (let ((_let_119 (_let_64 _let_15))) (let ((_let_120 (ASSUME :args (_let_64)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_118)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_120 _let_115) (SCOPE (FALSE_ELIM (TRANS _let_116 (FALSE_INTRO _let_120))) :args _let_119)) :args _let_119)) :args (true _let_118)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_16))) (REFL :args (_let_111)) (REFL :args (_let_109)) :args _let_51)) :args ((or _let_16 _let_109 _let_111))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_110) :args ((or (not _let_40) _let_17 _let_108))) _let_117 _let_107 :args (_let_17 false _let_40 false _let_65)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_67) _let_66 _let_117 :args (_let_64 true _let_41 false _let_40)) _let_63 :args (false false _let_17 true _let_16 false _let_15)) :args ((forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.strict_rel_str A) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.net_str B A)) (=> (tptp.strict_net_str B A) (= B (tptp.net_str_of A (tptp.the_carrier B) (tptp.the_InternalRel B) (tptp.the_mapping A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.complete_relstr A)) (and _let_2 _let_1 (tptp.up_complete_relstr A) (tptp.join_complete_relstr A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.join_complete_relstr A)) (and _let_2 _let_1 (tptp.lower_bounded_relstr A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.lower_bounded_relstr A))) (let ((_let_2 (tptp.with_suprema_relstr A))) (let ((_let_3 (tptp.antisymmetric_relstr A))) (let ((_let_4 (tptp.transitive_relstr A))) (let ((_let_5 (tptp.reflexive_relstr A))) (let ((_let_6 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 (tptp.up_complete_relstr A)) (and _let_6 _let_5 _let_4 _let_3 _let_2 (tptp.with_infima_relstr A) (tptp.complete_relstr A) _let_1 (tptp.upper_bounded_relstr A) (tptp.bounded_relstr A))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.antisymmetric_relstr A))) (let ((_let_2 (tptp.reflexive_relstr A))) (let ((_let_3 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_3 _let_2 _let_1 (tptp.join_complete_relstr A)) (and _let_3 _let_2 _let_1 (tptp.with_infima_relstr A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.upper_bounded_relstr A))) (let ((_let_2 (tptp.antisymmetric_relstr A))) (let ((_let_3 (tptp.reflexive_relstr A))) (let ((_let_4 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_4 _let_3 _let_2 _let_1 (tptp.join_complete_relstr A)) (and _let_4 _let_3 _let_2 (tptp.with_suprema_relstr A) _let_1)))))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.with_suprema_relstr A) (not (tptp.empty_carrier A))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (and (tptp.open_subset B A) (tptp.closed_subset B A))))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_1 (tptp.complete_relstr A)) (and _let_1 (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A)))))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.with_infima_relstr A) (not (tptp.empty_carrier A))))) (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (tptp.boundary_set B A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.trivial_carrier A)) (and _let_2 _let_1 (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.complete_relstr A))))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (tptp.nowhere_dense B A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_1 (tptp.complete_relstr A)) (and _let_1 (tptp.bounded_relstr A)))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.nowhere_dense B A) (tptp.boundary_set B A)))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.bounded_relstr A) (and (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.boundary_set B A))) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (and (tptp.closed_subset B A) _let_1) (and _let_1 (tptp.nowhere_dense B A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.trivial_carrier A)) (and _let_2 _let_1 (tptp.connected_relstr A))))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (and (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A)) (tptp.bounded_relstr A)))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.nowhere_dense B A))) (let ((_let_2 (tptp.open_subset B A))) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (and _let_2 _let_1) (and (tptp.empty B) _let_2 (tptp.closed_subset B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A) _let_1)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.with_suprema_relstr A))) (let ((_let_2 (tptp.reflexive_relstr A))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.up_complete_relstr A)) (and (not (tptp.empty_carrier A)) _let_2 _let_1 (tptp.upper_bounded_relstr A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.net_str B A)) (= (tptp.filter_of_net_str A B) (tptp.a_2_1_yellow19 A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (tptp.relation_of2 B A A) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.net_str_of A B C D))) (let ((_let_2 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_2) (tptp.relation_of2 D B _let_2)) (and (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (tptp.element (tptp.lim_points_of_net A B) (tptp.powerset (tptp.the_carrier A))))) true true _let_11 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (tptp.element (tptp.filter_of_net_str A B) (tptp.powerset (tptp.the_carrier (tptp.boole_POSet (tptp.cast_as_carrier_subset A))))))) true _let_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1)))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))) _let_9 true (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.net_str B A) (tptp.rel_str B))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.the_carrier B))) (let ((_let_3 (tptp.the_mapping A B))) (=> (and (tptp.one_sorted_str A) (tptp.net_str B A)) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))) (exists ((A $$unsorted)) (tptp.rel_str A)) (exists ((A $$unsorted)) (tptp.top_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (tptp.net_str B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))) (and _let_7 _let_6 (tptp.relation_empty_yielding tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (not (tptp.empty_carrier A)) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.lower_relstr_subset _let_1 A) (tptp.upper_relstr_subset _let_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.the_mapping A B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (and (not (tptp.empty _let_1)) (tptp.relation _let_1) (tptp.function _let_1) (tptp.quasi_total _let_1 (tptp.the_carrier B) (tptp.the_carrier A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.up_complete_relstr _let_1) (tptp.join_complete_relstr _let_1) (not (tptp.v1_yellow_3 _let_1)) (tptp.distributive_relstr _let_1) (tptp.heyting_relstr _let_1) (tptp.complemented_relstr _let_1) (tptp.boolean_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1)))) _let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (tptp.with_suprema_relstr A) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.directed_subset _let_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (=> (not (tptp.empty A)) (and (not (tptp.empty_carrier _let_1)) (not (tptp.trivial_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.up_complete_relstr _let_1) (tptp.join_complete_relstr _let_1) (not (tptp.v1_yellow_3 _let_1)) (tptp.distributive_relstr _let_1) (tptp.heyting_relstr _let_1) (tptp.complemented_relstr _let_1) (tptp.boolean_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.filter_of_net_str A B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (and (not (tptp.empty _let_1)) (tptp.upper_relstr_subset _let_1 (tptp.boole_POSet (tptp.cast_as_carrier_subset A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.rel_str A)) (not (tptp.empty (tptp.cast_as_carrier_subset A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (not (tptp.empty_carrier A)) (tptp.upper_bounded_relstr A) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.directed_subset _let_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.boole_POSet (tptp.cast_as_carrier_subset A)))) (let ((_let_2 (tptp.filter_of_net_str A B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (and (not (tptp.empty _let_2)) (tptp.filtered_subset _let_2 _let_1) (tptp.upper_relstr_subset _let_2 _let_1) (tptp.proper_element _let_2 (tptp.powerset (tptp.the_carrier _let_1)))))))) (and _let_7 _let_6) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (tptp.with_infima_relstr A) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.filtered_subset _let_1 A))))) _let_5 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (tptp.closed_subset (tptp.cast_as_carrier_subset A) A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lower_bounded_relstr A) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.filtered_subset _let_1 A))))) _let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.net_str_of A B C D))) (let ((_let_2 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (not (tptp.empty B)) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_2) (tptp.relation_of2 D B _let_2)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (tptp.topological_space A) (tptp.top_str A)) (and (tptp.open_subset _let_1 A) (tptp.closed_subset _let_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.directed_relstr _let_1) (tptp.up_complete_relstr _let_1) (tptp.join_complete_relstr _let_1) (not (tptp.v1_yellow_3 _let_1)) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1)))) (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.dense (tptp.cast_as_carrier_subset A) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.one_sorted_str B) (not (tptp.empty_carrier C)) (tptp.net_str C B)) (= (tptp.in A (tptp.a_2_1_yellow19 B C)) (exists ((D $$unsorted)) (and (tptp.element D (tptp.powerset (tptp.the_carrier B))) (= A D) (tptp.is_eventually_in B C D)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.rel_str_of A B) (tptp.rel_str_of C D)) (and (= A C) (= B D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_1) (tptp.relation_of2 D B _let_1)) (forall ((E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (= (tptp.net_str_of A B C D) (tptp.net_str_of E F G H)) (and (= A E) (= B F) (= C G) (= D H))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.filtered_subset B A) (tptp.upper_relstr_subset B A))))) (forall ((A $$unsorted)) (=> (and (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.directed_subset B A) (tptp.filtered_subset B A) (tptp.lower_relstr_subset B A) (tptp.upper_relstr_subset B A))))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.connected_relstr A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A) (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A) (tptp.bounded_relstr A) (tptp.up_complete_relstr A) (tptp.join_complete_relstr A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.complete_relstr A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset B A))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.directed_subset B A) (tptp.filtered_subset B A))))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (not (tptp.trivial_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A) (tptp.bounded_relstr A) (not (tptp.v1_yellow_3 A)) (tptp.distributive_relstr A) (tptp.heyting_relstr A) (tptp.complemented_relstr A) (tptp.boolean_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A) (tptp.trivial_carrier A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset B A) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.finite B) (tptp.directed_subset B A) (tptp.filtered_subset B A))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.powerset A))) (not (tptp.empty B)) (tptp.finite B)))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A) (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A) (tptp.bounded_relstr A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.open_subset B A) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (tptp.top_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.empty B) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A))))) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (and (tptp.net_str B A) (tptp.strict_net_str B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (not (tptp.trivial_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.upper_bounded_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (and (tptp.element B _let_1) (not (tptp.empty B)) (tptp.proper_element B _let_1) (tptp.filtered_subset B A) (tptp.upper_relstr_subset B A)))))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.transitive_relstr A) (tptp.directed_relstr A))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.empty B) (tptp.open_subset B A) (tptp.closed_subset B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A) (tptp.nowhere_dense B A))))) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (and (tptp.net_str B A) (not (tptp.empty_carrier B)) (tptp.reflexive_relstr B) (tptp.transitive_relstr B) (tptp.antisymmetric_relstr B) (tptp.strict_net_str B A) (tptp.directed_relstr B))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.lower_relstr_subset B A) (tptp.upper_relstr_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.lower_relstr_subset B A) (tptp.upper_relstr_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.directed_subset B A) (tptp.lower_relstr_subset B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_3 _let_2 _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.76  )
% 0.21/0.76  % SZS output end Proof for SEU395+1
% 0.21/0.76  % cvc5---1.0.5 exiting
% 0.21/0.76  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------