TSTP Solution File: SEU392+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU392+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 : Wed Jul 27 13:16:03 EDT 2022
% Result : Unknown 3.66s 3.84s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU392+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:59:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.00/3.18 ----- Otter 3.3f, August 2004 -----
% 3.00/3.18 The process was started by sandbox2 on n014.cluster.edu,
% 3.00/3.18 Wed Jul 27 07:59:09 2022
% 3.00/3.18 The command was "./otter". The process ID is 27587.
% 3.00/3.18
% 3.00/3.18 set(prolog_style_variables).
% 3.00/3.18 set(auto).
% 3.00/3.18 dependent: set(auto1).
% 3.00/3.18 dependent: set(process_input).
% 3.00/3.18 dependent: clear(print_kept).
% 3.00/3.18 dependent: clear(print_new_demod).
% 3.00/3.18 dependent: clear(print_back_demod).
% 3.00/3.18 dependent: clear(print_back_sub).
% 3.00/3.18 dependent: set(control_memory).
% 3.00/3.18 dependent: assign(max_mem, 12000).
% 3.00/3.18 dependent: assign(pick_given_ratio, 4).
% 3.00/3.18 dependent: assign(stats_level, 1).
% 3.00/3.18 dependent: assign(max_seconds, 10800).
% 3.00/3.18 clear(print_given).
% 3.00/3.18
% 3.00/3.18 formula_list(usable).
% 3.00/3.18 all A (A=A).
% 3.00/3.18 all A (rel_str(A)-> (strict_rel_str(A)->A=rel_str_of(the_carrier(A),the_InternalRel(A)))).
% 3.00/3.18 all A B (in(A,B)-> -in(B,A)).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A))).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&join_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&lower_bounded_relstr(A))).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&lower_bounded_relstr(A)&up_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A))).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&antisymmetric_relstr(A)&join_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&antisymmetric_relstr(A)&with_infima_relstr(A))).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&antisymmetric_relstr(A)&upper_bounded_relstr(A)&join_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&upper_bounded_relstr(A))).
% 3.00/3.18 all A (empty(A)->finite(A)).
% 3.00/3.18 all A (rel_str(A)-> (with_suprema_relstr(A)-> -empty_carrier(A))).
% 3.00/3.18 all A (empty(A)->relation(A)).
% 3.00/3.18 all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->open_subset(B,A)&closed_subset(B,A))))).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&complete_relstr(A)-> -empty_carrier(A)&with_suprema_relstr(A)&with_infima_relstr(A))).
% 3.00/3.18 all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 3.00/3.18 all A (rel_str(A)-> (with_infima_relstr(A)-> -empty_carrier(A))).
% 3.00/3.18 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->boundary_set(B,A))))).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&trivial_carrier(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&complete_relstr(A))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->nowhere_dense(B,A))))).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&complete_relstr(A)-> -empty_carrier(A)&bounded_relstr(A))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (nowhere_dense(B,A)->boundary_set(B,A))))).
% 3.00/3.18 all A (rel_str(A)-> (bounded_relstr(A)->lower_bounded_relstr(A)&upper_bounded_relstr(A))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)&boundary_set(B,A)->boundary_set(B,A)&nowhere_dense(B,A))))).
% 3.00/3.18 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&trivial_carrier(A)-> -empty_carrier(A)&reflexive_relstr(A)&connected_relstr(A))).
% 3.00/3.18 all A (rel_str(A)-> (lower_bounded_relstr(A)&upper_bounded_relstr(A)->bounded_relstr(A))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (open_subset(B,A)&nowhere_dense(B,A)->empty(B)&open_subset(B,A)&closed_subset(B,A)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)&nowhere_dense(B,A))))).
% 3.00/3.18 all A (rel_str(A)-> (reflexive_relstr(A)&with_suprema_relstr(A)&up_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&with_suprema_relstr(A)&upper_bounded_relstr(A))).
% 3.00/3.18 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (element(C,powerset(the_carrier(A)))-> (C=lim_points_of_net(A,B)<-> (all D (element(D,the_carrier(A))-> (in(D,C)<-> (all E (point_neighbourhood(E,A,D)->is_eventually_in(A,B,E)))))))))))).
% 3.00/3.18 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,powerset(the_carrier(A)))-> (point_neighbourhood(C,A,B)<->in(B,interior(A,C)))))))).
% 3.00/3.18 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)->filter_of_net_str(A,B)=a_2_1_yellow19(A,B)))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (all B C (is_a_convergence_point_of_set(A,B,C)<-> (all D (element(D,powerset(the_carrier(A)))-> (open_subset(D,A)&in(C,D)->in(D,B))))))).
% 3.00/3.18 all A B (relation_of2(B,A,A)->strict_rel_str(rel_str_of(A,B))&rel_str(rel_str_of(A,B))).
% 3.00/3.18 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)->element(lim_points_of_net(A,B),powerset(the_carrier(A)))).
% 3.00/3.18 all A B (top_str(A)&element(B,powerset(the_carrier(A)))->element(interior(A,B),powerset(the_carrier(A)))).
% 3.00/3.18 $T.
% 3.00/3.18 $T.
% 3.00/3.18 all A (one_sorted_str(A)->element(cast_as_carrier_subset(A),powerset(the_carrier(A)))).
% 3.00/3.18 all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&net_str(B,A)->element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))).
% 3.00/3.18 $T.
% 3.00/3.18 all A (strict_rel_str(boole_POSet(A))&rel_str(boole_POSet(A))).
% 3.00/3.18 all A (rel_str(A)->one_sorted_str(A)).
% 3.00/3.18 all A (top_str(A)->one_sorted_str(A)).
% 3.00/3.18 $T.
% 3.00/3.18 all A (one_sorted_str(A)-> (all B (net_str(B,A)->rel_str(B)))).
% 3.00/3.18 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))-> (all C (point_neighbourhood(C,A,B)->element(C,powerset(the_carrier(A)))))).
% 3.00/3.18 $T.
% 3.00/3.18 $T.
% 3.00/3.18 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 3.00/3.18 all A (rel_str(A)->relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))).
% 3.00/3.18 $T.
% 3.00/3.18 exists A rel_str(A).
% 3.00/3.18 exists A top_str(A).
% 3.00/3.18 exists A one_sorted_str(A).
% 3.00/3.18 all A (one_sorted_str(A)-> (exists B net_str(B,A))).
% 3.00/3.18 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))-> (exists C point_neighbourhood(C,A,B))).
% 3.00/3.18 all A B exists C relation_of2(C,A,B).
% 3.00/3.18 all A exists B element(B,A).
% 3.00/3.18 all A B exists C relation_of2_as_subset(C,A,B).
% 3.00/3.18 all A B (top_str(A)&boundary_set(B,A)&element(B,powerset(the_carrier(A)))->empty(interior(A,B))&v1_membered(interior(A,B))&v2_membered(interior(A,B))&v3_membered(interior(A,B))&v4_membered(interior(A,B))&v5_membered(interior(A,B))&boundary_set(interior(A,B),A)).
% 3.00/3.18 empty(empty_set).
% 3.00/3.18 relation(empty_set).
% 3.00/3.18 relation_empty_yielding(empty_set).
% 3.00/3.18 all A B (finite(A)&finite(B)->finite(cartesian_product2(A,B))).
% 3.00/3.18 all A (-empty_carrier(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&lower_relstr_subset(cast_as_carrier_subset(A),A)&upper_relstr_subset(cast_as_carrier_subset(A),A)).
% 3.00/3.18 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 3.00/3.18 all A (-empty(powerset(A))).
% 3.00/3.18 all A (-empty_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))&lower_bounded_relstr(boole_POSet(A))&upper_bounded_relstr(boole_POSet(A))&bounded_relstr(boole_POSet(A))&up_complete_relstr(boole_POSet(A))&join_complete_relstr(boole_POSet(A))& -v1_yellow_3(boole_POSet(A))&distributive_relstr(boole_POSet(A))&heyting_relstr(boole_POSet(A))&complemented_relstr(boole_POSet(A))&boolean_relstr(boole_POSet(A))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_relstr(boole_POSet(A))).
% 3.00/3.18 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(cast_as_carrier_subset(A))).
% 3.00/3.18 all A (with_suprema_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&directed_subset(cast_as_carrier_subset(A),A)).
% 3.00/3.18 all A (-empty(A)-> -empty_carrier(boole_POSet(A))& -trivial_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))&lower_bounded_relstr(boole_POSet(A))&upper_bounded_relstr(boole_POSet(A))&bounded_relstr(boole_POSet(A))&up_complete_relstr(boole_POSet(A))&join_complete_relstr(boole_POSet(A))& -v1_yellow_3(boole_POSet(A))&distributive_relstr(boole_POSet(A))&heyting_relstr(boole_POSet(A))&complemented_relstr(boole_POSet(A))&boolean_relstr(boole_POSet(A))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_relstr(boole_POSet(A))).
% 3.00/3.18 all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&net_str(B,A)-> -empty(filter_of_net_str(A,B))&upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))).
% 3.00/3.18 all A (-empty_carrier(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))).
% 3.00/3.18 all A (-empty_carrier(A)&upper_bounded_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&directed_subset(cast_as_carrier_subset(A),A)).
% 3.00/3.18 all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> -empty(filter_of_net_str(A,B))&filtered_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))&upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))&proper_element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))).
% 3.00/3.18 empty(empty_set).
% 3.00/3.18 relation(empty_set).
% 3.00/3.18 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 3.00/3.18 all A (with_infima_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&filtered_subset(cast_as_carrier_subset(A),A)).
% 3.00/3.18 all A (topological_space(A)&top_str(A)->closed_subset(cast_as_carrier_subset(A),A)).
% 3.00/3.18 all A (-empty_carrier(A)&lower_bounded_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&filtered_subset(cast_as_carrier_subset(A),A)).
% 3.00/3.18 all A B (topological_space(A)&top_str(A)&element(B,powerset(the_carrier(A)))->open_subset(interior(A,B),A)).
% 3.00/3.18 all A (-empty_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)->open_subset(cast_as_carrier_subset(A),A)&closed_subset(cast_as_carrier_subset(A),A)).
% 3.00/3.18 all A (-empty_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))&lower_bounded_relstr(boole_POSet(A))&upper_bounded_relstr(boole_POSet(A))&bounded_relstr(boole_POSet(A))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_relstr(boole_POSet(A))).
% 3.00/3.18 all A (-empty_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))&lower_bounded_relstr(boole_POSet(A))&upper_bounded_relstr(boole_POSet(A))&bounded_relstr(boole_POSet(A))&directed_relstr(boole_POSet(A))&up_complete_relstr(boole_POSet(A))&join_complete_relstr(boole_POSet(A))& -v1_yellow_3(boole_POSet(A))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_relstr(boole_POSet(A))).
% 3.00/3.18 all A (top_str(A)->dense(cast_as_carrier_subset(A),A)).
% 3.00/3.18 all A B C (-empty_carrier(B)&one_sorted_str(B)& -empty_carrier(C)&net_str(C,B)-> (in(A,a_2_1_yellow19(B,C))<-> (exists D (element(D,powerset(the_carrier(B)))&A=D&is_eventually_in(B,C,D))))).
% 3.00/3.18 all A B (relation_of2(B,A,A)-> (all C D (rel_str_of(A,B)=rel_str_of(C,D)->A=C&B=D))).
% 3.00/3.18 all A (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&filtered_subset(B,A)&upper_relstr_subset(B,A)))).
% 3.00/3.18 all A (reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&directed_subset(B,A)&filtered_subset(B,A)&lower_relstr_subset(B,A)&upper_relstr_subset(B,A)))).
% 3.00/3.18 exists A (rel_str(A)& -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&connected_relstr(A)).
% 3.00/3.18 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A)).
% 3.00/3.18 exists A (-empty(A)&finite(A)).
% 3.00/3.18 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&complete_relstr(A)).
% 3.00/3.18 exists A (empty(A)&relation(A)).
% 3.00/3.18 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&open_subset(B,A)))).
% 3.00/3.18 all A (rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&directed_subset(B,A)&filtered_subset(B,A)))).
% 3.00/3.18 exists A (rel_str(A)& -empty_carrier(A)& -trivial_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)& -v1_yellow_3(A)&distributive_relstr(A)&heyting_relstr(A)&complemented_relstr(A)&boolean_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)).
% 3.00/3.18 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&trivial_carrier(A)).
% 3.00/3.18 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)).
% 3.00/3.18 exists A (-empty(A)&relation(A)).
% 3.00/3.18 all A exists B (element(B,powerset(A))&empty(B)).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&open_subset(B,A)&closed_subset(B,A)))).
% 3.00/3.18 all A (-empty_carrier(A)&reflexive_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&finite(B)&directed_subset(B,A)&filtered_subset(B,A)))).
% 3.00/3.18 all A exists B (element(B,powerset(powerset(A)))& -empty(B)&finite(B)).
% 3.00/3.18 exists A (rel_str(A)& -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)).
% 3.00/3.18 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 3.00/3.18 exists A (relation(A)&relation_empty_yielding(A)).
% 3.00/3.18 exists A (one_sorted_str(A)& -empty_carrier(A)).
% 3.00/3.18 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&open_subset(B,A)&closed_subset(B,A)))).
% 3.00/3.18 all A (one_sorted_str(A)-> (exists B (element(B,powerset(powerset(the_carrier(A))))& -empty(B)&finite(B)))).
% 3.00/3.18 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 3.00/3.18 all A (top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&empty(B)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)))).
% 3.00/3.18 all A (-empty_carrier(A)& -trivial_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&upper_bounded_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&proper_element(B,powerset(the_carrier(A)))&filtered_subset(B,A)&upper_relstr_subset(B,A)))).
% 3.00/3.18 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&transitive_relstr(A)&directed_relstr(A)).
% 3.00/3.18 all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&empty(B)&open_subset(B,A)&closed_subset(B,A)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)&nowhere_dense(B,A)))).
% 3.00/3.18 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&closed_subset(B,A)))).
% 3.00/3.18 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&closed_subset(B,A)))).
% 3.00/3.18 all A (rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&lower_relstr_subset(B,A)&upper_relstr_subset(B,A)))).
% 3.00/3.18 all A (-empty_carrier(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&lower_relstr_subset(B,A)&upper_relstr_subset(B,A)))).
% 3.00/3.18 all A (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&directed_subset(B,A)&lower_relstr_subset(B,A)))).
% 3.00/3.18 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 3.00/3.18 all A B subset(A,A).
% 3.00/3.18 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C (in(C,filter_of_net_str(A,B))<->is_eventually_in(A,B,C)&element(C,powerset(the_carrier(A)))))))).
% 3.00/3.18 -(all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (element(C,the_carrier(A))-> (in(C,lim_points_of_net(A,B))<->is_a_convergence_point_of_set(A,filter_of_net_str(A,B),C)))))))).
% 3.00/3.18 all A B (in(A,B)->element(A,B)).
% 3.00/3.18 all A B (element(A,B)->empty(B)|in(A,B)).
% 3.00/3.18 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 3.00/3.18 all A B (element(A,powerset(B))<->subset(A,B)).
% 3.00/3.18 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset(interior(A,B),B)))).
% 3.00/3.18 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 3.00/3.18 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (all C (element(C,the_carrier(A))-> (open_subset(B,A)&in(C,B)->point_neighbourhood(B,A,C))))))).
% 3.00/3.18 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 3.00/3.18 all A (empty(A)->A=empty_set).
% 3.00/3.18 all A B (-(in(A,B)&empty(B))).
% 3.00/3.18 all A B (-(empty(A)&A!=B&empty(B))).
% 3.00/3.18 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C D (subset(C,D)-> (is_eventually_in(A,B,C)->is_eventually_in(A,B,D))& (is_often_in(A,B,C)->is_often_in(A,B,D))))))).
% 3.00/3.18 end_of_list.
% 3.00/3.18
% 3.00/3.18 -------> usable clausifies to:
% 3.00/3.18
% 3.00/3.18 list(usable).
% 3.00/3.18 0 [] A=A.
% 3.00/3.18 0 [] -rel_str(A)| -strict_rel_str(A)|A=rel_str_of(the_carrier(A),the_InternalRel(A)).
% 3.00/3.18 0 [] -in(A,B)| -in(B,A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|up_complete_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|join_complete_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -join_complete_relstr(A)|lower_bounded_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|with_infima_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|complete_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|bounded_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -join_complete_relstr(A)|with_infima_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -join_complete_relstr(A)|with_suprema_relstr(A).
% 3.00/3.18 0 [] -empty(A)|finite(A).
% 3.00/3.18 0 [] -rel_str(A)| -with_suprema_relstr(A)| -empty_carrier(A).
% 3.00/3.18 0 [] -empty(A)|relation(A).
% 3.00/3.18 0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|open_subset(B,A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|closed_subset(B,A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_suprema_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_infima_relstr(A).
% 3.00/3.18 0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 3.00/3.18 0 [] -rel_str(A)| -with_infima_relstr(A)| -empty_carrier(A).
% 3.00/3.18 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|boundary_set(B,A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|transitive_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|antisymmetric_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|complete_relstr(A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|nowhere_dense(B,A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|bounded_relstr(A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -nowhere_dense(B,A)|boundary_set(B,A).
% 3.00/3.18 0 [] -rel_str(A)| -bounded_relstr(A)|lower_bounded_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)| -bounded_relstr(A)|upper_bounded_relstr(A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)| -boundary_set(B,A)|nowhere_dense(B,A).
% 3.00/3.18 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|connected_relstr(A).
% 3.00/3.18 0 [] -rel_str(A)| -lower_bounded_relstr(A)| -upper_bounded_relstr(A)|bounded_relstr(A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|empty(B).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|closed_subset(B,A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v1_membered(B).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v2_membered(B).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v3_membered(B).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v4_membered(B).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v5_membered(B).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|boundary_set(B,A).
% 3.00/3.18 0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)| -empty_carrier(A).
% 3.00/3.18 0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C!=lim_points_of_net(A,B)| -element(D,the_carrier(A))| -in(D,C)| -point_neighbourhood(E,A,D)|is_eventually_in(A,B,E).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C!=lim_points_of_net(A,B)| -element(D,the_carrier(A))|in(D,C)|point_neighbourhood($f1(A,B,C,D),A,D).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C!=lim_points_of_net(A,B)| -element(D,the_carrier(A))|in(D,C)| -is_eventually_in(A,B,$f1(A,B,C,D)).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C=lim_points_of_net(A,B)|element($f3(A,B,C),the_carrier(A)).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C=lim_points_of_net(A,B)|in($f3(A,B,C),C)| -point_neighbourhood(X1,A,$f3(A,B,C))|is_eventually_in(A,B,X1).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C=lim_points_of_net(A,B)| -in($f3(A,B,C),C)|point_neighbourhood($f2(A,B,C),A,$f3(A,B,C)).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C=lim_points_of_net(A,B)| -in($f3(A,B,C),C)| -is_eventually_in(A,B,$f2(A,B,C)).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -element(C,powerset(the_carrier(A)))| -point_neighbourhood(C,A,B)|in(B,interior(A,C)).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -element(C,powerset(the_carrier(A)))|point_neighbourhood(C,A,B)| -in(B,interior(A,C)).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|filter_of_net_str(A,B)=a_2_1_yellow19(A,B).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -is_a_convergence_point_of_set(A,B,C)| -element(D,powerset(the_carrier(A)))| -open_subset(D,A)| -in(C,D)|in(D,B).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)|is_a_convergence_point_of_set(A,B,C)|element($f4(A,B,C),powerset(the_carrier(A))).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)|is_a_convergence_point_of_set(A,B,C)|open_subset($f4(A,B,C),A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)|is_a_convergence_point_of_set(A,B,C)|in(C,$f4(A,B,C)).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)|is_a_convergence_point_of_set(A,B,C)| -in($f4(A,B,C),B).
% 3.00/3.18 0 [] -relation_of2(B,A,A)|strict_rel_str(rel_str_of(A,B)).
% 3.00/3.18 0 [] -relation_of2(B,A,A)|rel_str(rel_str_of(A,B)).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)|element(lim_points_of_net(A,B),powerset(the_carrier(A))).
% 3.00/3.18 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|element(interior(A,B),powerset(the_carrier(A))).
% 3.00/3.18 0 [] $T.
% 3.00/3.18 0 [] $T.
% 3.00/3.18 0 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))).
% 3.00/3.18 0 [] $T.
% 3.00/3.18 0 [] strict_rel_str(boole_POSet(A)).
% 3.00/3.18 0 [] rel_str(boole_POSet(A)).
% 3.00/3.18 0 [] -rel_str(A)|one_sorted_str(A).
% 3.00/3.18 0 [] -top_str(A)|one_sorted_str(A).
% 3.00/3.18 0 [] $T.
% 3.00/3.18 0 [] -one_sorted_str(A)| -net_str(B,A)|rel_str(B).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -point_neighbourhood(C,A,B)|element(C,powerset(the_carrier(A))).
% 3.00/3.18 0 [] $T.
% 3.00/3.18 0 [] $T.
% 3.00/3.18 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 3.00/3.18 0 [] -rel_str(A)|relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)).
% 3.00/3.18 0 [] $T.
% 3.00/3.18 0 [] rel_str($c1).
% 3.00/3.18 0 [] top_str($c2).
% 3.00/3.18 0 [] one_sorted_str($c3).
% 3.00/3.18 0 [] -one_sorted_str(A)|net_str($f5(A),A).
% 3.00/3.18 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|point_neighbourhood($f6(A,B),A,B).
% 3.00/3.18 0 [] relation_of2($f7(A,B),A,B).
% 3.00/3.18 0 [] element($f8(A),A).
% 3.00/3.18 0 [] relation_of2_as_subset($f9(A,B),A,B).
% 3.00/3.18 0 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|empty(interior(A,B)).
% 3.00/3.18 0 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v1_membered(interior(A,B)).
% 3.00/3.18 0 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v2_membered(interior(A,B)).
% 3.00/3.18 0 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v3_membered(interior(A,B)).
% 3.00/3.18 0 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v4_membered(interior(A,B)).
% 3.00/3.18 0 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v5_membered(interior(A,B)).
% 3.00/3.18 0 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|boundary_set(interior(A,B),A).
% 3.00/3.18 0 [] empty(empty_set).
% 3.00/3.18 0 [] relation(empty_set).
% 3.00/3.18 0 [] relation_empty_yielding(empty_set).
% 3.00/3.18 0 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 3.00/3.18 0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.00/3.18 0 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 3.00/3.18 0 [] -empty(powerset(A)).
% 3.00/3.18 0 [] -empty_carrier(boole_POSet(A)).
% 3.00/3.18 0 [] strict_rel_str(boole_POSet(A)).
% 3.00/3.18 0 [] reflexive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] transitive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] up_complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] join_complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] -v1_yellow_3(boole_POSet(A)).
% 3.00/3.18 0 [] distributive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] heyting_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] complemented_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] boolean_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] with_suprema_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] with_infima_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.00/3.18 0 [] -with_suprema_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.00/3.18 0 [] -with_suprema_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] empty(A)| -empty_carrier(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)| -trivial_carrier(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|strict_rel_str(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|reflexive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|transitive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|antisymmetric_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|lower_bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|upper_bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|up_complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|join_complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)| -v1_yellow_3(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|distributive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|heyting_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|complemented_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|boolean_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|with_suprema_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|with_infima_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty(A)|complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -empty(filter_of_net_str(A,B)).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A))).
% 3.00/3.18 0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.00/3.18 0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.00/3.18 0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -empty(filter_of_net_str(A,B)).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)|filtered_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A))).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)|upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A))).
% 3.00/3.18 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)|proper_element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))).
% 3.00/3.18 0 [] empty(empty_set).
% 3.00/3.18 0 [] relation(empty_set).
% 3.00/3.18 0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 3.00/3.18 0 [] -with_infima_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.00/3.18 0 [] -with_infima_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)|closed_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.00/3.18 0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))|open_subset(interior(A,B),A).
% 3.00/3.18 0 [] -empty_carrier(boole_POSet(A)).
% 3.00/3.18 0 [] strict_rel_str(boole_POSet(A)).
% 3.00/3.18 0 [] reflexive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] transitive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)|open_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)|closed_subset(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] -empty_carrier(boole_POSet(A)).
% 3.00/3.18 0 [] strict_rel_str(boole_POSet(A)).
% 3.00/3.18 0 [] reflexive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] transitive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] with_suprema_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] with_infima_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] -empty_carrier(boole_POSet(A)).
% 3.00/3.18 0 [] strict_rel_str(boole_POSet(A)).
% 3.00/3.18 0 [] reflexive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] transitive_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] bounded_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] directed_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] up_complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] join_complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] -v1_yellow_3(boole_POSet(A)).
% 3.00/3.18 0 [] with_suprema_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] with_infima_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] complete_relstr(boole_POSet(A)).
% 3.00/3.18 0 [] -top_str(A)|dense(cast_as_carrier_subset(A),A).
% 3.00/3.18 0 [] empty_carrier(B)| -one_sorted_str(B)|empty_carrier(C)| -net_str(C,B)| -in(A,a_2_1_yellow19(B,C))|element($f10(A,B,C),powerset(the_carrier(B))).
% 3.00/3.18 0 [] empty_carrier(B)| -one_sorted_str(B)|empty_carrier(C)| -net_str(C,B)| -in(A,a_2_1_yellow19(B,C))|A=$f10(A,B,C).
% 3.00/3.18 0 [] empty_carrier(B)| -one_sorted_str(B)|empty_carrier(C)| -net_str(C,B)| -in(A,a_2_1_yellow19(B,C))|is_eventually_in(B,C,$f10(A,B,C)).
% 3.00/3.18 0 [] empty_carrier(B)| -one_sorted_str(B)|empty_carrier(C)| -net_str(C,B)|in(A,a_2_1_yellow19(B,C))| -element(D,powerset(the_carrier(B)))|A!=D| -is_eventually_in(B,C,D).
% 3.00/3.18 0 [] -relation_of2(B,A,A)|rel_str_of(A,B)!=rel_str_of(C,D)|A=C.
% 3.00/3.18 0 [] -relation_of2(B,A,A)|rel_str_of(A,B)!=rel_str_of(C,D)|B=D.
% 3.00/3.18 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f11(A),powerset(the_carrier(A))).
% 3.00/3.18 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f11(A)).
% 3.00/3.18 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|filtered_subset($f11(A),A).
% 3.00/3.18 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|upper_relstr_subset($f11(A),A).
% 3.00/3.18 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|element($f12(A),powerset(the_carrier(A))).
% 3.00/3.18 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)| -empty($f12(A)).
% 3.00/3.18 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|directed_subset($f12(A),A).
% 3.00/3.18 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|filtered_subset($f12(A),A).
% 3.00/3.18 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|lower_relstr_subset($f12(A),A).
% 3.00/3.18 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|upper_relstr_subset($f12(A),A).
% 3.00/3.18 0 [] rel_str($c4).
% 3.00/3.18 0 [] -empty_carrier($c4).
% 3.00/3.18 0 [] reflexive_relstr($c4).
% 3.00/3.18 0 [] transitive_relstr($c4).
% 3.00/3.18 0 [] antisymmetric_relstr($c4).
% 3.00/3.18 0 [] connected_relstr($c4).
% 3.00/3.18 0 [] rel_str($c5).
% 3.00/3.18 0 [] -empty_carrier($c5).
% 3.00/3.18 0 [] strict_rel_str($c5).
% 3.00/3.18 0 [] reflexive_relstr($c5).
% 3.00/3.18 0 [] transitive_relstr($c5).
% 3.00/3.18 0 [] antisymmetric_relstr($c5).
% 3.00/3.18 0 [] with_suprema_relstr($c5).
% 3.00/3.18 0 [] with_infima_relstr($c5).
% 3.00/3.18 0 [] complete_relstr($c5).
% 3.00/3.18 0 [] lower_bounded_relstr($c5).
% 3.00/3.18 0 [] upper_bounded_relstr($c5).
% 3.00/3.18 0 [] bounded_relstr($c5).
% 3.00/3.18 0 [] up_complete_relstr($c5).
% 3.00/3.18 0 [] join_complete_relstr($c5).
% 3.00/3.18 0 [] -empty($c6).
% 3.00/3.18 0 [] finite($c6).
% 3.00/3.18 0 [] rel_str($c7).
% 3.00/3.18 0 [] -empty_carrier($c7).
% 3.00/3.18 0 [] strict_rel_str($c7).
% 3.00/3.18 0 [] reflexive_relstr($c7).
% 3.00/3.18 0 [] transitive_relstr($c7).
% 3.00/3.18 0 [] antisymmetric_relstr($c7).
% 3.00/3.18 0 [] complete_relstr($c7).
% 3.00/3.18 0 [] empty($c8).
% 3.00/3.18 0 [] relation($c8).
% 3.00/3.18 0 [] empty(A)|element($f13(A),powerset(A)).
% 3.00/3.18 0 [] empty(A)| -empty($f13(A)).
% 3.00/3.18 0 [] -topological_space(A)| -top_str(A)|element($f14(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|open_subset($f14(A),A).
% 3.00/3.19 0 [] -rel_str(A)|element($f15(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] -rel_str(A)|directed_subset($f15(A),A).
% 3.00/3.19 0 [] -rel_str(A)|filtered_subset($f15(A),A).
% 3.00/3.19 0 [] rel_str($c9).
% 3.00/3.19 0 [] -empty_carrier($c9).
% 3.00/3.19 0 [] -trivial_carrier($c9).
% 3.00/3.19 0 [] strict_rel_str($c9).
% 3.00/3.19 0 [] reflexive_relstr($c9).
% 3.00/3.19 0 [] transitive_relstr($c9).
% 3.00/3.19 0 [] antisymmetric_relstr($c9).
% 3.00/3.19 0 [] lower_bounded_relstr($c9).
% 3.00/3.19 0 [] upper_bounded_relstr($c9).
% 3.00/3.19 0 [] bounded_relstr($c9).
% 3.00/3.19 0 [] -v1_yellow_3($c9).
% 3.00/3.19 0 [] distributive_relstr($c9).
% 3.00/3.19 0 [] heyting_relstr($c9).
% 3.00/3.19 0 [] complemented_relstr($c9).
% 3.00/3.19 0 [] boolean_relstr($c9).
% 3.00/3.19 0 [] with_suprema_relstr($c9).
% 3.00/3.19 0 [] with_infima_relstr($c9).
% 3.00/3.19 0 [] rel_str($c10).
% 3.00/3.19 0 [] -empty_carrier($c10).
% 3.00/3.19 0 [] strict_rel_str($c10).
% 3.00/3.19 0 [] reflexive_relstr($c10).
% 3.00/3.19 0 [] transitive_relstr($c10).
% 3.00/3.19 0 [] antisymmetric_relstr($c10).
% 3.00/3.19 0 [] with_suprema_relstr($c10).
% 3.00/3.19 0 [] with_infima_relstr($c10).
% 3.00/3.19 0 [] complete_relstr($c10).
% 3.00/3.19 0 [] trivial_carrier($c10).
% 3.00/3.19 0 [] rel_str($c11).
% 3.00/3.19 0 [] -empty_carrier($c11).
% 3.00/3.19 0 [] strict_rel_str($c11).
% 3.00/3.19 0 [] reflexive_relstr($c11).
% 3.00/3.19 0 [] transitive_relstr($c11).
% 3.00/3.19 0 [] antisymmetric_relstr($c11).
% 3.00/3.19 0 [] with_suprema_relstr($c11).
% 3.00/3.19 0 [] with_infima_relstr($c11).
% 3.00/3.19 0 [] complete_relstr($c11).
% 3.00/3.19 0 [] -empty($c12).
% 3.00/3.19 0 [] relation($c12).
% 3.00/3.19 0 [] element($f16(A),powerset(A)).
% 3.00/3.19 0 [] empty($f16(A)).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|element($f17(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|open_subset($f17(A),A).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|closed_subset($f17(A),A).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|element($f18(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -empty($f18(A)).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|finite($f18(A)).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|directed_subset($f18(A),A).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|filtered_subset($f18(A),A).
% 3.00/3.19 0 [] element($f19(A),powerset(powerset(A))).
% 3.00/3.19 0 [] -empty($f19(A)).
% 3.00/3.19 0 [] finite($f19(A)).
% 3.00/3.19 0 [] rel_str($c13).
% 3.00/3.19 0 [] -empty_carrier($c13).
% 3.00/3.19 0 [] reflexive_relstr($c13).
% 3.00/3.19 0 [] transitive_relstr($c13).
% 3.00/3.19 0 [] antisymmetric_relstr($c13).
% 3.00/3.19 0 [] with_suprema_relstr($c13).
% 3.00/3.19 0 [] with_infima_relstr($c13).
% 3.00/3.19 0 [] complete_relstr($c13).
% 3.00/3.19 0 [] lower_bounded_relstr($c13).
% 3.00/3.19 0 [] upper_bounded_relstr($c13).
% 3.00/3.19 0 [] bounded_relstr($c13).
% 3.00/3.19 0 [] empty(A)|element($f20(A),powerset(A)).
% 3.00/3.19 0 [] empty(A)| -empty($f20(A)).
% 3.00/3.19 0 [] empty(A)|finite($f20(A)).
% 3.00/3.19 0 [] relation($c14).
% 3.00/3.19 0 [] relation_empty_yielding($c14).
% 3.00/3.19 0 [] one_sorted_str($c15).
% 3.00/3.19 0 [] -empty_carrier($c15).
% 3.00/3.19 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|element($f21(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -empty($f21(A)).
% 3.00/3.19 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|open_subset($f21(A),A).
% 3.00/3.19 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|closed_subset($f21(A),A).
% 3.00/3.19 0 [] -one_sorted_str(A)|element($f22(A),powerset(powerset(the_carrier(A)))).
% 3.00/3.19 0 [] -one_sorted_str(A)| -empty($f22(A)).
% 3.00/3.19 0 [] -one_sorted_str(A)|finite($f22(A)).
% 3.00/3.19 0 [] empty(A)|element($f23(A),powerset(A)).
% 3.00/3.19 0 [] empty(A)| -empty($f23(A)).
% 3.00/3.19 0 [] empty(A)|finite($f23(A)).
% 3.00/3.19 0 [] -top_str(A)|element($f24(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] -top_str(A)|empty($f24(A)).
% 3.00/3.19 0 [] -top_str(A)|v1_membered($f24(A)).
% 3.00/3.19 0 [] -top_str(A)|v2_membered($f24(A)).
% 3.00/3.19 0 [] -top_str(A)|v3_membered($f24(A)).
% 3.00/3.19 0 [] -top_str(A)|v4_membered($f24(A)).
% 3.00/3.19 0 [] -top_str(A)|v5_membered($f24(A)).
% 3.00/3.19 0 [] -top_str(A)|boundary_set($f24(A),A).
% 3.00/3.19 0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|element($f25(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty($f25(A)).
% 3.00/3.19 0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|proper_element($f25(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|filtered_subset($f25(A),A).
% 3.00/3.19 0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|upper_relstr_subset($f25(A),A).
% 3.00/3.19 0 [] rel_str($c16).
% 3.00/3.19 0 [] -empty_carrier($c16).
% 3.00/3.19 0 [] strict_rel_str($c16).
% 3.00/3.19 0 [] transitive_relstr($c16).
% 3.00/3.19 0 [] directed_relstr($c16).
% 3.00/3.19 0 [] empty_carrier(A)| -one_sorted_str(A)|element($f26(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f26(A)).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|element($f27(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|empty($f27(A)).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|open_subset($f27(A),A).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|closed_subset($f27(A),A).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|v1_membered($f27(A)).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|v2_membered($f27(A)).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|v3_membered($f27(A)).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|v4_membered($f27(A)).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|v5_membered($f27(A)).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|boundary_set($f27(A),A).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|nowhere_dense($f27(A),A).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|element($f28(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] -topological_space(A)| -top_str(A)|closed_subset($f28(A),A).
% 3.00/3.19 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|element($f29(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -empty($f29(A)).
% 3.00/3.19 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|closed_subset($f29(A),A).
% 3.00/3.19 0 [] -rel_str(A)|element($f30(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] -rel_str(A)|lower_relstr_subset($f30(A),A).
% 3.00/3.19 0 [] -rel_str(A)|upper_relstr_subset($f30(A),A).
% 3.00/3.19 0 [] empty_carrier(A)| -rel_str(A)|element($f31(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)| -rel_str(A)| -empty($f31(A)).
% 3.00/3.19 0 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset($f31(A),A).
% 3.00/3.19 0 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset($f31(A),A).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f32(A),powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f32(A)).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|directed_subset($f32(A),A).
% 3.00/3.19 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|lower_relstr_subset($f32(A),A).
% 3.00/3.19 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 3.00/3.19 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 3.00/3.19 0 [] subset(A,A).
% 3.00/3.19 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,filter_of_net_str(A,B))|is_eventually_in(A,B,C).
% 3.00/3.19 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,filter_of_net_str(A,B))|element(C,powerset(the_carrier(A))).
% 3.00/3.19 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|in(C,filter_of_net_str(A,B))| -is_eventually_in(A,B,C)| -element(C,powerset(the_carrier(A))).
% 3.00/3.19 0 [] -empty_carrier($c19).
% 3.00/3.19 0 [] topological_space($c19).
% 3.00/3.19 0 [] top_str($c19).
% 3.00/3.19 0 [] -empty_carrier($c18).
% 3.00/3.19 0 [] transitive_relstr($c18).
% 3.00/3.19 0 [] directed_relstr($c18).
% 3.00/3.19 0 [] net_str($c18,$c19).
% 3.00/3.19 0 [] element($c17,the_carrier($c19)).
% 3.00/3.19 0 [] in($c17,lim_points_of_net($c19,$c18))|is_a_convergence_point_of_set($c19,filter_of_net_str($c19,$c18),$c17).
% 3.00/3.19 0 [] -in($c17,lim_points_of_net($c19,$c18))| -is_a_convergence_point_of_set($c19,filter_of_net_str($c19,$c18),$c17).
% 3.00/3.19 0 [] -in(A,B)|element(A,B).
% 3.00/3.19 0 [] -element(A,B)|empty(B)|in(A,B).
% 3.00/3.19 0 [] in($f33(A,B),A)|in($f33(A,B),B)|A=B.
% 3.00/3.19 0 [] -in($f33(A,B),A)| -in($f33(A,B),B)|A=B.
% 3.00/3.19 0 [] -element(A,powerset(B))|subset(A,B).
% 3.00/3.19 0 [] element(A,powerset(B))| -subset(A,B).
% 3.00/3.19 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|subset(interior(A,B),B).
% 3.00/3.19 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 3.00/3.19 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -element(C,the_carrier(A))| -open_subset(B,A)| -in(C,B)|point_neighbourhood(B,A,C).
% 3.00/3.19 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 3.00/3.19 0 [] -empty(A)|A=empty_set.
% 3.00/3.19 0 [] -in(A,B)| -empty(B).
% 3.00/3.19 0 [] -empty(A)|A=B| -empty(B).
% 3.00/3.19 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -subset(C,D)| -is_eventually_in(A,B,C)|is_eventually_in(A,B,D).
% 3.00/3.19 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -subset(C,D)| -is_often_in(A,B,C)|is_often_in(A,B,D).
% 3.00/3.19 end_of_list.
% 3.00/3.19
% 3.00/3.19 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=13.
% 3.00/3.19
% 3.00/3.19 This ia a non-Horn set with equality. The strategy will be
% 3.00/3.19 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.00/3.19 deletion, with positive clauses in sos and nonpositive
% 3.00/3.19 clauses in usable.
% 3.00/3.19
% 3.00/3.19 dependent: set(knuth_bendix).
% 3.00/3.19 dependent: set(anl_eq).
% 3.00/3.19 dependent: set(para_from).
% 3.00/3.19 dependent: set(para_into).
% 3.00/3.19 dependent: clear(para_from_right).
% 3.00/3.19 dependent: clear(para_into_right).
% 3.00/3.19 dependent: set(para_from_vars).
% 3.00/3.19 dependent: set(eq_units_both_ways).
% 3.00/3.19 dependent: set(dynamic_demod_all).
% 3.00/3.19 dependent: set(dynamic_demod).
% 3.00/3.19 dependent: set(order_eq).
% 3.00/3.19 dependent: set(back_demod).
% 3.00/3.19 dependent: set(lrpo).
% 3.00/3.19 dependent: set(hyper_res).
% 3.00/3.19 dependent: set(unit_deletion).
% 3.00/3.19 dependent: set(factor).
% 3.00/3.19
% 3.00/3.19 ------------> process usable:
% 3.00/3.19 ** KEPT (pick-wt=11): 2 [copy,1,flip.3] -rel_str(A)| -strict_rel_str(A)|rel_str_of(the_carrier(A),the_InternalRel(A))=A.
% 3.00/3.19 ** KEPT (pick-wt=6): 3 [] -in(A,B)| -in(B,A).
% 3.00/3.19 ** KEPT (pick-wt=10): 4 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|up_complete_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=10): 5 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|join_complete_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=10): 6 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -join_complete_relstr(A)|lower_bounded_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=18): 7 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|with_infima_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=18): 8 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|complete_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=18): 9 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=18): 10 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|bounded_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=12): 11 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -join_complete_relstr(A)|with_infima_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=14): 12 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -join_complete_relstr(A)|with_suprema_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=4): 13 [] -empty(A)|finite(A).
% 3.00/3.19 ** KEPT (pick-wt=6): 14 [] -rel_str(A)| -with_suprema_relstr(A)| -empty_carrier(A).
% 3.00/3.19 ** KEPT (pick-wt=4): 15 [] -empty(A)|relation(A).
% 3.00/3.19 ** KEPT (pick-wt=8): 16 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 3.00/3.19 ** KEPT (pick-wt=14): 17 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|open_subset(B,A).
% 3.00/3.19 ** KEPT (pick-wt=14): 18 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|closed_subset(B,A).
% 3.00/3.19 ** KEPT (pick-wt=8): 19 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_suprema_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=8): 20 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_infima_relstr(A).
% 3.00/3.19 ** KEPT (pick-wt=8): 21 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 3.00/3.19 ** KEPT (pick-wt=6): 22 [] -rel_str(A)| -with_infima_relstr(A)| -empty_carrier(A).
% 3.00/3.19 ** KEPT (pick-wt=12): 23 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|boundary_set(B,A).
% 3.06/3.19 ** KEPT (pick-wt=10): 24 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|transitive_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=10): 25 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|antisymmetric_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=10): 26 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|complete_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=14): 27 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|nowhere_dense(B,A).
% 3.06/3.19 ** KEPT (pick-wt=8): 28 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|bounded_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=15): 29 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -nowhere_dense(B,A)|boundary_set(B,A).
% 3.06/3.19 ** KEPT (pick-wt=6): 30 [] -rel_str(A)| -bounded_relstr(A)|lower_bounded_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=6): 31 [] -rel_str(A)| -bounded_relstr(A)|upper_bounded_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=18): 32 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)| -boundary_set(B,A)|nowhere_dense(B,A).
% 3.06/3.19 ** KEPT (pick-wt=10): 33 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|connected_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=8): 34 [] -rel_str(A)| -lower_bounded_relstr(A)| -upper_bounded_relstr(A)|bounded_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=17): 35 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|empty(B).
% 3.06/3.19 ** KEPT (pick-wt=18): 36 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|closed_subset(B,A).
% 3.06/3.19 ** KEPT (pick-wt=17): 37 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v1_membered(B).
% 3.06/3.19 ** KEPT (pick-wt=17): 38 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v2_membered(B).
% 3.06/3.19 ** KEPT (pick-wt=17): 39 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v3_membered(B).
% 3.06/3.19 ** KEPT (pick-wt=17): 40 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v4_membered(B).
% 3.06/3.19 ** KEPT (pick-wt=17): 41 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v5_membered(B).
% 3.06/3.19 Following clause subsumed by 29 during input processing: 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|boundary_set(B,A).
% 3.06/3.19 Following clause subsumed by 14 during input processing: 0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)| -empty_carrier(A).
% 3.06/3.19 ** KEPT (pick-wt=10): 42 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 3.06/3.19 ** KEPT (pick-wt=40): 43 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C!=lim_points_of_net(A,B)| -element(D,the_carrier(A))| -in(D,C)| -point_neighbourhood(E,A,D)|is_eventually_in(A,B,E).
% 3.06/3.19 ** KEPT (pick-wt=40): 44 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C!=lim_points_of_net(A,B)| -element(D,the_carrier(A))|in(D,C)|point_neighbourhood($f1(A,B,C,D),A,D).
% 3.06/3.19 ** KEPT (pick-wt=40): 45 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C!=lim_points_of_net(A,B)| -element(D,the_carrier(A))|in(D,C)| -is_eventually_in(A,B,$f1(A,B,C,D)).
% 3.06/3.19 ** KEPT (pick-wt=32): 46 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C=lim_points_of_net(A,B)|element($f3(A,B,C),the_carrier(A)).
% 3.06/3.19 ** KEPT (pick-wt=42): 47 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C=lim_points_of_net(A,B)|in($f3(A,B,C),C)| -point_neighbourhood(D,A,$f3(A,B,C))|is_eventually_in(A,B,D).
% 3.06/3.19 ** KEPT (pick-wt=41): 48 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C=lim_points_of_net(A,B)| -in($f3(A,B,C),C)|point_neighbourhood($f2(A,B,C),A,$f3(A,B,C)).
% 3.06/3.19 ** KEPT (pick-wt=38): 49 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -element(C,powerset(the_carrier(A)))|C=lim_points_of_net(A,B)| -in($f3(A,B,C),C)| -is_eventually_in(A,B,$f2(A,B,C)).
% 3.06/3.19 ** KEPT (pick-wt=24): 50 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -element(C,powerset(the_carrier(A)))| -point_neighbourhood(C,A,B)|in(B,interior(A,C)).
% 3.06/3.19 ** KEPT (pick-wt=24): 51 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -element(C,powerset(the_carrier(A)))|point_neighbourhood(C,A,B)| -in(B,interior(A,C)).
% 3.06/3.19 ** KEPT (pick-wt=16): 52 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|filter_of_net_str(A,B)=a_2_1_yellow19(A,B).
% 3.06/3.19 ** KEPT (pick-wt=22): 53 [] -topological_space(A)| -top_str(A)| -is_a_convergence_point_of_set(A,B,C)| -element(D,powerset(the_carrier(A)))| -open_subset(D,A)| -in(C,D)|in(D,B).
% 3.06/3.19 ** KEPT (pick-wt=16): 54 [] -topological_space(A)| -top_str(A)|is_a_convergence_point_of_set(A,B,C)|element($f4(A,B,C),powerset(the_carrier(A))).
% 3.06/3.19 ** KEPT (pick-wt=14): 55 [] -topological_space(A)| -top_str(A)|is_a_convergence_point_of_set(A,B,C)|open_subset($f4(A,B,C),A).
% 3.06/3.19 ** KEPT (pick-wt=14): 56 [] -topological_space(A)| -top_str(A)|is_a_convergence_point_of_set(A,B,C)|in(C,$f4(A,B,C)).
% 3.06/3.19 ** KEPT (pick-wt=14): 57 [] -topological_space(A)| -top_str(A)|is_a_convergence_point_of_set(A,B,C)| -in($f4(A,B,C),B).
% 3.06/3.19 ** KEPT (pick-wt=8): 58 [] -relation_of2(A,B,B)|strict_rel_str(rel_str_of(B,A)).
% 3.06/3.19 ** KEPT (pick-wt=8): 59 [] -relation_of2(A,B,B)|rel_str(rel_str_of(B,A)).
% 3.06/3.19 ** KEPT (pick-wt=22): 60 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)|element(lim_points_of_net(A,B),powerset(the_carrier(A))).
% 3.06/3.19 ** KEPT (pick-wt=14): 61 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|element(interior(A,B),powerset(the_carrier(A))).
% 3.06/3.19 ** KEPT (pick-wt=8): 62 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 3.06/3.19 ** KEPT (pick-wt=18): 63 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))).
% 3.06/3.19 ** KEPT (pick-wt=4): 64 [] -rel_str(A)|one_sorted_str(A).
% 3.06/3.19 ** KEPT (pick-wt=4): 65 [] -top_str(A)|one_sorted_str(A).
% 3.06/3.19 ** KEPT (pick-wt=7): 66 [] -one_sorted_str(A)| -net_str(B,A)|rel_str(B).
% 3.06/3.19 ** KEPT (pick-wt=19): 67 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -point_neighbourhood(C,A,B)|element(C,powerset(the_carrier(A))).
% 3.06/3.19 ** KEPT (pick-wt=10): 68 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 3.06/3.19 ** KEPT (pick-wt=9): 69 [] -rel_str(A)|relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)).
% 3.06/3.19 ** KEPT (pick-wt=6): 70 [] -one_sorted_str(A)|net_str($f5(A),A).
% 3.06/3.19 ** KEPT (pick-wt=16): 71 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|point_neighbourhood($f6(A,B),A,B).
% 3.06/3.19 ** KEPT (pick-wt=14): 72 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|empty(interior(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=14): 73 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v1_membered(interior(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=14): 74 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v2_membered(interior(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=14): 75 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v3_membered(interior(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=14): 76 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v4_membered(interior(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=14): 77 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|v5_membered(interior(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=15): 78 [] -top_str(A)| -boundary_set(B,A)| -element(B,powerset(the_carrier(A)))|boundary_set(interior(A,B),A).
% 3.06/3.19 ** KEPT (pick-wt=8): 79 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=7): 80 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.06/3.19 ** KEPT (pick-wt=8): 81 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset(cast_as_carrier_subset(A),A).
% 3.06/3.19 ** KEPT (pick-wt=8): 82 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset(cast_as_carrier_subset(A),A).
% 3.06/3.19 ** KEPT (pick-wt=7): 83 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 3.06/3.19 ** KEPT (pick-wt=3): 84 [] -empty(powerset(A)).
% 3.06/3.19 ** KEPT (pick-wt=3): 85 [] -empty_carrier(boole_POSet(A)).
% 3.06/3.19 ** KEPT (pick-wt=3): 86 [] -v1_yellow_3(boole_POSet(A)).
% 3.06/3.19 ** KEPT (pick-wt=7): 87 [] empty_carrier(A)| -one_sorted_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.06/3.19 ** KEPT (pick-wt=7): 88 [] -with_suprema_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.06/3.19 ** KEPT (pick-wt=8): 89 [] -with_suprema_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 3.06/3.19 Following clause subsumed by 85 during input processing: 0 [] empty(A)| -empty_carrier(boole_POSet(A)).
% 3.06/3.19 ** KEPT (pick-wt=5): 90 [] empty(A)| -trivial_carrier(boole_POSet(A)).
% 3.06/3.19 Following clause subsumed by 86 during input processing: 0 [] empty(A)| -v1_yellow_3(boole_POSet(A)).
% 3.06/3.19 ** KEPT (pick-wt=13): 91 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -empty(filter_of_net_str(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=16): 92 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A))).
% 3.06/3.19 Following clause subsumed by 80 during input processing: 0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.06/3.19 Following clause subsumed by 80 during input processing: 0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.06/3.19 ** KEPT (pick-wt=10): 93 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 3.06/3.19 Following clause subsumed by 91 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)| -empty(filter_of_net_str(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=20): 94 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)|filtered_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A))).
% 3.06/3.19 Following clause subsumed by 92 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)|upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A))).
% 3.06/3.19 ** KEPT (pick-wt=22): 95 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -transitive_relstr(B)| -directed_relstr(B)| -net_str(B,A)|proper_element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))).
% 3.06/3.19 ** KEPT (pick-wt=8): 96 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 3.06/3.19 ** KEPT (pick-wt=7): 97 [] -with_infima_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.06/3.19 ** KEPT (pick-wt=8): 98 [] -with_infima_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 3.06/3.19 ** KEPT (pick-wt=8): 99 [] -topological_space(A)| -top_str(A)|closed_subset(cast_as_carrier_subset(A),A).
% 3.06/3.19 Following clause subsumed by 80 during input processing: 0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.06/3.19 ** KEPT (pick-wt=10): 100 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 3.06/3.19 ** KEPT (pick-wt=14): 101 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))|open_subset(interior(A,B),A).
% 3.06/3.20 Following clause subsumed by 85 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 3.06/3.20 ** KEPT (pick-wt=8): 102 [] -topological_space(A)| -top_str(A)|open_subset(cast_as_carrier_subset(A),A).
% 3.06/3.20 Following clause subsumed by 99 during input processing: 0 [] -topological_space(A)| -top_str(A)|closed_subset(cast_as_carrier_subset(A),A).
% 3.06/3.20 Following clause subsumed by 85 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 3.06/3.20 Following clause subsumed by 85 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 3.06/3.20 Following clause subsumed by 86 during input processing: 0 [] -v1_yellow_3(boole_POSet(A)).
% 3.06/3.20 ** KEPT (pick-wt=6): 103 [] -top_str(A)|dense(cast_as_carrier_subset(A),A).
% 3.06/3.20 ** KEPT (pick-wt=22): 104 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,a_2_1_yellow19(A,B))|element($f10(C,A,B),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=20): 106 [copy,105,flip.6] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,a_2_1_yellow19(A,B))|$f10(C,A,B)=C.
% 3.06/3.20 ** KEPT (pick-wt=21): 107 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,a_2_1_yellow19(A,B))|is_eventually_in(A,B,$f10(C,A,B)).
% 3.06/3.20 ** KEPT (pick-wt=26): 108 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|in(C,a_2_1_yellow19(A,B))| -element(D,powerset(the_carrier(A)))|C!=D| -is_eventually_in(A,B,D).
% 3.06/3.20 ** KEPT (pick-wt=14): 109 [] -relation_of2(A,B,B)|rel_str_of(B,A)!=rel_str_of(C,D)|B=C.
% 3.06/3.20 ** KEPT (pick-wt=14): 110 [] -relation_of2(A,B,B)|rel_str_of(B,A)!=rel_str_of(C,D)|A=D.
% 3.06/3.20 ** KEPT (pick-wt=14): 111 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f11(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=11): 112 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f11(A)).
% 3.06/3.20 ** KEPT (pick-wt=12): 113 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|filtered_subset($f11(A),A).
% 3.06/3.20 ** KEPT (pick-wt=12): 114 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|upper_relstr_subset($f11(A),A).
% 3.06/3.20 ** KEPT (pick-wt=18): 115 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|element($f12(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=15): 116 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)| -empty($f12(A)).
% 3.06/3.20 ** KEPT (pick-wt=16): 117 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|directed_subset($f12(A),A).
% 3.06/3.20 ** KEPT (pick-wt=16): 118 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|filtered_subset($f12(A),A).
% 3.06/3.20 ** KEPT (pick-wt=16): 119 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|lower_relstr_subset($f12(A),A).
% 3.06/3.20 ** KEPT (pick-wt=16): 120 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|upper_relstr_subset($f12(A),A).
% 3.06/3.20 ** KEPT (pick-wt=2): 121 [] -empty_carrier($c4).
% 3.06/3.20 ** KEPT (pick-wt=2): 122 [] -empty_carrier($c5).
% 3.06/3.20 ** KEPT (pick-wt=2): 123 [] -empty($c6).
% 3.06/3.20 ** KEPT (pick-wt=2): 124 [] -empty_carrier($c7).
% 3.06/3.20 ** KEPT (pick-wt=5): 125 [] empty(A)| -empty($f13(A)).
% 3.06/3.20 ** KEPT (pick-wt=10): 126 [] -topological_space(A)| -top_str(A)|element($f14(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=8): 127 [] -topological_space(A)| -top_str(A)|open_subset($f14(A),A).
% 3.06/3.20 ** KEPT (pick-wt=8): 128 [] -rel_str(A)|element($f15(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=6): 129 [] -rel_str(A)|directed_subset($f15(A),A).
% 3.06/3.20 ** KEPT (pick-wt=6): 130 [] -rel_str(A)|filtered_subset($f15(A),A).
% 3.06/3.20 ** KEPT (pick-wt=2): 131 [] -empty_carrier($c9).
% 3.06/3.20 ** KEPT (pick-wt=2): 132 [] -trivial_carrier($c9).
% 3.06/3.20 ** KEPT (pick-wt=2): 133 [] -v1_yellow_3($c9).
% 3.06/3.20 ** KEPT (pick-wt=2): 134 [] -empty_carrier($c10).
% 3.06/3.20 ** KEPT (pick-wt=2): 135 [] -empty_carrier($c11).
% 3.06/3.20 ** KEPT (pick-wt=2): 136 [] -empty($c12).
% 3.06/3.20 ** KEPT (pick-wt=10): 137 [] -topological_space(A)| -top_str(A)|element($f17(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=8): 138 [] -topological_space(A)| -top_str(A)|open_subset($f17(A),A).
% 3.06/3.20 ** KEPT (pick-wt=8): 139 [] -topological_space(A)| -top_str(A)|closed_subset($f17(A),A).
% 3.06/3.20 ** KEPT (pick-wt=12): 140 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|element($f18(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=9): 141 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -empty($f18(A)).
% 3.06/3.20 ** KEPT (pick-wt=9): 142 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|finite($f18(A)).
% 3.06/3.20 ** KEPT (pick-wt=10): 143 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|directed_subset($f18(A),A).
% 3.06/3.20 ** KEPT (pick-wt=10): 144 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|filtered_subset($f18(A),A).
% 3.06/3.20 ** KEPT (pick-wt=3): 145 [] -empty($f19(A)).
% 3.06/3.20 ** KEPT (pick-wt=2): 146 [] -empty_carrier($c13).
% 3.06/3.20 ** KEPT (pick-wt=5): 147 [] empty(A)| -empty($f20(A)).
% 3.06/3.20 ** KEPT (pick-wt=2): 148 [] -empty_carrier($c15).
% 3.06/3.20 ** KEPT (pick-wt=12): 149 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|element($f21(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=9): 150 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -empty($f21(A)).
% 3.06/3.20 ** KEPT (pick-wt=10): 151 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|open_subset($f21(A),A).
% 3.06/3.20 ** KEPT (pick-wt=10): 152 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|closed_subset($f21(A),A).
% 3.06/3.20 ** KEPT (pick-wt=9): 153 [] -one_sorted_str(A)|element($f22(A),powerset(powerset(the_carrier(A)))).
% 3.06/3.20 ** KEPT (pick-wt=5): 154 [] -one_sorted_str(A)| -empty($f22(A)).
% 3.06/3.20 ** KEPT (pick-wt=5): 155 [] -one_sorted_str(A)|finite($f22(A)).
% 3.06/3.20 ** KEPT (pick-wt=5): 156 [] empty(A)| -empty($f23(A)).
% 3.06/3.20 ** KEPT (pick-wt=8): 157 [] -top_str(A)|element($f24(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=5): 158 [] -top_str(A)|empty($f24(A)).
% 3.06/3.20 ** KEPT (pick-wt=5): 159 [] -top_str(A)|v1_membered($f24(A)).
% 3.06/3.20 ** KEPT (pick-wt=5): 160 [] -top_str(A)|v2_membered($f24(A)).
% 3.06/3.20 ** KEPT (pick-wt=5): 161 [] -top_str(A)|v3_membered($f24(A)).
% 3.06/3.20 ** KEPT (pick-wt=5): 162 [] -top_str(A)|v4_membered($f24(A)).
% 3.06/3.20 ** KEPT (pick-wt=5): 163 [] -top_str(A)|v5_membered($f24(A)).
% 3.06/3.20 ** KEPT (pick-wt=6): 164 [] -top_str(A)|boundary_set($f24(A),A).
% 3.06/3.20 ** KEPT (pick-wt=20): 165 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|element($f25(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=17): 166 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty($f25(A)).
% 3.06/3.20 ** KEPT (pick-wt=20): 167 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|proper_element($f25(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=18): 168 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|filtered_subset($f25(A),A).
% 3.06/3.20 ** KEPT (pick-wt=18): 169 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|upper_relstr_subset($f25(A),A).
% 3.06/3.20 ** KEPT (pick-wt=2): 170 [] -empty_carrier($c16).
% 3.06/3.20 ** KEPT (pick-wt=10): 171 [] empty_carrier(A)| -one_sorted_str(A)|element($f26(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=7): 172 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f26(A)).
% 3.06/3.20 ** KEPT (pick-wt=10): 173 [] -topological_space(A)| -top_str(A)|element($f27(A),powerset(the_carrier(A))).
% 3.06/3.20 ** KEPT (pick-wt=7): 174 [] -topological_space(A)| -top_str(A)|empty($f27(A)).
% 3.06/3.20 ** KEPT (pick-wt=8): 175 [] -topological_space(A)| -top_str(A)|open_subset($f27(A),A).
% 3.06/3.20 ** KEPT (pick-wt=8): 176 [] -topological_space(A)| -top_str(A)|closed_subset($f27(A),A).
% 3.06/3.20 ** KEPT (pick-wt=7): 177 [] -topological_space(A)| -top_str(A)|v1_membered($f27(A)).
% 3.06/3.21 ** KEPT (pick-wt=7): 178 [] -topological_space(A)| -top_str(A)|v2_membered($f27(A)).
% 3.06/3.21 ** KEPT (pick-wt=7): 179 [] -topological_space(A)| -top_str(A)|v3_membered($f27(A)).
% 3.06/3.21 ** KEPT (pick-wt=7): 180 [] -topological_space(A)| -top_str(A)|v4_membered($f27(A)).
% 3.06/3.21 ** KEPT (pick-wt=7): 181 [] -topological_space(A)| -top_str(A)|v5_membered($f27(A)).
% 3.06/3.21 ** KEPT (pick-wt=8): 182 [] -topological_space(A)| -top_str(A)|boundary_set($f27(A),A).
% 3.06/3.21 ** KEPT (pick-wt=8): 183 [] -topological_space(A)| -top_str(A)|nowhere_dense($f27(A),A).
% 3.06/3.21 ** KEPT (pick-wt=10): 184 [] -topological_space(A)| -top_str(A)|element($f28(A),powerset(the_carrier(A))).
% 3.06/3.21 ** KEPT (pick-wt=8): 185 [] -topological_space(A)| -top_str(A)|closed_subset($f28(A),A).
% 3.06/3.21 ** KEPT (pick-wt=12): 186 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|element($f29(A),powerset(the_carrier(A))).
% 3.06/3.21 ** KEPT (pick-wt=9): 187 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -empty($f29(A)).
% 3.06/3.21 ** KEPT (pick-wt=10): 188 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|closed_subset($f29(A),A).
% 3.06/3.21 ** KEPT (pick-wt=8): 189 [] -rel_str(A)|element($f30(A),powerset(the_carrier(A))).
% 3.06/3.21 ** KEPT (pick-wt=6): 190 [] -rel_str(A)|lower_relstr_subset($f30(A),A).
% 3.06/3.21 ** KEPT (pick-wt=6): 191 [] -rel_str(A)|upper_relstr_subset($f30(A),A).
% 3.06/3.21 ** KEPT (pick-wt=10): 192 [] empty_carrier(A)| -rel_str(A)|element($f31(A),powerset(the_carrier(A))).
% 3.06/3.21 ** KEPT (pick-wt=7): 193 [] empty_carrier(A)| -rel_str(A)| -empty($f31(A)).
% 3.06/3.21 ** KEPT (pick-wt=8): 194 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset($f31(A),A).
% 3.06/3.21 ** KEPT (pick-wt=8): 195 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset($f31(A),A).
% 3.06/3.21 ** KEPT (pick-wt=14): 196 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f32(A),powerset(the_carrier(A))).
% 3.06/3.21 ** KEPT (pick-wt=11): 197 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f32(A)).
% 3.06/3.21 ** KEPT (pick-wt=12): 198 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|directed_subset($f32(A),A).
% 3.06/3.21 ** KEPT (pick-wt=12): 199 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|lower_relstr_subset($f32(A),A).
% 3.06/3.21 ** KEPT (pick-wt=8): 200 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 3.06/3.21 ** KEPT (pick-wt=8): 201 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 3.06/3.21 ** KEPT (pick-wt=18): 202 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,filter_of_net_str(A,B))|is_eventually_in(A,B,C).
% 3.06/3.21 ** KEPT (pick-wt=19): 203 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,filter_of_net_str(A,B))|element(C,powerset(the_carrier(A))).
% 3.06/3.21 ** KEPT (pick-wt=23): 204 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|in(C,filter_of_net_str(A,B))| -is_eventually_in(A,B,C)| -element(C,powerset(the_carrier(A))).
% 3.06/3.21 ** KEPT (pick-wt=2): 205 [] -empty_carrier($c19).
% 3.06/3.21 ** KEPT (pick-wt=2): 206 [] -empty_carrier($c18).
% 3.06/3.21 ** KEPT (pick-wt=11): 207 [] -in($c17,lim_points_of_net($c19,$c18))| -is_a_convergence_point_of_set($c19,filter_of_net_str($c19,$c18),$c17).
% 3.06/3.21 ** KEPT (pick-wt=6): 208 [] -in(A,B)|element(A,B).
% 3.06/3.21 ** KEPT (pick-wt=8): 209 [] -element(A,B)|empty(B)|in(A,B).
% 3.06/3.21 ** KEPT (pick-wt=13): 210 [] -in($f33(A,B),A)| -in($f33(A,B),B)|A=B.
% 3.06/3.21 ** KEPT (pick-wt=7): 211 [] -element(A,powerset(B))|subset(A,B).
% 3.06/3.21 ** KEPT (pick-wt=7): 212 [] element(A,powerset(B))| -subset(A,B).
% 3.06/3.21 ** KEPT (pick-wt=12): 213 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|subset(interior(A,B),B).
% 3.06/3.21 ** KEPT (pick-wt=10): 214 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 3.06/3.21 ** KEPT (pick-wt=25): 215 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -element(C,the_carrier(A))| -open_subset(B,A)| -in(C,B)|point_neighbourhood(B,A,C).
% 3.06/3.21 ** KEPT (pick-wt=9): 216 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 3.06/3.21 ** KEPT (pick-wt=5): 217 [] -empty(A)|A=empty_set.
% 3.06/3.21 ** KEPT (pick-wt=5): 218 [] -in(A,B)| -empty(B).
% 3.06/3.21 ** KEPT (pick-wt=7): 219 [] -empty(A)|A=B| -empty(B).
% 3.06/3.21 ** KEPT (pick-wt=20): 220 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -subset(C,D)| -is_eventually_in(A,B,C)|is_eventually_in(A,B,D).
% 3.06/3.21 ** KEPT (pick-wt=20): 221 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -subset(C,D)| -is_often_in(A,B,C)|is_often_in(A,B,D).
% 3.06/3.21 42 back subsumes 9.
% 3.06/3.21
% 3.06/3.21 ------------> process sos:
% 3.06/3.21 ** KEPT (pick-wt=3): 250 [] A=A.
% 3.06/3.21 ** KEPT (pick-wt=3): 251 [] strict_rel_str(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 252 [] rel_str(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=2): 253 [] rel_str($c1).
% 3.06/3.21 ** KEPT (pick-wt=2): 254 [] top_str($c2).
% 3.06/3.21 ** KEPT (pick-wt=2): 255 [] one_sorted_str($c3).
% 3.06/3.21 ** KEPT (pick-wt=6): 256 [] relation_of2($f7(A,B),A,B).
% 3.06/3.21 ** KEPT (pick-wt=4): 257 [] element($f8(A),A).
% 3.06/3.21 ** KEPT (pick-wt=6): 258 [] relation_of2_as_subset($f9(A,B),A,B).
% 3.06/3.21 ** KEPT (pick-wt=2): 259 [] empty(empty_set).
% 3.06/3.21 ** KEPT (pick-wt=2): 260 [] relation(empty_set).
% 3.06/3.21 ** KEPT (pick-wt=2): 261 [] relation_empty_yielding(empty_set).
% 3.06/3.21 Following clause subsumed by 251 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 262 [] reflexive_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 263 [] transitive_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 264 [] antisymmetric_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 265 [] lower_bounded_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 266 [] upper_bounded_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 267 [] bounded_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 268 [] up_complete_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 269 [] join_complete_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 270 [] distributive_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 271 [] heyting_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 272 [] complemented_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 273 [] boolean_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 274 [] with_suprema_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 275 [] with_infima_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 276 [] complete_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 251 during input processing: 0 [] empty(A)|strict_rel_str(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 262 during input processing: 0 [] empty(A)|reflexive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 263 during input processing: 0 [] empty(A)|transitive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 264 during input processing: 0 [] empty(A)|antisymmetric_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 265 during input processing: 0 [] empty(A)|lower_bounded_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 266 during input processing: 0 [] empty(A)|upper_bounded_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 267 during input processing: 0 [] empty(A)|bounded_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 268 during input processing: 0 [] empty(A)|up_complete_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 269 during input processing: 0 [] empty(A)|join_complete_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 270 during input processing: 0 [] empty(A)|distributive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 271 during input processing: 0 [] empty(A)|heyting_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 272 during input processing: 0 [] empty(A)|complemented_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 273 during input processing: 0 [] empty(A)|boolean_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 274 during input processing: 0 [] empty(A)|with_suprema_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 275 during input processing: 0 [] empty(A)|with_infima_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 276 during input processing: 0 [] empty(A)|complete_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 259 during input processing: 0 [] empty(empty_set).
% 3.06/3.21 Following clause subsumed by 260 during input processing: 0 [] relation(empty_set).
% 3.06/3.21 Following clause subsumed by 251 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 262 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 263 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 264 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 251 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 262 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 263 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 264 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 265 during input processing: 0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 266 during input processing: 0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 267 during input processing: 0 [] bounded_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 274 during input processing: 0 [] with_suprema_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 275 during input processing: 0 [] with_infima_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 276 during input processing: 0 [] complete_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 251 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 262 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 263 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 264 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 265 during input processing: 0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 266 during input processing: 0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 267 during input processing: 0 [] bounded_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=3): 277 [] directed_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 268 during input processing: 0 [] up_complete_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 269 during input processing: 0 [] join_complete_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 274 during input processing: 0 [] with_suprema_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 275 during input processing: 0 [] with_infima_relstr(boole_POSet(A)).
% 3.06/3.21 Following clause subsumed by 276 during input processing: 0 [] complete_relstr(boole_POSet(A)).
% 3.06/3.21 ** KEPT (pick-wt=2): 278 [] rel_str($c4).
% 3.06/3.21 ** KEPT (pick-wt=2): 279 [] reflexive_relstr($c4).
% 3.06/3.21 ** KEPT (pick-wt=2): 280 [] transitive_relstr($c4).
% 3.06/3.21 ** KEPT (pick-wt=2): 281 [] antisymmetric_relstr($c4).
% 3.06/3.21 ** KEPT (pick-wt=2): 282 [] connected_relstr($c4).
% 3.06/3.21 ** KEPT (pick-wt=2): 283 [] rel_str($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 284 [] strict_rel_str($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 285 [] reflexive_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 286 [] transitive_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 287 [] antisymmetric_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 288 [] with_suprema_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 289 [] with_infima_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 290 [] complete_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 291 [] lower_bounded_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 292 [] upper_bounded_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 293 [] bounded_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 294 [] up_complete_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 295 [] join_complete_relstr($c5).
% 3.06/3.21 ** KEPT (pick-wt=2): 296 [] finite($c6).
% 3.06/3.21 ** KEPT (pick-wt=2): 297 [] rel_str($c7).
% 3.06/3.21 ** KEPT (pick-wt=2): 298 [] strict_rel_str($c7).
% 3.06/3.21 ** KEPT (pick-wt=2): 299 [] reflexive_relstr($c7).
% 3.06/3.21 ** KEPT (pick-wt=2): 300 [] transitive_relstr($c7).
% 3.06/3.21 ** KEPT (pick-wt=2): 301 [] antisymmetric_relstr($c7).
% 3.06/3.21 ** KEPT (pick-wt=2): 302 [] complete_relstr($c7).
% 3.06/3.21 ** KEPT (pick-wt=2): 303 [] empty($c8).
% 3.06/3.21 ** KEPT (pick-wt=2): 304 [] relation($c8).
% 3.06/3.21 ** KEPT (pick-wt=7): 305 [] empty(A)|element($f13(A),powerset(A)).
% 3.06/3.21 ** KEPT (pick-wt=2): 306 [] rel_str($c9).
% 3.06/3.21 ** KEPT (pick-wt=2): 307 [] strict_rel_str($c9).
% 3.06/3.21 ** KEPT (pick-wt=2): 308 [] reflexive_relstr($c9).
% 3.06/3.21 ** KEPT (pick-wt=2): 309 [] transitive_relstr($c9).
% 3.06/3.21 ** KEPT (pick-wt=2): 310 [] antisymmetric_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 311 [] lower_bounded_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 312 [] upper_bounded_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 313 [] bounded_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 314 [] distributive_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 315 [] heyting_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 316 [] complemented_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 317 [] boolean_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 318 [] with_suprema_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 319 [] with_infima_relstr($c9).
% 3.66/3.84 ** KEPT (pick-wt=2): 320 [] rel_str($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 321 [] strict_rel_str($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 322 [] reflexive_relstr($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 323 [] transitive_relstr($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 324 [] antisymmetric_relstr($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 325 [] with_suprema_relstr($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 326 [] with_infima_relstr($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 327 [] complete_relstr($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 328 [] trivial_carrier($c10).
% 3.66/3.84 ** KEPT (pick-wt=2): 329 [] rel_str($c11).
% 3.66/3.84 ** KEPT (pick-wt=2): 330 [] strict_rel_str($c11).
% 3.66/3.84 ** KEPT (pick-wt=2): 331 [] reflexive_relstr($c11).
% 3.66/3.84 ** KEPT (pick-wt=2): 332 [] transitive_relstr($c11).
% 3.66/3.84 ** KEPT (pick-wt=2): 333 [] antisymmetric_relstr($c11).
% 3.66/3.84 ** KEPT (pick-wt=2): 334 [] with_suprema_relstr($c11).
% 3.66/3.84 ** KEPT (pick-wt=2): 335 [] with_infima_relstr($c11).
% 3.66/3.84 ** KEPT (pick-wt=2): 336 [] complete_relstr($c11).
% 3.66/3.84 ** KEPT (pick-wt=2): 337 [] relation($c12).
% 3.66/3.84 ** KEPT (pick-wt=5): 338 [] element($f16(A),powerset(A)).
% 3.66/3.84 ** KEPT (pick-wt=3): 339 [] empty($f16(A)).
% 3.66/3.84 ** KEPT (pick-wt=6): 340 [] element($f19(A),powerset(powerset(A))).
% 3.66/3.84 ** KEPT (pick-wt=3): 341 [] finite($f19(A)).
% 3.66/3.84 ** KEPT (pick-wt=2): 342 [] rel_str($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 343 [] reflexive_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 344 [] transitive_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 345 [] antisymmetric_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 346 [] with_suprema_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 347 [] with_infima_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 348 [] complete_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 349 [] lower_bounded_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 350 [] upper_bounded_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=2): 351 [] bounded_relstr($c13).
% 3.66/3.84 ** KEPT (pick-wt=7): 352 [] empty(A)|element($f20(A),powerset(A)).
% 3.66/3.84 ** KEPT (pick-wt=5): 353 [] empty(A)|finite($f20(A)).
% 3.66/3.84 ** KEPT (pick-wt=2): 354 [] relation($c14).
% 3.66/3.84 ** KEPT (pick-wt=2): 355 [] relation_empty_yielding($c14).
% 3.66/3.84 ** KEPT (pick-wt=2): 356 [] one_sorted_str($c15).
% 3.66/3.84 ** KEPT (pick-wt=7): 357 [] empty(A)|element($f23(A),powerset(A)).
% 3.66/3.84 ** KEPT (pick-wt=5): 358 [] empty(A)|finite($f23(A)).
% 3.66/3.84 ** KEPT (pick-wt=2): 359 [] rel_str($c16).
% 3.66/3.84 ** KEPT (pick-wt=2): 360 [] strict_rel_str($c16).
% 3.66/3.84 ** KEPT (pick-wt=2): 361 [] transitive_relstr($c16).
% 3.66/3.84 ** KEPT (pick-wt=2): 362 [] directed_relstr($c16).
% 3.66/3.84 ** KEPT (pick-wt=3): 363 [] subset(A,A).
% 3.66/3.84 ** KEPT (pick-wt=2): 364 [] topological_space($c19).
% 3.66/3.84 ** KEPT (pick-wt=2): 365 [] top_str($c19).
% 3.66/3.84 ** KEPT (pick-wt=2): 366 [] transitive_relstr($c18).
% 3.66/3.84 ** KEPT (pick-wt=2): 367 [] directed_relstr($c18).
% 3.66/3.84 ** KEPT (pick-wt=3): 368 [] net_str($c18,$c19).
% 3.66/3.84 ** KEPT (pick-wt=4): 369 [] element($c17,the_carrier($c19)).
% 3.66/3.84 ** KEPT (pick-wt=11): 370 [] in($c17,lim_points_of_net($c19,$c18))|is_a_convergence_point_of_set($c19,filter_of_net_str($c19,$c18),$c17).
% 3.66/3.84 ** KEPT (pick-wt=13): 371 [] in($f33(A,B),A)|in($f33(A,B),B)|A=B.
% 3.66/3.84 Following clause subsumed by 250 during input processing: 0 [copy,250,flip.1] A=A.
% 3.66/3.84 250 back subsumes 247.
% 3.66/3.84 250 back subsumes 246.
% 3.66/3.84
% 3.66/3.84 ======= end of input processing =======
% 3.66/3.84
% 3.66/3.84 =========== start of search ===========
% 3.66/3.84
% 3.66/3.84
% 3.66/3.84 Resetting weight limit to 2.
% 3.66/3.84
% 3.66/3.84
% 3.66/3.84 Resetting weight limit to 2.
% 3.66/3.84
% 3.66/3.84 sos_size=313
% 3.66/3.84
% 3.66/3.84 Search stopped because sos empty.
% 3.66/3.84
% 3.66/3.84
% 3.66/3.84 Search stopped because sos empty.
% 3.66/3.84
% 3.66/3.84 ============ end of search ============
% 3.66/3.84
% 3.66/3.84 -------------- statistics -------------
% 3.66/3.84 clauses given 363
% 3.66/3.84 clauses generated 21178
% 3.66/3.84 clauses kept 610
% 3.66/3.84 clauses forward subsumed 217
% 3.66/3.84 clauses back subsumed 3
% 3.66/3.84 Kbytes malloced 5859
% 3.66/3.84
% 3.66/3.84 ----------- times (seconds) -----------
% 3.66/3.84 user CPU time 0.66 (0 hr, 0 min, 0 sec)
% 3.66/3.84 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.66/3.84 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.66/3.84
% 3.66/3.84 Process 27587 finished Wed Jul 27 07:59:12 2022
% 3.66/3.84 Otter interrupted
% 3.66/3.84 PROOF NOT FOUND
%------------------------------------------------------------------------------