%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU393+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n027.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 3.95s 4.09s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU393+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12  % Command  : otter-tptp-script %s
% 0.12/0.32  % Computer : n027.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Wed Jul 27 08:09:21 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 3.32/3.51  ----- Otter 3.3f, August 2004 -----
% 3.32/3.51  The process was started by sandbox on n027.cluster.edu,
% 3.32/3.51  Wed Jul 27 08:09:21 2022
% 3.32/3.51  The command was "./otter".  The process ID is 10935.
% 3.32/3.51  
% 3.32/3.51  set(prolog_style_variables).
% 3.32/3.51  set(auto).
% 3.32/3.51     dependent: set(auto1).
% 3.32/3.51     dependent: set(process_input).
% 3.32/3.51     dependent: clear(print_kept).
% 3.32/3.51     dependent: clear(print_new_demod).
% 3.32/3.51     dependent: clear(print_back_demod).
% 3.32/3.51     dependent: clear(print_back_sub).
% 3.32/3.51     dependent: set(control_memory).
% 3.32/3.51     dependent: assign(max_mem, 12000).
% 3.32/3.51     dependent: assign(pick_given_ratio, 4).
% 3.32/3.51     dependent: assign(stats_level, 1).
% 3.32/3.51     dependent: assign(max_seconds, 10800).
% 3.32/3.51  clear(print_given).
% 3.32/3.51  
% 3.32/3.51  formula_list(usable).
% 3.32/3.51  all A (A=A).
% 3.32/3.51  all A (rel_str(A)-> (strict_rel_str(A)->A=rel_str_of(the_carrier(A),the_InternalRel(A)))).
% 3.32/3.51  all A B (one_sorted_str(A)&net_str(B,A)-> (strict_net_str(B,A)->B=net_str_of(A,the_carrier(B),the_InternalRel(B),the_mapping(A,B)))).
% 3.32/3.51  all A B (in(A,B)-> -in(B,A)).
% 3.32/3.51  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))).
% 3.32/3.51  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))).
% 3.32/3.51  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))).
% 3.32/3.51  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))).
% 3.32/3.51  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))).
% 3.32/3.51  all A (empty(A)->finite(A)).
% 3.32/3.51  all A (rel_str(A)-> (with_suprema_relstr(A)-> -empty_carrier(A))).
% 3.32/3.51  all A (empty(A)->relation(A)).
% 3.32/3.51  all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 3.32/3.51  all A (rel_str(A)-> (-empty_carrier(A)&complete_relstr(A)-> -empty_carrier(A)&with_suprema_relstr(A)&with_infima_relstr(A))).
% 3.32/3.51  all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 3.32/3.51  all A (rel_str(A)-> (with_infima_relstr(A)-> -empty_carrier(A))).
% 3.32/3.51  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))).
% 3.32/3.51  all A (rel_str(A)-> (-empty_carrier(A)&complete_relstr(A)-> -empty_carrier(A)&bounded_relstr(A))).
% 3.32/3.51  all A (rel_str(A)-> (bounded_relstr(A)->lower_bounded_relstr(A)&upper_bounded_relstr(A))).
% 3.32/3.51  all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&trivial_carrier(A)-> -empty_carrier(A)&reflexive_relstr(A)&connected_relstr(A))).
% 3.32/3.51  all A (rel_str(A)-> (lower_bounded_relstr(A)&upper_bounded_relstr(A)->bounded_relstr(A))).
% 3.32/3.51  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))).
% 3.32/3.51  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 3.32/3.51  all A B (A=B<->subset(A,B)&subset(B,A)).
% 3.32/3.51  all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C (is_eventually_in(A,B,C)<-> (exists D (element(D,the_carrier(B))& (all E (element(E,the_carrier(B))-> (related(B,D,E)->in(apply_netmap(A,B,E),C))))))))))).
% 3.32/3.51  all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 3.32/3.51  all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 3.32/3.51  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)))).
% 3.32/3.51  all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 3.32/3.51  all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty(B)&element(B,powerset(the_carrier(A)))-> (all C (-empty(C)&filtered_subset(C,boole_POSet(B))&upper_relstr_subset(C,boole_POSet(B))&element(C,powerset(the_carrier(boole_POSet(B))))-> (all D (-empty_carrier(D)&strict_net_str(D,A)&net_str(D,A)-> (D=net_of_bool_filter(A,B,C)<->the_carrier(D)=a_3_1_yellow19(A,B,C)& (all E (element(E,the_carrier(D))-> (all F (element(F,the_carrier(D))-> (related(D,E,F)<->subset(pair_second(F),pair_second(E)))))))& (all E (element(E,the_carrier(D))->apply_netmap(A,D,E)=pair_first(E))))))))))).
% 3.32/3.51  all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 3.32/3.51  all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C (element(C,the_carrier(B))->apply_netmap(A,B,C)=apply_on_structs(B,A,the_mapping(A,B),C)))))).
% 3.32/3.51  all A B (relation_of2(B,A,A)->strict_rel_str(rel_str_of(A,B))&rel_str(rel_str_of(A,B))).
% 3.32/3.51  all A B C D (one_sorted_str(A)&relation_of2(C,B,B)&function(D)&quasi_total(D,B,the_carrier(A))&relation_of2(D,B,the_carrier(A))->strict_net_str(net_str_of(A,B,C,D),A)&net_str(net_str_of(A,B,C,D),A)).
% 3.32/3.51  $T.
% 3.32/3.51  $T.
% 3.32/3.51  $T.
% 3.32/3.51  all A B C D (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&one_sorted_str(B)&function(C)&quasi_total(C,the_carrier(A),the_carrier(B))&relation_of2(C,the_carrier(A),the_carrier(B))&element(D,the_carrier(A))->element(apply_on_structs(A,B,C,D),the_carrier(B))).
% 3.32/3.51  all A relation(inclusion_relation(A)).
% 3.32/3.51  $T.
% 3.32/3.51  all A (reflexive(inclusion_order(A))&antisymmetric(inclusion_order(A))&transitive(inclusion_order(A))&v1_partfun1(inclusion_order(A),A,A)&relation_of2_as_subset(inclusion_order(A),A,A)).
% 3.32/3.51  $T.
% 3.32/3.51  $T.
% 3.32/3.51  all A (one_sorted_str(A)->element(cast_as_carrier_subset(A),powerset(the_carrier(A)))).
% 3.32/3.51  $T.
% 3.32/3.51  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)))))).
% 3.32/3.51  all A (strict_rel_str(incl_POSet(A))&rel_str(incl_POSet(A))).
% 3.32/3.51  $T.
% 3.32/3.51  all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&net_str(B,A)&element(C,the_carrier(B))->element(apply_netmap(A,B,C),the_carrier(A))).
% 3.32/3.51  all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty(B)&element(B,powerset(the_carrier(A)))& -empty(C)&filtered_subset(C,boole_POSet(B))&upper_relstr_subset(C,boole_POSet(B))&element(C,powerset(the_carrier(boole_POSet(B))))-> -empty_carrier(net_of_bool_filter(A,B,C))&strict_net_str(net_of_bool_filter(A,B,C),A)&net_str(net_of_bool_filter(A,B,C),A)).
% 3.32/3.51  all A (strict_rel_str(boole_POSet(A))&rel_str(boole_POSet(A))).
% 3.32/3.51  $T.
% 3.32/3.51  $T.
% 3.32/3.51  all A (rel_str(A)->one_sorted_str(A)).
% 3.32/3.51  $T.
% 3.32/3.51  all A (one_sorted_str(A)-> (all B (net_str(B,A)->rel_str(B)))).
% 3.32/3.51  $T.
% 3.32/3.51  all A B (-empty_carrier(A)&one_sorted_str(A)& -empty(B)&element(B,powerset(the_carrier(A)))-> (all C (element_as_carrier_subset(C,A,B)->element(C,the_carrier(A))))).
% 3.32/3.51  $T.
% 3.32/3.51  all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 3.32/3.51  all A (rel_str(A)->relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))).
% 3.32/3.51  $T.
% 3.32/3.51  all A B (one_sorted_str(A)&net_str(B,A)->function(the_mapping(A,B))&quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A))&relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A))).
% 3.32/3.51  exists A rel_str(A).
% 3.32/3.51  exists A one_sorted_str(A).
% 3.32/3.51  all A (one_sorted_str(A)-> (exists B net_str(B,A))).
% 3.32/3.51  all A B exists C relation_of2(C,A,B).
% 3.32/3.51  all A B (-empty_carrier(A)&one_sorted_str(A)& -empty(B)&element(B,powerset(the_carrier(A)))-> (exists C element_as_carrier_subset(C,A,B))).
% 3.32/3.51  all A exists B element(B,A).
% 3.32/3.51  all A B exists C relation_of2_as_subset(C,A,B).
% 3.32/3.51  all A B (finite(A)->finite(set_difference(A,B))).
% 3.32/3.51  empty(empty_set).
% 3.32/3.51  relation(empty_set).
% 3.32/3.51  relation_empty_yielding(empty_set).
% 3.32/3.51  all A B (finite(A)&finite(B)->finite(cartesian_product2(A,B))).
% 3.32/3.51  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)).
% 3.32/3.51  all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&net_str(B,A)-> -empty(the_mapping(A,B))&relation(the_mapping(A,B))&function(the_mapping(A,B))&quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A))).
% 3.32/3.51  all A (-empty(singleton(A))&finite(singleton(A))).
% 3.32/3.51  all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 3.32/3.51  all A (-empty(powerset(A))).
% 3.32/3.51  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))).
% 3.32/3.51  all A B (relation_of2(B,singleton(A),singleton(A))-> -empty_carrier(rel_str_of(singleton(A),B))&strict_rel_str(rel_str_of(singleton(A),B))&trivial_carrier(rel_str_of(singleton(A),B))).
% 3.32/3.51  all A B (-empty(unordered_pair(A,B))&finite(unordered_pair(A,B))).
% 3.32/3.51  all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(cast_as_carrier_subset(A))).
% 3.32/3.51  all A (-empty(singleton(A))).
% 3.32/3.51  all A (with_suprema_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&directed_subset(cast_as_carrier_subset(A),A)).
% 3.32/3.51  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))).
% 3.32/3.51  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)))).
% 3.32/3.51  all A (-empty_carrier(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))).
% 3.32/3.51  all A B (relation(A)&relation(B)->relation(set_difference(A,B))).
% 3.32/3.51  all A B (-empty(unordered_pair(A,B))).
% 3.32/3.51  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)).
% 3.32/3.51  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)))))).
% 3.32/3.51  empty(empty_set).
% 3.32/3.51  relation(empty_set).
% 3.32/3.51  all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 3.32/3.51  all A (with_infima_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&filtered_subset(cast_as_carrier_subset(A),A)).
% 3.32/3.51  all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty(B)&element(B,powerset(the_carrier(A)))& -empty(C)&filtered_subset(C,boole_POSet(B))&upper_relstr_subset(C,boole_POSet(B))&element(C,powerset(the_carrier(boole_POSet(B))))-> -empty_carrier(net_of_bool_filter(A,B,C))&reflexive_relstr(net_of_bool_filter(A,B,C))&transitive_relstr(net_of_bool_filter(A,B,C))&strict_net_str(net_of_bool_filter(A,B,C),A)).
% 3.32/3.51  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)).
% 3.32/3.51  all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty(B)&element(B,powerset(the_carrier(A)))& -empty(C)&filtered_subset(C,boole_POSet(B))&upper_relstr_subset(C,boole_POSet(B))&proper_element(C,powerset(the_carrier(boole_POSet(B))))&element(C,powerset(the_carrier(boole_POSet(B))))-> -empty_carrier(net_of_bool_filter(A,B,C))&reflexive_relstr(net_of_bool_filter(A,B,C))&transitive_relstr(net_of_bool_filter(A,B,C))&strict_net_str(net_of_bool_filter(A,B,C),A)&directed_relstr(net_of_bool_filter(A,B,C))).
% 3.32/3.51  all A (strict_rel_str(incl_POSet(A))&reflexive_relstr(incl_POSet(A))&transitive_relstr(incl_POSet(A))&antisymmetric_relstr(incl_POSet(A))).
% 3.32/3.51  all A B C D (one_sorted_str(A)& -empty(B)&relation_of2(C,B,B)&function(D)&quasi_total(D,B,the_carrier(A))&relation_of2(D,B,the_carrier(A))-> -empty_carrier(net_str_of(A,B,C,D))&strict_net_str(net_str_of(A,B,C,D),A)).
% 3.32/3.51  all A (-empty(A)-> -empty_carrier(incl_POSet(A))&strict_rel_str(incl_POSet(A))&reflexive_relstr(incl_POSet(A))&transitive_relstr(incl_POSet(A))&antisymmetric_relstr(incl_POSet(A))).
% 3.32/3.51  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))).
% 3.32/3.51  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))).
% 3.32/3.51  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))).
% 3.32/3.51  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))))).
% 3.32/3.51  all A B C (-empty_carrier(B)&one_sorted_str(B)& -empty(C)&filtered_subset(C,boole_POSet(cast_as_carrier_subset(B)))&upper_relstr_subset(C,boole_POSet(cast_as_carrier_subset(B)))&element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(B)))))-> (in(A,a_2_2_yellow19(B,C))<-> (exists D E (element(D,the_carrier(B))&element_as_carrier_subset(E,boole_POSet(cast_as_carrier_subset(B)),C)&A=ordered_pair(D,E)&in(D,E))))).
% 3.32/3.51  all A B C D (-empty_carrier(B)&one_sorted_str(B)& -empty(C)&element(C,powerset(the_carrier(B)))& -empty(D)&filtered_subset(D,boole_POSet(C))&upper_relstr_subset(D,boole_POSet(C))&element(D,powerset(the_carrier(boole_POSet(C))))-> (in(A,a_3_1_yellow19(B,C,D))<-> (exists E F (element(E,the_carrier(B))&element_as_carrier_subset(F,boole_POSet(C),D)&A=ordered_pair(E,F)&in(E,F))))).
% 3.32/3.51  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))).
% 3.32/3.51  all A B C D (one_sorted_str(A)&relation_of2(C,B,B)&function(D)&quasi_total(D,B,the_carrier(A))&relation_of2(D,B,the_carrier(A))-> (all E F G H (net_str_of(A,B,C,D)=net_str_of(E,F,G,H)->A=E&B=F&C=G&D=H))).
% 3.32/3.51  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)))).
% 3.32/3.51  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)))).
% 3.32/3.51  exists A (rel_str(A)& -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&connected_relstr(A)).
% 3.32/3.51  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)).
% 3.32/3.51  exists A (-empty(A)&finite(A)).
% 3.32/3.51  exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&complete_relstr(A)).
% 3.32/3.51  exists A (empty(A)&relation(A)).
% 3.32/3.51  all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 3.32/3.51  all A (rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&directed_subset(B,A)&filtered_subset(B,A)))).
% 3.32/3.52  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)).
% 3.32/3.52  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)).
% 3.32/3.52  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)).
% 3.32/3.52  exists A (-empty(A)&relation(A)).
% 3.32/3.52  all A exists B (element(B,powerset(A))&empty(B)).
% 3.32/3.52  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)))).
% 3.32/3.52  all A exists B (element(B,powerset(powerset(A)))& -empty(B)&finite(B)).
% 3.32/3.52  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)).
% 3.32/3.52  all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 3.32/3.52  exists A (relation(A)&relation_empty_yielding(A)).
% 3.32/3.52  exists A (one_sorted_str(A)& -empty_carrier(A)).
% 3.32/3.52  all A (one_sorted_str(A)-> (exists B (element(B,powerset(powerset(the_carrier(A))))& -empty(B)&finite(B)))).
% 3.32/3.52  all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 3.32/3.52  all A (one_sorted_str(A)-> (exists B (net_str(B,A)&strict_net_str(B,A)))).
% 3.32/3.52  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)))).
% 3.32/3.52  exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&transitive_relstr(A)&directed_relstr(A)).
% 3.32/3.52  all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 3.32/3.52  all A (one_sorted_str(A)-> (exists B (net_str(B,A)& -empty_carrier(B)&reflexive_relstr(B)&transitive_relstr(B)&antisymmetric_relstr(B)&strict_net_str(B,A)&directed_relstr(B)))).
% 3.32/3.52  all A (rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&lower_relstr_subset(B,A)&upper_relstr_subset(B,A)))).
% 3.32/3.52  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)))).
% 3.32/3.52  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)))).
% 3.32/3.52  all A B C D (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&one_sorted_str(B)&function(C)&quasi_total(C,the_carrier(A),the_carrier(B))&relation_of2(C,the_carrier(A),the_carrier(B))&element(D,the_carrier(A))->apply_on_structs(A,B,C,D)=apply(C,D)).
% 3.32/3.52  all A (inclusion_order(A)=inclusion_relation(A)).
% 3.32/3.52  all A B (-empty_carrier(A)&one_sorted_str(A)& -empty(B)&element(B,powerset(the_carrier(A)))-> (all C (element_as_carrier_subset(C,A,B)<->element(C,B)))).
% 3.32/3.52  all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 3.32/3.52  all A B C (-empty_carrier(A)&reflexive_relstr(A)&rel_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))-> (related_reflexive(A,B,C)<->related(A,B,C))).
% 3.32/3.52  all A B subset(A,A).
% 3.32/3.52  all A B C (-empty_carrier(A)&reflexive_relstr(A)&rel_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->related_reflexive(A,B,B)).
% 3.32/3.52  all A B (element(B,powerset(the_carrier(boole_POSet(A))))-> (upper_relstr_subset(B,boole_POSet(A))<-> (all C D (subset(C,D)&subset(D,A)&in(C,B)->in(D,B))))).
% 3.32/3.52  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)))))))).
% 3.32/3.52  all A (one_sorted_str(A)->cast_as_carrier_subset(A)=the_carrier(A)).
% 3.32/3.52  -(all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty(B)&filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))&upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))&element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))->set_difference(B,singleton(empty_set))=filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)))))).
% 3.32/3.52  all A B (in(A,B)->element(A,B)).
% 3.32/3.52  all A (the_carrier(incl_POSet(A))=A&the_InternalRel(incl_POSet(A))=inclusion_order(A)).
% 3.32/3.52  all A B (element(A,B)->empty(B)|in(A,B)).
% 3.32/3.52  all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 3.32/3.52  all A (set_difference(A,empty_set)=A).
% 3.32/3.52  all A B (element(A,powerset(B))<->subset(A,B)).
% 3.32/3.52  all A (set_difference(empty_set,A)=empty_set).
% 3.32/3.52  all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 3.32/3.52  all A (boole_POSet(A)=incl_POSet(powerset(A))).
% 3.32/3.52  all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 3.32/3.52  all A (empty(A)->A=empty_set).
% 3.32/3.52  all A B (-(in(A,B)&empty(B))).
% 3.32/3.52  all A B (pair_first(ordered_pair(A,B))=A&pair_second(ordered_pair(A,B))=B).
% 3.32/3.52  all A B (-(empty(A)&A!=B&empty(B))).
% 3.32/3.52  end_of_list.
% 3.32/3.52  
% 3.32/3.52  -------> usable clausifies to:
% 3.32/3.52  
% 3.32/3.52  list(usable).
% 3.32/3.52  0 [] A=A.
% 3.32/3.52  0 [] -rel_str(A)| -strict_rel_str(A)|A=rel_str_of(the_carrier(A),the_InternalRel(A)).
% 3.32/3.52  0 [] -one_sorted_str(A)| -net_str(B,A)| -strict_net_str(B,A)|B=net_str_of(A,the_carrier(B),the_InternalRel(B),the_mapping(A,B)).
% 3.32/3.52  0 [] -in(A,B)| -in(B,A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|up_complete_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|join_complete_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -join_complete_relstr(A)|lower_bounded_relstr(A).
% 3.32/3.52  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).
% 3.32/3.52  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).
% 3.32/3.52  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).
% 3.32/3.52  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).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -join_complete_relstr(A)|with_infima_relstr(A).
% 3.32/3.52  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).
% 3.32/3.52  0 [] -empty(A)|finite(A).
% 3.32/3.52  0 [] -rel_str(A)| -with_suprema_relstr(A)| -empty_carrier(A).
% 3.32/3.52  0 [] -empty(A)|relation(A).
% 3.32/3.52  0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_suprema_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_infima_relstr(A).
% 3.32/3.52  0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 3.32/3.52  0 [] -rel_str(A)| -with_infima_relstr(A)| -empty_carrier(A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|transitive_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|antisymmetric_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|complete_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|bounded_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)| -bounded_relstr(A)|lower_bounded_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)| -bounded_relstr(A)|upper_bounded_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|connected_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)| -lower_bounded_relstr(A)| -upper_bounded_relstr(A)|bounded_relstr(A).
% 3.32/3.52  0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)| -empty_carrier(A).
% 3.32/3.52  0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 3.32/3.52  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 3.32/3.52  0 [] A!=B|subset(A,B).
% 3.32/3.52  0 [] A!=B|subset(B,A).
% 3.32/3.52  0 [] A=B| -subset(A,B)| -subset(B,A).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -is_eventually_in(A,B,C)|element($f1(A,B,C),the_carrier(B)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -is_eventually_in(A,B,C)| -element(E,the_carrier(B))| -related(B,$f1(A,B,C),E)|in(apply_netmap(A,B,E),C).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|is_eventually_in(A,B,C)| -element(D,the_carrier(B))|element($f2(A,B,C,D),the_carrier(B)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|is_eventually_in(A,B,C)| -element(D,the_carrier(B))|related(B,D,$f2(A,B,C,D)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|is_eventually_in(A,B,C)| -element(D,the_carrier(B))| -in(apply_netmap(A,B,$f2(A,B,C,D)),C).
% 3.32/3.52  0 [] B!=singleton(A)| -in(C,B)|C=A.
% 3.32/3.52  0 [] B!=singleton(A)|in(C,B)|C!=A.
% 3.32/3.52  0 [] B=singleton(A)|in($f3(A,B),B)|$f3(A,B)=A.
% 3.32/3.52  0 [] B=singleton(A)| -in($f3(A,B),B)|$f3(A,B)!=A.
% 3.32/3.52  0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 3.32/3.52  0 [] subset(A,B)|in($f4(A,B),A).
% 3.32/3.52  0 [] subset(A,B)| -in($f4(A,B),B).
% 3.32/3.52  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).
% 3.32/3.52  0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 3.32/3.52  0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 3.32/3.52  0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 3.32/3.52  0 [] C=set_difference(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A).
% 3.32/3.52  0 [] C=set_difference(A,B)|in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 3.32/3.52  0 [] C=set_difference(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D!=net_of_bool_filter(A,B,C)|the_carrier(D)=a_3_1_yellow19(A,B,C).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D!=net_of_bool_filter(A,B,C)| -element(E,the_carrier(D))| -element(F,the_carrier(D))| -related(D,E,F)|subset(pair_second(F),pair_second(E)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D!=net_of_bool_filter(A,B,C)| -element(E,the_carrier(D))| -element(F,the_carrier(D))|related(D,E,F)| -subset(pair_second(F),pair_second(E)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D!=net_of_bool_filter(A,B,C)| -element(X1,the_carrier(D))|apply_netmap(A,D,X1)=pair_first(X1).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|element($f7(A,B,C,D),the_carrier(D))|element($f8(A,B,C,D),the_carrier(D)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|element($f7(A,B,C,D),the_carrier(D))|apply_netmap(A,D,$f8(A,B,C,D))!=pair_first($f8(A,B,C,D)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|element($f6(A,B,C,D),the_carrier(D))|element($f8(A,B,C,D),the_carrier(D)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|element($f6(A,B,C,D),the_carrier(D))|apply_netmap(A,D,$f8(A,B,C,D))!=pair_first($f8(A,B,C,D)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|related(D,$f7(A,B,C,D),$f6(A,B,C,D))|subset(pair_second($f6(A,B,C,D)),pair_second($f7(A,B,C,D)))|element($f8(A,B,C,D),the_carrier(D)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|related(D,$f7(A,B,C,D),$f6(A,B,C,D))|subset(pair_second($f6(A,B,C,D)),pair_second($f7(A,B,C,D)))|apply_netmap(A,D,$f8(A,B,C,D))!=pair_first($f8(A,B,C,D)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)| -related(D,$f7(A,B,C,D),$f6(A,B,C,D))| -subset(pair_second($f6(A,B,C,D)),pair_second($f7(A,B,C,D)))|element($f8(A,B,C,D),the_carrier(D)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)| -related(D,$f7(A,B,C,D),$f6(A,B,C,D))| -subset(pair_second($f6(A,B,C,D)),pair_second($f7(A,B,C,D)))|apply_netmap(A,D,$f8(A,B,C,D))!=pair_first($f8(A,B,C,D)).
% 3.32/3.52  0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -element(C,the_carrier(B))|apply_netmap(A,B,C)=apply_on_structs(B,A,the_mapping(A,B),C).
% 3.32/3.52  0 [] -relation_of2(B,A,A)|strict_rel_str(rel_str_of(A,B)).
% 3.32/3.52  0 [] -relation_of2(B,A,A)|rel_str(rel_str_of(A,B)).
% 3.32/3.52  0 [] -one_sorted_str(A)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))|strict_net_str(net_str_of(A,B,C,D),A).
% 3.32/3.52  0 [] -one_sorted_str(A)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))|net_str(net_str_of(A,B,C,D),A).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -one_sorted_str(B)| -function(C)| -quasi_total(C,the_carrier(A),the_carrier(B))| -relation_of2(C,the_carrier(A),the_carrier(B))| -element(D,the_carrier(A))|element(apply_on_structs(A,B,C,D),the_carrier(B)).
% 3.32/3.52  0 [] relation(inclusion_relation(A)).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] reflexive(inclusion_order(A)).
% 3.32/3.52  0 [] antisymmetric(inclusion_order(A)).
% 3.32/3.52  0 [] transitive(inclusion_order(A)).
% 3.32/3.52  0 [] v1_partfun1(inclusion_order(A),A,A).
% 3.32/3.52  0 [] relation_of2_as_subset(inclusion_order(A),A,A).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  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))))).
% 3.32/3.52  0 [] strict_rel_str(incl_POSet(A)).
% 3.32/3.52  0 [] rel_str(incl_POSet(A)).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -element(C,the_carrier(B))|element(apply_netmap(A,B,C),the_carrier(A)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))| -empty_carrier(net_of_bool_filter(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|strict_net_str(net_of_bool_filter(A,B,C),A).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|net_str(net_of_bool_filter(A,B,C),A).
% 3.32/3.52  0 [] strict_rel_str(boole_POSet(A)).
% 3.32/3.52  0 [] rel_str(boole_POSet(A)).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] -rel_str(A)|one_sorted_str(A).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] -one_sorted_str(A)| -net_str(B,A)|rel_str(B).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))| -element_as_carrier_subset(C,A,B)|element(C,the_carrier(A)).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 3.32/3.52  0 [] -rel_str(A)|relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)).
% 3.32/3.52  0 [] $T.
% 3.32/3.52  0 [] -one_sorted_str(A)| -net_str(B,A)|function(the_mapping(A,B)).
% 3.32/3.52  0 [] -one_sorted_str(A)| -net_str(B,A)|quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 3.32/3.52  0 [] -one_sorted_str(A)| -net_str(B,A)|relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 3.32/3.52  0 [] rel_str($c1).
% 3.32/3.52  0 [] one_sorted_str($c2).
% 3.32/3.52  0 [] -one_sorted_str(A)|net_str($f9(A),A).
% 3.32/3.52  0 [] relation_of2($f10(A,B),A,B).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|element_as_carrier_subset($f11(A,B),A,B).
% 3.32/3.52  0 [] element($f12(A),A).
% 3.32/3.52  0 [] relation_of2_as_subset($f13(A,B),A,B).
% 3.32/3.52  0 [] -finite(A)|finite(set_difference(A,B)).
% 3.32/3.52  0 [] empty(empty_set).
% 3.32/3.52  0 [] relation(empty_set).
% 3.32/3.52  0 [] relation_empty_yielding(empty_set).
% 3.32/3.52  0 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 3.32/3.52  0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.52  0 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset(cast_as_carrier_subset(A),A).
% 3.32/3.52  0 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset(cast_as_carrier_subset(A),A).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -empty(the_mapping(A,B)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|relation(the_mapping(A,B)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|function(the_mapping(A,B)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 3.32/3.52  0 [] -empty(singleton(A)).
% 3.32/3.52  0 [] finite(singleton(A)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 3.32/3.52  0 [] -empty(powerset(A)).
% 3.32/3.52  0 [] -empty_carrier(boole_POSet(A)).
% 3.32/3.52  0 [] strict_rel_str(boole_POSet(A)).
% 3.32/3.52  0 [] reflexive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] transitive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] up_complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] join_complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] -v1_yellow_3(boole_POSet(A)).
% 3.32/3.52  0 [] distributive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] heyting_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] complemented_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] boolean_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] with_suprema_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] with_infima_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] -relation_of2(B,singleton(A),singleton(A))| -empty_carrier(rel_str_of(singleton(A),B)).
% 3.32/3.52  0 [] -relation_of2(B,singleton(A),singleton(A))|strict_rel_str(rel_str_of(singleton(A),B)).
% 3.32/3.52  0 [] -relation_of2(B,singleton(A),singleton(A))|trivial_carrier(rel_str_of(singleton(A),B)).
% 3.32/3.52  0 [] -empty(unordered_pair(A,B)).
% 3.32/3.52  0 [] finite(unordered_pair(A,B)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.52  0 [] -empty(singleton(A)).
% 3.32/3.52  0 [] -with_suprema_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.52  0 [] -with_suprema_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 3.32/3.52  0 [] empty(A)| -empty_carrier(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)| -trivial_carrier(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|strict_rel_str(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|reflexive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|transitive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|antisymmetric_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|lower_bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|upper_bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|up_complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|join_complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)| -v1_yellow_3(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|distributive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|heyting_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|complemented_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|boolean_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|with_suprema_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|with_infima_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty(A)|complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -empty(filter_of_net_str(A,B)).
% 3.32/3.52  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))).
% 3.32/3.52  0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.52  0 [] -relation(A)| -relation(B)|relation(set_difference(A,B)).
% 3.32/3.52  0 [] -empty(unordered_pair(A,B)).
% 3.32/3.52  0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.52  0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 3.32/3.52  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)).
% 3.32/3.52  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))).
% 3.32/3.52  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))).
% 3.32/3.52  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))))).
% 3.32/3.52  0 [] empty(empty_set).
% 3.32/3.52  0 [] relation(empty_set).
% 3.32/3.52  0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 3.32/3.52  0 [] -with_infima_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.52  0 [] -with_infima_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))| -empty_carrier(net_of_bool_filter(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|reflexive_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|transitive_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|strict_net_str(net_of_bool_filter(A,B,C),A).
% 3.32/3.52  0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.52  0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))| -empty_carrier(net_of_bool_filter(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))|reflexive_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))|transitive_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))|strict_net_str(net_of_bool_filter(A,B,C),A).
% 3.32/3.52  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))|directed_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.52  0 [] strict_rel_str(incl_POSet(A)).
% 3.32/3.52  0 [] reflexive_relstr(incl_POSet(A)).
% 3.32/3.52  0 [] transitive_relstr(incl_POSet(A)).
% 3.32/3.52  0 [] antisymmetric_relstr(incl_POSet(A)).
% 3.32/3.52  0 [] -one_sorted_str(A)|empty(B)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))| -empty_carrier(net_str_of(A,B,C,D)).
% 3.32/3.52  0 [] -one_sorted_str(A)|empty(B)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))|strict_net_str(net_str_of(A,B,C,D),A).
% 3.32/3.52  0 [] empty(A)| -empty_carrier(incl_POSet(A)).
% 3.32/3.52  0 [] empty(A)|strict_rel_str(incl_POSet(A)).
% 3.32/3.52  0 [] empty(A)|reflexive_relstr(incl_POSet(A)).
% 3.32/3.52  0 [] empty(A)|transitive_relstr(incl_POSet(A)).
% 3.32/3.52  0 [] empty(A)|antisymmetric_relstr(incl_POSet(A)).
% 3.32/3.52  0 [] -empty_carrier(boole_POSet(A)).
% 3.32/3.52  0 [] strict_rel_str(boole_POSet(A)).
% 3.32/3.52  0 [] reflexive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] transitive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] -empty_carrier(boole_POSet(A)).
% 3.32/3.52  0 [] strict_rel_str(boole_POSet(A)).
% 3.32/3.52  0 [] reflexive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] transitive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] with_suprema_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] with_infima_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] -empty_carrier(boole_POSet(A)).
% 3.32/3.52  0 [] strict_rel_str(boole_POSet(A)).
% 3.32/3.52  0 [] reflexive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] transitive_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] bounded_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] directed_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] up_complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] join_complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] -v1_yellow_3(boole_POSet(A)).
% 3.32/3.52  0 [] with_suprema_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] with_infima_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] complete_relstr(boole_POSet(A)).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty_carrier(C)| -net_str(C,B)| -in(A,a_2_1_yellow19(B,C))|element($f14(A,B,C),powerset(the_carrier(B))).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty_carrier(C)| -net_str(C,B)| -in(A,a_2_1_yellow19(B,C))|A=$f14(A,B,C).
% 3.32/3.52  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,$f14(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty_carrier(C)| -net_str(C,B)|in(A,a_2_1_yellow19(B,C))| -element(D,powerset(the_carrier(B)))|A!=D| -is_eventually_in(B,C,D).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -filtered_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -upper_relstr_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(B)))))| -in(A,a_2_2_yellow19(B,C))|element($f16(A,B,C),the_carrier(B)).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -filtered_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -upper_relstr_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(B)))))| -in(A,a_2_2_yellow19(B,C))|element_as_carrier_subset($f15(A,B,C),boole_POSet(cast_as_carrier_subset(B)),C).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -filtered_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -upper_relstr_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(B)))))| -in(A,a_2_2_yellow19(B,C))|A=ordered_pair($f16(A,B,C),$f15(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -filtered_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -upper_relstr_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(B)))))| -in(A,a_2_2_yellow19(B,C))|in($f16(A,B,C),$f15(A,B,C)).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -filtered_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -upper_relstr_subset(C,boole_POSet(cast_as_carrier_subset(B)))| -element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(B)))))|in(A,a_2_2_yellow19(B,C))| -element(D,the_carrier(B))| -element_as_carrier_subset(E,boole_POSet(cast_as_carrier_subset(B)),C)|A!=ordered_pair(D,E)| -in(D,E).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -element(C,powerset(the_carrier(B)))|empty(D)| -filtered_subset(D,boole_POSet(C))| -upper_relstr_subset(D,boole_POSet(C))| -element(D,powerset(the_carrier(boole_POSet(C))))| -in(A,a_3_1_yellow19(B,C,D))|element($f18(A,B,C,D),the_carrier(B)).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -element(C,powerset(the_carrier(B)))|empty(D)| -filtered_subset(D,boole_POSet(C))| -upper_relstr_subset(D,boole_POSet(C))| -element(D,powerset(the_carrier(boole_POSet(C))))| -in(A,a_3_1_yellow19(B,C,D))|element_as_carrier_subset($f17(A,B,C,D),boole_POSet(C),D).
% 3.32/3.52  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -element(C,powerset(the_carrier(B)))|empty(D)| -filtered_subset(D,boole_POSet(C))| -upper_relstr_subset(D,boole_POSet(C))| -element(D,powerset(the_carrier(boole_POSet(C))))| -in(A,a_3_1_yellow19(B,C,D))|A=ordered_pair($f18(A,B,C,D),$f17(A,B,C,D)).
% 3.32/3.53  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -element(C,powerset(the_carrier(B)))|empty(D)| -filtered_subset(D,boole_POSet(C))| -upper_relstr_subset(D,boole_POSet(C))| -element(D,powerset(the_carrier(boole_POSet(C))))| -in(A,a_3_1_yellow19(B,C,D))|in($f18(A,B,C,D),$f17(A,B,C,D)).
% 3.32/3.53  0 [] empty_carrier(B)| -one_sorted_str(B)|empty(C)| -element(C,powerset(the_carrier(B)))|empty(D)| -filtered_subset(D,boole_POSet(C))| -upper_relstr_subset(D,boole_POSet(C))| -element(D,powerset(the_carrier(boole_POSet(C))))|in(A,a_3_1_yellow19(B,C,D))| -element(E,the_carrier(B))| -element_as_carrier_subset(F,boole_POSet(C),D)|A!=ordered_pair(E,F)| -in(E,F).
% 3.32/3.53  0 [] -relation_of2(B,A,A)|rel_str_of(A,B)!=rel_str_of(C,D)|A=C.
% 3.32/3.53  0 [] -relation_of2(B,A,A)|rel_str_of(A,B)!=rel_str_of(C,D)|B=D.
% 3.32/3.53  0 [] -one_sorted_str(A)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))|net_str_of(A,B,C,D)!=net_str_of(E,F,G,H)|A=E.
% 3.32/3.53  0 [] -one_sorted_str(A)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))|net_str_of(A,B,C,D)!=net_str_of(E,F,G,H)|B=F.
% 3.32/3.53  0 [] -one_sorted_str(A)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))|net_str_of(A,B,C,D)!=net_str_of(E,F,G,H)|C=G.
% 3.32/3.53  0 [] -one_sorted_str(A)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))|net_str_of(A,B,C,D)!=net_str_of(E,F,G,H)|D=H.
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f19(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f19(A)).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|filtered_subset($f19(A),A).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|upper_relstr_subset($f19(A),A).
% 3.32/3.53  0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|element($f20(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)| -empty($f20(A)).
% 3.32/3.53  0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|directed_subset($f20(A),A).
% 3.32/3.53  0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|filtered_subset($f20(A),A).
% 3.32/3.53  0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|lower_relstr_subset($f20(A),A).
% 3.32/3.53  0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|upper_relstr_subset($f20(A),A).
% 3.32/3.53  0 [] rel_str($c3).
% 3.32/3.53  0 [] -empty_carrier($c3).
% 3.32/3.53  0 [] reflexive_relstr($c3).
% 3.32/3.53  0 [] transitive_relstr($c3).
% 3.32/3.53  0 [] antisymmetric_relstr($c3).
% 3.32/3.53  0 [] connected_relstr($c3).
% 3.32/3.53  0 [] rel_str($c4).
% 3.32/3.53  0 [] -empty_carrier($c4).
% 3.32/3.53  0 [] strict_rel_str($c4).
% 3.32/3.53  0 [] reflexive_relstr($c4).
% 3.32/3.53  0 [] transitive_relstr($c4).
% 3.32/3.53  0 [] antisymmetric_relstr($c4).
% 3.32/3.53  0 [] with_suprema_relstr($c4).
% 3.32/3.53  0 [] with_infima_relstr($c4).
% 3.32/3.53  0 [] complete_relstr($c4).
% 3.32/3.53  0 [] lower_bounded_relstr($c4).
% 3.32/3.53  0 [] upper_bounded_relstr($c4).
% 3.32/3.53  0 [] bounded_relstr($c4).
% 3.32/3.53  0 [] up_complete_relstr($c4).
% 3.32/3.53  0 [] join_complete_relstr($c4).
% 3.32/3.53  0 [] -empty($c5).
% 3.32/3.53  0 [] finite($c5).
% 3.32/3.53  0 [] rel_str($c6).
% 3.32/3.53  0 [] -empty_carrier($c6).
% 3.32/3.53  0 [] strict_rel_str($c6).
% 3.32/3.53  0 [] reflexive_relstr($c6).
% 3.32/3.53  0 [] transitive_relstr($c6).
% 3.32/3.53  0 [] antisymmetric_relstr($c6).
% 3.32/3.53  0 [] complete_relstr($c6).
% 3.32/3.53  0 [] empty($c7).
% 3.32/3.53  0 [] relation($c7).
% 3.32/3.53  0 [] empty(A)|element($f21(A),powerset(A)).
% 3.32/3.53  0 [] empty(A)| -empty($f21(A)).
% 3.32/3.53  0 [] -rel_str(A)|element($f22(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] -rel_str(A)|directed_subset($f22(A),A).
% 3.32/3.53  0 [] -rel_str(A)|filtered_subset($f22(A),A).
% 3.32/3.53  0 [] rel_str($c8).
% 3.32/3.53  0 [] -empty_carrier($c8).
% 3.32/3.53  0 [] -trivial_carrier($c8).
% 3.32/3.53  0 [] strict_rel_str($c8).
% 3.32/3.53  0 [] reflexive_relstr($c8).
% 3.32/3.53  0 [] transitive_relstr($c8).
% 3.32/3.53  0 [] antisymmetric_relstr($c8).
% 3.32/3.53  0 [] lower_bounded_relstr($c8).
% 3.32/3.53  0 [] upper_bounded_relstr($c8).
% 3.32/3.53  0 [] bounded_relstr($c8).
% 3.32/3.53  0 [] -v1_yellow_3($c8).
% 3.32/3.53  0 [] distributive_relstr($c8).
% 3.32/3.53  0 [] heyting_relstr($c8).
% 3.32/3.53  0 [] complemented_relstr($c8).
% 3.32/3.53  0 [] boolean_relstr($c8).
% 3.32/3.53  0 [] with_suprema_relstr($c8).
% 3.32/3.53  0 [] with_infima_relstr($c8).
% 3.32/3.53  0 [] rel_str($c9).
% 3.32/3.53  0 [] -empty_carrier($c9).
% 3.32/3.53  0 [] strict_rel_str($c9).
% 3.32/3.53  0 [] reflexive_relstr($c9).
% 3.32/3.53  0 [] transitive_relstr($c9).
% 3.32/3.53  0 [] antisymmetric_relstr($c9).
% 3.32/3.53  0 [] with_suprema_relstr($c9).
% 3.32/3.53  0 [] with_infima_relstr($c9).
% 3.32/3.53  0 [] complete_relstr($c9).
% 3.32/3.53  0 [] trivial_carrier($c9).
% 3.32/3.53  0 [] rel_str($c10).
% 3.32/3.53  0 [] -empty_carrier($c10).
% 3.32/3.53  0 [] strict_rel_str($c10).
% 3.32/3.53  0 [] reflexive_relstr($c10).
% 3.32/3.53  0 [] transitive_relstr($c10).
% 3.32/3.53  0 [] antisymmetric_relstr($c10).
% 3.32/3.53  0 [] with_suprema_relstr($c10).
% 3.32/3.53  0 [] with_infima_relstr($c10).
% 3.32/3.53  0 [] complete_relstr($c10).
% 3.32/3.53  0 [] -empty($c11).
% 3.32/3.53  0 [] relation($c11).
% 3.32/3.53  0 [] element($f23(A),powerset(A)).
% 3.32/3.53  0 [] empty($f23(A)).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|element($f24(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -empty($f24(A)).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|finite($f24(A)).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|directed_subset($f24(A),A).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|filtered_subset($f24(A),A).
% 3.32/3.53  0 [] element($f25(A),powerset(powerset(A))).
% 3.32/3.53  0 [] -empty($f25(A)).
% 3.32/3.53  0 [] finite($f25(A)).
% 3.32/3.53  0 [] rel_str($c12).
% 3.32/3.53  0 [] -empty_carrier($c12).
% 3.32/3.53  0 [] reflexive_relstr($c12).
% 3.32/3.53  0 [] transitive_relstr($c12).
% 3.32/3.53  0 [] antisymmetric_relstr($c12).
% 3.32/3.53  0 [] with_suprema_relstr($c12).
% 3.32/3.53  0 [] with_infima_relstr($c12).
% 3.32/3.53  0 [] complete_relstr($c12).
% 3.32/3.53  0 [] lower_bounded_relstr($c12).
% 3.32/3.53  0 [] upper_bounded_relstr($c12).
% 3.32/3.53  0 [] bounded_relstr($c12).
% 3.32/3.53  0 [] empty(A)|element($f26(A),powerset(A)).
% 3.32/3.53  0 [] empty(A)| -empty($f26(A)).
% 3.32/3.53  0 [] empty(A)|finite($f26(A)).
% 3.32/3.53  0 [] relation($c13).
% 3.32/3.53  0 [] relation_empty_yielding($c13).
% 3.32/3.53  0 [] one_sorted_str($c14).
% 3.32/3.53  0 [] -empty_carrier($c14).
% 3.32/3.53  0 [] -one_sorted_str(A)|element($f27(A),powerset(powerset(the_carrier(A)))).
% 3.32/3.53  0 [] -one_sorted_str(A)| -empty($f27(A)).
% 3.32/3.53  0 [] -one_sorted_str(A)|finite($f27(A)).
% 3.32/3.53  0 [] empty(A)|element($f28(A),powerset(A)).
% 3.32/3.53  0 [] empty(A)| -empty($f28(A)).
% 3.32/3.53  0 [] empty(A)|finite($f28(A)).
% 3.32/3.53  0 [] -one_sorted_str(A)|net_str($f29(A),A).
% 3.32/3.53  0 [] -one_sorted_str(A)|strict_net_str($f29(A),A).
% 3.32/3.53  0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|element($f30(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty($f30(A)).
% 3.32/3.53  0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|proper_element($f30(A),powerset(the_carrier(A))).
% 3.32/3.53  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($f30(A),A).
% 3.32/3.53  0 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|upper_relstr_subset($f30(A),A).
% 3.32/3.53  0 [] rel_str($c15).
% 3.32/3.53  0 [] -empty_carrier($c15).
% 3.32/3.53  0 [] strict_rel_str($c15).
% 3.32/3.53  0 [] transitive_relstr($c15).
% 3.32/3.53  0 [] directed_relstr($c15).
% 3.32/3.53  0 [] empty_carrier(A)| -one_sorted_str(A)|element($f31(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f31(A)).
% 3.32/3.53  0 [] -one_sorted_str(A)|net_str($f32(A),A).
% 3.32/3.53  0 [] -one_sorted_str(A)| -empty_carrier($f32(A)).
% 3.32/3.53  0 [] -one_sorted_str(A)|reflexive_relstr($f32(A)).
% 3.32/3.53  0 [] -one_sorted_str(A)|transitive_relstr($f32(A)).
% 3.32/3.53  0 [] -one_sorted_str(A)|antisymmetric_relstr($f32(A)).
% 3.32/3.53  0 [] -one_sorted_str(A)|strict_net_str($f32(A),A).
% 3.32/3.53  0 [] -one_sorted_str(A)|directed_relstr($f32(A)).
% 3.32/3.53  0 [] -rel_str(A)|element($f33(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] -rel_str(A)|lower_relstr_subset($f33(A),A).
% 3.32/3.53  0 [] -rel_str(A)|upper_relstr_subset($f33(A),A).
% 3.32/3.53  0 [] empty_carrier(A)| -rel_str(A)|element($f34(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] empty_carrier(A)| -rel_str(A)| -empty($f34(A)).
% 3.32/3.53  0 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset($f34(A),A).
% 3.32/3.53  0 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset($f34(A),A).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f35(A),powerset(the_carrier(A))).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f35(A)).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|directed_subset($f35(A),A).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|lower_relstr_subset($f35(A),A).
% 3.32/3.53  0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -one_sorted_str(B)| -function(C)| -quasi_total(C,the_carrier(A),the_carrier(B))| -relation_of2(C,the_carrier(A),the_carrier(B))| -element(D,the_carrier(A))|apply_on_structs(A,B,C,D)=apply(C,D).
% 3.32/3.53  0 [] inclusion_order(A)=inclusion_relation(A).
% 3.32/3.53  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))| -element_as_carrier_subset(C,A,B)|element(C,B).
% 3.32/3.53  0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|element_as_carrier_subset(C,A,B)| -element(C,B).
% 3.32/3.53  0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 3.32/3.53  0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))| -related_reflexive(A,B,C)|related(A,B,C).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|related_reflexive(A,B,C)| -related(A,B,C).
% 3.32/3.53  0 [] subset(A,A).
% 3.32/3.53  0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|related_reflexive(A,B,B).
% 3.32/3.53  0 [] -element(B,powerset(the_carrier(boole_POSet(A))))| -upper_relstr_subset(B,boole_POSet(A))| -subset(C,D)| -subset(D,A)| -in(C,B)|in(D,B).
% 3.32/3.53  0 [] -element(B,powerset(the_carrier(boole_POSet(A))))|upper_relstr_subset(B,boole_POSet(A))|subset($f37(A,B),$f36(A,B)).
% 3.32/3.53  0 [] -element(B,powerset(the_carrier(boole_POSet(A))))|upper_relstr_subset(B,boole_POSet(A))|subset($f36(A,B),A).
% 3.32/3.53  0 [] -element(B,powerset(the_carrier(boole_POSet(A))))|upper_relstr_subset(B,boole_POSet(A))|in($f37(A,B),B).
% 3.32/3.53  0 [] -element(B,powerset(the_carrier(boole_POSet(A))))|upper_relstr_subset(B,boole_POSet(A))| -in($f36(A,B),B).
% 3.32/3.53  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).
% 3.32/3.53  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))).
% 3.32/3.53  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))).
% 3.32/3.53  0 [] -one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A).
% 3.32/3.53  0 [] -empty_carrier($c17).
% 3.32/3.53  0 [] one_sorted_str($c17).
% 3.32/3.53  0 [] -empty($c16).
% 3.32/3.53  0 [] filtered_subset($c16,boole_POSet(cast_as_carrier_subset($c17))).
% 3.32/3.53  0 [] upper_relstr_subset($c16,boole_POSet(cast_as_carrier_subset($c17))).
% 3.32/3.53  0 [] element($c16,powerset(the_carrier(boole_POSet(cast_as_carrier_subset($c17))))).
% 3.32/3.53  0 [] set_difference($c16,singleton(empty_set))!=filter_of_net_str($c17,net_of_bool_filter($c17,cast_as_carrier_subset($c17),$c16)).
% 3.32/3.53  0 [] -in(A,B)|element(A,B).
% 3.32/3.53  0 [] the_carrier(incl_POSet(A))=A.
% 3.32/3.53  0 [] the_InternalRel(incl_POSet(A))=inclusion_order(A).
% 3.32/3.53  0 [] -element(A,B)|empty(B)|in(A,B).
% 3.32/3.53  0 [] in($f38(A,B),A)|in($f38(A,B),B)|A=B.
% 3.32/3.53  0 [] -in($f38(A,B),A)| -in($f38(A,B),B)|A=B.
% 3.32/3.53  0 [] set_difference(A,empty_set)=A.
% 3.32/3.53  0 [] -element(A,powerset(B))|subset(A,B).
% 3.32/3.53  0 [] element(A,powerset(B))| -subset(A,B).
% 3.32/3.53  0 [] set_difference(empty_set,A)=empty_set.
% 3.32/3.53  0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 3.32/3.53  0 [] boole_POSet(A)=incl_POSet(powerset(A)).
% 3.32/3.53  0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 3.32/3.53  0 [] -empty(A)|A=empty_set.
% 3.32/3.53  0 [] -in(A,B)| -empty(B).
% 3.32/3.53  0 [] pair_first(ordered_pair(A,B))=A.
% 3.32/3.53  0 [] pair_second(ordered_pair(A,B))=B.
% 3.32/3.53  0 [] -empty(A)|A=B| -empty(B).
% 3.32/3.53  end_of_list.
% 3.32/3.53  
% 3.32/3.53  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=16.
% 3.32/3.53  
% 3.32/3.53  This ia a non-Horn set with equality.  The strategy will be
% 3.32/3.53  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.32/3.53  deletion, with positive clauses in sos and nonpositive
% 3.32/3.53  clauses in usable.
% 3.32/3.53  
% 3.32/3.53     dependent: set(knuth_bendix).
% 3.32/3.53     dependent: set(anl_eq).
% 3.32/3.53     dependent: set(para_from).
% 3.32/3.53     dependent: set(para_into).
% 3.32/3.53     dependent: clear(para_from_right).
% 3.32/3.53     dependent: clear(para_into_right).
% 3.32/3.53     dependent: set(para_from_vars).
% 3.32/3.53     dependent: set(eq_units_both_ways).
% 3.32/3.53     dependent: set(dynamic_demod_all).
% 3.32/3.53     dependent: set(dynamic_demod).
% 3.32/3.53     dependent: set(order_eq).
% 3.32/3.53     dependent: set(back_demod).
% 3.32/3.53     dependent: set(lrpo).
% 3.32/3.53     dependent: set(hyper_res).
% 3.32/3.53     dependent: set(unit_deletion).
% 3.32/3.53     dependent: set(factor).
% 3.32/3.53  
% 3.32/3.53  ------------> process usable:
% 3.32/3.53  ** 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.
% 3.32/3.53  ** KEPT (pick-wt=19): 4 [copy,3,flip.4] -one_sorted_str(A)| -net_str(B,A)| -strict_net_str(B,A)|net_str_of(A,the_carrier(B),the_InternalRel(B),the_mapping(A,B))=B.
% 3.32/3.53  ** KEPT (pick-wt=6): 5 [] -in(A,B)| -in(B,A).
% 3.32/3.53  ** KEPT (pick-wt=10): 6 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|up_complete_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=10): 7 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|join_complete_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=10): 8 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -join_complete_relstr(A)|lower_bounded_relstr(A).
% 3.32/3.53  ** 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)|with_infima_relstr(A).
% 3.32/3.53  ** 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)|complete_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=18): 11 [] -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).
% 3.32/3.53  ** KEPT (pick-wt=18): 12 [] -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).
% 3.32/3.53  ** KEPT (pick-wt=12): 13 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -join_complete_relstr(A)|with_infima_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=14): 14 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -join_complete_relstr(A)|with_suprema_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=4): 15 [] -empty(A)|finite(A).
% 3.32/3.53  ** KEPT (pick-wt=6): 16 [] -rel_str(A)| -with_suprema_relstr(A)| -empty_carrier(A).
% 3.32/3.53  ** KEPT (pick-wt=4): 17 [] -empty(A)|relation(A).
% 3.32/3.53  ** KEPT (pick-wt=8): 18 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 3.32/3.53  ** KEPT (pick-wt=8): 19 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_suprema_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=8): 20 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_infima_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=8): 21 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 3.32/3.53  ** KEPT (pick-wt=6): 22 [] -rel_str(A)| -with_infima_relstr(A)| -empty_carrier(A).
% 3.32/3.53  ** KEPT (pick-wt=10): 23 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|transitive_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=10): 24 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|antisymmetric_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=10): 25 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|complete_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=8): 26 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|bounded_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=6): 27 [] -rel_str(A)| -bounded_relstr(A)|lower_bounded_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=6): 28 [] -rel_str(A)| -bounded_relstr(A)|upper_bounded_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=10): 29 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|connected_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=8): 30 [] -rel_str(A)| -lower_bounded_relstr(A)| -upper_bounded_relstr(A)|bounded_relstr(A).
% 3.32/3.53    Following clause subsumed by 16 during input processing: 0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)| -empty_carrier(A).
% 3.32/3.53  ** KEPT (pick-wt=10): 31 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 3.32/3.53  ** KEPT (pick-wt=6): 32 [] A!=B|subset(A,B).
% 3.32/3.53  ** KEPT (pick-wt=6): 33 [] A!=B|subset(B,A).
% 3.32/3.53  ** KEPT (pick-wt=9): 34 [] A=B| -subset(A,B)| -subset(B,A).
% 3.32/3.53  ** KEPT (pick-wt=20): 35 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -is_eventually_in(A,B,C)|element($f1(A,B,C),the_carrier(B)).
% 3.32/3.53  ** KEPT (pick-wt=30): 36 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -is_eventually_in(A,B,C)| -element(D,the_carrier(B))| -related(B,$f1(A,B,C),D)|in(apply_netmap(A,B,D),C).
% 3.32/3.53  ** KEPT (pick-wt=25): 37 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|is_eventually_in(A,B,C)| -element(D,the_carrier(B))|element($f2(A,B,C,D),the_carrier(B)).
% 3.32/3.53  ** KEPT (pick-wt=25): 38 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|is_eventually_in(A,B,C)| -element(D,the_carrier(B))|related(B,D,$f2(A,B,C,D)).
% 3.32/3.53  ** KEPT (pick-wt=27): 39 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|is_eventually_in(A,B,C)| -element(D,the_carrier(B))| -in(apply_netmap(A,B,$f2(A,B,C,D)),C).
% 3.32/3.53  ** KEPT (pick-wt=10): 40 [] A!=singleton(B)| -in(C,A)|C=B.
% 3.32/3.53  ** KEPT (pick-wt=10): 41 [] A!=singleton(B)|in(C,A)|C!=B.
% 3.32/3.53  ** KEPT (pick-wt=14): 42 [] A=singleton(B)| -in($f3(B,A),A)|$f3(B,A)!=B.
% 3.32/3.53  ** KEPT (pick-wt=9): 43 [] -subset(A,B)| -in(C,A)|in(C,B).
% 3.32/3.53  ** KEPT (pick-wt=8): 44 [] subset(A,B)| -in($f4(A,B),B).
% 3.32/3.53  ** KEPT (pick-wt=16): 45 [] 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).
% 3.32/3.53  ** KEPT (pick-wt=11): 46 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 3.32/3.53  ** KEPT (pick-wt=11): 47 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 3.32/3.53  ** KEPT (pick-wt=14): 48 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 3.32/3.53  ** KEPT (pick-wt=17): 49 [] A=set_difference(B,C)|in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 3.32/3.53  ** KEPT (pick-wt=23): 50 [] A=set_difference(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 3.32/3.53  ** KEPT (pick-wt=48): 51 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D!=net_of_bool_filter(A,B,C)|the_carrier(D)=a_3_1_yellow19(A,B,C).
% 3.32/3.53  ** KEPT (pick-wt=58): 52 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D!=net_of_bool_filter(A,B,C)| -element(E,the_carrier(D))| -element(F,the_carrier(D))| -related(D,E,F)|subset(pair_second(F),pair_second(E)).
% 3.32/3.53  ** KEPT (pick-wt=58): 53 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D!=net_of_bool_filter(A,B,C)| -element(E,the_carrier(D))| -element(F,the_carrier(D))|related(D,E,F)| -subset(pair_second(F),pair_second(E)).
% 3.32/3.53  ** KEPT (pick-wt=52): 54 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D!=net_of_bool_filter(A,B,C)| -element(E,the_carrier(D))|apply_netmap(A,D,E)=pair_first(E).
% 3.32/3.53  ** KEPT (pick-wt=64): 55 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|element($f7(A,B,C,D),the_carrier(D))|element($f8(A,B,C,D),the_carrier(D)).
% 3.32/3.53  ** KEPT (pick-wt=71): 57 [copy,56,flip.15] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|element($f7(A,B,C,D),the_carrier(D))|pair_first($f8(A,B,C,D))!=apply_netmap(A,D,$f8(A,B,C,D)).
% 3.32/3.53  ** KEPT (pick-wt=64): 58 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|element($f6(A,B,C,D),the_carrier(D))|element($f8(A,B,C,D),the_carrier(D)).
% 3.32/3.53  ** KEPT (pick-wt=71): 60 [copy,59,flip.15] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|element($f6(A,B,C,D),the_carrier(D))|pair_first($f8(A,B,C,D))!=apply_netmap(A,D,$f8(A,B,C,D)).
% 3.32/3.53  ** KEPT (pick-wt=81): 61 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|related(D,$f7(A,B,C,D),$f6(A,B,C,D))|subset(pair_second($f6(A,B,C,D)),pair_second($f7(A,B,C,D)))|element($f8(A,B,C,D),the_carrier(D)).
% 3.32/3.53  ** KEPT (pick-wt=88): 63 [copy,62,flip.16] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)|related(D,$f7(A,B,C,D),$f6(A,B,C,D))|subset(pair_second($f6(A,B,C,D)),pair_second($f7(A,B,C,D)))|pair_first($f8(A,B,C,D))!=apply_netmap(A,D,$f8(A,B,C,D)).
% 3.32/3.53  ** KEPT (pick-wt=81): 64 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)| -related(D,$f7(A,B,C,D),$f6(A,B,C,D))| -subset(pair_second($f6(A,B,C,D)),pair_second($f7(A,B,C,D)))|element($f8(A,B,C,D),the_carrier(D)).
% 3.32/3.53  ** KEPT (pick-wt=88): 66 [copy,65,flip.16] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|empty_carrier(D)| -strict_net_str(D,A)| -net_str(D,A)|D=net_of_bool_filter(A,B,C)|the_carrier(D)!=a_3_1_yellow19(A,B,C)| -related(D,$f7(A,B,C,D),$f6(A,B,C,D))| -subset(pair_second($f6(A,B,C,D)),pair_second($f7(A,B,C,D)))|pair_first($f8(A,B,C,D))!=apply_netmap(A,D,$f8(A,B,C,D)).
% 3.32/3.53  ** KEPT (pick-wt=25): 67 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -element(C,the_carrier(B))|apply_netmap(A,B,C)=apply_on_structs(B,A,the_mapping(A,B),C).
% 3.32/3.53  ** KEPT (pick-wt=8): 68 [] -relation_of2(A,B,B)|strict_rel_str(rel_str_of(B,A)).
% 3.32/3.53  ** KEPT (pick-wt=8): 69 [] -relation_of2(A,B,B)|rel_str(rel_str_of(B,A)).
% 3.32/3.53  ** KEPT (pick-wt=25): 70 [] -one_sorted_str(A)| -relation_of2(B,C,C)| -function(D)| -quasi_total(D,C,the_carrier(A))| -relation_of2(D,C,the_carrier(A))|strict_net_str(net_str_of(A,C,B,D),A).
% 3.32/3.53  ** KEPT (pick-wt=25): 71 [] -one_sorted_str(A)| -relation_of2(B,C,C)| -function(D)| -quasi_total(D,C,the_carrier(A))| -relation_of2(D,C,the_carrier(A))|net_str(net_str_of(A,C,B,D),A).
% 3.32/3.53  ** KEPT (pick-wt=34): 72 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -one_sorted_str(B)| -function(C)| -quasi_total(C,the_carrier(A),the_carrier(B))| -relation_of2(C,the_carrier(A),the_carrier(B))| -element(D,the_carrier(A))|element(apply_on_structs(A,B,C,D),the_carrier(B)).
% 3.32/3.54  ** KEPT (pick-wt=8): 73 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 3.32/3.54  ** KEPT (pick-wt=18): 74 [] 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))))).
% 3.32/3.54  ** KEPT (pick-wt=20): 75 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -element(C,the_carrier(B))|element(apply_netmap(A,B,C),the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=32): 76 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))| -empty_carrier(net_of_bool_filter(A,B,C)).
% 3.32/3.54  ** KEPT (pick-wt=33): 77 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|strict_net_str(net_of_bool_filter(A,B,C),A).
% 3.32/3.54  ** KEPT (pick-wt=33): 78 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|net_str(net_of_bool_filter(A,B,C),A).
% 3.32/3.54  ** KEPT (pick-wt=4): 79 [] -rel_str(A)|one_sorted_str(A).
% 3.32/3.54  ** KEPT (pick-wt=7): 80 [] -one_sorted_str(A)| -net_str(B,A)|rel_str(B).
% 3.32/3.54  ** KEPT (pick-wt=19): 81 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))| -element_as_carrier_subset(C,A,B)|element(C,the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=10): 82 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 3.32/3.54  ** KEPT (pick-wt=9): 83 [] -rel_str(A)|relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=9): 84 [] -one_sorted_str(A)| -net_str(B,A)|function(the_mapping(A,B)).
% 3.32/3.54  ** KEPT (pick-wt=13): 85 [] -one_sorted_str(A)| -net_str(B,A)|quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=13): 86 [] -one_sorted_str(A)| -net_str(B,A)|relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=6): 87 [] -one_sorted_str(A)|net_str($f9(A),A).
% 3.32/3.54  ** KEPT (pick-wt=17): 88 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|element_as_carrier_subset($f11(A,B),A,B).
% 3.32/3.54  ** KEPT (pick-wt=6): 89 [] -finite(A)|finite(set_difference(A,B)).
% 3.32/3.54  ** KEPT (pick-wt=8): 90 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 3.32/3.54  ** KEPT (pick-wt=7): 91 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.54  ** KEPT (pick-wt=8): 92 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset(cast_as_carrier_subset(A),A).
% 3.32/3.54  ** KEPT (pick-wt=8): 93 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset(cast_as_carrier_subset(A),A).
% 3.32/3.54  ** KEPT (pick-wt=13): 94 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -empty(the_mapping(A,B)).
% 3.32/3.54  ** KEPT (pick-wt=13): 95 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|relation(the_mapping(A,B)).
% 3.32/3.54    Following clause subsumed by 84 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|function(the_mapping(A,B)).
% 3.32/3.54    Following clause subsumed by 85 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)|quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=3): 96 [] -empty(singleton(A)).
% 3.32/3.54  ** KEPT (pick-wt=7): 97 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=3): 98 [] -empty(powerset(A)).
% 3.32/3.54  ** KEPT (pick-wt=3): 99 [] -empty_carrier(boole_POSet(A)).
% 3.32/3.54  ** KEPT (pick-wt=3): 100 [] -v1_yellow_3(boole_POSet(A)).
% 3.32/3.54  ** KEPT (pick-wt=11): 101 [] -relation_of2(A,singleton(B),singleton(B))| -empty_carrier(rel_str_of(singleton(B),A)).
% 3.32/3.54    Following clause subsumed by 68 during input processing: 0 [] -relation_of2(A,singleton(B),singleton(B))|strict_rel_str(rel_str_of(singleton(B),A)).
% 3.32/3.54  ** KEPT (pick-wt=11): 102 [] -relation_of2(A,singleton(B),singleton(B))|trivial_carrier(rel_str_of(singleton(B),A)).
% 3.32/3.54  ** KEPT (pick-wt=4): 103 [] -empty(unordered_pair(A,B)).
% 3.32/3.54  ** KEPT (pick-wt=7): 104 [] empty_carrier(A)| -one_sorted_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.54    Following clause subsumed by 96 during input processing: 0 [] -empty(singleton(A)).
% 3.32/3.54  ** KEPT (pick-wt=7): 105 [] -with_suprema_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.54  ** KEPT (pick-wt=8): 106 [] -with_suprema_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 3.32/3.54    Following clause subsumed by 99 during input processing: 0 [] empty(A)| -empty_carrier(boole_POSet(A)).
% 3.32/3.54  ** KEPT (pick-wt=5): 107 [] empty(A)| -trivial_carrier(boole_POSet(A)).
% 3.32/3.54    Following clause subsumed by 100 during input processing: 0 [] empty(A)| -v1_yellow_3(boole_POSet(A)).
% 3.32/3.54  ** KEPT (pick-wt=13): 108 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -empty(filter_of_net_str(A,B)).
% 3.32/3.54  ** KEPT (pick-wt=16): 109 [] 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))).
% 3.32/3.54    Following clause subsumed by 91 during input processing: 0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.54  ** KEPT (pick-wt=8): 110 [] -relation(A)| -relation(B)|relation(set_difference(A,B)).
% 3.32/3.54    Following clause subsumed by 103 during input processing: 0 [] -empty(unordered_pair(A,B)).
% 3.32/3.54    Following clause subsumed by 91 during input processing: 0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.54  ** KEPT (pick-wt=10): 111 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 3.32/3.54    Following clause subsumed by 108 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)).
% 3.32/3.54  ** KEPT (pick-wt=20): 112 [] 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))).
% 3.32/3.54    Following clause subsumed by 109 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))).
% 3.32/3.54  ** KEPT (pick-wt=22): 113 [] 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))))).
% 3.32/3.54  ** KEPT (pick-wt=8): 114 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 3.32/3.54  ** KEPT (pick-wt=7): 115 [] -with_infima_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.54  ** KEPT (pick-wt=8): 116 [] -with_infima_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 3.32/3.54    Following clause subsumed by 76 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))| -empty_carrier(net_of_bool_filter(A,B,C)).
% 3.32/3.54  ** KEPT (pick-wt=32): 117 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|reflexive_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.54  ** KEPT (pick-wt=32): 118 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|transitive_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.54    Following clause subsumed by 77 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|strict_net_str(net_of_bool_filter(A,B,C),A).
% 3.32/3.54    Following clause subsumed by 91 during input processing: 0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 3.32/3.54  ** KEPT (pick-wt=10): 119 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 3.32/3.54    Following clause subsumed by 76 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))| -empty_carrier(net_of_bool_filter(A,B,C)).
% 3.32/3.54    Following clause subsumed by 117 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))|reflexive_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.54    Following clause subsumed by 118 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))|transitive_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.54    Following clause subsumed by 77 during input processing: 0 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))|strict_net_str(net_of_bool_filter(A,B,C),A).
% 3.32/3.54  ** KEPT (pick-wt=38): 120 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -proper_element(C,powerset(the_carrier(boole_POSet(B))))| -element(C,powerset(the_carrier(boole_POSet(B))))|directed_relstr(net_of_bool_filter(A,B,C)).
% 3.32/3.54  ** KEPT (pick-wt=26): 121 [] -one_sorted_str(A)|empty(B)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))| -empty_carrier(net_str_of(A,B,C,D)).
% 3.32/3.54    Following clause subsumed by 70 during input processing: 0 [] -one_sorted_str(A)|empty(B)| -relation_of2(C,B,B)| -function(D)| -quasi_total(D,B,the_carrier(A))| -relation_of2(D,B,the_carrier(A))|strict_net_str(net_str_of(A,B,C,D),A).
% 3.32/3.54  ** KEPT (pick-wt=5): 122 [] empty(A)| -empty_carrier(incl_POSet(A)).
% 3.32/3.54    Following clause subsumed by 99 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 3.32/3.54    Following clause subsumed by 99 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 3.32/3.54    Following clause subsumed by 99 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 3.32/3.54    Following clause subsumed by 100 during input processing: 0 [] -v1_yellow_3(boole_POSet(A)).
% 3.32/3.54  ** KEPT (pick-wt=22): 123 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,a_2_1_yellow19(A,B))|element($f14(C,A,B),powerset(the_carrier(A))).
% 3.32/3.54  ** KEPT (pick-wt=20): 125 [copy,124,flip.6] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,a_2_1_yellow19(A,B))|$f14(C,A,B)=C.
% 3.32/3.54  ** KEPT (pick-wt=21): 126 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -net_str(B,A)| -in(C,a_2_1_yellow19(A,B))|is_eventually_in(A,B,$f14(C,A,B)).
% 3.32/3.54  ** KEPT (pick-wt=26): 127 [] 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).
% 3.32/3.54  ** KEPT (pick-wt=35): 128 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))| -in(C,a_2_2_yellow19(A,B))|element($f16(C,A,B),the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=37): 129 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))| -in(C,a_2_2_yellow19(A,B))|element_as_carrier_subset($f15(C,A,B),boole_POSet(cast_as_carrier_subset(A)),B).
% 3.32/3.54  ** KEPT (pick-wt=39): 131 [copy,130,flip.8] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))| -in(C,a_2_2_yellow19(A,B))|ordered_pair($f16(C,A,B),$f15(C,A,B))=C.
% 3.32/3.54  ** KEPT (pick-wt=37): 132 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))| -in(C,a_2_2_yellow19(A,B))|in($f16(C,A,B),$f15(C,A,B)).
% 3.32/3.54  ** KEPT (pick-wt=46): 133 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))| -element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))|in(C,a_2_2_yellow19(A,B))| -element(D,the_carrier(A))| -element_as_carrier_subset(E,boole_POSet(cast_as_carrier_subset(A)),B)|C!=ordered_pair(D,E)| -in(D,E).
% 3.32/3.54  ** KEPT (pick-wt=41): 134 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))| -in(D,a_3_1_yellow19(A,B,C))|element($f18(D,A,B,C),the_carrier(A)).
% 3.32/3.54  ** KEPT (pick-wt=42): 135 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))| -in(D,a_3_1_yellow19(A,B,C))|element_as_carrier_subset($f17(D,A,B,C),boole_POSet(B),C).
% 3.32/3.54  ** KEPT (pick-wt=46): 137 [copy,136,flip.10] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))| -in(D,a_3_1_yellow19(A,B,C))|ordered_pair($f18(D,A,B,C),$f17(D,A,B,C))=D.
% 3.32/3.54  ** KEPT (pick-wt=44): 138 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))| -in(D,a_3_1_yellow19(A,B,C))|in($f18(D,A,B,C),$f17(D,A,B,C)).
% 3.32/3.54  ** KEPT (pick-wt=50): 139 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|empty(C)| -filtered_subset(C,boole_POSet(B))| -upper_relstr_subset(C,boole_POSet(B))| -element(C,powerset(the_carrier(boole_POSet(B))))|in(D,a_3_1_yellow19(A,B,C))| -element(E,the_carrier(A))| -element_as_carrier_subset(F,boole_POSet(B),C)|D!=ordered_pair(E,F)| -in(E,F).
% 3.32/3.54  ** KEPT (pick-wt=14): 140 [] -relation_of2(A,B,B)|rel_str_of(B,A)!=rel_str_of(C,D)|B=C.
% 3.32/3.54  ** KEPT (pick-wt=14): 141 [] -relation_of2(A,B,B)|rel_str_of(B,A)!=rel_str_of(C,D)|A=D.
% 3.32/3.54  ** KEPT (pick-wt=32): 142 [] -one_sorted_str(A)| -relation_of2(B,C,C)| -function(D)| -quasi_total(D,C,the_carrier(A))| -relation_of2(D,C,the_carrier(A))|net_str_of(A,C,B,D)!=net_str_of(E,F,G,H)|A=E.
% 3.32/3.54  ** KEPT (pick-wt=32): 143 [] -one_sorted_str(A)| -relation_of2(B,C,C)| -function(D)| -quasi_total(D,C,the_carrier(A))| -relation_of2(D,C,the_carrier(A))|net_str_of(A,C,B,D)!=net_str_of(E,F,G,H)|C=F.
% 3.32/3.54  ** KEPT (pick-wt=32): 144 [] -one_sorted_str(A)| -relation_of2(B,C,C)| -function(D)| -quasi_total(D,C,the_carrier(A))| -relation_of2(D,C,the_carrier(A))|net_str_of(A,C,B,D)!=net_str_of(E,F,G,H)|B=G.
% 3.32/3.55  ** KEPT (pick-wt=32): 145 [] -one_sorted_str(A)| -relation_of2(B,C,C)| -function(D)| -quasi_total(D,C,the_carrier(A))| -relation_of2(D,C,the_carrier(A))|net_str_of(A,C,B,D)!=net_str_of(E,F,G,H)|D=H.
% 3.32/3.55  ** KEPT (pick-wt=14): 146 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f19(A),powerset(the_carrier(A))).
% 3.32/3.55  ** KEPT (pick-wt=11): 147 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f19(A)).
% 3.32/3.55  ** KEPT (pick-wt=12): 148 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|filtered_subset($f19(A),A).
% 3.32/3.55  ** KEPT (pick-wt=12): 149 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|upper_relstr_subset($f19(A),A).
% 3.32/3.55  ** KEPT (pick-wt=18): 150 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|element($f20(A),powerset(the_carrier(A))).
% 3.32/3.55  ** KEPT (pick-wt=15): 151 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)| -empty($f20(A)).
% 3.32/3.55  ** KEPT (pick-wt=16): 152 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|directed_subset($f20(A),A).
% 3.32/3.55  ** KEPT (pick-wt=16): 153 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|filtered_subset($f20(A),A).
% 3.32/3.55  ** KEPT (pick-wt=16): 154 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|lower_relstr_subset($f20(A),A).
% 3.32/3.55  ** KEPT (pick-wt=16): 155 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|upper_relstr_subset($f20(A),A).
% 3.32/3.55  ** KEPT (pick-wt=2): 156 [] -empty_carrier($c3).
% 3.32/3.55  ** KEPT (pick-wt=2): 157 [] -empty_carrier($c4).
% 3.32/3.55  ** KEPT (pick-wt=2): 158 [] -empty($c5).
% 3.32/3.55  ** KEPT (pick-wt=2): 159 [] -empty_carrier($c6).
% 3.32/3.55  ** KEPT (pick-wt=5): 160 [] empty(A)| -empty($f21(A)).
% 3.32/3.55  ** KEPT (pick-wt=8): 161 [] -rel_str(A)|element($f22(A),powerset(the_carrier(A))).
% 3.32/3.55  ** KEPT (pick-wt=6): 162 [] -rel_str(A)|directed_subset($f22(A),A).
% 3.32/3.55  ** KEPT (pick-wt=6): 163 [] -rel_str(A)|filtered_subset($f22(A),A).
% 3.32/3.55  ** KEPT (pick-wt=2): 164 [] -empty_carrier($c8).
% 3.32/3.55  ** KEPT (pick-wt=2): 165 [] -trivial_carrier($c8).
% 3.32/3.55  ** KEPT (pick-wt=2): 166 [] -v1_yellow_3($c8).
% 3.32/3.55  ** KEPT (pick-wt=2): 167 [] -empty_carrier($c9).
% 3.32/3.55  ** KEPT (pick-wt=2): 168 [] -empty_carrier($c10).
% 3.32/3.55  ** KEPT (pick-wt=2): 169 [] -empty($c11).
% 3.32/3.55  ** KEPT (pick-wt=12): 170 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|element($f24(A),powerset(the_carrier(A))).
% 3.32/3.55  ** KEPT (pick-wt=9): 171 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -empty($f24(A)).
% 3.32/3.55  ** KEPT (pick-wt=9): 172 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|finite($f24(A)).
% 3.32/3.55  ** KEPT (pick-wt=10): 173 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|directed_subset($f24(A),A).
% 3.32/3.55  ** KEPT (pick-wt=10): 174 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|filtered_subset($f24(A),A).
% 3.32/3.55  ** KEPT (pick-wt=3): 175 [] -empty($f25(A)).
% 3.32/3.55  ** KEPT (pick-wt=2): 176 [] -empty_carrier($c12).
% 3.32/3.55  ** KEPT (pick-wt=5): 177 [] empty(A)| -empty($f26(A)).
% 3.32/3.55  ** KEPT (pick-wt=2): 178 [] -empty_carrier($c14).
% 3.32/3.55  ** KEPT (pick-wt=9): 179 [] -one_sorted_str(A)|element($f27(A),powerset(powerset(the_carrier(A)))).
% 3.32/3.55  ** KEPT (pick-wt=5): 180 [] -one_sorted_str(A)| -empty($f27(A)).
% 3.32/3.55  ** KEPT (pick-wt=5): 181 [] -one_sorted_str(A)|finite($f27(A)).
% 3.32/3.55  ** KEPT (pick-wt=5): 182 [] empty(A)| -empty($f28(A)).
% 3.32/3.55  ** KEPT (pick-wt=6): 183 [] -one_sorted_str(A)|net_str($f29(A),A).
% 3.32/3.55  ** KEPT (pick-wt=6): 184 [] -one_sorted_str(A)|strict_net_str($f29(A),A).
% 3.32/3.55  ** KEPT (pick-wt=20): 185 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|element($f30(A),powerset(the_carrier(A))).
% 3.32/3.55  ** KEPT (pick-wt=17): 186 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty($f30(A)).
% 3.48/3.63  ** KEPT (pick-wt=20): 187 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|proper_element($f30(A),powerset(the_carrier(A))).
% 3.48/3.63  ** KEPT (pick-wt=18): 188 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|filtered_subset($f30(A),A).
% 3.48/3.63  ** KEPT (pick-wt=18): 189 [] empty_carrier(A)|trivial_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -rel_str(A)|upper_relstr_subset($f30(A),A).
% 3.48/3.63  ** KEPT (pick-wt=2): 190 [] -empty_carrier($c15).
% 3.48/3.63  ** KEPT (pick-wt=10): 191 [] empty_carrier(A)| -one_sorted_str(A)|element($f31(A),powerset(the_carrier(A))).
% 3.48/3.63  ** KEPT (pick-wt=7): 192 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f31(A)).
% 3.48/3.63  ** KEPT (pick-wt=6): 193 [] -one_sorted_str(A)|net_str($f32(A),A).
% 3.48/3.63  ** KEPT (pick-wt=5): 194 [] -one_sorted_str(A)| -empty_carrier($f32(A)).
% 3.48/3.63  ** KEPT (pick-wt=5): 195 [] -one_sorted_str(A)|reflexive_relstr($f32(A)).
% 3.48/3.63  ** KEPT (pick-wt=5): 196 [] -one_sorted_str(A)|transitive_relstr($f32(A)).
% 3.48/3.63  ** KEPT (pick-wt=5): 197 [] -one_sorted_str(A)|antisymmetric_relstr($f32(A)).
% 3.48/3.63  ** KEPT (pick-wt=6): 198 [] -one_sorted_str(A)|strict_net_str($f32(A),A).
% 3.48/3.63  ** KEPT (pick-wt=5): 199 [] -one_sorted_str(A)|directed_relstr($f32(A)).
% 3.48/3.63  ** KEPT (pick-wt=8): 200 [] -rel_str(A)|element($f33(A),powerset(the_carrier(A))).
% 3.48/3.63  ** KEPT (pick-wt=6): 201 [] -rel_str(A)|lower_relstr_subset($f33(A),A).
% 3.48/3.63  ** KEPT (pick-wt=6): 202 [] -rel_str(A)|upper_relstr_subset($f33(A),A).
% 3.48/3.63  ** KEPT (pick-wt=10): 203 [] empty_carrier(A)| -rel_str(A)|element($f34(A),powerset(the_carrier(A))).
% 3.48/3.63  ** KEPT (pick-wt=7): 204 [] empty_carrier(A)| -rel_str(A)| -empty($f34(A)).
% 3.48/3.63  ** KEPT (pick-wt=8): 205 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset($f34(A),A).
% 3.48/3.63  ** KEPT (pick-wt=8): 206 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset($f34(A),A).
% 3.48/3.63  ** KEPT (pick-wt=14): 207 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f35(A),powerset(the_carrier(A))).
% 3.48/3.63  ** KEPT (pick-wt=11): 208 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f35(A)).
% 3.48/3.63  ** KEPT (pick-wt=12): 209 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|directed_subset($f35(A),A).
% 3.48/3.63  ** KEPT (pick-wt=12): 210 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|lower_relstr_subset($f35(A),A).
% 3.48/3.63  ** KEPT (pick-wt=35): 211 [] empty_carrier(A)| -one_sorted_str(A)|empty_carrier(B)| -one_sorted_str(B)| -function(C)| -quasi_total(C,the_carrier(A),the_carrier(B))| -relation_of2(C,the_carrier(A),the_carrier(B))| -element(D,the_carrier(A))|apply_on_structs(A,B,C,D)=apply(C,D).
% 3.48/3.63  ** KEPT (pick-wt=18): 212 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))| -element_as_carrier_subset(C,A,B)|element(C,B).
% 3.48/3.63  ** KEPT (pick-wt=18): 213 [] empty_carrier(A)| -one_sorted_str(A)|empty(B)| -element(B,powerset(the_carrier(A)))|element_as_carrier_subset(C,A,B)| -element(C,B).
% 3.48/3.63  ** KEPT (pick-wt=8): 214 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 3.48/3.63  ** KEPT (pick-wt=8): 215 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 3.48/3.63  ** KEPT (pick-wt=22): 216 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))| -related_reflexive(A,B,C)|related(A,B,C).
% 3.48/3.63  ** KEPT (pick-wt=22): 217 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|related_reflexive(A,B,C)| -related(A,B,C).
% 3.48/3.63  ** KEPT (pick-wt=14): 219 [copy,218,factor_simp] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -element(B,the_carrier(A))|related_reflexive(A,B,B).
% 3.48/3.63  ** KEPT (pick-wt=22): 220 [] -element(A,powerset(the_carrier(boole_POSet(B))))| -upper_relstr_subset(A,boole_POSet(B))| -subset(C,D)| -subset(D,B)| -in(C,A)|in(D,A).
% 3.48/3.63  ** KEPT (pick-wt=17): 221 [] -element(A,powerset(the_carrier(boole_POSet(B))))|upper_relstr_subset(A,boole_POSet(B))|subset($f37(B,A),$f36(B,A)).
% 3.48/3.63  ** KEPT (pick-wt=15): 222 [] -element(A,powerset(the_carrier(boole_POSet(B))))|upper_relstr_subset(A,boole_POSet(B))|subset($f36(B,A),B).
% 3.48/3.63  ** KEPT (pick-wt=15): 223 [] -element(A,powerset(the_carrier(boole_POSet(B))))|upper_relstr_subset(A,boole_POSet(B))|in($f37(B,A),A).
% 3.48/3.63  ** KEPT (pick-wt=15): 224 [] -element(A,powerset(the_carrier(boole_POSet(B))))|upper_relstr_subset(A,boole_POSet(B))| -in($f36(B,A),A).
% 3.48/3.63  ** KEPT (pick-wt=18): 225 [] 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).
% 3.48/3.63  ** KEPT (pick-wt=19): 226 [] 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))).
% 3.48/3.63  ** KEPT (pick-wt=23): 227 [] 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))).
% 3.48/3.63  ** KEPT (pick-wt=7): 229 [copy,228,flip.2] -one_sorted_str(A)|the_carrier(A)=cast_as_carrier_subset(A).
% 3.48/3.63  ** KEPT (pick-wt=2): 230 [] -empty_carrier($c17).
% 3.48/3.63  ** KEPT (pick-wt=2): 231 [] -empty($c16).
% 3.48/3.63  ** KEPT (pick-wt=12): 232 [] set_difference($c16,singleton(empty_set))!=filter_of_net_str($c17,net_of_bool_filter($c17,cast_as_carrier_subset($c17),$c16)).
% 3.48/3.63  ** KEPT (pick-wt=6): 233 [] -in(A,B)|element(A,B).
% 3.48/3.63  ** KEPT (pick-wt=8): 234 [] -element(A,B)|empty(B)|in(A,B).
% 3.48/3.63  ** KEPT (pick-wt=13): 235 [] -in($f38(A,B),A)| -in($f38(A,B),B)|A=B.
% 3.48/3.63  ** KEPT (pick-wt=7): 236 [] -element(A,powerset(B))|subset(A,B).
% 3.48/3.63  ** KEPT (pick-wt=7): 237 [] element(A,powerset(B))| -subset(A,B).
% 3.48/3.63  ** KEPT (pick-wt=10): 238 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 3.48/3.63  ** KEPT (pick-wt=9): 239 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 3.48/3.63  ** KEPT (pick-wt=5): 240 [] -empty(A)|A=empty_set.
% 3.48/3.63  ** KEPT (pick-wt=5): 241 [] -in(A,B)| -empty(B).
% 3.48/3.63  ** KEPT (pick-wt=7): 242 [] -empty(A)|A=B| -empty(B).
% 3.48/3.63  31 back subsumes 11.
% 3.48/3.63  
% 3.48/3.63  ------------> process sos:
% 3.48/3.63  ** KEPT (pick-wt=3): 380 [] A=A.
% 3.48/3.63  ** KEPT (pick-wt=7): 381 [] unordered_pair(A,B)=unordered_pair(B,A).
% 3.48/3.63  ** KEPT (pick-wt=14): 382 [] A=singleton(B)|in($f3(B,A),A)|$f3(B,A)=B.
% 3.48/3.63  ** KEPT (pick-wt=8): 383 [] subset(A,B)|in($f4(A,B),A).
% 3.48/3.63  ** KEPT (pick-wt=17): 384 [] A=set_difference(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B).
% 3.48/3.63  ** KEPT (pick-wt=10): 386 [copy,385,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 3.48/3.63  ---> New Demodulator: 387 [new_demod,386] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 3.48/3.63  ** KEPT (pick-wt=3): 388 [] relation(inclusion_relation(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 389 [] reflexive(inclusion_order(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 390 [] antisymmetric(inclusion_order(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 391 [] transitive(inclusion_order(A)).
% 3.48/3.63  ** KEPT (pick-wt=5): 392 [] v1_partfun1(inclusion_order(A),A,A).
% 3.48/3.63  ** KEPT (pick-wt=5): 393 [] relation_of2_as_subset(inclusion_order(A),A,A).
% 3.48/3.63  ** KEPT (pick-wt=3): 394 [] strict_rel_str(incl_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 395 [] rel_str(incl_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 396 [] strict_rel_str(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 397 [] rel_str(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=2): 398 [] rel_str($c1).
% 3.48/3.63  ** KEPT (pick-wt=2): 399 [] one_sorted_str($c2).
% 3.48/3.63  ** KEPT (pick-wt=6): 400 [] relation_of2($f10(A,B),A,B).
% 3.48/3.63  ** KEPT (pick-wt=4): 401 [] element($f12(A),A).
% 3.48/3.63  ** KEPT (pick-wt=6): 402 [] relation_of2_as_subset($f13(A,B),A,B).
% 3.48/3.63  ** KEPT (pick-wt=2): 403 [] empty(empty_set).
% 3.48/3.63  ** KEPT (pick-wt=2): 404 [] relation(empty_set).
% 3.48/3.63  ** KEPT (pick-wt=2): 405 [] relation_empty_yielding(empty_set).
% 3.48/3.63  ** KEPT (pick-wt=3): 406 [] finite(singleton(A)).
% 3.48/3.63    Following clause subsumed by 396 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 407 [] reflexive_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 408 [] transitive_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 409 [] antisymmetric_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 410 [] lower_bounded_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 411 [] upper_bounded_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 412 [] bounded_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 413 [] up_complete_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 414 [] join_complete_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 415 [] distributive_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 416 [] heyting_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 417 [] complemented_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 418 [] boolean_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 419 [] with_suprema_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 420 [] with_infima_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 421 [] complete_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=4): 422 [] finite(unordered_pair(A,B)).
% 3.48/3.63    Following clause subsumed by 396 during input processing: 0 [] empty(A)|strict_rel_str(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 407 during input processing: 0 [] empty(A)|reflexive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 408 during input processing: 0 [] empty(A)|transitive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 409 during input processing: 0 [] empty(A)|antisymmetric_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 410 during input processing: 0 [] empty(A)|lower_bounded_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 411 during input processing: 0 [] empty(A)|upper_bounded_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 412 during input processing: 0 [] empty(A)|bounded_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 413 during input processing: 0 [] empty(A)|up_complete_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 414 during input processing: 0 [] empty(A)|join_complete_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 415 during input processing: 0 [] empty(A)|distributive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 416 during input processing: 0 [] empty(A)|heyting_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 417 during input processing: 0 [] empty(A)|complemented_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 418 during input processing: 0 [] empty(A)|boolean_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 419 during input processing: 0 [] empty(A)|with_suprema_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 420 during input processing: 0 [] empty(A)|with_infima_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 421 during input processing: 0 [] empty(A)|complete_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 403 during input processing: 0 [] empty(empty_set).
% 3.48/3.63    Following clause subsumed by 404 during input processing: 0 [] relation(empty_set).
% 3.48/3.63    Following clause subsumed by 394 during input processing: 0 [] strict_rel_str(incl_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 423 [] reflexive_relstr(incl_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 424 [] transitive_relstr(incl_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 425 [] antisymmetric_relstr(incl_POSet(A)).
% 3.48/3.63    Following clause subsumed by 394 during input processing: 0 [] empty(A)|strict_rel_str(incl_POSet(A)).
% 3.48/3.63    Following clause subsumed by 423 during input processing: 0 [] empty(A)|reflexive_relstr(incl_POSet(A)).
% 3.48/3.63    Following clause subsumed by 424 during input processing: 0 [] empty(A)|transitive_relstr(incl_POSet(A)).
% 3.48/3.63    Following clause subsumed by 425 during input processing: 0 [] empty(A)|antisymmetric_relstr(incl_POSet(A)).
% 3.48/3.63    Following clause subsumed by 396 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 407 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 408 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 409 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 396 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 407 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 408 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 409 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 410 during input processing: 0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 411 during input processing: 0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 412 during input processing: 0 [] bounded_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 419 during input processing: 0 [] with_suprema_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 420 during input processing: 0 [] with_infima_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 421 during input processing: 0 [] complete_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 396 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 407 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 408 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 409 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 410 during input processing: 0 [] lower_bounded_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 411 during input processing: 0 [] upper_bounded_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 412 during input processing: 0 [] bounded_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 426 [] directed_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 413 during input processing: 0 [] up_complete_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 414 during input processing: 0 [] join_complete_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 419 during input processing: 0 [] with_suprema_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 420 during input processing: 0 [] with_infima_relstr(boole_POSet(A)).
% 3.48/3.63    Following clause subsumed by 421 during input processing: 0 [] complete_relstr(boole_POSet(A)).
% 3.48/3.63  ** KEPT (pick-wt=2): 427 [] rel_str($c3).
% 3.48/3.63  ** KEPT (pick-wt=2): 428 [] reflexive_relstr($c3).
% 3.48/3.63  ** KEPT (pick-wt=2): 429 [] transitive_relstr($c3).
% 3.48/3.63  ** KEPT (pick-wt=2): 430 [] antisymmetric_relstr($c3).
% 3.48/3.63  ** KEPT (pick-wt=2): 431 [] connected_relstr($c3).
% 3.48/3.63  ** KEPT (pick-wt=2): 432 [] rel_str($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 433 [] strict_rel_str($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 434 [] reflexive_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 435 [] transitive_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 436 [] antisymmetric_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 437 [] with_suprema_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 438 [] with_infima_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 439 [] complete_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 440 [] lower_bounded_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 441 [] upper_bounded_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 442 [] bounded_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 443 [] up_complete_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 444 [] join_complete_relstr($c4).
% 3.48/3.63  ** KEPT (pick-wt=2): 445 [] finite($c5).
% 3.48/3.63  ** KEPT (pick-wt=2): 446 [] rel_str($c6).
% 3.48/3.63  ** KEPT (pick-wt=2): 447 [] strict_rel_str($c6).
% 3.48/3.63  ** KEPT (pick-wt=2): 448 [] reflexive_relstr($c6).
% 3.48/3.63  ** KEPT (pick-wt=2): 449 [] transitive_relstr($c6).
% 3.48/3.63  ** KEPT (pick-wt=2): 450 [] antisymmetric_relstr($c6).
% 3.48/3.63  ** KEPT (pick-wt=2): 451 [] complete_relstr($c6).
% 3.48/3.63  ** KEPT (pick-wt=2): 452 [] empty($c7).
% 3.48/3.63  ** KEPT (pick-wt=2): 453 [] relation($c7).
% 3.48/3.63  ** KEPT (pick-wt=7): 454 [] empty(A)|element($f21(A),powerset(A)).
% 3.48/3.63  ** KEPT (pick-wt=2): 455 [] rel_str($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 456 [] strict_rel_str($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 457 [] reflexive_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 458 [] transitive_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 459 [] antisymmetric_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 460 [] lower_bounded_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 461 [] upper_bounded_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 462 [] bounded_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 463 [] distributive_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 464 [] heyting_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 465 [] complemented_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 466 [] boolean_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 467 [] with_suprema_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 468 [] with_infima_relstr($c8).
% 3.48/3.63  ** KEPT (pick-wt=2): 469 [] rel_str($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 470 [] strict_rel_str($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 471 [] reflexive_relstr($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 472 [] transitive_relstr($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 473 [] antisymmetric_relstr($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 474 [] with_suprema_relstr($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 475 [] with_infima_relstr($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 476 [] complete_relstr($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 477 [] trivial_carrier($c9).
% 3.48/3.63  ** KEPT (pick-wt=2): 478 [] rel_str($c10).
% 3.48/3.63  ** KEPT (pick-wt=2): 479 [] strict_rel_str($c10).
% 3.48/3.63  ** KEPT (pick-wt=2): 480 [] reflexive_relstr($c10).
% 3.48/3.63  ** KEPT (pick-wt=2): 481 [] transitive_relstr($c10).
% 3.48/3.63  ** KEPT (pick-wt=2): 482 [] antisymmetric_relstr($c10).
% 3.48/3.63  ** KEPT (pick-wt=2): 483 [] with_suprema_relstr($c10).
% 3.48/3.63  ** KEPT (pick-wt=2): 484 [] with_infima_relstr($c10).
% 3.48/3.63  ** KEPT (pick-wt=2): 485 [] complete_relstr($c10).
% 3.48/3.63  ** KEPT (pick-wt=2): 486 [] relation($c11).
% 3.48/3.63  ** KEPT (pick-wt=5): 487 [] element($f23(A),powerset(A)).
% 3.48/3.63  ** KEPT (pick-wt=3): 488 [] empty($f23(A)).
% 3.48/3.63  ** KEPT (pick-wt=6): 489 [] element($f25(A),powerset(powerset(A))).
% 3.48/3.63  ** KEPT (pick-wt=3): 490 [] finite($f25(A)).
% 3.48/3.63  ** KEPT (pick-wt=2): 491 [] rel_str($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 492 [] reflexive_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 493 [] transitive_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 494 [] antisymmetric_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 495 [] with_suprema_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 496 [] with_infima_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 497 [] complete_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 498 [] lower_bounded_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 499 [] upper_bounded_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=2): 500 [] bounded_relstr($c12).
% 3.48/3.63  ** KEPT (pick-wt=7): 501 [] empty(A)|element($f26(A),powerset(A)).
% 3.48/3.63  ** KEPT (pick-wt=5): 502 [] empty(A)|finite($f26(A)).
% 3.48/3.63  ** KEPT (pick-wt=2): 503 [] relation($c13).
% 3.48/3.63  ** KEPT (pick-wt=2): 504 [] relation_empty_yielding($c13).
% 3.48/3.63  ** KEPT (pick-wt=2): 505 [] one_sorted_str($c14).
% 3.48/3.63  ** KEPT (pick-wt=7): 506 [] empty(A)|element($f28(A),powerset(A)).
% 3.48/3.63  ** KEPT (pick-wt=5): 507 [] empty(A)|finite($f28(A)).
% 3.48/3.63  ** KEPT (pick-wt=2): 508 [] rel_str($c15).
% 3.48/3.63  ** KEPT (pick-wt=2): 509 [] strict_rel_str($c15).
% 3.48/3.63  ** KEPT (pick-wt=2): 510 [] transitive_relstr($c15).
% 3.48/3.63  ** KEPT (pick-wt=2): 511 [] directed_relstr($c15).
% 3.48/3.63  ** KEPT (pick-wt=5): 513 [copy,512,flip.1] inclusion_relation(A)=inclusion_order(A).
% 3.48/3.63  ---> New Demodulator: 514 [new_demod,513] inclusion_relation(A)=inclusion_order(A).
% 3.48/3.63  ** KEPT (pick-wt=3): 515 [] subset(A,A).
% 3.48/3.63  ** KEPT (pick-wt=2): 516 [] one_sorted_str($c17).
% 3.48/3.63  ** KEPT (pick-wt=5): 517 [] filtered_subset($c16,boole_POSet(cast_as_carrier_subset($c17))).
% 3.48/3.63  ** KEPT (pick-wt=5): 518 [] upper_relstr_subset($c16,boole_POSet(cast_as_carrier_subset($c17))).
% 3.48/3.63  ** KEPT (pick-wt=7): 519 [] element($c16,powerset(the_carrier(boole_POSet(cast_as_carrier_subset($c17))))).
% 3.48/3.63  ** KEPT (pick-wt=5): 520 [] the_carrier(incl_POSet(A))=A.
% 3.48/3.63  ---> New Demodulator: 521 [new_demod,520] the_carrier(incl_POSet(A))=A.
% 3.48/3.63  ** KEPT (pick-wt=6): 522 [] the_InternalRel(incl_POSet(A))=inclusion_order(A).
% 3.48/3.63  ---> New Demodulator: 523 [new_demod,522] the_InternalRel(incl_POSet(A))=inclusion_order(A).
% 3.48/3.63  ** KEPT (pick-wt=13): 524 [] in($f38(A,B),A)|in($f38(A,B),B)|A=B.
% 3.48/3.63  ** KEPT (pick-wt=5): 525 [] set_difference(A,empty_set)=A.
% 3.48/3.63  ---> New Demodulator: 526 [new_demod,525] set_difference(A,empty_set)=A.
% 3.48/3.63  ** KEPT (pick-wt=5): 527 [] set_difference(empty_set,A)=empty_set.
% 3.48/3.63  ---> New Demodulator: 528 [new_demod,527] set_difference(empty_set,A)=empty_set.
% 3.48/3.63  ** KEPT (pick-wt=6): 530 [copy,529,flip.1] incl_POSet(powerset(A))=boole_POSet(A).
% 3.48/3.63  ---> New Demodulator: 531 [new_demod,530] incl_POSet(powerset(A))=boole_POSet(A).
% 3.48/3.63  ** KEPT (pick-wt=6): 532 [] pair_first(ordered_pair(A,B))=A.
% 3.48/3.63  ---> New Demodulator: 533 [new_demod,532] pair_first(ordered_pair(A,B))=A.
% 3.48/3.63  ** KEPT (pick-wt=6): 534 [] pair_second(ordered_pair(A,B))=B.
% 3.48/3.63  ---> New Demodulator: 535 [new_demod,534] pair_second(ordered_pair(A,B))=B.
% 3.48/3.63    Following clause subsumed by 380 during input processing: 0 [copy,380,flip.1] A=A.
% 3.48/3.63  380 back subsumes 345.
% 3.48/3.63  380 back subsumes 344.
% 3.48/3.63  380 back subsumes 244.
% 3.48/3.63    Following clause subsumed by 381 during input processing: 0 [copy,381,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 3.95/4.09  >>>> Starting back demodulation with 387.
% 3.95/4.09  >>>> Starting back demodulation with 514.
% 3.95/4.09      >> back demodulating 388 with 514.
% 3.95/4.09  515 back subsumes 377.
% 3.95/4.09  515 back subsumes 376.
% 3.95/4.09  515 back subsumes 352.
% 3.95/4.09  515 back subsumes 351.
% 3.95/4.09  515 back subsumes 350.
% 3.95/4.09  515 back subsumes 260.
% 3.95/4.09  >>>> Starting back demodulation with 521.
% 3.95/4.09  >>>> Starting back demodulation with 523.
% 3.95/4.09  >>>> Starting back demodulation with 526.
% 3.95/4.09  >>>> Starting back demodulation with 528.
% 3.95/4.09  >>>> Starting back demodulation with 531.
% 3.95/4.09  >>>> Starting back demodulation with 533.
% 3.95/4.09  >>>> Starting back demodulation with 535.
% 3.95/4.09  
% 3.95/4.09  ======= end of input processing =======
% 3.95/4.09  
% 3.95/4.09  =========== start of search ===========
% 3.95/4.09  
% 3.95/4.09  
% 3.95/4.09  Resetting weight limit to 2.
% 3.95/4.09  
% 3.95/4.09  
% 3.95/4.09  Resetting weight limit to 2.
% 3.95/4.09  
% 3.95/4.09  sos_size=144
% 3.95/4.09  
% 3.95/4.09  Search stopped because sos empty.
% 3.95/4.09  
% 3.95/4.09  
% 3.95/4.09  Search stopped because sos empty.
% 3.95/4.09  
% 3.95/4.09  ============ end of search ============
% 3.95/4.09  
% 3.95/4.09  -------------- statistics -------------
% 3.95/4.09  clauses given                176
% 3.95/4.09  clauses generated          17410
% 3.95/4.09  clauses kept                 545
% 3.95/4.09  clauses forward subsumed     229
% 3.95/4.09  clauses back subsumed         10
% 3.95/4.09  Kbytes malloced             6835
% 3.95/4.09  
% 3.95/4.09  ----------- times (seconds) -----------
% 3.95/4.09  user CPU time          0.59          (0 hr, 0 min, 0 sec)
% 3.95/4.09  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 3.95/4.09  wall-clock time        4             (0 hr, 0 min, 4 sec)
% 3.95/4.09  
% 3.95/4.09  Process 10935 finished Wed Jul 27 08:09:25 2022
% 3.95/4.09  Otter interrupted
% 3.95/4.09  PROOF NOT FOUND
%------------------------------------------------------------------------------