TSTP Solution File: SEU404+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU404+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:16:08 EDT 2022
% Result : Unknown 29.97s 29.88s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU404+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 07:44:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 29.04/28.89 ----- Otter 3.3f, August 2004 -----
% 29.04/28.89 The process was started by sandbox on n013.cluster.edu,
% 29.04/28.89 Wed Jul 27 07:44:45 2022
% 29.04/28.89 The command was "./otter". The process ID is 1334.
% 29.04/28.89
% 29.04/28.89 set(prolog_style_variables).
% 29.04/28.89 set(auto).
% 29.04/28.89 dependent: set(auto1).
% 29.04/28.89 dependent: set(process_input).
% 29.04/28.89 dependent: clear(print_kept).
% 29.04/28.89 dependent: clear(print_new_demod).
% 29.04/28.89 dependent: clear(print_back_demod).
% 29.04/28.89 dependent: clear(print_back_sub).
% 29.04/28.89 dependent: set(control_memory).
% 29.04/28.89 dependent: assign(max_mem, 12000).
% 29.04/28.89 dependent: assign(pick_given_ratio, 4).
% 29.04/28.89 dependent: assign(stats_level, 1).
% 29.04/28.89 dependent: assign(max_seconds, 10800).
% 29.04/28.89 clear(print_given).
% 29.04/28.89
% 29.04/28.89 formula_list(usable).
% 29.04/28.89 all A (A=A).
% 29.04/28.89 all A (rel_str(A)-> (strict_rel_str(A)->A=rel_str_of(the_carrier(A),the_InternalRel(A)))).
% 29.04/28.89 all A (latt_str(A)-> (strict_latt_str(A)->A=latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)))).
% 29.04/28.89 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)))).
% 29.04/28.89 all A B (in(A,B)-> -in(B,A)).
% 29.04/28.89 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 29.04/28.89 all A (v1_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)))).
% 29.04/28.89 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))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&boolean_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&upper_bounded_relstr(A)&distributive_relstr(A)&heyting_relstr(A))).
% 29.04/28.89 all A (v2_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)))).
% 29.04/28.89 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))).
% 29.04/28.89 all A (v3_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)&v1_rat_1(B)))).
% 29.04/28.89 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))).
% 29.04/28.89 all A (v4_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)&v1_int_1(B)&v1_rat_1(B)))).
% 29.04/28.89 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))).
% 29.04/28.89 all A (v5_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&natural(B)&v1_xreal_0(B)&v1_int_1(B)&v1_rat_1(B)))).
% 29.04/28.89 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))).
% 29.04/28.89 all A (empty(A)->v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 29.04/28.89 all A (v1_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)))).
% 29.04/28.89 all A (v2_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)))).
% 29.04/28.89 all A (v3_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)))).
% 29.04/28.89 all A (v4_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)))).
% 29.04/28.89 all A (ordinal(A)-> (all B (element(B,A)->epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)))).
% 29.04/28.89 all A (empty(A)->finite(A)).
% 29.04/28.89 all A (preboolean(A)->cup_closed(A)&diff_closed(A)).
% 29.04/28.89 all A (empty(A)->function(A)).
% 29.04/28.89 all A B C (relation_of2(C,A,B)-> (function(C)&v1_partfun1(C,A,B)->function(C)&quasi_total(C,A,B))).
% 29.04/28.89 all A (latt_str(A)-> (-empty_carrier(A)&lattice(A)&complete_latt_str(A)-> -empty_carrier(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A)&lattice(A)&lower_bounded_semilattstr(A)&upper_bounded_semilattstr(A)&bounded_lattstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (with_suprema_relstr(A)-> -empty_carrier(A))).
% 29.04/28.89 all A (latt_str(A)-> (-empty_carrier(A)&lattice(A)-> -empty_carrier(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A))).
% 29.04/28.89 all A (v5_membered(A)->v4_membered(A)).
% 29.04/28.89 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 29.04/28.89 all A (relation(A)&symmetric(A)&transitive(A)->relation(A)&reflexive(A)).
% 29.04/28.89 all A (empty(A)->relation(A)).
% 29.04/28.89 all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 29.04/28.89 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->open_subset(B,A)&closed_subset(B,A))))).
% 29.04/28.89 all A (-empty_carrier(A)&connected_relstr(A)&rel_str(A)-> (all B (element(B,powerset(the_carrier(A)))->directed_subset(B,A)&filtered_subset(B,A)))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&complete_relstr(A)-> -empty_carrier(A)&with_suprema_relstr(A)&with_infima_relstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&upper_bounded_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (empty_carrier(A)->v1_yellow_3(A))).
% 29.04/28.89 all A (v5_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)))).
% 29.04/28.89 all A (empty(A)&ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 29.04/28.89 all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 29.04/28.89 all A (cup_closed(A)&diff_closed(A)->preboolean(A)).
% 29.04/28.89 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 29.04/28.89 all A B C (relation_of2(C,A,B)-> (function(C)&quasi_total(C,A,B)&bijective(C,A,B)->function(C)&one_to_one(C)&quasi_total(C,A,B)&onto(C,A,B))).
% 29.04/28.89 all A (rel_str(A)-> (with_infima_relstr(A)-> -empty_carrier(A))).
% 29.04/28.89 all A (latt_str(A)-> (-empty_carrier(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A)-> -empty_carrier(A)&lattice(A))).
% 29.04/28.89 all A (v4_membered(A)->v3_membered(A)).
% 29.04/28.89 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 29.04/28.89 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->boundary_set(B,A))))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&connected_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)&connected_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A))).
% 29.04/28.89 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))).
% 29.04/28.89 all A (rel_str(A)-> (-v1_yellow_3(A)-> -empty_carrier(A))).
% 29.04/28.89 all A (element(A,omega)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 29.04/28.89 all A B C (relation_of2(C,A,B)-> (function(C)&one_to_one(C)&quasi_total(C,A,B)&onto(C,A,B)->function(C)&quasi_total(C,A,B)&bijective(C,A,B))).
% 29.04/28.89 all A (latt_str(A)-> (-empty_carrier(A)&lower_bounded_semilattstr(A)&upper_bounded_semilattstr(A)-> -empty_carrier(A)&bounded_lattstr(A))).
% 29.04/28.89 all A (v3_membered(A)->v2_membered(A)).
% 29.04/28.89 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 29.04/28.89 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->nowhere_dense(B,A))))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&trivial_carrier(A)&reflexive_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&v2_waybel_3(A))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&complete_relstr(A)-> -empty_carrier(A)&bounded_relstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)-> -empty_carrier(A)& -v1_yellow_3(A))).
% 29.04/28.89 all A B (relation_of2(B,A,A)-> (function(B)&v1_partfun1(B,A,A)&reflexive(B)&quasi_total(B,A,A)->function(B)&one_to_one(B)&quasi_total(B,A,A)&onto(B,A,A)&bijective(B,A,A))).
% 29.04/28.89 all A (latt_str(A)-> (-empty_carrier(A)&bounded_lattstr(A)-> -empty_carrier(A)&lower_bounded_semilattstr(A)&upper_bounded_semilattstr(A))).
% 29.04/28.89 all A (v2_membered(A)->v1_membered(A)).
% 29.04/28.89 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (nowhere_dense(B,A)->boundary_set(B,A))))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&v3_waybel_3(A)-> -empty_carrier(A)&reflexive_relstr(A)&up_complete_relstr(A)&v2_waybel_3(A))).
% 29.04/28.89 all A (rel_str(A)-> (reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&v3_waybel_3(A)&with_suprema_relstr(A)&with_infima_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A)& -v1_yellow_3(A)&v1_waybel_2(A)&v2_waybel_2(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (bounded_relstr(A)->lower_bounded_relstr(A)&upper_bounded_relstr(A))).
% 29.04/28.89 all A B (-empty(B)-> (all C (relation_of2(C,A,B)-> (function(C)&quasi_total(C,A,B)->function(C)&v1_partfun1(C,A,B)&quasi_total(C,A,B))))).
% 29.04/28.89 all A (latt_str(A)-> (-empty_carrier(A)&boolean_lattstr(A)-> -empty_carrier(A)&distributive_lattstr(A)&lower_bounded_semilattstr(A)&upper_bounded_semilattstr(A)&bounded_lattstr(A)&complemented_lattstr(A))).
% 29.04/28.89 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)&boundary_set(B,A)->boundary_set(B,A)&nowhere_dense(B,A))))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&trivial_carrier(A)-> -empty_carrier(A)&reflexive_relstr(A)&connected_relstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&heyting_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&lower_bounded_relstr(A)&up_complete_relstr(A)&v2_waybel_3(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&lower_bounded_relstr(A)&v3_waybel_3(A))).
% 29.04/28.89 all A (rel_str(A)-> (lower_bounded_relstr(A)&upper_bounded_relstr(A)->bounded_relstr(A))).
% 29.04/28.89 all A B (-empty(A)& -empty(B)-> (all C (relation_of2(C,A,B)-> (function(C)&quasi_total(C,A,B)->function(C)& -empty(C)&v1_partfun1(C,A,B)&quasi_total(C,A,B))))).
% 29.04/28.89 all A (latt_str(A)-> (-empty_carrier(A)&distributive_lattstr(A)&bounded_lattstr(A)&complemented_lattstr(A)-> -empty_carrier(A)&boolean_lattstr(A))).
% 29.04/28.89 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (open_subset(B,A)&nowhere_dense(B,A)->empty(B)&open_subset(B,A)&closed_subset(B,A)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)&nowhere_dense(B,A))))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&heyting_relstr(A)-> -empty_carrier(A)&distributive_relstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&complete_relstr(A)&connected_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&connected_relstr(A)&v2_waybel_3(A))).
% 29.04/28.89 all A (latt_str(A)-> (-empty_carrier(A)&lattice(A)&distributive_lattstr(A)-> -empty_carrier(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A)&lattice(A)&modular_lattstr(A))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&heyting_relstr(A)-> -empty_carrier(A)&upper_bounded_relstr(A))).
% 29.04/28.89 all A (transitive_relstr(A)&rel_str(A)-> (all B (subrelstr(B,A)-> (full_subrelstr(B,A)->transitive_relstr(B)&full_subrelstr(B,A))))).
% 29.04/28.89 all A (rel_str(A)-> (-empty_carrier(A)&boolean_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)&distributive_relstr(A)&complemented_relstr(A))).
% 29.04/28.90 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))).
% 29.04/28.90 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&bounded_relstr(A)&distributive_relstr(A)&complemented_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)&distributive_relstr(A)&complemented_relstr(A)&boolean_relstr(A))).
% 29.04/28.90 all A B C (-empty_carrier(A)&one_sorted_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->unordered_pair_as_carrier_subset(A,B,C)=unordered_pair_as_carrier_subset(A,C,B)).
% 29.04/28.90 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 29.04/28.90 all A B (set_union2(A,B)=set_union2(B,A)).
% 29.04/28.90 all A B C (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->join_commut(A,B,C)=join_commut(A,C,B)).
% 29.04/28.90 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 29.04/28.90 all A B C (-empty_carrier(A)&meet_commutative(A)&meet_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->meet_commut(A,B,C)=meet_commut(A,C,B)).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_union2(A,B,C)=subset_union2(A,C,B)).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_intersection2(A,B,C)=subset_intersection2(A,C,B)).
% 29.04/28.90 all A B (ordinal(A)&ordinal(B)->ordinal_subset(A,B)|ordinal_subset(B,A)).
% 29.04/28.90 all A B (relation(B)-> (B=identity_relation(A)<-> (all C D (in(ordered_pair(C,D),B)<->in(C,A)&C=D)))).
% 29.04/28.90 all A B (A=B<->subset(A,B)&subset(B,A)).
% 29.04/28.90 all A (rel_str(A)-> (all B C (element(C,the_carrier(A))-> (ex_inf_of_relstr_set(A,B)-> (C=meet_on_relstr(A,B)<->relstr_element_smaller(A,B,C)& (all D (element(D,the_carrier(A))-> (relstr_element_smaller(A,B,D)->related(A,D,C))))))))).
% 29.04/28.90 all A (one_sorted_str(A)->identity_on_carrier(A)=identity_as_relation_of(the_carrier(A))).
% 29.04/28.90 all A (relation(A)-> (all B C (relation(C)-> (C=relation_dom_restriction(A,B)<-> (all D E (in(ordered_pair(D,E),C)<->in(D,B)&in(ordered_pair(D,E),A))))))).
% 29.04/28.90 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))))))))))).
% 29.04/28.90 all A (rel_str(A)->bottom_of_relstr(A)=join_on_relstr(A,empty_set)).
% 29.04/28.90 all A (relation(A)&function(A)-> (all B C (C=relation_image(A,B)<-> (all D (in(D,C)<-> (exists E (in(E,relation_dom(A))&in(E,B)&D=apply(A,E)))))))).
% 29.04/28.90 all A B (relation(B)-> (all C (relation(C)-> (C=relation_rng_restriction(A,B)<-> (all D E (in(ordered_pair(D,E),C)<->in(E,A)&in(ordered_pair(D,E),B))))))).
% 29.04/28.90 all A (relation(A)-> (antisymmetric(A)<->is_antisymmetric_in(A,relation_field(A)))).
% 29.04/28.90 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C (is_often_in(A,B,C)<-> (all D (element(D,the_carrier(B))-> (exists E (element(E,the_carrier(B))&related(B,D,E)&in(apply_netmap(A,B,E),C)))))))))).
% 29.04/28.90 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (-empty_carrier(C)&transitive_relstr(C)&directed_relstr(C)&net_str(C,A)-> (subnet(C,A,B)<-> (exists D (function(D)&quasi_total(D,the_carrier(C),the_carrier(B))&relation_of2_as_subset(D,the_carrier(C),the_carrier(B))&the_mapping(A,C)=function_of_composition(the_carrier(C),the_carrier(B),the_carrier(A),D,the_mapping(A,B))& (all E (element(E,the_carrier(B))-> (exists F (element(F,the_carrier(C))& (all G (element(G,the_carrier(C))-> (related(C,F,G)->related(B,E,apply_on_set_and_struct(the_carrier(C),B,D,G))))))))))))))))).
% 29.04/28.90 all A (relation(A)&function(A)-> (all B C (C=relation_inverse_image(A,B)<-> (all D (in(D,C)<->in(D,relation_dom(A))&in(apply(A,D),B)))))).
% 29.04/28.90 all A (-empty_carrier(A)&meet_semilatt_str(A)-> (lower_bounded_semilattstr(A)<-> (exists B (element(B,the_carrier(A))& (all C (element(C,the_carrier(A))->meet(A,B,C)=B&meet(A,C,B)=B)))))).
% 29.04/28.90 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (all C (element(C,powerset(the_carrier(A)))-> (C=topstr_closure(A,B)<-> (all D (in(D,the_carrier(A))-> (in(D,C)<-> (all E (element(E,powerset(the_carrier(A)))-> -(open_subset(E,A)&in(D,E)&disjoint(B,E))))))))))))).
% 29.04/28.90 all A (relation(A)-> (all B C (C=relation_image(A,B)<-> (all D (in(D,C)<-> (exists E (in(ordered_pair(E,D),A)&in(E,B)))))))).
% 29.04/28.90 all A (rel_str(A)-> (all B (rel_str(B)-> (subrelstr(B,A)<->subset(the_carrier(B),the_carrier(A))&subset(the_InternalRel(B),the_InternalRel(A)))))).
% 29.04/28.90 all A (one_sorted_str(A)-> (all B (net_str(B,A)-> (all C D (strict_net_str(D,A)&subnetstr(D,A,B)-> (D=preimage_subnetstr(A,B,C)<->full_subrelstr(D,B)&subrelstr(D,B)&the_carrier(D)=function_invverse_img_as_carrier_subset(B,A,the_mapping(A,B),C))))))).
% 29.04/28.90 all A (relation(A)-> (all B C (C=relation_inverse_image(A,B)<-> (all D (in(D,C)<-> (exists E (in(ordered_pair(D,E),A)&in(E,B)))))))).
% 29.04/28.90 all A (relation(A)-> (connected(A)<->is_connected_in(A,relation_field(A)))).
% 29.04/28.90 all A (rel_str(A)-> (all B (subrelstr(B,A)-> (full_subrelstr(B,A)<->the_InternalRel(B)=relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)))))).
% 29.04/28.90 all A (-empty_carrier(A)&latt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (latt_set_smaller(A,B,C)<-> (all D (element(D,the_carrier(A))-> (in(D,C)->below(A,B,D))))))))).
% 29.04/28.90 all A (-empty_carrier(A)&meet_semilatt_str(A)-> (lower_bounded_semilattstr(A)-> (all B (element(B,the_carrier(A))-> (B=bottom_of_semilattstr(A)<-> (all C (element(C,the_carrier(A))->meet(A,B,C)=B&meet(A,C,B)=B))))))).
% 29.04/28.90 all A (relation(A)-> (transitive(A)<->is_transitive_in(A,relation_field(A)))).
% 29.04/28.90 all A (-empty_carrier(A)&latt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (latt_element_smaller(A,B,C)<-> (all D (element(D,the_carrier(A))-> (in(D,C)->below(A,D,B))))))))).
% 29.04/28.90 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (element(C,powerset(the_carrier(A)))-> (C=lim_points_of_net(A,B)<-> (all D (element(D,the_carrier(A))-> (in(D,C)<-> (all E (point_neighbourhood(E,A,D)->is_eventually_in(A,B,E)))))))))))).
% 29.04/28.90 all A (relation(A)&function(A)-> (all B C (apply_binary(A,B,C)=apply(A,ordered_pair(B,C))))).
% 29.04/28.90 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,powerset(the_carrier(A)))-> (point_neighbourhood(C,A,B)<->in(B,interior(A,C)))))))).
% 29.04/28.90 all A B C D (D=unordered_triple(A,B,C)<-> (all E (in(E,D)<-> -(E!=A&E!=B&E!=C)))).
% 29.04/28.90 all A (finite(A)<-> (exists B (relation(B)&function(B)&relation_rng(B)=A&in(relation_dom(B),omega)))).
% 29.04/28.90 all A (function(A)<-> (all B C D (in(ordered_pair(B,C),A)&in(ordered_pair(B,D),A)->C=D))).
% 29.04/28.90 all A B C (relation_of2_as_subset(C,A,B)-> ((B=empty_set->A=empty_set)-> (quasi_total(C,A,B)<->A=relation_dom_as_subset(A,B,C)))& (B=empty_set->A=empty_set| (quasi_total(C,A,B)<->C=empty_set))).
% 29.04/28.90 all A B (strict_latt_str(B)&latt_str(B)-> (B=boole_lattice(A)<->the_carrier(B)=powerset(A)& (all C (element(C,powerset(A))-> (all D (element(D,powerset(A))->apply_binary(the_L_join(B),C,D)=subset_union2(A,C,D)&apply_binary(the_L_meet(B),C,D)=subset_intersection2(A,C,D))))))).
% 29.04/28.90 all A (-empty_carrier(A)&join_semilatt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))->join(A,B,C)=apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C)))))).
% 29.04/28.90 all A ((exists B C (A=ordered_pair(B,C)))-> (all B (B=pair_first(A)<-> (all C D (A=ordered_pair(C,D)->B=C))))).
% 29.04/28.90 all A (succ(A)=set_union2(A,singleton(A))).
% 29.04/28.90 all A (top_str(A)-> (topological_space(A)<->in(the_carrier(A),the_topology(A))& (all B (element(B,powerset(powerset(the_carrier(A))))-> (subset(B,the_topology(A))->in(union_of_subsets(the_carrier(A),B),the_topology(A)))))& (all B (element(B,powerset(the_carrier(A)))-> (all C (element(C,powerset(the_carrier(A)))-> (in(B,the_topology(A))&in(C,the_topology(A))->in(subset_intersection2(the_carrier(A),B,C),the_topology(A))))))))).
% 29.04/28.90 all A (relation(A)<-> (all B (-(in(B,A)& (all C D (B!=ordered_pair(C,D))))))).
% 29.04/28.90 all A (relation(A)-> (all B (is_reflexive_in(A,B)<-> (all C (in(C,B)->in(ordered_pair(C,C),A)))))).
% 29.04/28.90 all A B C (relation_of2(C,A,B)<->subset(C,cartesian_product2(A,B))).
% 29.04/28.90 all A B ((A!=empty_set-> (B=set_meet(A)<-> (all C (in(C,B)<-> (all D (in(D,A)->in(C,D)))))))& (A=empty_set-> (B=set_meet(A)<->B=empty_set))).
% 29.04/28.90 all A (one_sorted_str(A)-> (empty_carrier(A)<->empty(the_carrier(A)))).
% 29.04/28.90 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 29.04/28.90 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))->interior(A,B)=subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B)))))).
% 29.04/28.90 all A (top_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> (open_subsets(B,A)<-> (all C (element(C,powerset(the_carrier(A)))-> (in(C,B)->open_subset(C,A)))))))).
% 29.04/28.90 all A (rel_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (directed_subset(B,A)<-> (all C (element(C,the_carrier(A))-> (all D (element(D,the_carrier(A))-> -(in(C,B)&in(D,B)& (all E (element(E,the_carrier(A))-> -(in(E,B)&related(A,C,E)&related(A,D,E))))))))))))).
% 29.04/28.90 all A (relation(A)-> (all B C (C=fiber(A,B)<-> (all D (in(D,C)<->D!=B&in(ordered_pair(D,B),A)))))).
% 29.04/28.90 all A B (relation(B)-> (B=inclusion_relation(A)<->relation_field(B)=A& (all C D (in(C,A)&in(D,A)-> (in(ordered_pair(C,D),B)<->subset(C,D)))))).
% 29.04/28.90 all A (A=empty_set<-> (all B (-in(B,A)))).
% 29.04/28.90 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,the_carrier(A))->neighborhood_system(A,B)=a_2_0_yellow19(A,B)))).
% 29.04/28.90 all A (incl_POSet(A)=rel_str_of(A,inclusion_order(A))).
% 29.04/28.90 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 29.04/28.90 all A (rel_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (upper_relstr_subset(B,A)<-> (all C (element(C,the_carrier(A))-> (all D (element(D,the_carrier(A))-> (in(C,B)&related(A,C,D)->in(D,B)))))))))).
% 29.04/28.90 all A (-empty_carrier(A)&latt_str(A)-> (-empty_carrier(A)&lattice(A)&complete_latt_str(A)&latt_str(A)-> (all B C (element(C,the_carrier(A))-> (C=join_of_latt_set(A,B)<->latt_element_smaller(A,C,B)& (all D (element(D,the_carrier(A))-> (latt_element_smaller(A,D,B)->below(A,C,D))))))))).
% 29.04/28.90 all A (-empty_carrier(A)&latt_str(A)-> (all B (meet_of_latt_set(A,B)=join_of_latt_set(A,a_2_2_lattice3(A,B))))).
% 29.04/28.90 all A (centered(A)<->A!=empty_set& (all B (-(B!=empty_set&subset(B,A)&finite(B)&set_meet(B)=empty_set)))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)->poset_of_lattice(A)=rel_str_of(the_carrier(A),k2_lattice3(A))).
% 29.04/28.90 all A (-empty_carrier(A)&meet_semilatt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))->meet(A,B,C)=apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C)))))).
% 29.04/28.90 all A ((exists B C (A=ordered_pair(B,C)))-> (all B (B=pair_second(A)<-> (all C D (A=ordered_pair(C,D)->B=D))))).
% 29.04/28.90 all A (epsilon_transitive(A)<-> (all B (in(B,A)->subset(B,A)))).
% 29.04/28.90 all A (one_sorted_str(A)->empty_carrier_subset(A)=empty_set).
% 29.04/28.90 all A (relation(A)-> (all B (relation(B)-> (A=B<-> (all C D (in(ordered_pair(C,D),A)<->in(ordered_pair(C,D),B))))))).
% 29.04/28.90 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 29.04/28.90 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 29.04/28.90 all A B (element(B,A)-> (proper_element(B,A)<->B!=union(A))).
% 29.04/28.90 all A (top_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> (closed_subsets(B,A)<-> (all C (element(C,powerset(the_carrier(A)))-> (in(C,B)->closed_subset(C,A)))))))).
% 29.04/28.90 all A (relation(A)-> (well_founded_relation(A)<-> (all B (-(subset(B,relation_field(A))&B!=empty_set& (all C (-(in(C,B)&disjoint(fiber(A,C),B))))))))).
% 29.04/28.90 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 29.04/28.90 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C (element(C,powerset(the_carrier(A)))-> (netstr_induced_subset(C,A,B)<-> (exists D (element(D,the_carrier(B))&C=relation_rng_as_subset(the_carrier(netstr_restr_to_element(A,B,D)),the_carrier(A),the_mapping(A,netstr_restr_to_element(A,B,D))))))))))).
% 29.04/28.90 all A (rel_str(A)-> (transitive_relstr(A)<-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (all D (element(D,the_carrier(A))-> (related(A,B,C)&related(A,C,D)->related(A,B,D)))))))))).
% 29.04/28.90 all A (boole_POSet(A)=poset_of_lattice(boole_lattice(A))).
% 29.04/28.90 all A B C (C=cartesian_product2(A,B)<-> (all D (in(D,C)<-> (exists E F (in(E,A)&in(F,B)&D=ordered_pair(E,F)))))).
% 29.04/28.90 all A (top_str(A)-> (compact_top_space(A)<-> (all B (element(B,powerset(powerset(the_carrier(A))))-> -(is_a_cover_of_carrier(A,B)&open_subsets(B,A)& (all C (element(C,powerset(powerset(the_carrier(A))))-> -(subset(C,B)&is_a_cover_of_carrier(A,C)&finite(C))))))))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)-> (all B (element(B,the_carrier(A))->cast_to_el_of_LattPOSet(A,B)=B))).
% 29.04/28.90 all A (-empty_carrier(A)&join_semilatt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (below(A,B,C)<->join(A,B,C)=C)))))).
% 29.04/28.90 all A (epsilon_connected(A)<-> (all B C (-(in(B,A)&in(C,A)& -in(B,C)&B!=C& -in(C,B))))).
% 29.04/28.90 all A (one_sorted_str(A)->cast_as_carrier_subset(A)=the_carrier(A)).
% 29.04/28.90 all A (relation(A)-> (all B (relation(B)-> (subset(A,B)<-> (all C D (in(ordered_pair(C,D),A)->in(ordered_pair(C,D),B))))))).
% 29.04/28.90 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 29.04/28.90 all A (relation(A)-> (all B (is_well_founded_in(A,B)<-> (all C (-(subset(C,B)&C!=empty_set& (all D (-(in(D,C)&disjoint(fiber(A,D),C)))))))))).
% 29.04/28.90 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 29.04/28.90 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)))).
% 29.04/28.90 all A (relation(A)&function(A)-> (all B C ((in(B,relation_dom(A))-> (C=apply(A,B)<->in(ordered_pair(B,C),A)))& (-in(B,relation_dom(A))-> (C=apply(A,B)<->C=empty_set))))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)-> (all B (element(B,the_carrier(poset_of_lattice(A)))->cast_to_el_of_lattice(A,B)=B))).
% 29.04/28.90 all A (ordinal(A)<->epsilon_transitive(A)&epsilon_connected(A)).
% 29.04/28.90 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 29.04/28.90 all A (relation(A)-> (all B (is_antisymmetric_in(A,B)<-> (all C D (in(C,B)&in(D,B)&in(ordered_pair(C,D),A)&in(ordered_pair(D,C),A)->C=D))))).
% 29.04/28.90 all A (cast_to_subset(A)=A).
% 29.04/28.90 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 29.04/28.90 all A (relation(A)-> (well_ordering(A)<->reflexive(A)&transitive(A)&antisymmetric(A)&connected(A)&well_founded_relation(A))).
% 29.04/28.90 all A B (e_quipotent(A,B)<-> (exists C (relation(C)&function(C)&one_to_one(C)&relation_dom(C)=A&relation_rng(C)=B))).
% 29.04/28.90 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 29.04/28.90 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))))))))))).
% 29.04/28.90 all A (rel_str(A)-> (lower_bounded_relstr(A)<-> (exists B (element(B,the_carrier(A))&relstr_element_smaller(A,the_carrier(A),B))))).
% 29.04/28.90 all A (relation(A)&function(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D (in(D,relation_dom(A))&C=apply(A,D)))))))).
% 29.04/28.90 all A (rel_str(A)-> (transitive_relstr(A)<->is_transitive_in(the_InternalRel(A),the_carrier(A)))).
% 29.04/28.90 all A (A=omega<->in(empty_set,A)&being_limit_ordinal(A)&ordinal(A)& (all B (ordinal(B)-> (in(empty_set,B)&being_limit_ordinal(B)->subset(A,B))))).
% 29.04/28.90 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (open_subset(B,A)<->in(B,the_topology(A)))))).
% 29.04/28.90 all A (relation(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(D,C),A))))))).
% 29.04/28.90 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 29.04/28.90 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 29.04/28.90 all A (topological_space(A)&top_str(A)-> (all B C (is_a_convergence_point_of_set(A,B,C)<-> (all D (element(D,powerset(the_carrier(A)))-> (open_subset(D,A)&in(C,D)->in(D,B))))))).
% 29.04/28.90 all A (relation(A)-> (all B (well_orders(A,B)<->is_reflexive_in(A,B)&is_transitive_in(A,B)&is_antisymmetric_in(A,B)&is_connected_in(A,B)&is_well_founded_in(A,B)))).
% 29.04/28.90 all A (-empty_carrier(A)&rel_str(A)-> (directed_relstr(A)<-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (exists D (element(D,the_carrier(A))&related(A,B,D)&related(A,C,D))))))))).
% 29.04/28.90 all A (rel_str(A)-> (antisymmetric_relstr(A)<->is_antisymmetric_in(the_InternalRel(A),the_carrier(A)))).
% 29.04/28.90 all A (being_limit_ordinal(A)<->A=union(A)).
% 29.04/28.90 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)<->open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A))))).
% 29.04/28.90 all A (relation(A)->relation_field(A)=set_union2(relation_dom(A),relation_rng(A))).
% 29.04/28.90 all A (relation(A)-> (all B (is_connected_in(A,B)<-> (all C D (-(in(C,B)&in(D,B)&C!=D& -in(ordered_pair(C,D),A)& -in(ordered_pair(D,C),A))))))).
% 29.04/28.90 all A (relation(A)-> (all B (relation_restriction(A,B)=set_intersection2(A,cartesian_product2(B,B))))).
% 29.04/28.90 all A (relation(A)-> (all B (relation(B)-> (B=relation_inverse(A)<-> (all C D (in(ordered_pair(C,D),B)<->in(ordered_pair(D,C),A))))))).
% 29.04/28.90 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))-> (all D (strict_net_str(D,A)&net_str(D,A)-> (D=netstr_restr_to_element(A,B,C)<-> (all E (in(E,the_carrier(D))<-> (exists F (element(F,the_carrier(B))&F=E&related(B,C,F)))))&the_InternalRel(D)=relation_restriction_as_relation_of(the_InternalRel(B),the_carrier(D))&the_mapping(A,D)=partfun_dom_restriction(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(D)))))))))).
% 29.04/28.90 all A (relation(A)-> (all B (relation(B)-> (all C (relation(C)&function(C)-> (relation_isomorphism(A,B,C)<->relation_dom(C)=relation_field(A)&relation_rng(C)=relation_field(B)&one_to_one(C)& (all D E (in(ordered_pair(D,E),A)<->in(D,relation_field(A))&in(E,relation_field(A))&in(ordered_pair(apply(C,D),apply(C,E)),B))))))))).
% 29.04/28.90 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 29.04/28.90 all A (rel_str(A)-> (all B (ex_sup_of_relstr_set(A,B)<-> (exists C (element(C,the_carrier(A))&relstr_set_smaller(A,B,C)& (all D (element(D,the_carrier(A))-> (relstr_set_smaller(A,B,D)->related(A,C,D))))& (all D (element(D,the_carrier(A))-> (relstr_set_smaller(A,B,D)& (all E (element(E,the_carrier(A))-> (relstr_set_smaller(A,B,E)->related(A,D,E))))->D=C)))))))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)->relation_of_lattice(A)=a_1_0_filter_1(A)).
% 29.04/28.90 all A (relation(A)&function(A)-> (one_to_one(A)<-> (all B C (in(B,relation_dom(A))&in(C,relation_dom(A))&apply(A,B)=apply(A,C)->B=C)))).
% 29.04/28.90 all A (rel_str(A)-> (all B C (element(C,the_carrier(A))-> (relstr_element_smaller(A,B,C)<-> (all D (element(D,the_carrier(A))-> (in(D,B)->related(A,C,D)))))))).
% 29.04/28.90 all A (-empty_carrier(A)&latt_str(A)-> (meet_absorbing(A)<-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))->join(A,meet(A,B,C),C)=C)))))).
% 29.04/28.90 all A (one_sorted_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> (is_a_cover_of_carrier(A,B)<->cast_as_carrier_subset(A)=union_of_subsets(the_carrier(A),B))))).
% 29.04/28.90 all A (relation(A)-> (all B (relation(B)-> (all C (relation(C)-> (C=relation_composition(A,B)<-> (all D E (in(ordered_pair(D,E),C)<-> (exists F (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B))))))))))).
% 29.04/28.90 all A (relation(A)-> (all B (is_transitive_in(A,B)<-> (all C D E (in(C,B)&in(D,B)&in(E,B)&in(ordered_pair(C,D),A)&in(ordered_pair(D,E),A)->in(ordered_pair(C,E),A)))))).
% 29.04/28.90 all A B (element(B,powerset(powerset(A)))-> (all C (element(C,powerset(powerset(A)))-> (C=complements_of_subsets(A,B)<-> (all D (element(D,powerset(A))-> (in(D,C)<->in(subset_complement(A,D),B)))))))).
% 29.04/28.90 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)))))).
% 29.04/28.90 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 29.04/28.90 all A (rel_str(A)-> (all B (ex_inf_of_relstr_set(A,B)<-> (exists C (element(C,the_carrier(A))&relstr_element_smaller(A,B,C)& (all D (element(D,the_carrier(A))-> (relstr_element_smaller(A,B,D)->related(A,D,C))))& (all D (element(D,the_carrier(A))-> (relstr_element_smaller(A,B,D)& (all E (element(E,the_carrier(A))-> (relstr_element_smaller(A,B,E)->related(A,E,D))))->D=C)))))))).
% 29.04/28.90 all A (one_sorted_str(A)-> (all B (net_str(B,A)-> (all C (net_str(C,A)-> (subnetstr(C,A,B)<->subrelstr(C,B)&the_mapping(A,C)=relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)))))))).
% 29.04/28.90 all A (relation(A)&function(A)-> (one_to_one(A)->function_inverse(A)=relation_inverse(A))).
% 29.04/28.90 all A (rel_str(A)-> (all B C (element(C,the_carrier(A))-> (relstr_set_smaller(A,B,C)<-> (all D (element(D,the_carrier(A))-> (in(D,B)->related(A,D,C)))))))).
% 29.04/28.90 all A (rel_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (related(A,B,C)<->in(ordered_pair(B,C),the_InternalRel(A)))))))).
% 29.04/28.90 all A (relation(A)-> (reflexive(A)<->is_reflexive_in(A,relation_field(A)))).
% 29.04/28.90 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C (element(C,the_carrier(A))-> (is_a_cluster_point_of_netstr(A,B,C)<-> (all D (point_neighbourhood(D,A,C)->is_often_in(A,B,D))))))))).
% 29.04/28.90 all A (rel_str(A)-> (all B C (element(C,the_carrier(A))-> (ex_sup_of_relstr_set(A,B)-> (C=join_on_relstr(A,B)<->relstr_set_smaller(A,B,C)& (all D (element(D,the_carrier(A))-> (relstr_set_smaller(A,B,D)->related(A,C,D))))))))).
% 29.04/28.90 all A (one_sorted_str(A)-> (all B (net_str(B,A)-> (all C (subnetstr(C,A,B)-> (full_subnetstr(C,A,B)<->full_subrelstr(C,B)&subrelstr(C,B))))))).
% 29.04/28.90 all A B (relation_of2(B,A,A)->strict_rel_str(rel_str_of(A,B))&rel_str(rel_str_of(A,B))).
% 29.04/28.90 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)).
% 29.04/28.90 all A B C (function(B)&quasi_total(B,cartesian_product2(A,A),A)&relation_of2(B,cartesian_product2(A,A),A)&function(C)&quasi_total(C,cartesian_product2(A,A),A)&relation_of2(C,cartesian_product2(A,A),A)->strict_latt_str(latt_str_of(A,B,C))&latt_str(latt_str_of(A,B,C))).
% 29.04/28.90 all A B C D (-empty_carrier(A)&lattice(A)&latt_str(A)& -empty_carrier(B)&lattice(B)&latt_str(B)&element(C,the_carrier(A))&element(D,the_carrier(B))->element(k10_filter_1(A,B,C,D),the_carrier(k8_filter_1(A,B)))).
% 29.04/28.90 $T.
% 29.04/28.90 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)->element(lim_points_of_net(A,B),powerset(the_carrier(A)))).
% 29.04/28.90 all A B (-empty_carrier(A)&latt_str(A)->element(join_of_latt_set(A,B),the_carrier(A))).
% 29.04/28.90 all A B (-empty_carrier(A)&latt_str(A)->element(meet_of_latt_set(A,B),the_carrier(A))).
% 29.04/28.90 $T.
% 29.04/28.90 all A B C D (-empty(A)& -empty(B)&element(C,A)&element(D,B)->element(ordered_pair_as_product_element(A,B,C,D),cartesian_product2(A,B))).
% 29.04/28.90 $T.
% 29.04/28.90 $T.
% 29.04/28.90 all A (strict_latt_str(boole_lattice(A))&latt_str(boole_lattice(A))).
% 29.04/28.90 all A B C (-empty_carrier(A)&join_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(join(A,B,C),the_carrier(A))).
% 29.04/28.90 $T.
% 29.04/28.90 $T.
% 29.04/28.90 all A element(k1_pcomps_1(A),powerset(powerset(A))).
% 29.04/28.90 all A (one_sorted_str(A)->element(empty_carrier_subset(A),powerset(the_carrier(A)))).
% 29.04/28.90 $T.
% 29.04/28.90 $T.
% 29.04/28.90 $T.
% 29.04/28.90 all A B (relation(A)->relation_of2_as_subset(relation_restriction_as_relation_of(A,B),B,B)).
% 29.04/28.90 all A B (top_str(A)&element(B,powerset(the_carrier(A)))->element(interior(A,B),powerset(the_carrier(A)))).
% 29.04/28.90 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))).
% 29.04/28.90 $T.
% 29.04/28.90 all A relation(inclusion_relation(A)).
% 29.04/28.90 $T.
% 29.04/28.90 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))->element(neighborhood_system(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))).
% 29.04/28.90 all A B (rel_str(A)->element(join_on_relstr(A,B),the_carrier(A))).
% 29.04/28.90 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)).
% 29.04/28.90 $T.
% 29.04/28.90 all A B C D E F (-empty(A)& -empty(B)&function(D)&quasi_total(D,cartesian_product2(A,B),C)&relation_of2(D,cartesian_product2(A,B),C)&element(E,A)&element(F,B)->element(apply_binary_as_element(A,B,C,D,E,F),C)).
% 29.04/28.90 all A (relation(A)&function(A)->relation(function_inverse(A))&function(function_inverse(A))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)->reflexive(k2_lattice3(A))&antisymmetric(k2_lattice3(A))&transitive(k2_lattice3(A))&v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A))&relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A))).
% 29.04/28.90 all A B C (-empty_carrier(A)&meet_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(meet(A,B,C),the_carrier(A))).
% 29.04/28.90 $T.
% 29.04/28.90 all A B C D (function(C)&relation_of2(C,A,B)->function(partfun_dom_restriction(A,B,C,D))&relation_of2_as_subset(partfun_dom_restriction(A,B,C,D),A,B)).
% 29.04/28.90 all A (one_sorted_str(A)->element(cast_as_carrier_subset(A),powerset(the_carrier(A)))).
% 29.04/28.90 $T.
% 29.04/28.90 all A B C (-empty_carrier(A)&one_sorted_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(unordered_pair_as_carrier_subset(A,B,C),powerset(the_carrier(A)))).
% 29.04/28.90 all A element(cast_to_subset(A),powerset(A)).
% 29.04/28.90 $T.
% 29.04/28.90 all A B (relation(A)->relation(relation_restriction(A,B))).
% 29.04/28.90 $T.
% 29.04/28.90 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)))))).
% 29.04/28.90 all A B (rel_str(A)->element(meet_on_relstr(A,B),the_carrier(A))).
% 29.04/28.90 all A (strict_rel_str(incl_POSet(A))&rel_str(incl_POSet(A))).
% 29.04/28.90 $T.
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)->strict_rel_str(poset_of_lattice(A))&reflexive_relstr(poset_of_lattice(A))&transitive_relstr(poset_of_lattice(A))&antisymmetric_relstr(poset_of_lattice(A))&rel_str(poset_of_lattice(A))).
% 29.04/28.90 all A B C (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(join_commut(A,B,C),the_carrier(A))).
% 29.04/28.90 $T.
% 29.04/28.90 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 29.04/28.90 $T.
% 29.04/28.90 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))).
% 29.04/28.90 $T.
% 29.04/28.90 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)).
% 29.04/28.90 all A (rel_str(A)->element(bottom_of_relstr(A),the_carrier(A))).
% 29.04/28.90 all A (strict_rel_str(boole_POSet(A))&rel_str(boole_POSet(A))).
% 29.04/28.90 all A B C D (-empty(A)& -empty_carrier(B)&rel_str(B)&function(C)&quasi_total(C,A,the_carrier(B))&relation_of2(C,A,the_carrier(B))&element(D,A)->element(apply_on_set_and_struct(A,B,C,D),the_carrier(B))).
% 29.04/28.90 all A B (-empty_carrier(A)&lattice(A)&latt_str(A)&element(B,the_carrier(A))->element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A)))).
% 29.04/28.90 all A B C (-empty_carrier(A)&meet_commutative(A)&meet_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(meet_commut(A,B,C),the_carrier(A))).
% 29.04/28.90 all A (relation(A)->relation(relation_inverse(A))).
% 29.04/28.90 all A B C (relation_of2(C,A,B)->element(relation_dom_as_subset(A,B,C),powerset(A))).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_union2(A,B,C),powerset(A))).
% 29.04/28.90 $T.
% 29.04/28.90 $T.
% 29.04/28.90 all A B (-empty_carrier(A)&lattice(A)&latt_str(A)&element(B,the_carrier(poset_of_lattice(A)))->element(cast_to_el_of_lattice(A,B),the_carrier(A))).
% 29.04/28.90 all A (-empty_carrier(A)&meet_semilatt_str(A)->element(bottom_of_semilattstr(A),the_carrier(A))).
% 29.04/28.90 $T.
% 29.04/28.90 all A B C D (one_sorted_str(A)&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(function_invverse_img_as_carrier_subset(A,B,C,D),powerset(the_carrier(A)))).
% 29.04/28.90 all A B (relation(A)&relation(B)->relation(relation_composition(A,B))).
% 29.04/28.90 all A B C (relation_of2(C,A,B)->element(relation_rng_as_subset(A,B,C),powerset(B))).
% 29.04/28.90 all A B (element(B,powerset(powerset(A)))->element(union_of_subsets(A,B),powerset(A))).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_intersection2(A,B,C),powerset(A))).
% 29.04/28.90 all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&net_str(B,A)&element(C,the_carrier(B))->strict_net_str(netstr_restr_to_element(A,B,C),A)&net_str(netstr_restr_to_element(A,B,C),A)).
% 29.04/28.90 all A (v1_partfun1(identity_as_relation_of(A),A,A)&relation_of2_as_subset(identity_as_relation_of(A),A,A)).
% 29.04/28.90 all A B (top_str(A)&element(B,powerset(the_carrier(A)))->element(topstr_closure(A,B),powerset(the_carrier(A)))).
% 29.04/28.90 all A relation(identity_relation(A)).
% 29.04/28.90 all A B (element(B,powerset(powerset(A)))->element(meet_of_subsets(A,B),powerset(A))).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_difference(A,B,C),powerset(A))).
% 29.04/28.90 all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)&element(C,the_carrier(B))->strict_net_str(subnetstr_of_element(A,B,C),A)&subnet(subnetstr_of_element(A,B,C),A,B)).
% 29.04/28.90 all A B C (one_sorted_str(A)&net_str(B,A)->strict_net_str(preimage_subnetstr(A,B,C),A)&subnetstr(preimage_subnetstr(A,B,C),A,B)).
% 29.04/28.90 all A B C D E (-empty(B)&function(D)&quasi_total(D,A,B)&relation_of2(D,A,B)&function(E)&quasi_total(E,B,C)&relation_of2(E,B,C)->function(function_of_composition(A,B,C,D,E))&quasi_total(function_of_composition(A,B,C,D,E),A,C)&relation_of2_as_subset(function_of_composition(A,B,C,D,E),A,C)).
% 29.04/28.90 all A (one_sorted_str(A)->function(identity_on_carrier(A))&quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A))&relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A))).
% 29.04/28.90 all A B (relation(A)->relation(relation_dom_restriction(A,B))).
% 29.04/28.90 all A B (element(B,powerset(powerset(A)))->element(complements_of_subsets(A,B),powerset(powerset(A)))).
% 29.04/28.90 all A B C D (-empty(A)& -empty_carrier(B)&one_sorted_str(B)&function(C)&quasi_total(C,A,the_carrier(B))&relation_of2(C,A,the_carrier(B))&element(D,A)->element(apply_on_set_and_struct2(A,B,C,D),the_carrier(B))).
% 29.04/28.90 all A B (-empty_carrier(A)&latt_str(A)& -empty_carrier(B)&latt_str(B)->strict_latt_str(k8_filter_1(A,B))&latt_str(k8_filter_1(A,B))).
% 29.04/28.90 all A B C D (-empty(A)&function(C)&quasi_total(C,A,B)&relation_of2(C,A,B)&element(D,A)->element(apply_as_element(A,B,C,D),B)).
% 29.04/28.90 all A B (relation(B)->relation(relation_rng_restriction(A,B))).
% 29.04/28.90 all A B C D (relation_of2(C,A,B)->relation_of2_as_subset(relation_dom_restr_as_relation_of(A,B,C,D),A,B)).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)->relation(relation_of_lattice(A))).
% 29.04/28.90 $T.
% 29.04/28.90 all A (meet_semilatt_str(A)->one_sorted_str(A)).
% 29.04/28.90 all A (rel_str(A)->one_sorted_str(A)).
% 29.04/28.90 all A (top_str(A)->one_sorted_str(A)).
% 29.04/28.90 $T.
% 29.04/28.90 all A (one_sorted_str(A)-> (all B (net_str(B,A)->rel_str(B)))).
% 29.04/28.90 all A (join_semilatt_str(A)->one_sorted_str(A)).
% 29.04/28.90 all A (latt_str(A)->meet_semilatt_str(A)&join_semilatt_str(A)).
% 29.04/28.90 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))-> (all C (point_neighbourhood(C,A,B)->element(C,powerset(the_carrier(A)))))).
% 29.04/28.90 $T.
% 29.04/28.90 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))))).
% 29.04/28.90 $T.
% 29.04/28.90 all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&net_str(B,A)-> (all C (netstr_induced_subset(C,A,B)->element(C,powerset(the_carrier(A)))))).
% 29.04/28.90 all A (rel_str(A)-> (all B (subrelstr(B,A)->rel_str(B)))).
% 29.04/28.90 all A B (one_sorted_str(A)&net_str(B,A)-> (all C (subnetstr(C,A,B)->net_str(C,A)))).
% 29.04/28.90 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 29.04/28.90 all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (subnet(C,A,B)-> -empty_carrier(C)&transitive_relstr(C)&directed_relstr(C)&net_str(C,A)))).
% 29.04/28.90 all A (meet_semilatt_str(A)->function(the_L_meet(A))&quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))&relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))).
% 29.04/28.90 all A (rel_str(A)->relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))).
% 29.04/28.90 all A (top_str(A)->element(the_topology(A),powerset(powerset(the_carrier(A))))).
% 29.04/28.90 $T.
% 29.04/28.90 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))).
% 29.04/28.90 all A (join_semilatt_str(A)->function(the_L_join(A))&quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))&relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))).
% 29.04/28.90 exists A meet_semilatt_str(A).
% 29.04/28.90 exists A rel_str(A).
% 29.04/28.90 exists A top_str(A).
% 29.04/28.90 exists A one_sorted_str(A).
% 29.04/28.90 all A (one_sorted_str(A)-> (exists B net_str(B,A))).
% 29.04/28.90 exists A join_semilatt_str(A).
% 29.04/28.90 exists A latt_str(A).
% 29.04/28.90 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))-> (exists C point_neighbourhood(C,A,B))).
% 29.04/28.90 all A B exists C relation_of2(C,A,B).
% 29.04/28.90 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))).
% 29.04/28.90 all A exists B element(B,A).
% 29.04/28.90 all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&net_str(B,A)-> (exists C netstr_induced_subset(C,A,B))).
% 29.04/28.90 all A (rel_str(A)-> (exists B subrelstr(B,A))).
% 29.04/28.90 all A B (one_sorted_str(A)&net_str(B,A)-> (exists C subnetstr(C,A,B))).
% 29.04/28.90 all A B exists C relation_of2_as_subset(C,A,B).
% 29.04/28.90 all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (exists C subnet(C,A,B))).
% 29.04/28.90 all A B (finite(B)->finite(set_intersection2(A,B))).
% 29.04/28.90 all A B (empty(A)&relation(B)->empty(relation_composition(B,A))&relation(relation_composition(B,A))).
% 29.04/28.90 all A B (top_str(A)&boundary_set(B,A)&element(B,powerset(the_carrier(A)))->empty(interior(A,B))&v1_membered(interior(A,B))&v2_membered(interior(A,B))&v3_membered(interior(A,B))&v4_membered(interior(A,B))&v5_membered(interior(A,B))&boundary_set(interior(A,B),A)).
% 29.04/28.90 all A B (finite(A)->finite(set_intersection2(A,B))).
% 29.04/28.90 all A (empty(A)->empty(relation_inverse(A))&relation(relation_inverse(A))).
% 29.04/28.90 all A B (finite(A)->finite(set_difference(A,B))).
% 29.04/28.90 empty(empty_set).
% 29.04/28.90 relation(empty_set).
% 29.04/28.90 relation_empty_yielding(empty_set).
% 29.04/28.90 all A B (relation(A)&function(A)&finite(B)->finite(relation_image(A,B))).
% 29.04/28.90 all A B (relation(A)&relation_empty_yielding(A)->relation(relation_dom_restriction(A,B))&relation_empty_yielding(relation_dom_restriction(A,B))).
% 29.04/28.90 all A (-v1_yellow_3(A)&rel_str(A)-> -empty(the_InternalRel(A))&relation(the_InternalRel(A))).
% 29.04/28.90 all A B (finite(A)&finite(B)->finite(cartesian_product2(A,B))).
% 29.04/28.90 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)).
% 29.04/28.90 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))).
% 29.04/28.90 all A B C (one_sorted_str(A)&transitive_relstr(B)&net_str(B,A)->transitive_relstr(preimage_subnetstr(A,B,C))&strict_net_str(preimage_subnetstr(A,B,C),A)&full_subnetstr(preimage_subnetstr(A,B,C),A,B)).
% 29.04/28.90 all A (-empty(singleton(A))&finite(singleton(A))).
% 29.04/28.90 all A (-empty(powerset(A))&cup_closed(powerset(A))&diff_closed(powerset(A))&preboolean(powerset(A))).
% 29.04/28.90 all A B (relation(A)&function(A)&relation(B)&function(B)->relation(relation_composition(A,B))&function(relation_composition(A,B))).
% 29.04/28.90 all A (-empty_carrier(boole_lattice(A))&strict_latt_str(boole_lattice(A))&join_commutative(boole_lattice(A))&join_associative(boole_lattice(A))&meet_commutative(boole_lattice(A))&meet_associative(boole_lattice(A))&meet_absorbing(boole_lattice(A))&join_absorbing(boole_lattice(A))&lattice(boole_lattice(A))&distributive_lattstr(boole_lattice(A))&modular_lattstr(boole_lattice(A))&lower_bounded_semilattstr(boole_lattice(A))&upper_bounded_semilattstr(boole_lattice(A))&bounded_lattstr(boole_lattice(A))&complemented_lattstr(boole_lattice(A))&boolean_lattstr(boole_lattice(A))&complete_latt_str(boole_lattice(A))).
% 29.04/28.90 all A (-empty_carrier(boole_lattice(A))&strict_latt_str(boole_lattice(A))).
% 29.04/28.90 all A B (-empty(A)&relation_of2(B,A,A)-> -empty_carrier(rel_str_of(A,B))&strict_rel_str(rel_str_of(A,B))).
% 29.04/28.90 all A (-empty(succ(A))).
% 29.04/28.90 epsilon_transitive(omega).
% 29.04/28.90 epsilon_connected(omega).
% 29.04/28.90 ordinal(omega).
% 29.04/28.90 -empty(omega).
% 29.04/28.90 all A (one_sorted_str(A)->empty(empty_carrier_subset(A))&v1_membered(empty_carrier_subset(A))&v2_membered(empty_carrier_subset(A))&v3_membered(empty_carrier_subset(A))&v4_membered(empty_carrier_subset(A))&v5_membered(empty_carrier_subset(A))).
% 29.04/28.90 all A B (relation(A)&relation(B)->relation(set_intersection2(A,B))).
% 29.04/28.90 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 29.04/28.90 all A (-empty(powerset(A))).
% 29.04/28.90 all A (topological_space(A)&top_str(A)->empty(empty_carrier_subset(A))&closed_subset(empty_carrier_subset(A),A)&v1_membered(empty_carrier_subset(A))&v2_membered(empty_carrier_subset(A))&v3_membered(empty_carrier_subset(A))&v4_membered(empty_carrier_subset(A))&v5_membered(empty_carrier_subset(A))).
% 29.04/28.90 all A (rel_str(A)->empty(empty_carrier_subset(A))&strongly_connected_rel_subset(empty_carrier_subset(A),A)&finite(empty_carrier_subset(A))&v1_membered(empty_carrier_subset(A))&v2_membered(empty_carrier_subset(A))&v3_membered(empty_carrier_subset(A))&v4_membered(empty_carrier_subset(A))&v5_membered(empty_carrier_subset(A))&directed_subset(empty_carrier_subset(A),A)&filtered_subset(empty_carrier_subset(A),A)).
% 29.04/28.90 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))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_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))&distributive_relstr(boole_POSet(A))).
% 29.04/28.90 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))).
% 29.04/28.90 empty(empty_set).
% 29.04/28.90 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))-> -empty(neighborhood_system(A,B))&filtered_subset(neighborhood_system(A,B),boole_POSet(cast_as_carrier_subset(A)))&upper_relstr_subset(neighborhood_system(A,B),boole_POSet(cast_as_carrier_subset(A)))&proper_element(neighborhood_system(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))).
% 29.04/28.90 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))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)-> -empty_carrier(poset_of_lattice(A))&strict_rel_str(poset_of_lattice(A))&reflexive_relstr(poset_of_lattice(A))&transitive_relstr(poset_of_lattice(A))&antisymmetric_relstr(poset_of_lattice(A))&with_suprema_relstr(poset_of_lattice(A))&with_infima_relstr(poset_of_lattice(A))).
% 29.04/28.90 all A B (-empty(ordered_pair(A,B))).
% 29.04/28.90 all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&directed_relstr(B)&net_str(B,A)&element(C,the_carrier(B))-> -empty_carrier(netstr_restr_to_element(A,B,C))&strict_net_str(netstr_restr_to_element(A,B,C),A)).
% 29.04/28.90 all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)&element(C,the_carrier(B))-> -empty_carrier(netstr_restr_to_element(A,B,C))&transitive_relstr(netstr_restr_to_element(A,B,C))&strict_net_str(netstr_restr_to_element(A,B,C),A)&directed_relstr(netstr_restr_to_element(A,B,C))).
% 29.04/28.90 all A B (v1_membered(A)->v1_membered(set_intersection2(A,B))).
% 29.04/28.90 all A B (v1_membered(A)->v1_membered(set_intersection2(B,A))).
% 29.04/28.90 all A B (v2_membered(A)->v1_membered(set_intersection2(A,B))&v2_membered(set_intersection2(A,B))).
% 29.04/28.90 all A (ordinal(A)&natural(A)-> -empty(succ(A))&epsilon_transitive(succ(A))&epsilon_connected(succ(A))&ordinal(succ(A))&natural(succ(A))).
% 29.04/28.90 all A B (-empty(unordered_pair(A,B))&finite(unordered_pair(A,B))).
% 29.04/28.90 all A (relation(identity_relation(A))&function(identity_relation(A))).
% 29.04/28.90 all A (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)->relation(the_L_join(A))&function(the_L_join(A))&quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))&v1_binop_1(the_L_join(A),the_carrier(A))&v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))).
% 29.04/28.90 all A (-empty_carrier(boole_lattice(A))&strict_latt_str(boole_lattice(A))&join_commutative(boole_lattice(A))&join_associative(boole_lattice(A))&meet_commutative(boole_lattice(A))&meet_associative(boole_lattice(A))&meet_absorbing(boole_lattice(A))&join_absorbing(boole_lattice(A))&lattice(boole_lattice(A))).
% 29.04/28.90 all A (reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&rel_str(A)->relation(the_InternalRel(A))&reflexive(the_InternalRel(A))&antisymmetric(the_InternalRel(A))&transitive(the_InternalRel(A))&v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A))).
% 29.04/28.90 relation(empty_set).
% 29.04/28.90 relation_empty_yielding(empty_set).
% 29.04/28.90 function(empty_set).
% 29.04/28.90 one_to_one(empty_set).
% 29.04/28.90 empty(empty_set).
% 29.04/28.90 epsilon_transitive(empty_set).
% 29.04/28.90 epsilon_connected(empty_set).
% 29.04/28.90 ordinal(empty_set).
% 29.04/28.90 all A (relation(identity_relation(A))&function(identity_relation(A))&reflexive(identity_relation(A))&symmetric(identity_relation(A))&antisymmetric(identity_relation(A))&transitive(identity_relation(A))).
% 29.04/28.90 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(cast_as_carrier_subset(A))).
% 29.04/28.90 all A B (relation(A)&relation(B)->relation(set_union2(A,B))).
% 29.04/28.90 all A (-empty(singleton(A))).
% 29.04/28.90 all A B (topological_space(A)&top_str(A)&element(B,powerset(the_carrier(A)))->closed_subset(topstr_closure(A,B),A)).
% 29.04/28.90 all A (with_suprema_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&directed_subset(cast_as_carrier_subset(A),A)).
% 29.04/28.90 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))).
% 29.04/28.90 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 29.04/28.90 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)))).
% 29.04/28.90 all A (-empty_carrier(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&upper_bounded_semilattstr(A)&latt_str(A)-> -empty_carrier(poset_of_lattice(A))&strict_rel_str(poset_of_lattice(A))&reflexive_relstr(poset_of_lattice(A))&transitive_relstr(poset_of_lattice(A))&antisymmetric_relstr(poset_of_lattice(A))&upper_bounded_relstr(poset_of_lattice(A))&with_suprema_relstr(poset_of_lattice(A))&with_infima_relstr(poset_of_lattice(A))).
% 29.04/28.90 all A B (v2_membered(A)->v1_membered(set_intersection2(B,A))&v2_membered(set_intersection2(B,A))).
% 29.04/28.90 all A B (v3_membered(A)->v1_membered(set_intersection2(A,B))&v2_membered(set_intersection2(A,B))&v3_membered(set_intersection2(A,B))).
% 29.04/28.90 all A B (v3_membered(A)->v1_membered(set_intersection2(B,A))&v2_membered(set_intersection2(B,A))&v3_membered(set_intersection2(B,A))).
% 29.04/28.90 all A B (v4_membered(A)->v1_membered(set_intersection2(A,B))&v2_membered(set_intersection2(A,B))&v3_membered(set_intersection2(A,B))&v4_membered(set_intersection2(A,B))).
% 29.04/28.90 all A B (v4_membered(A)->v1_membered(set_intersection2(B,A))&v2_membered(set_intersection2(B,A))&v3_membered(set_intersection2(B,A))&v4_membered(set_intersection2(B,A))).
% 29.04/28.90 all A B (v5_membered(A)->v1_membered(set_intersection2(A,B))&v2_membered(set_intersection2(A,B))&v3_membered(set_intersection2(A,B))&v4_membered(set_intersection2(A,B))&v5_membered(set_intersection2(A,B))).
% 29.04/28.90 all A B (v5_membered(A)->v1_membered(set_intersection2(B,A))&v2_membered(set_intersection2(B,A))&v3_membered(set_intersection2(B,A))&v4_membered(set_intersection2(B,A))&v5_membered(set_intersection2(B,A))).
% 29.04/28.90 all A B (v1_membered(A)->v1_membered(set_difference(A,B))).
% 29.04/28.90 all A B (v2_membered(A)->v1_membered(set_difference(A,B))&v2_membered(set_difference(A,B))).
% 29.04/28.90 all A B (v3_membered(A)->v1_membered(set_difference(A,B))&v2_membered(set_difference(A,B))&v3_membered(set_difference(A,B))).
% 29.04/28.90 all A (relation(A)&function(A)&one_to_one(A)->relation(relation_inverse(A))&function(relation_inverse(A))).
% 29.04/28.90 all A (-empty_carrier(A)&join_associative(A)&join_semilatt_str(A)->relation(the_L_join(A))&function(the_L_join(A))&quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))&v2_binop_1(the_L_join(A),the_carrier(A))&v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))).
% 29.04/28.90 all A (-empty_carrier(boole_lattice(A))&strict_latt_str(boole_lattice(A))&join_commutative(boole_lattice(A))&join_associative(boole_lattice(A))&meet_commutative(boole_lattice(A))&meet_associative(boole_lattice(A))&meet_absorbing(boole_lattice(A))&join_absorbing(boole_lattice(A))&lattice(boole_lattice(A))&distributive_lattstr(boole_lattice(A))&modular_lattstr(boole_lattice(A))&lower_bounded_semilattstr(boole_lattice(A))&upper_bounded_semilattstr(boole_lattice(A))&bounded_lattstr(boole_lattice(A))&complemented_lattstr(boole_lattice(A))&boolean_lattstr(boole_lattice(A))).
% 29.04/28.90 all A B C (-empty(A)&function(B)&quasi_total(B,cartesian_product2(A,A),A)&relation_of2(B,cartesian_product2(A,A),A)&function(C)&quasi_total(C,cartesian_product2(A,A),A)&relation_of2(C,cartesian_product2(A,A),A)-> -empty_carrier(latt_str_of(A,B,C))&strict_latt_str(latt_str_of(A,B,C))).
% 29.04/28.90 all A B (reflexive(B)&antisymmetric(B)&transitive(B)&v1_partfun1(B,A,A)&relation_of2(B,A,A)->strict_rel_str(rel_str_of(A,B))&reflexive_relstr(rel_str_of(A,B))&transitive_relstr(rel_str_of(A,B))&antisymmetric_relstr(rel_str_of(A,B))).
% 29.04/28.90 all A (ordinal(A)-> -empty(succ(A))&epsilon_transitive(succ(A))&epsilon_connected(succ(A))&ordinal(succ(A))).
% 29.04/28.90 all A B (relation(A)&relation(B)->relation(set_difference(A,B))).
% 29.04/28.90 all A B (-empty(unordered_pair(A,B))).
% 29.04/28.90 all A B (topological_space(A)&top_str(A)&closed_subset(B,A)&element(B,powerset(the_carrier(A)))->open_subset(subset_complement(the_carrier(A),B),A)).
% 29.04/28.90 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)).
% 29.04/28.90 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 29.04/28.90 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)))))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&lower_bounded_semilattstr(A)&latt_str(A)-> -empty_carrier(poset_of_lattice(A))&strict_rel_str(poset_of_lattice(A))&reflexive_relstr(poset_of_lattice(A))&transitive_relstr(poset_of_lattice(A))&antisymmetric_relstr(poset_of_lattice(A))&lower_bounded_relstr(poset_of_lattice(A))&with_suprema_relstr(poset_of_lattice(A))&with_infima_relstr(poset_of_lattice(A))).
% 29.04/28.90 all A B (v4_membered(A)->v1_membered(set_difference(A,B))&v2_membered(set_difference(A,B))&v3_membered(set_difference(A,B))&v4_membered(set_difference(A,B))).
% 29.04/28.90 all A B (v5_membered(A)->v1_membered(set_difference(A,B))&v2_membered(set_difference(A,B))&v3_membered(set_difference(A,B))&v4_membered(set_difference(A,B))&v5_membered(set_difference(A,B))).
% 29.04/28.90 all A B (relation(A)&function(A)->relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))).
% 29.04/28.90 all A (-empty_carrier(A)&meet_commutative(A)&meet_semilatt_str(A)->relation(the_L_meet(A))&function(the_L_meet(A))&quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))&v1_binop_1(the_L_meet(A),the_carrier(A))&v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)-> -empty_carrier(poset_of_lattice(A))&strict_rel_str(poset_of_lattice(A))&reflexive_relstr(poset_of_lattice(A))&transitive_relstr(poset_of_lattice(A))&antisymmetric_relstr(poset_of_lattice(A))).
% 29.04/28.90 all A (ordinal(A)->epsilon_transitive(union(A))&epsilon_connected(union(A))&ordinal(union(A))).
% 29.04/28.90 empty(empty_set).
% 29.04/28.90 relation(empty_set).
% 29.04/28.90 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 29.04/28.90 all A B (topological_space(A)&top_str(A)&open_subset(B,A)&element(B,powerset(the_carrier(A)))->closed_subset(subset_complement(the_carrier(A),B),A)).
% 29.04/28.90 all A (with_infima_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&filtered_subset(cast_as_carrier_subset(A),A)).
% 29.04/28.90 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)).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&complete_latt_str(A)&latt_str(A)-> -empty_carrier(poset_of_lattice(A))&strict_rel_str(poset_of_lattice(A))&reflexive_relstr(poset_of_lattice(A))&transitive_relstr(poset_of_lattice(A))&antisymmetric_relstr(poset_of_lattice(A))&lower_bounded_relstr(poset_of_lattice(A))&upper_bounded_relstr(poset_of_lattice(A))&bounded_relstr(poset_of_lattice(A))&with_suprema_relstr(poset_of_lattice(A))&with_infima_relstr(poset_of_lattice(A))&complete_relstr(poset_of_lattice(A))).
% 29.04/28.90 all A B (relation(B)&function(B)->relation(relation_rng_restriction(A,B))&function(relation_rng_restriction(A,B))).
% 29.04/28.90 all A (-empty_carrier(A)&meet_associative(A)&meet_semilatt_str(A)->relation(the_L_meet(A))&function(the_L_meet(A))&quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))&v2_binop_1(the_L_meet(A),the_carrier(A))&v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))).
% 29.04/28.90 all A (topological_space(A)&top_str(A)->closed_subset(cast_as_carrier_subset(A),A)).
% 29.04/28.90 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 29.04/28.90 all A (top_str(A)->empty(interior(A,empty_carrier_subset(A)))&v1_membered(interior(A,empty_carrier_subset(A)))&v2_membered(interior(A,empty_carrier_subset(A)))&v3_membered(interior(A,empty_carrier_subset(A)))&v4_membered(interior(A,empty_carrier_subset(A)))&v5_membered(interior(A,empty_carrier_subset(A)))).
% 29.04/28.90 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)).
% 29.04/28.90 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))).
% 29.04/28.90 all A (strict_rel_str(incl_POSet(A))&reflexive_relstr(incl_POSet(A))&transitive_relstr(incl_POSet(A))&antisymmetric_relstr(incl_POSet(A))).
% 29.04/28.90 empty(empty_set).
% 29.04/28.90 v1_membered(empty_set).
% 29.04/28.90 v2_membered(empty_set).
% 29.04/28.90 v3_membered(empty_set).
% 29.04/28.90 v4_membered(empty_set).
% 29.04/28.90 v5_membered(empty_set).
% 29.04/28.90 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 29.04/28.90 all A B (topological_space(A)&top_str(A)&element(B,powerset(the_carrier(A)))->open_subset(interior(A,B),A)).
% 29.04/28.90 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)).
% 29.04/28.90 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))).
% 29.04/28.90 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 29.04/28.90 all A (topological_space(A)&top_str(A)->empty(empty_carrier_subset(A))&open_subset(empty_carrier_subset(A),A)&closed_subset(empty_carrier_subset(A),A)&v1_membered(empty_carrier_subset(A))&v2_membered(empty_carrier_subset(A))&v3_membered(empty_carrier_subset(A))&v4_membered(empty_carrier_subset(A))&v5_membered(empty_carrier_subset(A))).
% 29.04/28.90 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))).
% 29.04/28.90 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 29.04/28.90 all A (topological_space(A)&top_str(A)->open_subset(cast_as_carrier_subset(A),A)&closed_subset(cast_as_carrier_subset(A),A)).
% 29.04/28.90 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))).
% 29.04/28.90 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))).
% 29.04/28.90 all A B (finite(A)&finite(B)->finite(set_union2(A,B))).
% 29.04/28.90 all A B (empty(A)&relation(B)->empty(relation_composition(A,B))&relation(relation_composition(A,B))).
% 29.04/28.90 all A (top_str(A)->dense(cast_as_carrier_subset(A),A)).
% 29.04/28.90 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))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_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))&distributive_relstr(boole_POSet(A))&complemented_relstr(boole_POSet(A))).
% 29.04/28.90 all A B (-empty_carrier(B)&lattice(B)&latt_str(B)-> (in(A,a_1_0_filter_1(B))<-> (exists C D (element(C,the_carrier(B))&element(D,the_carrier(B))&A=ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)&below_refl(B,C,D))))).
% 29.04/28.90 all A B C (-empty_carrier(B)&topological_space(B)&top_str(B)&element(C,the_carrier(B))-> (in(A,a_2_0_yellow19(B,C))<-> (exists D (point_neighbourhood(D,B,C)&A=D)))).
% 29.04/28.90 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))))).
% 29.04/28.90 all A B C (-empty_carrier(B)&latt_str(B)-> (in(A,a_2_2_lattice3(B,C))<-> (exists D (element(D,the_carrier(B))&A=D&latt_set_smaller(B,D,C))))).
% 29.04/28.90 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))))).
% 29.04/28.90 all A B C (-empty_carrier(B)&lattice(B)&complete_latt_str(B)&latt_str(B)-> (in(A,a_2_3_lattice3(B,C))<-> (exists D (element(D,the_carrier(B))&A=D&latt_set_smaller(B,D,C))))).
% 29.04/28.90 all A B C (-empty_carrier(B)&topological_space(B)&top_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)))&proper_element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(B)))))&element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(B)))))-> (in(A,a_2_3_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))))).
% 29.04/28.90 all A B C D (-empty_carrier(B)&one_sorted_str(B)& -empty_carrier(C)&net_str(C,B)&element(D,the_carrier(C))-> (in(A,a_3_0_waybel_9(B,C,D))<-> (exists E (element(E,the_carrier(C))&A=E&related(C,D,E))))).
% 29.04/28.90 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))))).
% 29.04/28.90 all A B C D (-empty_carrier(B)&topological_space(B)&top_str(B)& -empty_carrier(C)&transitive_relstr(C)&directed_relstr(C)&net_str(C,B)&element(D,the_carrier(C))-> (in(A,a_3_3_yellow19(B,C,D))<-> (exists E (element(E,the_carrier(C))&A=E&related(C,D,E))))).
% 29.04/28.90 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))).
% 29.04/28.90 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))).
% 29.04/28.90 all A B C (function(B)&quasi_total(B,cartesian_product2(A,A),A)&relation_of2(B,cartesian_product2(A,A),A)&function(C)&quasi_total(C,cartesian_product2(A,A),A)&relation_of2(C,cartesian_product2(A,A),A)-> (all D E F (latt_str_of(A,B,C)=latt_str_of(D,E,F)->A=D&B=E&C=F))).
% 29.04/28.90 all A B (set_union2(A,A)=A).
% 29.04/28.90 all A B (set_intersection2(A,A)=A).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_union2(A,B,B)=B).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_intersection2(A,B,B)=B).
% 29.04/28.90 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 29.04/28.90 all A (relation(A)->relation_inverse(relation_inverse(A))=A).
% 29.04/28.90 all A B (element(B,powerset(powerset(A)))->complements_of_subsets(A,complements_of_subsets(A,B))=B).
% 29.04/28.90 all A B (-proper_subset(A,A)).
% 29.04/28.90 all A (relation(A)-> (reflexive(A)<-> (all B (in(B,relation_field(A))->in(ordered_pair(B,B),A))))).
% 29.04/28.90 all A (singleton(A)!=empty_set).
% 29.04/28.90 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 29.04/28.90 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 29.04/28.90 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 29.04/28.90 all A B (relation(B)->subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))).
% 29.04/28.90 all A (relation(A)-> (transitive(A)<-> (all B C D (in(ordered_pair(B,C),A)&in(ordered_pair(C,D),A)->in(ordered_pair(B,D),A))))).
% 29.04/28.90 all A B (subset(singleton(A),B)<->in(A,B)).
% 29.04/28.90 all A B (relation(B)-> -(well_ordering(B)&e_quipotent(A,relation_field(B))& (all C (relation(C)-> -well_orders(C,A))))).
% 29.04/28.90 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 29.04/28.90 all A B (element(B,powerset(A))-> (all C (in(C,B)->in(C,A)))).
% 29.04/28.90 all A (relation(A)-> (antisymmetric(A)<-> (all B C (in(ordered_pair(B,C),A)&in(ordered_pair(C,B),A)->B=C)))).
% 29.04/28.90 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 29.04/28.90 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (all C (element(C,the_carrier(A))-> (in(C,subset_complement(the_carrier(A),B))<-> -in(C,B))))))).
% 29.04/28.90 all A (relation(A)-> (connected(A)<-> (all B C (-(in(B,relation_field(A))&in(C,relation_field(A))&B!=C& -in(ordered_pair(B,C),A)& -in(ordered_pair(C,B),A)))))).
% 29.04/28.90 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 29.04/28.90 all A B (in(A,B)->subset(A,union(B))).
% 29.04/28.90 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 29.04/28.90 all A B ((all C (in(C,A)->in(C,B)))->element(A,powerset(B))).
% 29.04/28.90 all A B C (relation(C)&function(C)-> (in(B,relation_dom(relation_dom_restriction(C,A)))<->in(B,relation_dom(C))&in(B,A))).
% 29.04/28.90 exists A (latt_str(A)& -empty_carrier(A)&strict_latt_str(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A)&lattice(A)&distributive_lattstr(A)&modular_lattstr(A)&lower_bounded_semilattstr(A)&upper_bounded_semilattstr(A)).
% 29.04/28.90 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)))).
% 29.04/28.90 exists A (latt_str(A)& -empty_carrier(A)&strict_latt_str(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A)&lattice(A)&lower_bounded_semilattstr(A)&upper_bounded_semilattstr(A)&bounded_lattstr(A)).
% 29.04/28.90 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)))).
% 29.04/28.90 exists A (latt_str(A)& -empty_carrier(A)&strict_latt_str(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A)&lattice(A)&lower_bounded_semilattstr(A)&upper_bounded_semilattstr(A)&bounded_lattstr(A)&complemented_lattstr(A)).
% 29.04/28.90 exists A (rel_str(A)& -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&connected_relstr(A)).
% 29.04/28.90 exists A (latt_str(A)& -empty_carrier(A)&strict_latt_str(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A)&lattice(A)&distributive_lattstr(A)&lower_bounded_semilattstr(A)&upper_bounded_semilattstr(A)&bounded_lattstr(A)&complemented_lattstr(A)&boolean_lattstr(A)).
% 29.04/28.90 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)).
% 29.04/28.90 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 29.04/28.90 exists A (-empty(A)&finite(A)).
% 29.04/28.90 exists A (relation(A)&function(A)).
% 29.04/28.90 all A B exists C (relation_of2(C,A,B)&relation(C)&function(C)&quasi_total(C,A,B)).
% 29.04/28.90 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&complete_relstr(A)).
% 29.04/28.90 exists A (-empty(A)&v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 29.04/28.90 exists A (rel_str(A)&strict_rel_str(A)).
% 29.04/28.90 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 29.04/28.90 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&being_limit_ordinal(A)).
% 29.04/28.90 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)).
% 29.04/28.90 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 29.04/28.90 exists A (empty(A)&relation(A)).
% 29.04/28.90 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 29.04/28.90 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&open_subset(B,A)))).
% 29.04/28.90 all A (rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&directed_subset(B,A)&filtered_subset(B,A)))).
% 29.04/28.90 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)&connected_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A)).
% 29.04/28.90 exists A (rel_str(A)& -empty_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)&up_complete_relstr(A)&join_complete_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&distributive_relstr(A)&v2_waybel_3(A)&v3_waybel_3(A)).
% 29.04/28.90 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)).
% 29.04/28.90 all A B (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (exists C (subnet(C,A,B)& -empty_carrier(C)&transitive_relstr(C)&strict_net_str(C,A)&directed_relstr(C)))).
% 29.04/28.90 exists A empty(A).
% 29.04/28.90 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)).
% 29.04/28.90 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)& -v1_yellow_3(A)).
% 29.04/28.90 all A exists B (element(B,powerset(A))&empty(B)&relation(B)&function(B)&one_to_one(B)&epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)&natural(B)&finite(B)).
% 29.04/28.90 exists A (relation(A)&empty(A)&function(A)).
% 29.04/28.90 all A exists B (relation_of2(B,A,A)&relation(B)&function(B)&one_to_one(B)&quasi_total(B,A,A)&onto(B,A,A)&bijective(B,A,A)).
% 29.04/28.90 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)).
% 29.04/28.90 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)).
% 29.04/28.90 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 29.04/28.90 all A B exists C (relation_of2(C,A,B)&relation(C)&function(C)).
% 29.04/28.90 exists A (-empty(A)&relation(A)).
% 29.04/28.90 all A exists B (element(B,powerset(A))&empty(B)).
% 29.04/28.90 all A exists B (element(B,powerset(A))& -proper_element(B,powerset(A))).
% 29.04/28.90 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&open_subset(B,A)&closed_subset(B,A)))).
% 29.04/28.90 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)))).
% 29.04/28.90 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)&v2_waybel_3(A)&v3_waybel_3(A)).
% 29.04/28.90 all A exists B (element(B,powerset(powerset(A)))& -empty(B)&finite(B)).
% 29.04/28.90 exists A (-empty(A)).
% 29.04/28.90 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)).
% 29.04/28.90 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 29.04/28.90 exists A (relation(A)&function(A)&one_to_one(A)).
% 29.04/28.90 exists A (latt_str(A)&strict_latt_str(A)).
% 29.04/28.90 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 29.04/28.90 all A exists B (relation_of2(B,A,A)&relation(B)&reflexive(B)&symmetric(B)&antisymmetric(B)&transitive(B)&v1_partfun1(B,A,A)).
% 29.04/28.90 exists A (relation(A)&relation_empty_yielding(A)).
% 29.04/28.90 exists A (one_sorted_str(A)& -empty_carrier(A)).
% 29.04/28.90 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&open_subset(B,A)&closed_subset(B,A)))).
% 29.04/28.90 all A (one_sorted_str(A)-> (exists B (element(B,powerset(powerset(the_carrier(A))))& -empty(B)&finite(B)))).
% 29.04/28.90 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 29.04/28.90 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 29.04/28.90 all A (top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&empty(B)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)))).
% 29.04/28.90 all A (one_sorted_str(A)-> (exists B (net_str(B,A)&strict_net_str(B,A)))).
% 29.04/28.90 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)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)&distributive_relstr(A)&heyting_relstr(A)&complemented_relstr(A)&boolean_relstr(A)).
% 29.04/28.90 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)))).
% 29.04/28.90 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&transitive_relstr(A)&directed_relstr(A)).
% 29.04/28.90 all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 29.04/28.90 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&empty(B)&open_subset(B,A)&closed_subset(B,A)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)&nowhere_dense(B,A)))).
% 29.04/28.90 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)))).
% 29.04/28.90 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)&upper_bounded_relstr(A)&distributive_relstr(A)&heyting_relstr(A)).
% 29.04/28.90 exists A (latt_str(A)& -empty_carrier(A)&strict_latt_str(A)).
% 29.04/28.90 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&closed_subset(B,A)))).
% 29.04/28.90 all A B (one_sorted_str(A)&net_str(B,A)-> (exists C (subnetstr(C,A,B)&strict_net_str(C,A)&full_subnetstr(C,A,B)))).
% 29.04/28.90 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&closed_subset(B,A)))).
% 29.04/28.90 all A (rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&lower_relstr_subset(B,A)&upper_relstr_subset(B,A)))).
% 29.04/28.90 all A B (one_sorted_str(A)& -empty_carrier(B)&net_str(B,A)-> (exists C (subnetstr(C,A,B)& -empty_carrier(C)&strict_net_str(C,A)&full_subnetstr(C,A,B)))).
% 29.04/28.90 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)))).
% 29.04/28.90 exists A (latt_str(A)& -empty_carrier(A)&strict_latt_str(A)&join_commutative(A)&join_associative(A)&meet_commutative(A)&meet_associative(A)&meet_absorbing(A)&join_absorbing(A)&lattice(A)).
% 29.04/28.90 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)))).
% 29.04/28.90 all A B C D (-empty_carrier(A)&lattice(A)&latt_str(A)& -empty_carrier(B)&lattice(B)&latt_str(B)&element(C,the_carrier(A))&element(D,the_carrier(B))->k10_filter_1(A,B,C,D)=ordered_pair(C,D)).
% 29.04/28.90 all A B C D (-empty(A)& -empty(B)&element(C,A)&element(D,B)->ordered_pair_as_product_element(A,B,C,D)=ordered_pair(C,D)).
% 29.04/28.90 all A (k1_pcomps_1(A)=powerset(A)).
% 29.04/28.90 all A B (relation(A)->relation_restriction_as_relation_of(A,B)=relation_restriction(A,B)).
% 29.04/28.90 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)).
% 29.04/28.90 all A (inclusion_order(A)=inclusion_relation(A)).
% 29.04/28.90 all A B C D E F (-empty(A)& -empty(B)&function(D)&quasi_total(D,cartesian_product2(A,B),C)&relation_of2(D,cartesian_product2(A,B),C)&element(E,A)&element(F,B)->apply_binary_as_element(A,B,C,D,E,F)=apply_binary(D,E,F)).
% 29.04/28.90 all A (-empty_carrier(A)&lattice(A)&latt_str(A)->k2_lattice3(A)=relation_of_lattice(A)).
% 29.04/28.90 all A B C D (function(C)&relation_of2(C,A,B)->partfun_dom_restriction(A,B,C,D)=relation_dom_restriction(C,D)).
% 29.04/28.90 all A B C (-empty_carrier(A)&one_sorted_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->unordered_pair_as_carrier_subset(A,B,C)=unordered_pair(B,C)).
% 29.04/28.90 all A B C (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->join_commut(A,B,C)=join(A,B,C)).
% 29.04/28.90 all A B C D (-empty(A)& -empty_carrier(B)&rel_str(B)&function(C)&quasi_total(C,A,the_carrier(B))&relation_of2(C,A,the_carrier(B))&element(D,A)->apply_on_set_and_struct(A,B,C,D)=apply(C,D)).
% 29.04/28.90 all A B C (-empty_carrier(A)&meet_commutative(A)&meet_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->meet_commut(A,B,C)=meet(A,B,C)).
% 29.04/28.90 all A B C (relation_of2(C,A,B)->relation_dom_as_subset(A,B,C)=relation_dom(C)).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_union2(A,B,C)=set_union2(B,C)).
% 29.04/28.90 all A B C D (one_sorted_str(A)&one_sorted_str(B)&function(C)&quasi_total(C,the_carrier(A),the_carrier(B))&relation_of2(C,the_carrier(A),the_carrier(B))->function_invverse_img_as_carrier_subset(A,B,C,D)=relation_inverse_image(C,D)).
% 29.04/28.90 all A B C (relation_of2(C,A,B)->relation_rng_as_subset(A,B,C)=relation_rng(C)).
% 29.04/28.90 all A B (element(B,powerset(powerset(A)))->union_of_subsets(A,B)=union(B)).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_intersection2(A,B,C)=set_intersection2(B,C)).
% 29.04/28.90 all A (identity_as_relation_of(A)=identity_relation(A)).
% 29.04/28.90 all A B (element(B,powerset(powerset(A)))->meet_of_subsets(A,B)=set_meet(B)).
% 29.04/28.90 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_difference(A,B,C)=set_difference(B,C)).
% 29.04/28.90 all A B C (-empty_carrier(A)&one_sorted_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)&element(C,the_carrier(B))->subnetstr_of_element(A,B,C)=netstr_restr_to_element(A,B,C)).
% 29.04/28.90 all A B C D E (-empty(B)&function(D)&quasi_total(D,A,B)&relation_of2(D,A,B)&function(E)&quasi_total(E,B,C)&relation_of2(E,B,C)->function_of_composition(A,B,C,D,E)=relation_composition(D,E)).
% 29.04/28.90 all A B C D (-empty(A)& -empty_carrier(B)&one_sorted_str(B)&function(C)&quasi_total(C,A,the_carrier(B))&relation_of2(C,A,the_carrier(B))&element(D,A)->apply_on_set_and_struct2(A,B,C,D)=apply(C,D)).
% 29.04/28.90 all A B C D (-empty(A)&function(C)&quasi_total(C,A,B)&relation_of2(C,A,B)&element(D,A)->apply_as_element(A,B,C,D)=apply(C,D)).
% 29.04/28.90 all A B C D (relation_of2(C,A,B)->relation_dom_restr_as_relation_of(A,B,C,D)=relation_dom_restriction(C,D)).
% 29.04/28.90 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)))).
% 29.04/28.90 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 29.04/28.90 all A B (ordinal(A)&ordinal(B)-> (ordinal_subset(A,B)<->subset(A,B))).
% 29.04/28.90 all A B (e_quipotent(A,B)<->are_e_quipotent(A,B)).
% 29.04/28.90 all A B C (-empty_carrier(A)&meet_commutative(A)&meet_absorbing(A)&join_absorbing(A)&latt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))-> (below_refl(A,B,C)<->below(A,B,C))).
% 29.04/28.90 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))).
% 29.04/28.90 all A B (ordinal(A)&ordinal(B)->ordinal_subset(A,A)).
% 29.04/28.90 all A B subset(A,A).
% 29.04/28.90 all A B e_quipotent(A,A).
% 29.04/28.90 all A B C (-empty_carrier(A)&meet_commutative(A)&meet_absorbing(A)&join_absorbing(A)&latt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->below_refl(A,B,B)).
% 29.04/28.90 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)).
% 29.04/28.90 all A B (-empty(A)&relation(B)-> ((all C D E (in(C,A)& (exists F (C=F&in(D,F)& (all G (in(G,F)->in(ordered_pair(D,G),B)))))&in(C,A)& (exists H (C=H&in(E,H)& (all I (in(I,H)->in(ordered_pair(E,I),B)))))->D=E))-> (exists C (relation(C)&function(C)& (all D E (in(ordered_pair(D,E),C)<->in(D,A)&in(D,A)& (exists J (D=J&in(E,J)& (all K (in(K,J)->in(ordered_pair(E,K),B))))))))))).
% 29.04/28.90 all A ((all B C D (in(B,A)&C=singleton(B)&in(B,A)&D=singleton(B)->C=D))-> (exists B (relation(B)&function(B)& (all C D (in(ordered_pair(C,D),B)<->in(C,A)&in(C,A)&D=singleton(C)))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> ((all C D E (in(C,complements_of_subsets(the_carrier(A),B))& (all F (element(F,powerset(the_carrier(A)))-> (F=C->D=subset_complement(the_carrier(A),F))))&in(C,complements_of_subsets(the_carrier(A),B))& (all G (element(G,powerset(the_carrier(A)))-> (G=C->E=subset_complement(the_carrier(A),G))))->D=E))-> (exists C (relation(C)&function(C)& (all D E (in(ordered_pair(D,E),C)<->in(D,complements_of_subsets(the_carrier(A),B))&in(D,complements_of_subsets(the_carrier(A),B))& (all H (element(H,powerset(the_carrier(A)))-> (H=D->E=subset_complement(the_carrier(A),H)))))))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> ((all C D E (in(C,B)& (all F (element(F,powerset(the_carrier(A)))-> (F=C->D=subset_complement(the_carrier(A),F))))&in(C,B)& (all G (element(G,powerset(the_carrier(A)))-> (G=C->E=subset_complement(the_carrier(A),G))))->D=E))-> (exists C (relation(C)&function(C)& (all D E (in(ordered_pair(D,E),C)<->in(D,B)&in(D,B)& (all H (element(H,powerset(the_carrier(A)))-> (H=D->E=subset_complement(the_carrier(A),H)))))))))).
% 29.04/28.90 all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> ((all D E F (in(D,C)& (exists G (E=G& (all H (in(H,G)<->in(H,the_carrier(B))& (exists I (netstr_induced_subset(I,A,B)& (exists J (element(J,the_carrier(B))&D=topstr_closure(A,I)&H=J&I=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,J)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,J)))))))))))&in(D,C)& (exists K (F=K& (all L (in(L,K)<->in(L,the_carrier(B))& (exists M (netstr_induced_subset(M,A,B)& (exists N (element(N,the_carrier(B))&D=topstr_closure(A,M)&L=N&M=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,N)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,N)))))))))))->E=F))-> (exists D (relation(D)&function(D)& (all E F (in(ordered_pair(E,F),D)<->in(E,C)&in(E,C)& (exists O (F=O& (all P (in(P,O)<->in(P,the_carrier(B))& (exists Q (netstr_induced_subset(Q,A,B)& (exists R (element(R,the_carrier(B))&E=topstr_closure(A,Q)&P=R&Q=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,R)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,R))))))))))))))))).
% 29.04/28.90 all A ((exists B (ordinal(B)&in(B,A)))-> (exists B (ordinal(B)&in(B,A)& (all C (ordinal(C)-> (in(C,A)->ordinal_subset(B,C))))))).
% 29.04/28.90 (in(empty_set,omega)-> (all A (element(A,powerset(powerset(empty_set)))-> -(A!=empty_set& (all B (-(in(B,A)& (all C (in(C,A)&subset(B,C)->C=B)))))))))& (all D (ordinal(D)-> ((in(D,omega)-> (all E (element(E,powerset(powerset(D)))-> -(E!=empty_set& (all F (-(in(F,E)& (all G (in(G,E)&subset(F,G)->G=F)))))))))-> (in(succ(D),omega)-> (all H (element(H,powerset(powerset(succ(D))))-> -(H!=empty_set& (all I (-(in(I,H)& (all J (in(J,H)&subset(I,J)->J=I))))))))))))& (all D (ordinal(D)-> (being_limit_ordinal(D)& (all K (ordinal(K)-> (in(K,D)-> (in(K,omega)-> (all L (element(L,powerset(powerset(K)))-> -(L!=empty_set& (all M (-(in(M,L)& (all N (in(N,L)&subset(M,N)->N=M))))))))))))->D=empty_set| (in(D,omega)-> (all O (element(O,powerset(powerset(D)))-> -(O!=empty_set& (all P (-(in(P,O)& (all Q (in(Q,O)&subset(P,Q)->Q=P))))))))))))-> (all D (ordinal(D)-> (in(D,omega)-> (all R (element(R,powerset(powerset(D)))-> -(R!=empty_set& (all S (-(in(S,R)& (all T (in(T,R)&subset(S,T)->T=S))))))))))).
% 29.04/28.90 all A B C (relation(B)&relation(C)&function(C)-> (exists D (relation(D)& (all E F (in(ordered_pair(E,F),D)<->in(E,A)&in(F,A)&in(ordered_pair(apply(C,E),apply(C,F)),B)))))).
% 29.04/28.90 all A B (-empty(A)&relation(B)-> ((all C D E (in(C,A)& (exists F (C=F&in(D,F)& (all G (in(G,F)->in(ordered_pair(D,G),B)))))&in(C,A)& (exists H (C=H&in(E,H)& (all I (in(I,H)->in(ordered_pair(E,I),B)))))->D=E))-> (exists C all D (in(D,C)<-> (exists E (in(E,A)&in(E,A)& (exists J (E=J&in(D,J)& (all K (in(K,J)->in(ordered_pair(D,K),B))))))))))).
% 29.04/28.90 all A B (-empty(A)&relation(B)-> (all C ((all D E F (D=E& (exists G H (ordered_pair(G,H)=E&in(G,A)& (exists I (G=I&in(H,I)& (all J (in(J,I)->in(ordered_pair(H,J),B)))))))&D=F& (exists K L (ordered_pair(K,L)=F&in(K,A)& (exists M (K=M&in(L,M)& (all N (in(N,M)->in(ordered_pair(L,N),B)))))))->E=F))-> (exists D all E (in(E,D)<-> (exists F (in(F,cartesian_product2(A,C))&F=E& (exists O P (ordered_pair(O,P)=E&in(O,A)& (exists Q (O=Q&in(P,Q)& (all R (in(R,Q)->in(ordered_pair(P,R),B)))))))))))))).
% 29.04/28.90 all A B C (-empty_carrier(A)&transitive_relstr(A)&rel_str(A)&element(B,powerset(the_carrier(A)))&finite(C)&element(C,powerset(B))-> ((all D E F (D=E& (exists G (G=E& (exists H (element(H,the_carrier(A))&in(H,B)&relstr_set_smaller(A,G,H)))))&D=F& (exists I (I=F& (exists J (element(J,the_carrier(A))&in(J,B)&relstr_set_smaller(A,I,J)))))->E=F))-> (exists D all E (in(E,D)<-> (exists F (in(F,powerset(C))&F=E& (exists K (K=E& (exists L (element(L,the_carrier(A))&in(L,B)&relstr_set_smaller(A,K,L))))))))))).
% 29.04/28.90 all A ((all B C D (in(B,A)&C=singleton(B)&in(B,A)&D=singleton(B)->C=D))-> (exists B all C (in(C,B)<-> (exists D (in(D,A)&in(D,A)&C=singleton(D)))))).
% 29.04/28.90 all A B ((all C D E (C=D& (exists F G (ordered_pair(F,G)=D&in(F,A)&G=singleton(F)))&C=E& (exists H I (ordered_pair(H,I)=E&in(H,A)&I=singleton(H)))->D=E))-> (exists C all D (in(D,C)<-> (exists E (in(E,cartesian_product2(A,B))&E=D& (exists J K (ordered_pair(J,K)=D&in(J,A)&K=singleton(J)))))))).
% 29.04/28.90 all A (ordinal(A)-> ((all B C D (B=C& (exists E (ordinal(E)&C=E& (in(E,omega)-> (all F (element(F,powerset(powerset(E)))-> -(F!=empty_set& (all G (-(in(G,F)& (all H (in(H,F)&subset(G,H)->H=G)))))))))))&B=D& (exists I (ordinal(I)&D=I& (in(I,omega)-> (all J (element(J,powerset(powerset(I)))-> -(J!=empty_set& (all K (-(in(K,J)& (all L (in(L,J)&subset(K,L)->L=K)))))))))))->C=D))-> (exists B all C (in(C,B)<-> (exists D (in(D,succ(A))&D=C& (exists M (ordinal(M)&C=M& (in(M,omega)-> (all N (element(N,powerset(powerset(M)))-> -(N!=empty_set& (all O (-(in(O,N)& (all P (in(P,N)&subset(O,P)->P=O))))))))))))))))).
% 29.04/28.90 all A B (topological_space(A)&top_str(A)&element(B,powerset(the_carrier(A)))-> ((all C D E (C=D& (exists F (element(F,powerset(the_carrier(A)))&F=D&closed_subset(F,A)&subset(B,D)))&C=E& (exists G (element(G,powerset(the_carrier(A)))&G=E&closed_subset(G,A)&subset(B,E)))->D=E))-> (exists C all D (in(D,C)<-> (exists E (in(E,powerset(the_carrier(A)))&E=D& (exists H (element(H,powerset(the_carrier(A)))&H=D&closed_subset(H,A)&subset(B,D))))))))).
% 29.04/28.90 all A B (topological_space(A)&top_str(A)&element(B,powerset(powerset(the_carrier(A))))-> ((all C D E (C=D&in(set_difference(cast_as_carrier_subset(A),D),B)&C=E&in(set_difference(cast_as_carrier_subset(A),E),B)->D=E))-> (exists C all D (in(D,C)<-> (exists E (in(E,powerset(the_carrier(A)))&E=D&in(set_difference(cast_as_carrier_subset(A),D),B))))))).
% 29.04/28.90 all A B (ordinal(A)&element(B,powerset(powerset(succ(A))))-> ((all C D E (C=D& (exists F (in(F,B)&D=set_difference(F,singleton(A))))&C=E& (exists G (in(G,B)&E=set_difference(G,singleton(A))))->D=E))-> (exists C all D (in(D,C)<-> (exists E (in(E,powerset(A))&E=D& (exists H (in(H,B)&D=set_difference(H,singleton(A)))))))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> ((all C D E (in(C,complements_of_subsets(the_carrier(A),B))& (all F (element(F,powerset(the_carrier(A)))-> (F=C->D=subset_complement(the_carrier(A),F))))&in(C,complements_of_subsets(the_carrier(A),B))& (all G (element(G,powerset(the_carrier(A)))-> (G=C->E=subset_complement(the_carrier(A),G))))->D=E))-> (exists C all D (in(D,C)<-> (exists E (in(E,complements_of_subsets(the_carrier(A),B))&in(E,complements_of_subsets(the_carrier(A),B))& (all H (element(H,powerset(the_carrier(A)))-> (H=E->D=subset_complement(the_carrier(A),H)))))))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> (all C ((all D E F (D=E& (exists G H (ordered_pair(G,H)=E&in(G,complements_of_subsets(the_carrier(A),B))& (all I (element(I,powerset(the_carrier(A)))-> (I=G->H=subset_complement(the_carrier(A),I))))))&D=F& (exists J K (ordered_pair(J,K)=F&in(J,complements_of_subsets(the_carrier(A),B))& (all L (element(L,powerset(the_carrier(A)))-> (L=J->K=subset_complement(the_carrier(A),L))))))->E=F))-> (exists D all E (in(E,D)<-> (exists F (in(F,cartesian_product2(complements_of_subsets(the_carrier(A),B),C))&F=E& (exists M N (ordered_pair(M,N)=E&in(M,complements_of_subsets(the_carrier(A),B))& (all O (element(O,powerset(the_carrier(A)))-> (O=M->N=subset_complement(the_carrier(A),O))))))))))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> ((all C D E (in(C,B)& (all F (element(F,powerset(the_carrier(A)))-> (F=C->D=subset_complement(the_carrier(A),F))))&in(C,B)& (all G (element(G,powerset(the_carrier(A)))-> (G=C->E=subset_complement(the_carrier(A),G))))->D=E))-> (exists C all D (in(D,C)<-> (exists E (in(E,B)&in(E,B)& (all H (element(H,powerset(the_carrier(A)))-> (H=E->D=subset_complement(the_carrier(A),H)))))))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> (all C ((all D E F (D=E& (exists G H (ordered_pair(G,H)=E&in(G,B)& (all I (element(I,powerset(the_carrier(A)))-> (I=G->H=subset_complement(the_carrier(A),I))))))&D=F& (exists J K (ordered_pair(J,K)=F&in(J,B)& (all L (element(L,powerset(the_carrier(A)))-> (L=J->K=subset_complement(the_carrier(A),L))))))->E=F))-> (exists D all E (in(E,D)<-> (exists F (in(F,cartesian_product2(B,C))&F=E& (exists M N (ordered_pair(M,N)=E&in(M,B)& (all O (element(O,powerset(the_carrier(A)))-> (O=M->N=subset_complement(the_carrier(A),O))))))))))))).
% 29.04/28.90 all A B C (relation(B)&relation(C)&function(C)-> ((all D E F (D=E& (exists G H (E=ordered_pair(G,H)&in(ordered_pair(apply(C,G),apply(C,H)),B)))&D=F& (exists I J (F=ordered_pair(I,J)&in(ordered_pair(apply(C,I),apply(C,J)),B)))->E=F))-> (exists D all E (in(E,D)<-> (exists F (in(F,cartesian_product2(A,A))&F=E& (exists K L (E=ordered_pair(K,L)&in(ordered_pair(apply(C,K),apply(C,L)),B))))))))).
% 29.04/28.90 all A ((all B C D (B=C&ordinal(C)&B=D&ordinal(D)->C=D))-> (exists B all C (in(C,B)<-> (exists D (in(D,A)&D=C&ordinal(C)))))).
% 29.04/28.90 all A B C (element(B,powerset(powerset(A)))&relation(C)&function(C)-> ((all D E F (D=E&in(relation_image(C,E),B)&D=F&in(relation_image(C,F),B)->E=F))-> (exists D all E (in(E,D)<-> (exists F (in(F,powerset(relation_dom(C)))&F=E&in(relation_image(C,E),B))))))).
% 29.04/28.90 all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all D ((all E F G (E=F& (exists H (netstr_induced_subset(H,A,B)& (exists I (element(I,the_carrier(B))&D=topstr_closure(A,H)&F=I&H=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,I)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,I)))))))&E=G& (exists J (netstr_induced_subset(J,A,B)& (exists K (element(K,the_carrier(B))&D=topstr_closure(A,J)&G=K&J=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,K)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,K)))))))->F=G))-> (exists E all F (in(F,E)<-> (exists G (in(G,the_carrier(B))&G=F& (exists L (netstr_induced_subset(L,A,B)& (exists M (element(M,the_carrier(B))&D=topstr_closure(A,L)&F=M&L=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,M)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,M)))))))))))))).
% 29.04/28.90 all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> ((all D E F (in(D,C)& (exists G (E=G& (all H (in(H,G)<->in(H,the_carrier(B))& (exists I (netstr_induced_subset(I,A,B)& (exists J (element(J,the_carrier(B))&D=topstr_closure(A,I)&H=J&I=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,J)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,J)))))))))))&in(D,C)& (exists K (F=K& (all L (in(L,K)<->in(L,the_carrier(B))& (exists M (netstr_induced_subset(M,A,B)& (exists N (element(N,the_carrier(B))&D=topstr_closure(A,M)&L=N&M=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,N)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,N)))))))))))->E=F))-> (exists D all E (in(E,D)<-> (exists F (in(F,C)&in(F,C)& (exists O (E=O& (all P (in(P,O)<->in(P,the_carrier(B))& (exists Q (netstr_induced_subset(Q,A,B)& (exists R (element(R,the_carrier(B))&F=topstr_closure(A,Q)&P=R&Q=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,R)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,R))))))))))))))))).
% 29.04/28.90 all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all D ((all E F G (E=F& (exists H I (ordered_pair(H,I)=F&in(H,C)& (exists J (I=J& (all K (in(K,J)<->in(K,the_carrier(B))& (exists L (netstr_induced_subset(L,A,B)& (exists M (element(M,the_carrier(B))&H=topstr_closure(A,L)&K=M&L=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,M)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,M)))))))))))))&E=G& (exists N O (ordered_pair(N,O)=G&in(N,C)& (exists P (O=P& (all Q (in(Q,P)<->in(Q,the_carrier(B))& (exists R (netstr_induced_subset(R,A,B)& (exists S (element(S,the_carrier(B))&N=topstr_closure(A,R)&Q=S&R=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,S)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,S)))))))))))))->F=G))-> (exists E all F (in(F,E)<-> (exists G (in(G,cartesian_product2(C,D))&G=F& (exists T U (ordered_pair(T,U)=F&in(T,C)& (exists V (U=V& (all W (in(W,V)<->in(W,the_carrier(B))& (exists X (netstr_induced_subset(X,A,B)& (exists Y (element(Y,the_carrier(B))&T=topstr_closure(A,X)&W=Y&X=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,Y)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,Y)))))))))))))))))))).
% 29.04/28.90 all A B (ordinal(B)-> ((all C D E (C=D& (exists F (ordinal(F)&D=F&in(F,A)))&C=E& (exists G (ordinal(G)&E=G&in(G,A)))->D=E))-> (exists C all D (in(D,C)<-> (exists E (in(E,succ(B))&E=D& (exists H (ordinal(H)&D=H&in(H,A))))))))).
% 29.04/28.90 -(all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> ((all D (-(in(D,C)& (all E (-(in(E,the_carrier(B))& (exists F (netstr_induced_subset(F,A,B)& (exists G (element(G,the_carrier(B))&D=topstr_closure(A,F)&E=G&F=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,G)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,G)))))))))))))-> (exists D (relation(D)&function(D)&relation_dom(D)=C&subset(relation_rng(D),the_carrier(B))& (all E (in(E,C)-> (exists H (netstr_induced_subset(H,A,B)& (exists I (element(I,the_carrier(B))&E=topstr_closure(A,H)&apply(D,E)=I&H=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,I)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,I)))))))))))))).
% 29.04/28.90 all A B (-empty(A)&relation(B)-> (all C exists D all E (in(E,D)<->in(E,cartesian_product2(A,C))& (exists F G (ordered_pair(F,G)=E&in(F,A)& (exists H (F=H&in(G,H)& (all I (in(I,H)->in(ordered_pair(G,I),B)))))))))).
% 29.04/28.90 all A B C (-empty_carrier(A)&transitive_relstr(A)&rel_str(A)&element(B,powerset(the_carrier(A)))&finite(C)&element(C,powerset(B))-> (exists D all E (in(E,D)<->in(E,powerset(C))& (exists F (F=E& (exists G (element(G,the_carrier(A))&in(G,B)&relstr_set_smaller(A,F,G)))))))).
% 29.04/28.90 all A B exists C all D (in(D,C)<->in(D,cartesian_product2(A,B))& (exists E F (ordered_pair(E,F)=D&in(E,A)&F=singleton(E)))).
% 29.04/28.90 all A (ordinal(A)-> (exists B all C (in(C,B)<->in(C,succ(A))& (exists D (ordinal(D)&C=D& (in(D,omega)-> (all E (element(E,powerset(powerset(D)))-> -(E!=empty_set& (all F (-(in(F,E)& (all G (in(G,E)&subset(F,G)->G=F)))))))))))))).
% 29.04/28.90 all A B (topological_space(A)&top_str(A)&element(B,powerset(the_carrier(A)))-> (exists C all D (in(D,C)<->in(D,powerset(the_carrier(A)))& (exists E (element(E,powerset(the_carrier(A)))&E=D&closed_subset(E,A)&subset(B,D)))))).
% 29.04/28.90 all A B (topological_space(A)&top_str(A)&element(B,powerset(powerset(the_carrier(A))))-> (exists C all D (in(D,C)<->in(D,powerset(the_carrier(A)))&in(set_difference(cast_as_carrier_subset(A),D),B)))).
% 29.04/28.90 all A B (ordinal(A)&element(B,powerset(powerset(succ(A))))-> (exists C all D (in(D,C)<->in(D,powerset(A))& (exists E (in(E,B)&D=set_difference(E,singleton(A))))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> (all C exists D all E (in(E,D)<->in(E,cartesian_product2(complements_of_subsets(the_carrier(A),B),C))& (exists F G (ordered_pair(F,G)=E&in(F,complements_of_subsets(the_carrier(A),B))& (all H (element(H,powerset(the_carrier(A)))-> (H=F->G=subset_complement(the_carrier(A),H))))))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> (all C exists D all E (in(E,D)<->in(E,cartesian_product2(B,C))& (exists F G (ordered_pair(F,G)=E&in(F,B)& (all H (element(H,powerset(the_carrier(A)))-> (H=F->G=subset_complement(the_carrier(A),H))))))))).
% 29.04/28.90 all A B C (relation(B)&relation(C)&function(C)-> (exists D all E (in(E,D)<->in(E,cartesian_product2(A,A))& (exists F G (E=ordered_pair(F,G)&in(ordered_pair(apply(C,F),apply(C,G)),B)))))).
% 29.04/28.90 all A exists B all C (in(C,B)<->in(C,A)&ordinal(C)).
% 29.04/28.90 all A B C (element(B,powerset(powerset(A)))&relation(C)&function(C)-> (exists D all E (in(E,D)<->in(E,powerset(relation_dom(C)))&in(relation_image(C,E),B)))).
% 29.04/28.90 all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all D exists E all F (in(F,E)<->in(F,the_carrier(B))& (exists G (netstr_induced_subset(G,A,B)& (exists H (element(H,the_carrier(B))&D=topstr_closure(A,G)&F=H&G=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,H)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,H)))))))))).
% 29.04/28.90 all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all D exists E all F (in(F,E)<->in(F,cartesian_product2(C,D))& (exists G H (ordered_pair(G,H)=F&in(G,C)& (exists I (H=I& (all J (in(J,I)<->in(J,the_carrier(B))& (exists K (netstr_induced_subset(K,A,B)& (exists L (element(L,the_carrier(B))&G=topstr_closure(A,K)&J=L&K=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,L)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,L)))))))))))))))).
% 29.04/28.90 all A B (ordinal(B)-> (exists C all D (in(D,C)<->in(D,succ(B))& (exists E (ordinal(E)&D=E&in(E,A)))))).
% 29.04/28.90 all A B C (-empty_carrier(A)&transitive_relstr(A)&rel_str(A)&element(B,powerset(the_carrier(A)))&finite(C)&element(C,powerset(B))-> (finite(C)& (exists D (element(D,the_carrier(A))&in(D,B)&relstr_set_smaller(A,empty_set,D)))& (all E F (in(E,C)&subset(F,C)& (exists G (element(G,the_carrier(A))&in(G,B)&relstr_set_smaller(A,F,G)))-> (exists H (element(H,the_carrier(A))&in(H,B)&relstr_set_smaller(A,set_union2(F,singleton(E)),H)))))-> (exists I (element(I,the_carrier(A))&in(I,B)&relstr_set_smaller(A,C,I))))).
% 29.04/28.90 all A B (-empty(A)&relation(B)-> ((all C D E (in(C,A)& (exists F (C=F&in(D,F)& (all G (in(G,F)->in(ordered_pair(D,G),B)))))& (exists H (C=H&in(E,H)& (all I (in(I,H)->in(ordered_pair(E,I),B)))))->D=E))& (all C (-(in(C,A)& (all D (-(exists J (C=J&in(D,J)& (all K (in(K,J)->in(ordered_pair(D,K),B))))))))))-> (exists C (relation(C)&function(C)&relation_dom(C)=A& (all D (in(D,A)-> (exists L (D=L&in(apply(C,D),L)& (all M (in(M,L)->in(ordered_pair(apply(C,D),M),B))))))))))).
% 29.04/28.90 all A ((all B C D (in(B,A)&C=singleton(B)&D=singleton(B)->C=D))& (all B (-(in(B,A)& (all C (C!=singleton(B))))))-> (exists B (relation(B)&function(B)&relation_dom(B)=A& (all C (in(C,A)->apply(B,C)=singleton(C)))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> ((all C D E (in(C,complements_of_subsets(the_carrier(A),B))& (all F (element(F,powerset(the_carrier(A)))-> (F=C->D=subset_complement(the_carrier(A),F))))& (all G (element(G,powerset(the_carrier(A)))-> (G=C->E=subset_complement(the_carrier(A),G))))->D=E))& (all C (-(in(C,complements_of_subsets(the_carrier(A),B))& (all D (-(all H (element(H,powerset(the_carrier(A)))-> (H=C->D=subset_complement(the_carrier(A),H)))))))))-> (exists C (relation(C)&function(C)&relation_dom(C)=complements_of_subsets(the_carrier(A),B)& (all D (in(D,complements_of_subsets(the_carrier(A),B))-> (all I (element(I,powerset(the_carrier(A)))-> (I=D->apply(C,D)=subset_complement(the_carrier(A),I)))))))))).
% 29.04/28.90 all A B (one_sorted_str(A)&element(B,powerset(powerset(the_carrier(A))))-> ((all C D E (in(C,B)& (all F (element(F,powerset(the_carrier(A)))-> (F=C->D=subset_complement(the_carrier(A),F))))& (all G (element(G,powerset(the_carrier(A)))-> (G=C->E=subset_complement(the_carrier(A),G))))->D=E))& (all C (-(in(C,B)& (all D (-(all H (element(H,powerset(the_carrier(A)))-> (H=C->D=subset_complement(the_carrier(A),H)))))))))-> (exists C (relation(C)&function(C)&relation_dom(C)=B& (all D (in(D,B)-> (all I (element(I,powerset(the_carrier(A)))-> (I=D->apply(C,D)=subset_complement(the_carrier(A),I)))))))))).
% 29.04/28.91 all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> ((all D E F (in(D,C)& (exists G (E=G& (all H (in(H,G)<->in(H,the_carrier(B))& (exists I (netstr_induced_subset(I,A,B)& (exists J (element(J,the_carrier(B))&D=topstr_closure(A,I)&H=J&I=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,J)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,J)))))))))))& (exists K (F=K& (all L (in(L,K)<->in(L,the_carrier(B))& (exists M (netstr_induced_subset(M,A,B)& (exists N (element(N,the_carrier(B))&D=topstr_closure(A,M)&L=N&M=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,N)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,N)))))))))))->E=F))& (all D (-(in(D,C)& (all E (-(exists O (E=O& (all P (in(P,O)<->in(P,the_carrier(B))& (exists Q (netstr_induced_subset(Q,A,B)& (exists R (element(R,the_carrier(B))&D=topstr_closure(A,Q)&P=R&Q=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,R)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,R))))))))))))))))-> (exists D (relation(D)&function(D)&relation_dom(D)=C& (all E (in(E,C)-> (exists S (apply(D,E)=S& (all T (in(T,S)<->in(T,the_carrier(B))& (exists U (netstr_induced_subset(U,A,B)& (exists V (element(V,the_carrier(B))&E=topstr_closure(A,U)&T=V&U=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,V)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,V))))))))))))))))).
% 29.04/28.91 (all A (ordinal(A)-> ((all B (ordinal(B)-> (in(B,A)-> (in(B,omega)-> (all C (element(C,powerset(powerset(B)))-> -(C!=empty_set& (all D (-(in(D,C)& (all E (in(E,C)&subset(D,E)->E=D))))))))))))-> (in(A,omega)-> (all F (element(F,powerset(powerset(A)))-> -(F!=empty_set& (all G (-(in(G,F)& (all H (in(H,F)&subset(G,H)->H=G))))))))))))-> (all A (ordinal(A)-> (in(A,omega)-> (all I (element(I,powerset(powerset(A)))-> -(I!=empty_set& (all J (-(in(J,I)& (all K (in(K,I)&subset(J,K)->K=J))))))))))).
% 29.04/28.91 all A B C (-empty_carrier(A)&topological_space(A)&top_str(A)& -empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all D E F ((all G (in(G,E)<->in(G,the_carrier(B))& (exists H (netstr_induced_subset(H,A,B)& (exists I (element(I,the_carrier(B))&D=topstr_closure(A,H)&G=I&H=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,I)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,I)))))))))& (all G (in(G,F)<->in(G,the_carrier(B))& (exists J (netstr_induced_subset(J,A,B)& (exists K (element(K,the_carrier(B))&D=topstr_closure(A,J)&G=K&J=relation_rng_as_subset(the_carrier(subnetstr_of_element(A,B,K)),the_carrier(A),the_mapping(A,subnetstr_of_element(A,B,K)))))))))->E=F))).
% 29.04/28.91 all A exists B (relation(B)&function(B)&relation_dom(B)=A& (all C (in(C,A)->apply(B,C)=singleton(C)))).
% 29.04/28.91 all A B (topological_space(A)&top_str(A)&element(B,powerset(the_carrier(A)))-> (exists C (element(C,powerset(powerset(the_carrier(A))))& (all D (element(D,powerset(the_carrier(A)))-> (in(D,C)<-> (exists E (element(E,powerset(the_carrier(A)))&E=D&closed_subset(E,A)&subset(B,D))))))))).
% 29.04/28.91 all A B (topological_space(A)&top_str(A)&element(B,powerset(powerset(the_carrier(A))))-> (exists C (element(C,powerset(powerset(the_carrier(A))))& (all D (element(D,powerset(the_carrier(A)))-> (in(D,C)<->in(set_difference(cast_as_carrier_subset(A),D),B))))))).
% 29.04/28.91 all A B (disjoint(A,B)->disjoint(B,A)).
% 29.04/28.91 all A B (e_quipotent(A,B)->e_quipotent(B,A)).
% 29.04/28.91 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 29.04/28.91 all A in(A,succ(A)).
% 29.04/28.91 all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set)& -(complements_of_subsets(A,B)!=empty_set&B=empty_set)).
% 29.04/28.91 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 29.04/28.91 all A B C (relation(C)-> (in(A,relation_rng(relation_rng_restriction(B,C)))<->in(A,B)&in(A,relation_rng(C)))).
% 29.04/28.91 all A B (relation(B)->subset(relation_rng(relation_rng_restriction(A,B)),A)).
% 29.04/28.91 all A B (relation(B)->subset(relation_rng_restriction(A,B),B)).
% 29.04/28.91 all A B (relation(B)->subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))).
% 29.04/28.91 all A B C (subset(A,B)->subset(cartesian_product2(A,C),cartesian_product2(B,C))&subset(cartesian_product2(C,A),cartesian_product2(C,B))).
% 29.04/28.91 all A B (relation(B)->relation_rng(relation_rng_restriction(A,B))=set_intersection2(relation_rng(B),A)).
% 29.04/28.91 all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 29.04/28.91 all A B (element(B,powerset(powerset(A)))-> (B!=empty_set->meet_of_subsets(A,complements_of_subsets(A,B))=subset_complement(A,union_of_subsets(A,B)))).
% 29.04/28.91 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))))).
% 29.04/28.91 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)))))))).
% 29.04/28.91 all A (one_sorted_str(A)->cast_as_carrier_subset(A)=the_carrier(A)).
% 29.04/28.91 all A B C (relation_of2_as_subset(C,A,B)->subset(relation_dom(C),A)&subset(relation_rng(C),B)).
% 29.04/28.91 all A B (element(B,powerset(powerset(A)))-> (B!=empty_set->union_of_subsets(A,complements_of_subsets(A,B))=subset_complement(A,meet_of_subsets(A,B)))).
% 29.04/28.91 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))->the_carrier(netstr_restr_to_element(A,B,C))=a_3_0_waybel_9(A,B,C)))))).
% 29.04/28.91 all A B (subset(A,B)->set_union2(A,B)=B).
% 29.04/28.91 all A exists B (in(A,B)& (all C D (in(C,B)&subset(D,C)->in(D,B)))& (all C (in(C,B)->in(powerset(C),B)))& (all C (-(subset(C,B)& -are_e_quipotent(C,B)& -in(C,B))))).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (compact_top_space(A)<-> (all B (element(B,powerset(powerset(the_carrier(A))))-> -(centered(B)&closed_subsets(B,A)&meet_of_subsets(the_carrier(A),B)=empty_set))))).
% 29.04/28.91 all A B (subset(A,B)&finite(B)->finite(A)).
% 29.04/28.91 all A (one_sorted_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> (finite(complements_of_subsets(the_carrier(A),B))<->finite(B))))).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (element(C,the_carrier(A))-> (in(C,lim_points_of_net(A,B))<->is_a_convergence_point_of_set(A,filter_of_net_str(A,B),C))))))).
% 29.04/28.91 all A B C (relation(C)->relation_dom_restriction(relation_rng_restriction(A,C),B)=relation_rng_restriction(A,relation_dom_restriction(C,B))).
% 29.04/28.91 all A B C (relation(C)-> (in(A,relation_image(C,B))<-> (exists D (in(D,relation_dom(C))&in(ordered_pair(D,A),C)&in(D,B))))).
% 29.04/28.91 all A B (relation(B)->subset(relation_image(B,A),relation_rng(B))).
% 29.04/28.91 all A B (relation(B)&function(B)->subset(relation_image(B,relation_inverse_image(B,A)),A)).
% 29.04/28.91 all A B (relation(B)->relation_image(B,A)=relation_image(B,set_intersection2(relation_dom(B),A))).
% 29.04/28.91 all A B (relation(B)-> (subset(A,relation_dom(B))->subset(A,relation_inverse_image(B,relation_image(B,A))))).
% 29.04/28.91 all A (relation(A)->relation_image(A,relation_dom(A))=relation_rng(A)).
% 29.04/28.91 all A B (relation(B)&function(B)-> (subset(A,relation_rng(B))->relation_image(B,relation_inverse_image(B,A))=A)).
% 29.04/28.91 all A B C D (relation_of2_as_subset(D,C,A)-> (subset(relation_rng(D),B)->relation_of2_as_subset(D,C,B))).
% 29.04/28.91 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))))).
% 29.04/28.91 all A B (finite(A)->finite(set_intersection2(A,B))).
% 29.04/28.91 all A (one_sorted_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A))=B))).
% 29.04/28.91 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)))&proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))&element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))->B=filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B))))).
% 29.04/28.91 all A (antisymmetric_relstr(A)&rel_str(A)-> (all B (ex_sup_of_relstr_set(A,B)<-> (exists C (element(C,the_carrier(A))&relstr_set_smaller(A,B,C)& (all D (element(D,the_carrier(A))-> (relstr_set_smaller(A,B,D)->related(A,C,D))))))))).
% 29.04/28.91 all A (relation(A)-> (all B (relation(B)->relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A))))).
% 29.04/28.91 all A B C (relation(C)-> (in(A,relation_inverse_image(C,B))<-> (exists D (in(D,relation_rng(C))&in(ordered_pair(A,D),C)&in(D,B))))).
% 29.04/28.91 all A B (relation(B)->subset(relation_inverse_image(B,A),relation_dom(B))).
% 29.04/28.91 all A B C D (relation_of2_as_subset(D,C,A)-> (subset(A,B)->relation_of2_as_subset(D,C,B))).
% 29.04/28.91 all A (top_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> (closed_subsets(B,A)<->open_subsets(complements_of_subsets(the_carrier(A),B),A))))).
% 29.04/28.91 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&directed_relstr(B)&net_str(B,A)-> (all C (element(C,the_carrier(B))-> (all D (element(D,the_carrier(B))-> (all E (element(E,the_carrier(netstr_restr_to_element(A,B,C)))-> (D=E->apply_netmap(A,B,D)=apply_netmap(A,netstr_restr_to_element(A,B,C),E))))))))))).
% 29.04/28.91 all A B C (relation(C)-> (in(A,relation_restriction(C,B))<->in(A,C)&in(A,cartesian_product2(B,B)))).
% 29.04/28.91 all A (antisymmetric_relstr(A)&rel_str(A)-> (all B (ex_inf_of_relstr_set(A,B)<-> (exists C (element(C,the_carrier(A))&relstr_element_smaller(A,B,C)& (all D (element(D,the_carrier(A))-> (relstr_element_smaller(A,B,D)->related(A,D,C))))))))).
% 29.04/28.91 all A B (relation(B)-> -(A!=empty_set&subset(A,relation_rng(B))&relation_inverse_image(B,A)=empty_set)).
% 29.04/28.91 all A B C (relation(C)-> (subset(A,B)->subset(relation_inverse_image(C,A),relation_inverse_image(C,B)))).
% 29.04/28.91 all A B (relation(B)&function(B)-> (finite(A)->finite(relation_image(B,A)))).
% 29.04/28.91 all A (one_sorted_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset_complement(the_carrier(A),B)=subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)))).
% 29.04/28.91 all A (top_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> (open_subsets(B,A)<->closed_subsets(complements_of_subsets(the_carrier(A),B),A))))).
% 29.04/28.91 all A B (relation(B)->relation_restriction(B,A)=relation_dom_restriction(relation_rng_restriction(A,B),A)).
% 29.04/28.91 all A B subset(set_intersection2(A,B),A).
% 29.04/28.91 all A (finite(A)-> (all B (element(B,powerset(powerset(A)))-> -(B!=empty_set& (all C (-(in(C,B)& (all D (in(D,B)&subset(C,D)->D=C))))))))).
% 29.04/28.91 all A B (relation(B)->relation_restriction(B,A)=relation_rng_restriction(A,relation_dom_restriction(B,A))).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_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)))&proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))&element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))-> (all C (element(C,the_carrier(A))-> (in(C,lim_points_of_net(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)))<->is_a_convergence_point_of_set(A,B,C))))))).
% 29.04/28.91 all A (bottom_of_relstr(boole_POSet(A))=empty_set).
% 29.04/28.91 all A B C (relation(C)-> (in(A,relation_field(relation_restriction(C,B)))->in(A,relation_field(C))&in(A,B))).
% 29.04/28.91 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 29.04/28.91 all A (one_sorted_str(A)-> (all B (net_str(B,A)-> (all C (subnetstr(C,A,B)->subset(the_carrier(C),the_carrier(B))))))).
% 29.04/28.91 all A (set_union2(A,empty_set)=A).
% 29.04/28.91 all A B (element(B,the_carrier(boole_lattice(A)))-> (all C (element(C,the_carrier(boole_lattice(A)))->join(boole_lattice(A),B,C)=set_union2(B,C)&meet(boole_lattice(A),B,C)=set_intersection2(B,C)))).
% 29.04/28.91 all A B (in(A,B)->element(A,B)).
% 29.04/28.91 all A (-empty_carrier(A)&transitive_relstr(A)&rel_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (-empty(B)&directed_subset(B,A)<-> (all C (finite(C)&element(C,powerset(B))-> (exists D (element(D,the_carrier(A))&in(D,B)&relstr_set_smaller(A,C,D))))))))).
% 29.04/28.91 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 29.04/28.91 all A (the_carrier(incl_POSet(A))=A&the_InternalRel(incl_POSet(A))=inclusion_order(A)).
% 29.04/28.91 powerset(empty_set)=singleton(empty_set).
% 29.04/28.91 all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_dom(C))&in(B,relation_rng(C)))).
% 29.04/28.91 all A B (relation(B)->subset(relation_field(relation_restriction(B,A)),relation_field(B))&subset(relation_field(relation_restriction(B,A)),A)).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,powerset(the_carrier(A)))-> (in(B,topstr_closure(A,C))-> (all D (-empty(D)&filtered_subset(D,boole_POSet(cast_as_carrier_subset(A)))&upper_relstr_subset(D,boole_POSet(cast_as_carrier_subset(A)))&proper_element(D,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))&element(D,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))-> (D=neighborhood_system(A,B)->is_often_in(A,net_of_bool_filter(A,cast_as_carrier_subset(A),D),C)))))))))).
% 29.04/28.91 all A (one_sorted_str(A)-> (all B (net_str(B,A)-> (all C (subnetstr(C,A,B)-> (all D (element(D,the_carrier(B))-> (all E (element(E,the_carrier(B))-> (all F (element(F,the_carrier(C))-> (all G (element(G,the_carrier(C))-> (D=F&E=G&related(C,F,G)->related(B,D,E))))))))))))))).
% 29.04/28.91 all A B (relation(B)&function(B)-> (all C (relation(C)&function(C)-> (in(A,relation_dom(relation_composition(C,B)))<->in(A,relation_dom(C))&in(apply(C,A),relation_dom(B)))))).
% 29.04/28.91 all A B C D (function(D)&quasi_total(D,A,B)&relation_of2_as_subset(D,A,B)-> (all E (relation(E)&function(E)-> (in(C,A)->B=empty_set|apply(relation_composition(D,E),C)=apply(E,apply(D,C)))))).
% 29.04/28.91 all A (epsilon_transitive(A)-> (all B (ordinal(B)-> (proper_subset(A,B)->in(A,B))))).
% 29.04/28.91 all A (relation(A)->subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))).
% 29.04/28.91 all A B C (relation(C)->subset(fiber(relation_restriction(C,A),B),fiber(C,B))).
% 29.04/28.91 all A (one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C (-empty_carrier(C)&full_subnetstr(C,A,B)&subnetstr(C,A,B)-> (all D (element(D,the_carrier(B))-> (all E (element(E,the_carrier(B))-> (all F (element(F,the_carrier(C))-> (all G (element(G,the_carrier(C))-> (D=F&E=G&related(B,D,E)->related(C,F,G))))))))))))))).
% 29.04/28.91 all A B (relation(B)&function(B)-> (all C (relation(C)&function(C)-> (in(A,relation_dom(relation_composition(C,B)))->apply(relation_composition(C,B),A)=apply(B,apply(C,A)))))).
% 29.04/28.91 all A (one_sorted_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B))=B))).
% 29.04/28.91 all A B C (relation_of2_as_subset(C,B,A)-> ((all D (-(in(D,B)& (all E (-in(ordered_pair(D,E),C))))))<->relation_dom_as_subset(B,A,C)=B)).
% 29.04/28.91 all A B (relation(B)-> (reflexive(B)->reflexive(relation_restriction(B,A)))).
% 29.04/28.91 all A B (relation(B)&function(B)-> (all C (relation(C)&function(C)-> (in(A,relation_dom(B))->apply(relation_composition(B,C),A)=apply(C,apply(B,A)))))).
% 29.04/28.91 all A (-empty_carrier(A)&meet_commutative(A)&meet_absorbing(A)&latt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))->below(A,meet_commut(A,B,C),B)))))).
% 29.04/28.91 all A B (ordinal(B)-> (in(A,B)->ordinal(A))).
% 29.04/28.91 all A B C (relation_of2_as_subset(C,A,B)-> ((all D (-(in(D,B)& (all E (-in(ordered_pair(E,D),C))))))<->relation_rng_as_subset(A,B,C)=B)).
% 29.04/28.91 all A B (relation(B)-> (connected(B)->connected(relation_restriction(B,A)))).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (all C (element(C,the_carrier(A))-> (in(C,topstr_closure(A,B))<-> (exists D (-empty_carrier(D)&transitive_relstr(D)&directed_relstr(D)&net_str(D,A)&is_eventually_in(A,D,B)&is_a_cluster_point_of_netstr(A,D,C))))))))).
% 29.04/28.91 all A (ordinal(A)-> (all B (ordinal(B)-> -(-in(A,B)&A!=B& -in(B,A))))).
% 29.04/28.91 all A B (relation(B)-> (transitive(B)->transitive(relation_restriction(B,A)))).
% 29.04/28.91 all A (antisymmetric_relstr(A)&rel_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (related(A,B,C)&related(A,C,B)->B=C)))))).
% 29.04/28.91 all A (relation(A)-> (all B (relation(B)-> (subset(A,B)->subset(relation_dom(A),relation_dom(B))&subset(relation_rng(A),relation_rng(B)))))).
% 29.04/28.91 all A B (relation(B)-> (antisymmetric(B)->antisymmetric(relation_restriction(B,A)))).
% 29.04/28.91 all A B (relation(B)-> (well_orders(B,A)->relation_field(relation_restriction(B,A))=A&well_ordering(relation_restriction(B,A)))).
% 29.04/28.91 all A (relation(A)&function(A)-> (finite(relation_dom(A))->finite(relation_rng(A)))).
% 29.04/28.91 all A (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (below(A,B,C)&below(A,C,B)->B=C)))))).
% 29.04/28.91 all A (transitive_relstr(A)&rel_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (all D (element(D,the_carrier(A))-> (related(A,B,C)&related(A,C,D)->related(A,B,D))))))))).
% 29.04/28.91 all A exists B (relation(B)&well_orders(B,A)).
% 29.04/28.91 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 29.04/28.91 all A B (-empty_carrier(B)&lattice(B)&latt_str(B)-> (all C (element(C,the_carrier(B))-> (latt_set_smaller(B,C,A)<->relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)))))).
% 29.04/28.91 all A (-empty(A)-> -((all B (-(in(B,A)&B=empty_set)))& (all B (relation(B)&function(B)-> -(relation_dom(B)=A& (all C (in(C,A)->in(apply(B,C),C)))))))).
% 29.04/28.91 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 29.04/28.91 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (is_eventually_in(A,B,C)->is_often_in(A,B,C)))))).
% 29.04/28.91 all A B (-empty_carrier(B)&lattice(B)&latt_str(B)-> (all C (element(C,the_carrier(poset_of_lattice(B)))-> (relstr_element_smaller(poset_of_lattice(B),A,C)<->latt_set_smaller(B,cast_to_el_of_lattice(B,C),A))))).
% 29.04/28.91 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)<->open_subset(subset_complement(the_carrier(A),B),A))))).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (element(C,the_carrier(A))-> (in(C,lim_points_of_net(A,B))->is_a_cluster_point_of_netstr(A,B,C))))))).
% 29.04/28.91 all A (-empty_carrier(A)&lattice(A)&complete_latt_str(A)&latt_str(A)-> (all B (join_of_latt_set(A,B)=join_on_relstr(poset_of_lattice(A),B)&meet_of_latt_set(A,B)=meet_on_relstr(poset_of_lattice(A),B)))).
% 29.04/28.91 all A (set_intersection2(A,empty_set)=empty_set).
% 29.04/28.91 all A B (element(B,the_carrier(boole_lattice(A)))-> (all C (element(C,the_carrier(boole_lattice(A)))-> (below(boole_lattice(A),B,C)<->subset(B,C))))).
% 29.04/28.91 all A B (element(A,B)->empty(B)|in(A,B)).
% 29.04/28.91 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 29.04/28.91 all A reflexive(inclusion_relation(A)).
% 29.04/28.91 all A subset(empty_set,A).
% 29.04/28.91 all A (-empty(A)-> (all B (-empty(B)&filtered_subset(B,boole_POSet(A))&upper_relstr_subset(B,boole_POSet(A))&proper_element(B,powerset(the_carrier(boole_POSet(A))))&element(B,powerset(the_carrier(boole_POSet(A))))-> (all C (-(in(C,B)&empty(C))))))).
% 29.04/28.91 all A B (element(B,the_carrier(boole_POSet(A)))-> (all C (element(C,the_carrier(boole_POSet(A)))-> (related_reflexive(boole_POSet(A),B,C)<->subset(B,C))))).
% 29.04/28.91 all A B (-empty_carrier(B)&lattice(B)&latt_str(B)-> (all C (element(C,the_carrier(B))-> (latt_element_smaller(B,C,A)<->relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)))))).
% 29.04/28.91 all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_field(C))&in(B,relation_field(C)))).
% 29.04/28.91 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (open_subset(B,A)<->closed_subset(subset_complement(the_carrier(A),B),A))))).
% 29.04/28.91 all A (antisymmetric_relstr(A)&rel_str(A)-> (all B (element(B,the_carrier(A))-> (all C ((B=join_on_relstr(A,C)&ex_sup_of_relstr_set(A,C)->relstr_set_smaller(A,C,B)& (all D (element(D,the_carrier(A))-> (relstr_set_smaller(A,C,D)->related(A,B,D)))))& (relstr_set_smaller(A,C,B)& (all D (element(D,the_carrier(A))-> (relstr_set_smaller(A,C,D)->related(A,B,D))))->B=join_on_relstr(A,C)&ex_sup_of_relstr_set(A,C))))))).
% 29.04/28.91 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (is_often_in(A,B,C)-> -empty_carrier(preimage_subnetstr(A,B,C))&directed_relstr(preimage_subnetstr(A,B,C))))))).
% 29.04/28.91 all A B (-empty_carrier(B)&lattice(B)&latt_str(B)-> (all C (element(C,the_carrier(poset_of_lattice(B)))-> (relstr_set_smaller(poset_of_lattice(B),A,C)<->latt_element_smaller(B,cast_to_el_of_lattice(B,C),A))))).
% 29.04/28.91 all A ((all B (in(B,A)->ordinal(B)&subset(B,A)))->ordinal(A)).
% 29.04/28.91 all A B (relation(B)-> (well_founded_relation(B)->well_founded_relation(relation_restriction(B,A)))).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (element(C,the_carrier(A))-> (is_a_cluster_point_of_netstr(A,B,C)<-> (all D (netstr_induced_subset(D,A,B)->in(C,topstr_closure(A,D)))))))))).
% 29.04/28.91 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (is_often_in(A,B,C)->subnet(preimage_subnetstr(A,B,C),A,B)))))).
% 29.04/28.91 all A (-empty_carrier(A)&lattice(A)&latt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A))<->below_refl(A,B,C))))))).
% 29.04/28.91 all A B (ordinal(B)-> -(subset(A,B)&A!=empty_set& (all C (ordinal(C)-> -(in(C,A)& (all D (ordinal(D)-> (in(D,A)->ordinal_subset(C,D))))))))).
% 29.04/28.91 all A B (relation(B)-> (well_ordering(B)->well_ordering(relation_restriction(B,A)))).
% 29.04/28.91 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C D (subnet(D,A,B)-> (D=preimage_subnetstr(A,B,C)->is_eventually_in(A,D,C))))))).
% 29.04/28.91 all A (ordinal(A)-> (all B (ordinal(B)-> (in(A,B)<->ordinal_subset(succ(A),B))))).
% 29.04/28.91 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 29.04/28.91 all A B C D (ordered_pair(A,B)=ordered_pair(C,D)->A=C&B=D).
% 29.04/28.91 all A B (relation(B)&function(B)-> (B=identity_relation(A)<->relation_dom(B)=A& (all C (in(C,A)->apply(B,C)=C)))).
% 29.04/28.91 all A (-empty_carrier(A)&lattice(A)&complete_latt_str(A)&latt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (B=meet_of_latt_set(A,C)<->latt_set_smaller(A,B,C)& (all D (element(D,the_carrier(A))-> (latt_set_smaller(A,D,C)->below_refl(A,D,B))))))))).
% 29.04/28.91 all A B (in(B,A)->apply(identity_relation(A),B)=B).
% 29.04/28.91 all A B subset(set_difference(A,B),A).
% 29.04/28.91 all A (relation(A)->relation_rng(A)=relation_dom(relation_inverse(A))&relation_dom(A)=relation_rng(relation_inverse(A))).
% 29.04/28.91 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 29.04/28.91 all A B (subset(singleton(A),B)<->in(A,B)).
% 29.04/28.91 all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C)).
% 29.04/28.91 all A B (relation(B)-> (well_ordering(B)&subset(A,relation_field(B))->relation_field(relation_restriction(B,A))=A)).
% 29.04/28.91 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 29.04/28.91 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 29.04/28.91 all A (set_difference(A,empty_set)=A).
% 29.04/28.91 all A (lower_bounded_semilattstr(boole_lattice(A))&bottom_of_semilattstr(boole_lattice(A))=empty_set).
% 29.04/28.91 all A B C (-(in(A,B)&in(B,C)&in(C,A))).
% 29.04/28.91 all A B (element(A,powerset(B))<->subset(A,B)).
% 29.04/28.91 all A transitive(inclusion_relation(A)).
% 29.04/28.91 all A B (-(-disjoint(A,B)& (all C (-(in(C,A)&in(C,B)))))& -((exists C (in(C,A)&in(C,B)))&disjoint(A,B))).
% 29.04/28.91 all A (subset(A,empty_set)->A=empty_set).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,the_carrier(A))-> (all C (in(C,neighborhood_system(A,B))<->point_neighbourhood(C,A,B)))))).
% 29.04/28.91 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 29.04/28.91 all A (ordinal(A)-> (being_limit_ordinal(A)<-> (all B (ordinal(B)-> (in(B,A)->in(succ(B),A)))))).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (subnet(C,A,B)->subset(lim_points_of_net(A,B),lim_points_of_net(A,C))))))).
% 29.04/28.91 all A (ordinal(A)-> -(-being_limit_ordinal(A)& (all B (ordinal(B)->A!=succ(B))))& -((exists B (ordinal(B)&A=succ(B)))&being_limit_ordinal(A))).
% 29.04/28.91 all A (-empty_carrier(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&rel_str(A)->ex_sup_of_relstr_set(A,empty_set)&ex_inf_of_relstr_set(A,the_carrier(A))).
% 29.04/28.91 all A B (element(B,powerset(A))-> (all C (element(C,powerset(A))-> (disjoint(B,C)<->subset(B,subset_complement(A,C)))))).
% 29.04/28.91 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> ((all C (element(C,powerset(the_carrier(A)))-> (in(C,B)->closed_subset(C,A))))->closed_subset(meet_of_subsets(the_carrier(A),B),A))))).
% 29.04/28.91 all A (relation(A)-> (all B (relation(B)->subset(relation_dom(relation_composition(A,B)),relation_dom(A))))).
% 29.04/28.91 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset(interior(A,B),B)))).
% 29.04/28.91 all A (-empty_carrier(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&rel_str(A)-> (all B (element(B,the_carrier(A))->related(A,bottom_of_relstr(A),B)))).
% 29.04/28.91 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (all C (in(C,the_carrier(A))-> (in(C,topstr_closure(A,B))<-> (all D (element(D,powerset(the_carrier(A)))-> (closed_subset(D,A)&subset(B,D)->in(C,D)))))))))).
% 29.04/28.91 all A (relation(A)-> (all B (relation(B)->subset(relation_rng(relation_composition(A,B)),relation_rng(B))))).
% 29.04/28.91 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 29.04/28.91 all A B C D (function(D)&quasi_total(D,A,B)&relation_of2_as_subset(D,A,B)-> (B!=empty_set-> (all E (in(E,relation_inverse_image(D,C))<->in(E,A)&in(apply(D,E),C))))).
% 29.04/28.91 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (exists C (element(C,powerset(powerset(the_carrier(A))))& (all D (element(D,powerset(the_carrier(A)))-> (in(D,C)<->closed_subset(D,A)&subset(B,D))))&topstr_closure(A,B)=meet_of_subsets(the_carrier(A),C)))))).
% 29.04/28.91 all A (relation(A)-> (all B (relation(B)-> (subset(relation_rng(A),relation_dom(B))->relation_dom(relation_composition(A,B))=relation_dom(A))))).
% 29.04/28.91 all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set)).
% 29.04/28.91 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 29.04/28.91 all A (relation(A)-> (all B (relation(B)-> (subset(relation_dom(A),relation_rng(B))->relation_rng(relation_composition(B,A))=relation_rng(A))))).
% 29.04/28.91 all A B (element(B,powerset(powerset(A)))-> (B!=empty_set->subset_difference(A,cast_to_subset(A),union_of_subsets(A,B))=meet_of_subsets(A,complements_of_subsets(A,B)))).
% 29.04/28.91 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset(B,topstr_closure(A,B))))).
% 29.04/28.91 all A B (element(B,powerset(powerset(A)))-> (B!=empty_set->union_of_subsets(A,complements_of_subsets(A,B))=subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)))).
% 29.04/28.91 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 29.04/28.91 all A (relation(A)-> (all B (relation(B)-> (all C (relation(C)&function(C)-> (relation_isomorphism(A,B,C)->relation_isomorphism(B,A,function_inverse(C)))))))).
% 29.04/28.91 all A (set_difference(empty_set,A)=empty_set).
% 29.04/28.91 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 29.04/28.91 all A (the_carrier(boole_POSet(A))=powerset(A)).
% 29.04/28.91 all A (ordinal(A)->connected(inclusion_relation(A))).
% 29.04/28.91 all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B))).
% 29.04/28.91 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,the_carrier(A))-> (all C (upper_relstr_subset(C,boole_POSet(cast_as_carrier_subset(A)))&element(C,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))-> (is_a_convergence_point_of_set(A,C,B)<->subset(neighborhood_system(A,B),C))))))).
% 29.04/28.91 all A (boole_POSet(A)=incl_POSet(powerset(A))).
% 29.04/28.91 all A (-empty_carrier(A)&lattice(A)&complete_latt_str(A)&latt_str(A)-> -empty_carrier(A)&lattice(A)&lower_bounded_semilattstr(A)&latt_str(A)&bottom_of_semilattstr(A)=join_of_latt_set(A,empty_set)).
% 29.04/28.91 all A (A!=empty_set-> (all B (element(B,powerset(A))-> (all C (element(C,A)-> (-in(C,B)->in(C,subset_complement(A,B)))))))).
% 29.04/28.91 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))->open_subset(interior(A,B),A)))).
% 29.04/28.91 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)->topstr_closure(A,B)=B)& (topological_space(A)&topstr_closure(A,B)=B->closed_subset(B,A))))).
% 29.04/28.91 all A (relation(A)-> (all B (relation(B)-> (all C (relation(C)&function(C)-> (relation_isomorphism(A,B,C)-> (reflexive(A)->reflexive(B))& (transitive(A)->transitive(B))& (connected(A)->connected(B))& (antisymmetric(A)->antisymmetric(B))& (well_founded_relation(A)->well_founded_relation(B)))))))).
% 29.97/29.88 all A (relation(A)&function(A)-> (one_to_one(A)-> (all B (relation(B)&function(B)-> (B=function_inverse(A)<->relation_dom(B)=relation_rng(A)& (all C D ((in(C,relation_rng(A))&D=apply(B,C)->in(D,relation_dom(A))&C=apply(A,D))& (in(D,relation_dom(A))&C=apply(A,D)->in(C,relation_rng(A))&D=apply(B,C))))))))).
% 29.97/29.88 all A B C (element(C,powerset(A))-> -(in(B,subset_complement(A,C))&in(B,C))).
% 29.97/29.88 all A (relation(A)-> (all B (relation(B)-> (all C (relation(C)&function(C)-> (well_ordering(A)&relation_isomorphism(A,B,C)->well_ordering(B))))))).
% 29.97/29.88 all A (relation(A)&function(A)-> (one_to_one(A)->relation_rng(A)=relation_dom(function_inverse(A))&relation_dom(A)=relation_rng(function_inverse(A)))).
% 29.97/29.88 all A (topological_space(A)&top_str(A)-> (all B (top_str(B)-> (all C (element(C,powerset(the_carrier(A)))-> (all D (element(D,powerset(the_carrier(B)))-> (open_subset(D,B)->interior(B,D)=D)& (interior(A,C)=C->open_subset(C,A))))))))).
% 29.97/29.88 all A (relation(A)-> ((all B C (-in(ordered_pair(B,C),A)))->A=empty_set)).
% 29.97/29.88 all A B (relation(B)&function(B)-> (one_to_one(B)&in(A,relation_rng(B))->A=apply(B,apply(function_inverse(B),A))&A=apply(relation_composition(function_inverse(B),B),A))).
% 29.97/29.88 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (all C (element(C,the_carrier(A))-> (open_subset(B,A)&in(C,B)->point_neighbourhood(B,A,C))))))).
% 29.97/29.88 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 29.97/29.88 all A B (element(B,powerset(A))-> (proper_element(B,powerset(A))<->B!=A)).
% 29.97/29.88 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> -(is_a_cover_of_carrier(A,B)&B=empty_set)))).
% 29.97/29.88 all A (relation(A)-> (well_founded_relation(A)<->is_well_founded_in(A,relation_field(A)))).
% 29.97/29.88 all A antisymmetric(inclusion_relation(A)).
% 29.97/29.88 relation_dom(empty_set)=empty_set.
% 29.97/29.88 relation_rng(empty_set)=empty_set.
% 29.97/29.88 all A B (-(subset(A,B)&proper_subset(B,A))).
% 29.97/29.88 all A (rel_str(A)-> (all B (subrelstr(B,A)-> (all C (element(C,the_carrier(A))-> (all D (element(D,the_carrier(A))-> (all E (element(E,the_carrier(B))-> (all F (element(F,the_carrier(B))-> (E=C&F=D&related(B,E,F)->related(A,C,D))))))))))))).
% 29.97/29.88 all A (rel_str(A)-> (all B (full_subrelstr(B,A)&subrelstr(B,A)-> (all C (element(C,the_carrier(A))-> (all D (element(D,the_carrier(A))-> (all E (element(E,the_carrier(B))-> (all F (element(F,the_carrier(B))-> (E=C&F=D&related(A,C,D)&in(E,the_carrier(B))&in(F,the_carrier(B))->related(B,E,F))))))))))))).
% 29.97/29.88 all A (relation(A)&function(A)-> (one_to_one(A)->one_to_one(function_inverse(A)))).
% 29.97/29.88 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 29.97/29.88 all A (relation(A)-> (relation_dom(A)=empty_set|relation_rng(A)=empty_set->A=empty_set)).
% 29.97/29.88 all A (relation(A)-> (relation_dom(A)=empty_set<->relation_rng(A)=empty_set)).
% 29.97/29.88 all A B (set_difference(A,singleton(B))=A<-> -in(B,A)).
% 29.97/29.88 all A B (relation(B)&function(B)-> (all C (relation(C)&function(C)-> (B=relation_dom_restriction(C,A)<->relation_dom(B)=set_intersection2(relation_dom(C),A)& (all D (in(D,relation_dom(B))->apply(B,D)=apply(C,D))))))).
% 29.97/29.88 all A (unordered_pair(A,A)=singleton(A)).
% 29.97/29.88 all A (empty(A)->A=empty_set).
% 29.97/29.88 all A B C D (function(D)&quasi_total(D,A,B)&relation_of2_as_subset(D,A,B)-> (in(C,A)->B=empty_set|in(apply(D,C),relation_rng(D)))).
% 29.97/29.88 all A (ordinal(A)->well_founded_relation(inclusion_relation(A))).
% 29.97/29.88 all A (rel_str(A)-> (all B (element(B,the_carrier(A))->relstr_set_smaller(A,empty_set,B)&relstr_element_smaller(A,empty_set,B)))).
% 29.97/29.88 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (all C (element(C,the_carrier(A))-> (in(C,topstr_closure(A,B))<-> (all D (point_neighbourhood(D,A,C)-> -disjoint(D,B))))))))).
% 29.97/29.88 all A B (subset(singleton(A),singleton(B))->A=B).
% 29.97/29.88 all A B C (relation(C)&function(C)-> (in(B,relation_dom(relation_dom_restriction(C,A)))->apply(relation_dom_restriction(C,A
% 29.97/29.88 Search stopped in tp_alloc by max_mem option.
% 29.97/29.88 ),B)=apply(C,B))).
% 29.97/29.88 all A (relation_dom(identity_relation(A))=A&relation_rng(identity_relation(A))=A).
% 29.97/29.88 all A B C (relation(C)&function(C)-> (in(B,A)->apply(relation_dom_restriction(C,A),B)=apply(C,B))).
% 29.97/29.88 all A B C D (relation(D)-> (in(ordered_pair(A,B),relation_composition(identity_relation(C),D))<->in(A,C)&in(ordered_pair(A,B),D))).
% 29.97/29.88 all A B (-(in(A,B)&empty(B))).
% 29.97/29.88 all A (-empty_carrier(A)&lattice(A)&latt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (below_refl(A,B,C)<->related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C)))))))).
% 29.97/29.88 all A B (pair_first(ordered_pair(A,B))=A&pair_second(ordered_pair(A,B))=B).
% 29.97/29.88 all A B (-(in(A,B)& (all C (-(in(C,B)& (all D (-(in(D,B)&in(D,C))))))))).
% 29.97/29.88 all A (ordinal(A)->well_ordering(inclusion_relation(A))).
% 29.97/29.88 all A B subset(A,set_union2(A,B)).
% 29.97/29.88 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 29.97/29.88 all A B C (relation(C)-> (in(A,relation_dom(relation_dom_restriction(C,B)))<->in(A,B)&in(A,relation_dom(C)))).
% 29.97/29.88 all A B (relation(B)->subset(relation_dom_restriction(B,A),B)).
% 29.97/29.88 all A B (-(empty(A)&A!=B&empty(B))).
% 29.97/29.88 all A B C (relation(C)&function(C)-> (in(ordered_pair(A,B),C)<->in(A,relation_dom(C))&B=apply(C,A))).
% 29.97/29.88 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&net_str(B,A)-> (all C D (subset(C,D)-> (is_eventually_in(A,B,C)->is_eventually_in(A,B,D))& (is_often_in(A,B,C)->is_often_in(A,B,D))))))).
% 29.97/29.88 all A (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&rel_str(A)-> (all B (-empty(B)&filtered_subset(B,A)&upper_relstr_subset(B,A)&element(B,powerset(the_carrier(A)))-> (proper_element(B,powerset(the_carrier(A)))<-> -in(bottom_of_relstr(A),B))))).
% 29.97/29.88 all A (relation(A)-> (well_orders(A,relation_field(A))<->well_ordering(A))).
% 29.97/29.88 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 29.97/29.88 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 29.97/29.88 all A B (relation(B)->relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A)).
% 29.97/29.88 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (element(B,the_carrier(A))->apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B)=B))).
% 29.97/29.88 all A B (in(A,B)->subset(A,union(B))).
% 29.97/29.88 all A B (relation(B)->relation_dom_restriction(B,A)=relation_composition(identity_relation(A),B)).
% 29.97/29.88 all A B (relation(B)->subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))).
% 29.97/29.88 all A (union(powerset(A))=A).
% 29.97/29.88 all A B C D (function(D)&quasi_total(D,A,B)&relation_of2_as_subset(D,A,B)-> (subset(B,C)->B=empty_set&A!=empty_set|function(D)&quasi_total(D,A,C)&relation_of2_as_subset(D,A,C))).
% 29.97/29.88 all A exists B (in(A,B)& (all C D (in(C,B)&subset(D,C)->in(D,B)))& (all C (-(in(C,B)& (all D (-(in(D,B)& (all E (subset(E,C)->in(E,D)))))))))& (all C (-(subset(C,B)& -are_e_quipotent(C,B)& -in(C,B))))).
% 29.97/29.88 all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (-empty_carrier(B)&transitive_relstr(B)&directed_relstr(B)&net_str(B,A)-> (all C (netstr_induced_subset(C,A,B)->is_eventually_in(A,B,C)))))).
% 29.97/29.88 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 29.97/29.88 end_of_list.
% 29.97/29.88
% 29.97/29.88 Search stopped in tp_alloc by max_mem option.
% 29.97/29.88
% 29.97/29.88 ============ end of search ============
% 29.97/29.88
% 29.97/29.88 -------------- statistics -------------
% 29.97/29.88 clauses given 0
% 29.97/29.88 clauses generated 0
% 29.97/29.88 clauses kept 0
% 29.97/29.88 clauses forward subsumed 0
% 29.97/29.88 clauses back subsumed 0
% 29.97/29.88 Kbytes malloced 11718
% 29.97/29.88
% 29.97/29.88 ----------- times (seconds) -----------
% 29.97/29.88 user CPU time 1.05 (0 hr, 0 min, 1 sec)
% 29.97/29.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 29.97/29.88 wall-clock time 29 (0 hr, 0 min, 29 sec)
% 29.97/29.88
% 29.97/29.88 Process 1334 finished Wed Jul 27 07:45:14 2022
% 29.97/29.88 Otter interrupted
% 29.97/29.88 PROOF NOT FOUND
%------------------------------------------------------------------------------