TSTP Solution File: SEU261+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU261+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 13:15:22 EDT 2022
% Result : Theorem 8.41s 8.57s
% Output : Refutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 18
% Syntax : Number of clauses : 30 ( 19 unt; 0 nHn; 30 RR)
% Number of literals : 76 ( 0 equ; 47 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(169,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) ),
file('SEU261+2.p',unknown),
[] ).
cnf(170,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) ),
file('SEU261+2.p',unknown),
[] ).
cnf(171,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) ),
file('SEU261+2.p',unknown),
[] ).
cnf(172,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| connected(A) ),
file('SEU261+2.p',unknown),
[] ).
cnf(173,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) ),
file('SEU261+2.p',unknown),
[] ).
cnf(174,axiom,
( ~ relation(A)
| well_ordering(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ antisymmetric(A)
| ~ connected(A)
| ~ well_founded_relation(A) ),
file('SEU261+2.p',unknown),
[] ).
cnf(484,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ reflexive(A)
| reflexive(B) ),
file('SEU261+2.p',unknown),
[] ).
cnf(485,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ transitive(A)
| transitive(B) ),
file('SEU261+2.p',unknown),
[] ).
cnf(486,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ connected(A)
| connected(B) ),
file('SEU261+2.p',unknown),
[] ).
cnf(487,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ antisymmetric(A)
| antisymmetric(B) ),
file('SEU261+2.p',unknown),
[] ).
cnf(488,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ well_founded_relation(A)
| well_founded_relation(B) ),
file('SEU261+2.p',unknown),
[] ).
cnf(504,axiom,
~ well_ordering(dollar_c14),
file('SEU261+2.p',unknown),
[] ).
cnf(880,axiom,
relation(dollar_c15),
file('SEU261+2.p',unknown),
[] ).
cnf(881,axiom,
relation(dollar_c14),
file('SEU261+2.p',unknown),
[] ).
cnf(882,axiom,
relation(dollar_c13),
file('SEU261+2.p',unknown),
[] ).
cnf(883,axiom,
function(dollar_c13),
file('SEU261+2.p',unknown),
[] ).
cnf(884,axiom,
well_ordering(dollar_c15),
file('SEU261+2.p',unknown),
[] ).
cnf(885,axiom,
relation_isomorphism(dollar_c15,dollar_c14,dollar_c13),
file('SEU261+2.p',unknown),
[] ).
cnf(991,plain,
well_founded_relation(dollar_c15),
inference(hyper,[status(thm)],[884,173,880]),
[iquote('hyper,884,173,880')] ).
cnf(992,plain,
connected(dollar_c15),
inference(hyper,[status(thm)],[884,172,880]),
[iquote('hyper,884,172,880')] ).
cnf(993,plain,
antisymmetric(dollar_c15),
inference(hyper,[status(thm)],[884,171,880]),
[iquote('hyper,884,171,880')] ).
cnf(994,plain,
transitive(dollar_c15),
inference(hyper,[status(thm)],[884,170,880]),
[iquote('hyper,884,170,880')] ).
cnf(995,plain,
reflexive(dollar_c15),
inference(hyper,[status(thm)],[884,169,880]),
[iquote('hyper,884,169,880')] ).
cnf(998,plain,
well_founded_relation(dollar_c14),
inference(hyper,[status(thm)],[885,488,880,881,882,883,991]),
[iquote('hyper,885,488,880,881,882,883,991')] ).
cnf(999,plain,
antisymmetric(dollar_c14),
inference(hyper,[status(thm)],[885,487,880,881,882,883,993]),
[iquote('hyper,885,487,880,881,882,883,993')] ).
cnf(1000,plain,
connected(dollar_c14),
inference(hyper,[status(thm)],[885,486,880,881,882,883,992]),
[iquote('hyper,885,486,880,881,882,883,992')] ).
cnf(1001,plain,
transitive(dollar_c14),
inference(hyper,[status(thm)],[885,485,880,881,882,883,994]),
[iquote('hyper,885,485,880,881,882,883,994')] ).
cnf(1002,plain,
reflexive(dollar_c14),
inference(hyper,[status(thm)],[885,484,880,881,882,883,995]),
[iquote('hyper,885,484,880,881,882,883,995')] ).
cnf(1004,plain,
well_ordering(dollar_c14),
inference(hyper,[status(thm)],[1002,174,881,1001,999,1000,998]),
[iquote('hyper,1002,174,881,1001,999,1000,998')] ).
cnf(1005,plain,
$false,
inference(binary,[status(thm)],[1004,504]),
[iquote('binary,1004.1,504.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU261+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 08:05:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.38/4.49 ----- Otter 3.3f, August 2004 -----
% 4.38/4.49 The process was started by sandbox on n016.cluster.edu,
% 4.38/4.49 Wed Jul 27 08:05:22 2022
% 4.38/4.49 The command was "./otter". The process ID is 2029.
% 4.38/4.49
% 4.38/4.49 set(prolog_style_variables).
% 4.38/4.49 set(auto).
% 4.38/4.49 dependent: set(auto1).
% 4.38/4.49 dependent: set(process_input).
% 4.38/4.49 dependent: clear(print_kept).
% 4.38/4.49 dependent: clear(print_new_demod).
% 4.38/4.49 dependent: clear(print_back_demod).
% 4.38/4.49 dependent: clear(print_back_sub).
% 4.38/4.49 dependent: set(control_memory).
% 4.38/4.49 dependent: assign(max_mem, 12000).
% 4.38/4.49 dependent: assign(pick_given_ratio, 4).
% 4.38/4.49 dependent: assign(stats_level, 1).
% 4.38/4.49 dependent: assign(max_seconds, 10800).
% 4.38/4.49 clear(print_given).
% 4.38/4.49
% 4.38/4.49 formula_list(usable).
% 4.38/4.49 all A (A=A).
% 4.38/4.49 all A B (in(A,B)-> -in(B,A)).
% 4.38/4.49 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 4.38/4.49 all A (empty(A)->function(A)).
% 4.38/4.49 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 4.38/4.49 all A (empty(A)->relation(A)).
% 4.38/4.49 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 4.38/4.49 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 4.38/4.49 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 4.38/4.49 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 4.38/4.49 all A B (set_union2(A,B)=set_union2(B,A)).
% 4.38/4.49 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 4.38/4.49 all A B (ordinal(A)&ordinal(B)->ordinal_subset(A,B)|ordinal_subset(B,A)).
% 4.38/4.49 all A B (relation(B)-> (B=identity_relation(A)<-> (all C D (in(ordered_pair(C,D),B)<->in(C,A)&C=D)))).
% 4.38/4.49 all A B (A=B<->subset(A,B)&subset(B,A)).
% 4.38/4.49 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))))))).
% 4.38/4.49 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)))))))).
% 4.38/4.49 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))))))).
% 4.38/4.49 all A (relation(A)-> (antisymmetric(A)<->is_antisymmetric_in(A,relation_field(A)))).
% 4.38/4.49 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)))))).
% 4.38/4.49 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)))))))).
% 4.38/4.49 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)))))))).
% 4.38/4.49 all A (relation(A)-> (connected(A)<->is_connected_in(A,relation_field(A)))).
% 4.38/4.49 all A (relation(A)-> (transitive(A)<->is_transitive_in(A,relation_field(A)))).
% 4.38/4.49 all A B C D (D=unordered_triple(A,B,C)<-> (all E (in(E,D)<-> -(E!=A&E!=B&E!=C)))).
% 4.38/4.49 all A (succ(A)=set_union2(A,singleton(A))).
% 4.38/4.49 all A (relation(A)<-> (all B (-(in(B,A)& (all C D (B!=ordered_pair(C,D))))))).
% 4.38/4.49 all A (relation(A)-> (all B (is_reflexive_in(A,B)<-> (all C (in(C,B)->in(ordered_pair(C,C),A)))))).
% 4.38/4.49 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))).
% 4.38/4.49 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 4.38/4.49 all A (relation(A)-> (all B C (C=fiber(A,B)<-> (all D (in(D,C)<->D!=B&in(ordered_pair(D,B),A)))))).
% 4.38/4.49 all A (A=empty_set<-> (all B (-in(B,A)))).
% 4.38/4.49 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 4.38/4.49 all A (epsilon_transitive(A)<-> (all B (in(B,A)->subset(B,A)))).
% 4.38/4.49 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))))))).
% 4.38/4.49 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 4.38/4.49 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 4.38/4.49 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))))))))).
% 4.38/4.49 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 4.38/4.49 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)))))).
% 4.38/4.49 all A (epsilon_connected(A)<-> (all B C (-(in(B,A)&in(C,A)& -in(B,C)&B!=C& -in(C,B))))).
% 4.38/4.49 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))))))).
% 4.38/4.49 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 4.38/4.49 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)))))))))).
% 4.38/4.49 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 4.38/4.49 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))))).
% 4.38/4.49 all A (ordinal(A)<->epsilon_transitive(A)&epsilon_connected(A)).
% 4.38/4.49 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 4.38/4.49 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))))).
% 4.38/4.49 all A (cast_to_subset(A)=A).
% 4.38/4.49 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 4.38/4.49 all A (relation(A)-> (well_ordering(A)<->reflexive(A)&transitive(A)&antisymmetric(A)&connected(A)&well_founded_relation(A))).
% 4.38/4.49 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 4.38/4.49 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)))))))).
% 4.38/4.49 all A (relation(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(D,C),A))))))).
% 4.38/4.49 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 4.38/4.49 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 4.38/4.49 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)))).
% 4.38/4.49 all A (being_limit_ordinal(A)<->A=union(A)).
% 4.38/4.49 all A (relation(A)->relation_field(A)=set_union2(relation_dom(A),relation_rng(A))).
% 4.38/4.49 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))))))).
% 4.38/4.49 all A (relation(A)-> (all B (relation_restriction(A,B)=set_intersection2(A,cartesian_product2(B,B))))).
% 4.38/4.49 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))))))).
% 4.38/4.49 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))))))))).
% 4.38/4.49 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 4.38/4.49 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)))).
% 4.38/4.49 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))))))))))).
% 4.38/4.49 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)))))).
% 4.38/4.49 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)))))))).
% 4.38/4.49 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 4.38/4.49 all A (relation(A)&function(A)-> (one_to_one(A)->function_inverse(A)=relation_inverse(A))).
% 4.38/4.49 all A (relation(A)-> (reflexive(A)<->is_reflexive_in(A,relation_field(A)))).
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 all A (relation(A)&function(A)->relation(function_inverse(A))&function(function_inverse(A))).
% 4.38/4.49 $T.
% 4.38/4.49 all A element(cast_to_subset(A),powerset(A)).
% 4.38/4.49 $T.
% 4.38/4.49 all A B (relation(A)->relation(relation_restriction(A,B))).
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 all A (relation(A)->relation(relation_inverse(A))).
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 all A B (relation(A)&relation(B)->relation(relation_composition(A,B))).
% 4.38/4.49 all A B (element(B,powerset(powerset(A)))->element(union_of_subsets(A,B),powerset(A))).
% 4.38/4.49 all A relation(identity_relation(A)).
% 4.38/4.49 all A B (element(B,powerset(powerset(A)))->element(meet_of_subsets(A,B),powerset(A))).
% 4.38/4.49 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_difference(A,B,C),powerset(A))).
% 4.38/4.49 all A B (relation(A)->relation(relation_dom_restriction(A,B))).
% 4.38/4.49 all A B (element(B,powerset(powerset(A)))->element(complements_of_subsets(A,B),powerset(powerset(A)))).
% 4.38/4.49 all A B (relation(B)->relation(relation_rng_restriction(A,B))).
% 4.38/4.49 $T.
% 4.38/4.49 $T.
% 4.38/4.49 all A exists B element(B,A).
% 4.38/4.49 all A B (empty(A)&relation(B)->empty(relation_composition(B,A))&relation(relation_composition(B,A))).
% 4.38/4.49 all A (empty(A)->empty(relation_inverse(A))&relation(relation_inverse(A))).
% 4.38/4.49 empty(empty_set).
% 4.38/4.49 relation(empty_set).
% 4.38/4.49 relation_empty_yielding(empty_set).
% 4.38/4.49 all A B (relation(A)&relation_empty_yielding(A)->relation(relation_dom_restriction(A,B))&relation_empty_yielding(relation_dom_restriction(A,B))).
% 4.38/4.49 all A B (relation(A)&function(A)&relation(B)&function(B)->relation(relation_composition(A,B))&function(relation_composition(A,B))).
% 4.38/4.49 all A (-empty(succ(A))).
% 4.38/4.49 all A B (relation(A)&relation(B)->relation(set_intersection2(A,B))).
% 4.38/4.49 all A (-empty(powerset(A))).
% 4.38/4.49 empty(empty_set).
% 4.38/4.49 all A B (-empty(ordered_pair(A,B))).
% 4.38/4.49 all A (relation(identity_relation(A))&function(identity_relation(A))).
% 4.38/4.49 relation(empty_set).
% 4.38/4.49 relation_empty_yielding(empty_set).
% 4.38/4.49 function(empty_set).
% 4.38/4.49 one_to_one(empty_set).
% 4.38/4.49 empty(empty_set).
% 4.38/4.49 epsilon_transitive(empty_set).
% 4.38/4.49 epsilon_connected(empty_set).
% 4.38/4.49 ordinal(empty_set).
% 4.38/4.49 all A B (relation(A)&relation(B)->relation(set_union2(A,B))).
% 4.38/4.49 all A (-empty(singleton(A))).
% 4.38/4.49 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 4.38/4.49 all A (relation(A)&function(A)&one_to_one(A)->relation(relation_inverse(A))&function(relation_inverse(A))).
% 4.38/4.49 all A (ordinal(A)-> -empty(succ(A))&epsilon_transitive(succ(A))&epsilon_connected(succ(A))&ordinal(succ(A))).
% 4.38/4.49 all A B (relation(A)&relation(B)->relation(set_difference(A,B))).
% 4.38/4.49 all A B (-empty(unordered_pair(A,B))).
% 4.38/4.49 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 4.38/4.49 all A B (relation(A)&function(A)->relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))).
% 4.38/4.49 all A (ordinal(A)->epsilon_transitive(union(A))&epsilon_connected(union(A))&ordinal(union(A))).
% 4.38/4.49 empty(empty_set).
% 4.38/4.49 relation(empty_set).
% 4.38/4.49 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 4.38/4.49 all A B (relation(B)&function(B)->relation(relation_rng_restriction(A,B))&function(relation_rng_restriction(A,B))).
% 4.38/4.49 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 4.38/4.49 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 4.38/4.49 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 4.38/4.49 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 4.38/4.49 all A B (empty(A)&relation(B)->empty(relation_composition(A,B))&relation(relation_composition(A,B))).
% 4.38/4.49 all A B (set_union2(A,A)=A).
% 4.38/4.49 all A B (set_intersection2(A,A)=A).
% 4.38/4.49 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 4.38/4.49 all A (relation(A)->relation_inverse(relation_inverse(A))=A).
% 4.38/4.49 all A B (element(B,powerset(powerset(A)))->complements_of_subsets(A,complements_of_subsets(A,B))=B).
% 4.38/4.49 all A B (-proper_subset(A,A)).
% 4.38/4.49 all A (relation(A)-> (reflexive(A)<-> (all B (in(B,relation_field(A))->in(ordered_pair(B,B),A))))).
% 4.38/4.49 all A (singleton(A)!=empty_set).
% 4.38/4.49 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 4.38/4.49 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 4.38/4.49 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 4.38/4.49 all A B (relation(B)->subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))).
% 4.38/4.49 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))))).
% 4.38/4.49 all A B (subset(singleton(A),B)<->in(A,B)).
% 4.38/4.49 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 4.38/4.49 all A B (element(B,powerset(A))-> (all C (in(C,B)->in(C,A)))).
% 4.38/4.49 all A (relation(A)-> (antisymmetric(A)<-> (all B C (in(ordered_pair(B,C),A)&in(ordered_pair(C,B),A)->B=C)))).
% 4.38/4.49 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 4.38/4.49 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)))))).
% 4.38/4.49 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 4.38/4.49 all A B (in(A,B)->subset(A,union(B))).
% 4.38/4.49 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 4.38/4.49 all A B ((all C (in(C,A)->in(C,B)))->element(A,powerset(B))).
% 4.38/4.49 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))).
% 4.38/4.49 exists A (relation(A)&function(A)).
% 4.38/4.49 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 4.38/4.49 exists A (empty(A)&relation(A)).
% 4.38/4.49 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 4.38/4.49 exists A empty(A).
% 4.38/4.49 exists A (relation(A)&empty(A)&function(A)).
% 4.38/4.49 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 4.38/4.49 exists A (-empty(A)&relation(A)).
% 4.38/4.49 all A exists B (element(B,powerset(A))&empty(B)).
% 4.38/4.49 exists A (-empty(A)).
% 4.38/4.49 exists A (relation(A)&function(A)&one_to_one(A)).
% 4.38/4.49 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 4.38/4.49 exists A (relation(A)&relation_empty_yielding(A)).
% 4.38/4.49 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 4.38/4.49 all A B (element(B,powerset(powerset(A)))->union_of_subsets(A,B)=union(B)).
% 4.38/4.49 all A B (element(B,powerset(powerset(A)))->meet_of_subsets(A,B)=set_meet(B)).
% 4.38/4.49 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_difference(A,B,C)=set_difference(B,C)).
% 4.38/4.49 all A B (ordinal(A)&ordinal(B)-> (ordinal_subset(A,B)<->subset(A,B))).
% 4.38/4.49 all A B (ordinal(A)&ordinal(B)->ordinal_subset(A,A)).
% 4.38/4.49 all A B subset(A,A).
% 4.38/4.49 all A B (disjoint(A,B)->disjoint(B,A)).
% 4.38/4.49 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 4.38/4.49 all A in(A,succ(A)).
% 4.38/4.49 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 4.38/4.49 all A B C (relation(C)-> (in(A,relation_rng(relation_rng_restriction(B,C)))<->in(A,B)&in(A,relation_rng(C)))).
% 4.38/4.49 all A B (relation(B)->subset(relation_rng(relation_rng_restriction(A,B)),A)).
% 4.38/4.49 all A B (relation(B)->subset(relation_rng_restriction(A,B),B)).
% 4.38/4.49 all A B (relation(B)->subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))).
% 4.38/4.49 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))).
% 4.38/4.49 all A B (relation(B)->relation_rng(relation_rng_restriction(A,B))=set_intersection2(relation_rng(B),A)).
% 4.38/4.49 all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 4.38/4.49 all A B (subset(A,B)->set_union2(A,B)=B).
% 4.38/4.49 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))))).
% 4.38/4.49 all A B C (relation(C)->relation_dom_restriction(relation_rng_restriction(A,C),B)=relation_rng_restriction(A,relation_dom_restriction(C,B))).
% 4.38/4.49 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))))).
% 4.38/4.49 all A B (relation(B)->subset(relation_image(B,A),relation_rng(B))).
% 4.38/4.49 all A B (relation(B)&function(B)->subset(relation_image(B,relation_inverse_image(B,A)),A)).
% 4.38/4.49 all A B (relation(B)->relation_image(B,A)=relation_image(B,set_intersection2(relation_dom(B),A))).
% 4.38/4.49 all A B (relation(B)-> (subset(A,relation_dom(B))->subset(A,relation_inverse_image(B,relation_image(B,A))))).
% 4.38/4.49 all A (relation(A)->relation_image(A,relation_dom(A))=relation_rng(A)).
% 4.38/4.49 all A B (relation(B)&function(B)-> (subset(A,relation_rng(B))->relation_image(B,relation_inverse_image(B,A))=A)).
% 4.38/4.49 all A (relation(A)-> (all B (relation(B)->relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A))))).
% 4.38/4.49 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))))).
% 4.38/4.49 all A B (relation(B)->subset(relation_inverse_image(B,A),relation_dom(B))).
% 4.38/4.49 all A B C (relation(C)-> (in(A,relation_restriction(C,B))<->in(A,C)&in(A,cartesian_product2(B,B)))).
% 4.38/4.49 all A B (relation(B)-> -(A!=empty_set&subset(A,relation_rng(B))&relation_inverse_image(B,A)=empty_set)).
% 4.38/4.49 all A B C (relation(C)-> (subset(A,B)->subset(relation_inverse_image(C,A),relation_inverse_image(C,B)))).
% 4.38/4.49 all A B (relation(B)->relation_restriction(B,A)=relation_dom_restriction(relation_rng_restriction(A,B),A)).
% 4.38/4.49 all A B subset(set_intersection2(A,B),A).
% 4.38/4.49 all A B (relation(B)->relation_restriction(B,A)=relation_rng_restriction(A,relation_dom_restriction(B,A))).
% 4.38/4.49 all A B C (relation(C)-> (in(A,relation_field(relation_restriction(C,B)))->in(A,relation_field(C))&in(A,B))).
% 4.38/4.49 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 4.38/4.49 all A (set_union2(A,empty_set)=A).
% 4.38/4.49 all A B (in(A,B)->element(A,B)).
% 4.38/4.49 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 4.38/4.49 powerset(empty_set)=singleton(empty_set).
% 4.38/4.49 all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_dom(C))&in(B,relation_rng(C)))).
% 4.38/4.49 all A B (relation(B)->subset(relation_field(relation_restriction(B,A)),relation_field(B))&subset(relation_field(relation_restriction(B,A)),A)).
% 4.38/4.49 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)))))).
% 4.38/4.49 all A (epsilon_transitive(A)-> (all B (ordinal(B)-> (proper_subset(A,B)->in(A,B))))).
% 4.38/4.49 all A (relation(A)->subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))).
% 4.38/4.49 all A B C (relation(C)->subset(fiber(relation_restriction(C,A),B),fiber(C,B))).
% 4.38/4.49 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)))))).
% 4.38/4.49 all A B (relation(B)-> (reflexive(B)->reflexive(relation_restriction(B,A)))).
% 4.38/4.49 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)))))).
% 4.38/4.49 all A B (ordinal(B)-> (in(A,B)->ordinal(A))).
% 4.38/4.49 all A B (relation(B)-> (connected(B)->connected(relation_restriction(B,A)))).
% 4.38/4.49 all A (ordinal(A)-> (all B (ordinal(B)-> -(-in(A,B)&A!=B& -in(B,A))))).
% 4.38/4.49 all A B (relation(B)-> (transitive(B)->transitive(relation_restriction(B,A)))).
% 4.38/4.49 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)))))).
% 4.38/4.49 all A B (relation(B)-> (antisymmetric(B)->antisymmetric(relation_restriction(B,A)))).
% 4.38/4.49 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 4.38/4.49 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 4.38/4.49 all A (set_intersection2(A,empty_set)=empty_set).
% 4.38/4.49 all A B (element(A,B)->empty(B)|in(A,B)).
% 4.38/4.49 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 4.38/4.49 all A subset(empty_set,A).
% 4.38/4.49 all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_field(C))&in(B,relation_field(C)))).
% 4.38/4.49 all A ((all B (in(B,A)->ordinal(B)&subset(B,A)))->ordinal(A)).
% 4.38/4.49 all A B (relation(B)-> (well_founded_relation(B)->well_founded_relation(relation_restriction(B,A)))).
% 4.38/4.49 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))))))))).
% 4.38/4.49 all A B (relation(B)-> (well_ordering(B)->well_ordering(relation_restriction(B,A)))).
% 4.38/4.49 all A (ordinal(A)-> (all B (ordinal(B)-> (in(A,B)<->ordinal_subset(succ(A),B))))).
% 4.38/4.49 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 4.38/4.49 all A B C D (ordered_pair(A,B)=ordered_pair(C,D)->A=C&B=D).
% 4.38/4.49 all A B (relation(B)&function(B)-> (B=identity_relation(A)<->relation_dom(B)=A& (all C (in(C,A)->apply(B,C)=C)))).
% 4.38/4.49 all A B (in(B,A)->apply(identity_relation(A),B)=B).
% 4.38/4.49 all A B subset(set_difference(A,B),A).
% 4.38/4.49 all A (relation(A)->relation_rng(A)=relation_dom(relation_inverse(A))&relation_dom(A)=relation_rng(relation_inverse(A))).
% 4.38/4.49 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 4.38/4.49 all A B (subset(singleton(A),B)<->in(A,B)).
% 4.38/4.49 all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C)).
% 4.38/4.49 all A B (relation(B)-> (well_ordering(B)&subset(A,relation_field(B))->relation_field(relation_restriction(B,A))=A)).
% 4.38/4.49 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 4.38/4.49 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 4.38/4.49 all A (set_difference(A,empty_set)=A).
% 4.38/4.49 all A B C (-(in(A,B)&in(B,C)&in(C,A))).
% 4.38/4.49 all A B (element(A,powerset(B))<->subset(A,B)).
% 4.38/4.49 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))).
% 4.38/4.50 all A (subset(A,empty_set)->A=empty_set).
% 4.38/4.50 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 4.38/4.50 all A (ordinal(A)-> (being_limit_ordinal(A)<-> (all B (ordinal(B)-> (in(B,A)->in(succ(B),A)))))).
% 4.38/4.50 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))).
% 4.38/4.50 all A B (element(B,powerset(A))-> (all C (element(C,powerset(A))-> (disjoint(B,C)<->subset(B,subset_complement(A,C)))))).
% 4.38/4.50 all A (relation(A)-> (all B (relation(B)->subset(relation_dom(relation_composition(A,B)),relation_dom(A))))).
% 4.38/4.50 all A (relation(A)-> (all B (relation(B)->subset(relation_rng(relation_composition(A,B)),relation_rng(B))))).
% 4.38/4.50 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 4.38/4.50 all A (relation(A)-> (all B (relation(B)-> (subset(relation_rng(A),relation_dom(B))->relation_dom(relation_composition(A,B))=relation_dom(A))))).
% 4.38/4.50 all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set)).
% 4.38/4.50 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 4.38/4.50 all A (relation(A)-> (all B (relation(B)-> (subset(relation_dom(A),relation_rng(B))->relation_rng(relation_composition(B,A))=relation_rng(A))))).
% 4.38/4.50 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)))).
% 4.38/4.50 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)))).
% 4.38/4.50 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 4.38/4.50 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)))))))).
% 4.38/4.50 all A (set_difference(empty_set,A)=empty_set).
% 4.38/4.50 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 4.38/4.50 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))).
% 4.38/4.50 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)))))))).
% 4.38/4.50 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)))))))).
% 4.38/4.50 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))))))))).
% 4.38/4.50 all A B C (element(C,powerset(A))-> -(in(B,subset_complement(A,C))&in(B,C))).
% 4.38/4.50 -(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)))))))).
% 4.38/4.50 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)))).
% 4.38/4.50 all A (relation(A)-> ((all B C (-in(ordered_pair(B,C),A)))->A=empty_set)).
% 4.38/4.50 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))).
% 4.38/4.50 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 4.38/4.50 all A (relation(A)-> (well_founded_relation(A)<->is_well_founded_in(A,relation_field(A)))).
% 4.38/4.50 relation_dom(empty_set)=empty_set.
% 4.38/4.50 relation_rng(empty_set)=empty_set.
% 4.38/4.50 all A B (-(subset(A,B)&proper_subset(B,A))).
% 4.38/4.50 all A (relation(A)&function(A)-> (one_to_one(A)->one_to_one(function_inverse(A)))).
% 4.38/4.50 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 4.38/4.50 all A (relation(A)-> (relation_dom(A)=empty_set|relation_rng(A)=empty_set->A=empty_set)).
% 4.38/4.50 all A (relation(A)-> (relation_dom(A)=empty_set<->relation_rng(A)=empty_set)).
% 4.38/4.50 all A B (set_difference(A,singleton(B))=A<-> -in(B,A)).
% 4.38/4.50 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))))))).
% 4.38/4.50 all A (unordered_pair(A,A)=singleton(A)).
% 4.38/4.50 all A (empty(A)->A=empty_set).
% 4.38/4.50 all A B (subset(singleton(A),singleton(B))->A=B).
% 4.38/4.50 all A B C (relation(C)&function(C)-> (in(B,relation_dom(relation_dom_restriction(C,A)))->apply(relation_dom_restriction(C,A),B)=apply(C,B))).
% 4.38/4.50 all A (relation_dom(identity_relation(A))=A&relation_rng(identity_relation(A))=A).
% 4.38/4.50 all A B C (relation(C)&function(C)-> (in(B,A)->apply(relation_dom_restriction(C,A),B)=apply(C,B))).
% 4.38/4.50 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))).
% 4.38/4.50 all A B (-(in(A,B)&empty(B))).
% 4.38/4.50 all A B (-(in(A,B)& (all C (-(in(C,B)& (all D (-(in(D,B)&in(D,C))))))))).
% 4.38/4.50 all A B subset(A,set_union2(A,B)).
% 4.38/4.50 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 4.38/4.50 all A B C (relation(C)-> (in(A,relation_dom(relation_dom_restriction(C,B)))<->in(A,B)&in(A,relation_dom(C)))).
% 4.38/4.50 all A B (relation(B)->subset(relation_dom_restriction(B,A),B)).
% 4.38/4.50 all A B (-(empty(A)&A!=B&empty(B))).
% 4.38/4.50 all A B C (relation(C)&function(C)-> (in(ordered_pair(A,B),C)<->in(A,relation_dom(C))&B=apply(C,A))).
% 4.38/4.50 all A (relation(A)-> (well_orders(A,relation_field(A))<->well_ordering(A))).
% 4.38/4.50 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 4.38/4.50 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 4.38/4.50 all A B (relation(B)->relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A)).
% 4.38/4.50 all A B (in(A,B)->subset(A,union(B))).
% 4.38/4.50 all A B (relation(B)->relation_dom_restriction(B,A)=relation_composition(identity_relation(A),B)).
% 4.38/4.50 all A B (relation(B)->subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))).
% 4.38/4.50 all A (union(powerset(A))=A).
% 4.38/4.50 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))))).
% 4.38/4.50 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 4.38/4.50 end_of_list.
% 4.38/4.50
% 4.38/4.50 -------> usable clausifies to:
% 4.38/4.50
% 4.38/4.50 list(usable).
% 4.38/4.50 0 [] A=A.
% 4.38/4.50 0 [] -in(A,B)| -in(B,A).
% 4.38/4.50 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 4.38/4.50 0 [] -empty(A)|function(A).
% 4.38/4.50 0 [] -ordinal(A)|epsilon_transitive(A).
% 4.38/4.50 0 [] -ordinal(A)|epsilon_connected(A).
% 4.38/4.50 0 [] -empty(A)|relation(A).
% 4.38/4.50 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 4.38/4.50 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 4.38/4.50 0 [] -empty(A)|epsilon_transitive(A).
% 4.38/4.50 0 [] -empty(A)|epsilon_connected(A).
% 4.38/4.50 0 [] -empty(A)|ordinal(A).
% 4.38/4.50 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 4.38/4.50 0 [] set_union2(A,B)=set_union2(B,A).
% 4.38/4.50 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 4.38/4.50 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)|ordinal_subset(B,A).
% 4.38/4.50 0 [] -relation(B)|B!=identity_relation(A)| -in(ordered_pair(C,D),B)|in(C,A).
% 4.38/4.50 0 [] -relation(B)|B!=identity_relation(A)| -in(ordered_pair(C,D),B)|C=D.
% 4.38/4.50 0 [] -relation(B)|B!=identity_relation(A)|in(ordered_pair(C,D),B)| -in(C,A)|C!=D.
% 4.38/4.50 0 [] -relation(B)|B=identity_relation(A)|in(ordered_pair($f2(A,B),$f1(A,B)),B)|in($f2(A,B),A).
% 4.38/4.50 0 [] -relation(B)|B=identity_relation(A)|in(ordered_pair($f2(A,B),$f1(A,B)),B)|$f2(A,B)=$f1(A,B).
% 4.38/4.50 0 [] -relation(B)|B=identity_relation(A)| -in(ordered_pair($f2(A,B),$f1(A,B)),B)| -in($f2(A,B),A)|$f2(A,B)!=$f1(A,B).
% 4.38/4.50 0 [] A!=B|subset(A,B).
% 4.38/4.50 0 [] A!=B|subset(B,A).
% 4.38/4.50 0 [] A=B| -subset(A,B)| -subset(B,A).
% 4.38/4.50 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)| -in(ordered_pair(D,E),C)|in(D,B).
% 4.38/4.50 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,E),A).
% 4.38/4.50 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)|in(ordered_pair(D,E),C)| -in(D,B)| -in(ordered_pair(D,E),A).
% 4.38/4.50 0 [] -relation(A)| -relation(C)|C=relation_dom_restriction(A,B)|in(ordered_pair($f4(A,B,C),$f3(A,B,C)),C)|in($f4(A,B,C),B).
% 4.38/4.50 0 [] -relation(A)| -relation(C)|C=relation_dom_restriction(A,B)|in(ordered_pair($f4(A,B,C),$f3(A,B,C)),C)|in(ordered_pair($f4(A,B,C),$f3(A,B,C)),A).
% 4.38/4.50 0 [] -relation(A)| -relation(C)|C=relation_dom_restriction(A,B)| -in(ordered_pair($f4(A,B,C),$f3(A,B,C)),C)| -in($f4(A,B,C),B)| -in(ordered_pair($f4(A,B,C),$f3(A,B,C)),A).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C!=relation_image(A,B)| -in(D,C)|in($f5(A,B,C,D),relation_dom(A)).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C!=relation_image(A,B)| -in(D,C)|in($f5(A,B,C,D),B).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C!=relation_image(A,B)| -in(D,C)|D=apply(A,$f5(A,B,C,D)).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C!=relation_image(A,B)|in(D,C)| -in(E,relation_dom(A))| -in(E,B)|D!=apply(A,E).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C=relation_image(A,B)|in($f7(A,B,C),C)|in($f6(A,B,C),relation_dom(A)).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C=relation_image(A,B)|in($f7(A,B,C),C)|in($f6(A,B,C),B).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C=relation_image(A,B)|in($f7(A,B,C),C)|$f7(A,B,C)=apply(A,$f6(A,B,C)).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C=relation_image(A,B)| -in($f7(A,B,C),C)| -in(X1,relation_dom(A))| -in(X1,B)|$f7(A,B,C)!=apply(A,X1).
% 4.38/4.50 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)| -in(ordered_pair(D,E),C)|in(E,A).
% 4.38/4.50 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,E),B).
% 4.38/4.50 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)|in(ordered_pair(D,E),C)| -in(E,A)| -in(ordered_pair(D,E),B).
% 4.38/4.50 0 [] -relation(B)| -relation(C)|C=relation_rng_restriction(A,B)|in(ordered_pair($f9(A,B,C),$f8(A,B,C)),C)|in($f8(A,B,C),A).
% 4.38/4.50 0 [] -relation(B)| -relation(C)|C=relation_rng_restriction(A,B)|in(ordered_pair($f9(A,B,C),$f8(A,B,C)),C)|in(ordered_pair($f9(A,B,C),$f8(A,B,C)),B).
% 4.38/4.50 0 [] -relation(B)| -relation(C)|C=relation_rng_restriction(A,B)| -in(ordered_pair($f9(A,B,C),$f8(A,B,C)),C)| -in($f8(A,B,C),A)| -in(ordered_pair($f9(A,B,C),$f8(A,B,C)),B).
% 4.38/4.50 0 [] -relation(A)| -antisymmetric(A)|is_antisymmetric_in(A,relation_field(A)).
% 4.38/4.50 0 [] -relation(A)|antisymmetric(A)| -is_antisymmetric_in(A,relation_field(A)).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C!=relation_inverse_image(A,B)| -in(D,C)|in(D,relation_dom(A)).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C!=relation_inverse_image(A,B)| -in(D,C)|in(apply(A,D),B).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C!=relation_inverse_image(A,B)|in(D,C)| -in(D,relation_dom(A))| -in(apply(A,D),B).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C=relation_inverse_image(A,B)|in($f10(A,B,C),C)|in($f10(A,B,C),relation_dom(A)).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C=relation_inverse_image(A,B)|in($f10(A,B,C),C)|in(apply(A,$f10(A,B,C)),B).
% 4.38/4.50 0 [] -relation(A)| -function(A)|C=relation_inverse_image(A,B)| -in($f10(A,B,C),C)| -in($f10(A,B,C),relation_dom(A))| -in(apply(A,$f10(A,B,C)),B).
% 4.38/4.50 0 [] -relation(A)|C!=relation_image(A,B)| -in(D,C)|in(ordered_pair($f11(A,B,C,D),D),A).
% 4.38/4.50 0 [] -relation(A)|C!=relation_image(A,B)| -in(D,C)|in($f11(A,B,C,D),B).
% 4.38/4.50 0 [] -relation(A)|C!=relation_image(A,B)|in(D,C)| -in(ordered_pair(E,D),A)| -in(E,B).
% 4.38/4.50 0 [] -relation(A)|C=relation_image(A,B)|in($f13(A,B,C),C)|in(ordered_pair($f12(A,B,C),$f13(A,B,C)),A).
% 4.38/4.50 0 [] -relation(A)|C=relation_image(A,B)|in($f13(A,B,C),C)|in($f12(A,B,C),B).
% 4.38/4.50 0 [] -relation(A)|C=relation_image(A,B)| -in($f13(A,B,C),C)| -in(ordered_pair(X2,$f13(A,B,C)),A)| -in(X2,B).
% 4.38/4.50 0 [] -relation(A)|C!=relation_inverse_image(A,B)| -in(D,C)|in(ordered_pair(D,$f14(A,B,C,D)),A).
% 4.38/4.50 0 [] -relation(A)|C!=relation_inverse_image(A,B)| -in(D,C)|in($f14(A,B,C,D),B).
% 4.38/4.50 0 [] -relation(A)|C!=relation_inverse_image(A,B)|in(D,C)| -in(ordered_pair(D,E),A)| -in(E,B).
% 4.38/4.50 0 [] -relation(A)|C=relation_inverse_image(A,B)|in($f16(A,B,C),C)|in(ordered_pair($f16(A,B,C),$f15(A,B,C)),A).
% 4.38/4.50 0 [] -relation(A)|C=relation_inverse_image(A,B)|in($f16(A,B,C),C)|in($f15(A,B,C),B).
% 4.38/4.50 0 [] -relation(A)|C=relation_inverse_image(A,B)| -in($f16(A,B,C),C)| -in(ordered_pair($f16(A,B,C),X3),A)| -in(X3,B).
% 4.38/4.50 0 [] -relation(A)| -connected(A)|is_connected_in(A,relation_field(A)).
% 4.38/4.50 0 [] -relation(A)|connected(A)| -is_connected_in(A,relation_field(A)).
% 4.38/4.50 0 [] -relation(A)| -transitive(A)|is_transitive_in(A,relation_field(A)).
% 4.38/4.50 0 [] -relation(A)|transitive(A)| -is_transitive_in(A,relation_field(A)).
% 4.38/4.50 0 [] D!=unordered_triple(A,B,C)| -in(E,D)|E=A|E=B|E=C.
% 4.38/4.50 0 [] D!=unordered_triple(A,B,C)|in(E,D)|E!=A.
% 4.38/4.50 0 [] D!=unordered_triple(A,B,C)|in(E,D)|E!=B.
% 4.38/4.50 0 [] D!=unordered_triple(A,B,C)|in(E,D)|E!=C.
% 4.38/4.50 0 [] D=unordered_triple(A,B,C)|in($f17(A,B,C,D),D)|$f17(A,B,C,D)=A|$f17(A,B,C,D)=B|$f17(A,B,C,D)=C.
% 4.38/4.50 0 [] D=unordered_triple(A,B,C)| -in($f17(A,B,C,D),D)|$f17(A,B,C,D)!=A.
% 4.38/4.50 0 [] D=unordered_triple(A,B,C)| -in($f17(A,B,C,D),D)|$f17(A,B,C,D)!=B.
% 4.38/4.50 0 [] D=unordered_triple(A,B,C)| -in($f17(A,B,C,D),D)|$f17(A,B,C,D)!=C.
% 4.38/4.50 0 [] succ(A)=set_union2(A,singleton(A)).
% 4.38/4.50 0 [] -relation(A)| -in(B,A)|B=ordered_pair($f19(A,B),$f18(A,B)).
% 4.38/4.50 0 [] relation(A)|in($f20(A),A).
% 4.38/4.50 0 [] relation(A)|$f20(A)!=ordered_pair(C,D).
% 4.38/4.50 0 [] -relation(A)| -is_reflexive_in(A,B)| -in(C,B)|in(ordered_pair(C,C),A).
% 4.38/4.50 0 [] -relation(A)|is_reflexive_in(A,B)|in($f21(A,B),B).
% 4.38/4.50 0 [] -relation(A)|is_reflexive_in(A,B)| -in(ordered_pair($f21(A,B),$f21(A,B)),A).
% 4.38/4.50 0 [] A=empty_set|B!=set_meet(A)| -in(C,B)| -in(D,A)|in(C,D).
% 4.38/4.50 0 [] A=empty_set|B!=set_meet(A)|in(C,B)|in($f22(A,B,C),A).
% 4.38/4.50 0 [] A=empty_set|B!=set_meet(A)|in(C,B)| -in(C,$f22(A,B,C)).
% 4.38/4.50 0 [] A=empty_set|B=set_meet(A)|in($f24(A,B),B)| -in(X4,A)|in($f24(A,B),X4).
% 4.38/4.50 0 [] A=empty_set|B=set_meet(A)| -in($f24(A,B),B)|in($f23(A,B),A).
% 4.38/4.50 0 [] A=empty_set|B=set_meet(A)| -in($f24(A,B),B)| -in($f24(A,B),$f23(A,B)).
% 4.38/4.50 0 [] A!=empty_set|B!=set_meet(A)|B=empty_set.
% 4.38/4.50 0 [] A!=empty_set|B=set_meet(A)|B!=empty_set.
% 4.38/4.50 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 4.38/4.50 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 4.38/4.50 0 [] B=singleton(A)|in($f25(A,B),B)|$f25(A,B)=A.
% 4.38/4.50 0 [] B=singleton(A)| -in($f25(A,B),B)|$f25(A,B)!=A.
% 4.38/4.50 0 [] -relation(A)|C!=fiber(A,B)| -in(D,C)|D!=B.
% 4.38/4.50 0 [] -relation(A)|C!=fiber(A,B)| -in(D,C)|in(ordered_pair(D,B),A).
% 4.38/4.50 0 [] -relation(A)|C!=fiber(A,B)|in(D,C)|D=B| -in(ordered_pair(D,B),A).
% 4.38/4.50 0 [] -relation(A)|C=fiber(A,B)|in($f26(A,B,C),C)|$f26(A,B,C)!=B.
% 4.38/4.50 0 [] -relation(A)|C=fiber(A,B)|in($f26(A,B,C),C)|in(ordered_pair($f26(A,B,C),B),A).
% 4.38/4.50 0 [] -relation(A)|C=fiber(A,B)| -in($f26(A,B,C),C)|$f26(A,B,C)=B| -in(ordered_pair($f26(A,B,C),B),A).
% 4.38/4.50 0 [] A!=empty_set| -in(B,A).
% 4.38/4.50 0 [] A=empty_set|in($f27(A),A).
% 4.38/4.50 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 4.38/4.50 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 4.38/4.50 0 [] B=powerset(A)|in($f28(A,B),B)|subset($f28(A,B),A).
% 4.38/4.50 0 [] B=powerset(A)| -in($f28(A,B),B)| -subset($f28(A,B),A).
% 4.38/4.50 0 [] -epsilon_transitive(A)| -in(B,A)|subset(B,A).
% 4.38/4.50 0 [] epsilon_transitive(A)|in($f29(A),A).
% 4.38/4.50 0 [] epsilon_transitive(A)| -subset($f29(A),A).
% 4.38/4.50 0 [] -relation(A)| -relation(B)|A!=B| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 4.38/4.50 0 [] -relation(A)| -relation(B)|A!=B|in(ordered_pair(C,D),A)| -in(ordered_pair(C,D),B).
% 4.38/4.50 0 [] -relation(A)| -relation(B)|A=B|in(ordered_pair($f31(A,B),$f30(A,B)),A)|in(ordered_pair($f31(A,B),$f30(A,B)),B).
% 4.38/4.50 0 [] -relation(A)| -relation(B)|A=B| -in(ordered_pair($f31(A,B),$f30(A,B)),A)| -in(ordered_pair($f31(A,B),$f30(A,B)),B).
% 4.38/4.50 0 [] empty(A)| -element(B,A)|in(B,A).
% 4.38/4.50 0 [] empty(A)|element(B,A)| -in(B,A).
% 4.38/4.50 0 [] -empty(A)| -element(B,A)|empty(B).
% 4.38/4.50 0 [] -empty(A)|element(B,A)| -empty(B).
% 4.38/4.50 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 4.38/4.50 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 4.38/4.50 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 4.38/4.50 0 [] C=unordered_pair(A,B)|in($f32(A,B,C),C)|$f32(A,B,C)=A|$f32(A,B,C)=B.
% 4.38/4.50 0 [] C=unordered_pair(A,B)| -in($f32(A,B,C),C)|$f32(A,B,C)!=A.
% 4.38/4.50 0 [] C=unordered_pair(A,B)| -in($f32(A,B,C),C)|$f32(A,B,C)!=B.
% 4.38/4.50 0 [] -relation(A)| -well_founded_relation(A)| -subset(B,relation_field(A))|B=empty_set|in($f33(A,B),B).
% 4.38/4.50 0 [] -relation(A)| -well_founded_relation(A)| -subset(B,relation_field(A))|B=empty_set|disjoint(fiber(A,$f33(A,B)),B).
% 4.38/4.50 0 [] -relation(A)|well_founded_relation(A)|subset($f34(A),relation_field(A)).
% 4.38/4.50 0 [] -relation(A)|well_founded_relation(A)|$f34(A)!=empty_set.
% 4.38/4.50 0 [] -relation(A)|well_founded_relation(A)| -in(C,$f34(A))| -disjoint(fiber(A,C),$f34(A)).
% 4.38/4.50 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 4.38/4.50 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 4.38/4.50 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 4.38/4.50 0 [] C=set_union2(A,B)|in($f35(A,B,C),C)|in($f35(A,B,C),A)|in($f35(A,B,C),B).
% 4.38/4.50 0 [] C=set_union2(A,B)| -in($f35(A,B,C),C)| -in($f35(A,B,C),A).
% 4.38/4.50 0 [] C=set_union2(A,B)| -in($f35(A,B,C),C)| -in($f35(A,B,C),B).
% 4.38/4.50 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f37(A,B,C,D),A).
% 4.38/4.50 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f36(A,B,C,D),B).
% 4.38/4.50 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f37(A,B,C,D),$f36(A,B,C,D)).
% 4.38/4.51 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 4.38/4.51 0 [] C=cartesian_product2(A,B)|in($f40(A,B,C),C)|in($f39(A,B,C),A).
% 4.38/4.51 0 [] C=cartesian_product2(A,B)|in($f40(A,B,C),C)|in($f38(A,B,C),B).
% 4.38/4.51 0 [] C=cartesian_product2(A,B)|in($f40(A,B,C),C)|$f40(A,B,C)=ordered_pair($f39(A,B,C),$f38(A,B,C)).
% 4.38/4.51 0 [] C=cartesian_product2(A,B)| -in($f40(A,B,C),C)| -in(X5,A)| -in(X6,B)|$f40(A,B,C)!=ordered_pair(X5,X6).
% 4.38/4.51 0 [] -epsilon_connected(A)| -in(B,A)| -in(C,A)|in(B,C)|B=C|in(C,B).
% 4.38/4.51 0 [] epsilon_connected(A)|in($f42(A),A).
% 4.38/4.51 0 [] epsilon_connected(A)|in($f41(A),A).
% 4.38/4.51 0 [] epsilon_connected(A)| -in($f42(A),$f41(A)).
% 4.38/4.51 0 [] epsilon_connected(A)|$f42(A)!=$f41(A).
% 4.38/4.51 0 [] epsilon_connected(A)| -in($f41(A),$f42(A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -subset(A,B)| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|subset(A,B)|in(ordered_pair($f44(A,B),$f43(A,B)),A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|subset(A,B)| -in(ordered_pair($f44(A,B),$f43(A,B)),B).
% 4.38/4.51 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 4.38/4.51 0 [] subset(A,B)|in($f45(A,B),A).
% 4.38/4.51 0 [] subset(A,B)| -in($f45(A,B),B).
% 4.38/4.51 0 [] -relation(A)| -is_well_founded_in(A,B)| -subset(C,B)|C=empty_set|in($f46(A,B,C),C).
% 4.38/4.51 0 [] -relation(A)| -is_well_founded_in(A,B)| -subset(C,B)|C=empty_set|disjoint(fiber(A,$f46(A,B,C)),C).
% 4.38/4.51 0 [] -relation(A)|is_well_founded_in(A,B)|subset($f47(A,B),B).
% 4.38/4.51 0 [] -relation(A)|is_well_founded_in(A,B)|$f47(A,B)!=empty_set.
% 4.38/4.51 0 [] -relation(A)|is_well_founded_in(A,B)| -in(D,$f47(A,B))| -disjoint(fiber(A,D),$f47(A,B)).
% 4.38/4.51 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 4.38/4.51 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 4.38/4.51 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 4.38/4.51 0 [] C=set_intersection2(A,B)|in($f48(A,B,C),C)|in($f48(A,B,C),A).
% 4.38/4.51 0 [] C=set_intersection2(A,B)|in($f48(A,B,C),C)|in($f48(A,B,C),B).
% 4.38/4.51 0 [] C=set_intersection2(A,B)| -in($f48(A,B,C),C)| -in($f48(A,B,C),A)| -in($f48(A,B,C),B).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C!=apply(A,B)|in(ordered_pair(B,C),A).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C=apply(A,B)| -in(ordered_pair(B,C),A).
% 4.38/4.51 0 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C!=apply(A,B)|C=empty_set.
% 4.38/4.51 0 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C=apply(A,B)|C!=empty_set.
% 4.38/4.51 0 [] -ordinal(A)|epsilon_transitive(A).
% 4.38/4.51 0 [] -ordinal(A)|epsilon_connected(A).
% 4.38/4.51 0 [] ordinal(A)| -epsilon_transitive(A)| -epsilon_connected(A).
% 4.38/4.51 0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f49(A,B,C)),A).
% 4.38/4.51 0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 4.38/4.51 0 [] -relation(A)|B=relation_dom(A)|in($f51(A,B),B)|in(ordered_pair($f51(A,B),$f50(A,B)),A).
% 4.38/4.51 0 [] -relation(A)|B=relation_dom(A)| -in($f51(A,B),B)| -in(ordered_pair($f51(A,B),X7),A).
% 4.38/4.51 0 [] -relation(A)| -is_antisymmetric_in(A,B)| -in(C,B)| -in(D,B)| -in(ordered_pair(C,D),A)| -in(ordered_pair(D,C),A)|C=D.
% 4.38/4.51 0 [] -relation(A)|is_antisymmetric_in(A,B)|in($f53(A,B),B).
% 4.38/4.51 0 [] -relation(A)|is_antisymmetric_in(A,B)|in($f52(A,B),B).
% 4.38/4.51 0 [] -relation(A)|is_antisymmetric_in(A,B)|in(ordered_pair($f53(A,B),$f52(A,B)),A).
% 4.38/4.51 0 [] -relation(A)|is_antisymmetric_in(A,B)|in(ordered_pair($f52(A,B),$f53(A,B)),A).
% 4.38/4.51 0 [] -relation(A)|is_antisymmetric_in(A,B)|$f53(A,B)!=$f52(A,B).
% 4.38/4.51 0 [] cast_to_subset(A)=A.
% 4.38/4.51 0 [] B!=union(A)| -in(C,B)|in(C,$f54(A,B,C)).
% 4.38/4.51 0 [] B!=union(A)| -in(C,B)|in($f54(A,B,C),A).
% 4.38/4.51 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 4.38/4.51 0 [] B=union(A)|in($f56(A,B),B)|in($f56(A,B),$f55(A,B)).
% 4.38/4.51 0 [] B=union(A)|in($f56(A,B),B)|in($f55(A,B),A).
% 4.38/4.51 0 [] B=union(A)| -in($f56(A,B),B)| -in($f56(A,B),X8)| -in(X8,A).
% 4.38/4.51 0 [] -relation(A)| -well_ordering(A)|reflexive(A).
% 4.38/4.51 0 [] -relation(A)| -well_ordering(A)|transitive(A).
% 4.38/4.51 0 [] -relation(A)| -well_ordering(A)|antisymmetric(A).
% 4.38/4.51 0 [] -relation(A)| -well_ordering(A)|connected(A).
% 4.38/4.51 0 [] -relation(A)| -well_ordering(A)|well_founded_relation(A).
% 4.38/4.51 0 [] -relation(A)|well_ordering(A)| -reflexive(A)| -transitive(A)| -antisymmetric(A)| -connected(A)| -well_founded_relation(A).
% 4.38/4.51 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 4.38/4.51 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 4.38/4.51 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 4.38/4.51 0 [] C=set_difference(A,B)|in($f57(A,B,C),C)|in($f57(A,B,C),A).
% 4.38/4.51 0 [] C=set_difference(A,B)|in($f57(A,B,C),C)| -in($f57(A,B,C),B).
% 4.38/4.51 0 [] C=set_difference(A,B)| -in($f57(A,B,C),C)| -in($f57(A,B,C),A)|in($f57(A,B,C),B).
% 4.38/4.51 0 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|in($f58(A,B,C),relation_dom(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|C=apply(A,$f58(A,B,C)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|B!=relation_rng(A)|in(C,B)| -in(D,relation_dom(A))|C!=apply(A,D).
% 4.38/4.51 0 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f60(A,B),B)|in($f59(A,B),relation_dom(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f60(A,B),B)|$f60(A,B)=apply(A,$f59(A,B)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|B=relation_rng(A)| -in($f60(A,B),B)| -in(X9,relation_dom(A))|$f60(A,B)!=apply(A,X9).
% 4.38/4.51 0 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f61(A,B,C),C),A).
% 4.38/4.51 0 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 4.38/4.51 0 [] -relation(A)|B=relation_rng(A)|in($f63(A,B),B)|in(ordered_pair($f62(A,B),$f63(A,B)),A).
% 4.38/4.51 0 [] -relation(A)|B=relation_rng(A)| -in($f63(A,B),B)| -in(ordered_pair(X10,$f63(A,B)),A).
% 4.38/4.51 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 4.38/4.51 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 4.38/4.51 0 [] -relation(A)| -well_orders(A,B)|is_reflexive_in(A,B).
% 4.38/4.51 0 [] -relation(A)| -well_orders(A,B)|is_transitive_in(A,B).
% 4.38/4.51 0 [] -relation(A)| -well_orders(A,B)|is_antisymmetric_in(A,B).
% 4.38/4.51 0 [] -relation(A)| -well_orders(A,B)|is_connected_in(A,B).
% 4.38/4.51 0 [] -relation(A)| -well_orders(A,B)|is_well_founded_in(A,B).
% 4.38/4.51 0 [] -relation(A)|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).
% 4.38/4.51 0 [] -being_limit_ordinal(A)|A=union(A).
% 4.38/4.51 0 [] being_limit_ordinal(A)|A!=union(A).
% 4.38/4.51 0 [] -relation(A)|relation_field(A)=set_union2(relation_dom(A),relation_rng(A)).
% 4.38/4.51 0 [] -relation(A)| -is_connected_in(A,B)| -in(C,B)| -in(D,B)|C=D|in(ordered_pair(C,D),A)|in(ordered_pair(D,C),A).
% 4.38/4.51 0 [] -relation(A)|is_connected_in(A,B)|in($f65(A,B),B).
% 4.38/4.51 0 [] -relation(A)|is_connected_in(A,B)|in($f64(A,B),B).
% 4.38/4.51 0 [] -relation(A)|is_connected_in(A,B)|$f65(A,B)!=$f64(A,B).
% 4.38/4.51 0 [] -relation(A)|is_connected_in(A,B)| -in(ordered_pair($f65(A,B),$f64(A,B)),A).
% 4.38/4.51 0 [] -relation(A)|is_connected_in(A,B)| -in(ordered_pair($f64(A,B),$f65(A,B)),A).
% 4.38/4.51 0 [] -relation(A)|relation_restriction(A,B)=set_intersection2(A,cartesian_product2(B,B)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|B!=relation_inverse(A)| -in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|B!=relation_inverse(A)|in(ordered_pair(C,D),B)| -in(ordered_pair(D,C),A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|B=relation_inverse(A)|in(ordered_pair($f67(A,B),$f66(A,B)),B)|in(ordered_pair($f66(A,B),$f67(A,B)),A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|B=relation_inverse(A)| -in(ordered_pair($f67(A,B),$f66(A,B)),B)| -in(ordered_pair($f66(A,B),$f67(A,B)),A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|relation_dom(C)=relation_field(A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|relation_rng(C)=relation_field(B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|one_to_one(C).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -in(ordered_pair(D,E),A)|in(D,relation_field(A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -in(ordered_pair(D,E),A)|in(E,relation_field(A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -in(ordered_pair(D,E),A)|in(ordered_pair(apply(C,D),apply(C,E)),B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|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).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -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)|in(ordered_pair($f69(A,B,C),$f68(A,B,C)),A)|in($f69(A,B,C),relation_field(A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)|relation_isomorphism(A,B,C)|relation_dom(C)!=relation_field(A)|relation_rng(C)!=relation_field(B)| -one_to_one(C)|in(ordered_pair($f69(A,B,C),$f68(A,B,C)),A)|in($f68(A,B,C),relation_field(A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -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)|in(ordered_pair($f69(A,B,C),$f68(A,B,C)),A)|in(ordered_pair(apply(C,$f69(A,B,C)),apply(C,$f68(A,B,C))),B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -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)| -in(ordered_pair($f69(A,B,C),$f68(A,B,C)),A)| -in($f69(A,B,C),relation_field(A))| -in($f68(A,B,C),relation_field(A))| -in(ordered_pair(apply(C,$f69(A,B,C)),apply(C,$f68(A,B,C))),B).
% 4.38/4.51 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 4.38/4.51 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_dom(A))| -in(C,relation_dom(A))|apply(A,B)!=apply(A,C)|B=C.
% 4.38/4.51 0 [] -relation(A)| -function(A)|one_to_one(A)|in($f71(A),relation_dom(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|one_to_one(A)|in($f70(A),relation_dom(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|one_to_one(A)|apply(A,$f71(A))=apply(A,$f70(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|one_to_one(A)|$f71(A)!=$f70(A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,$f72(A,B,C,D,E)),A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair($f72(A,B,C,D,E),E),B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)|in(ordered_pair(D,E),C)| -in(ordered_pair(D,F),A)| -in(ordered_pair(F,E),B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f75(A,B,C),$f74(A,B,C)),C)|in(ordered_pair($f75(A,B,C),$f73(A,B,C)),A).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f75(A,B,C),$f74(A,B,C)),C)|in(ordered_pair($f73(A,B,C),$f74(A,B,C)),B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)| -in(ordered_pair($f75(A,B,C),$f74(A,B,C)),C)| -in(ordered_pair($f75(A,B,C),X11),A)| -in(ordered_pair(X11,$f74(A,B,C)),B).
% 4.38/4.51 0 [] -relation(A)| -is_transitive_in(A,B)| -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).
% 4.38/4.51 0 [] -relation(A)|is_transitive_in(A,B)|in($f78(A,B),B).
% 4.38/4.51 0 [] -relation(A)|is_transitive_in(A,B)|in($f77(A,B),B).
% 4.38/4.51 0 [] -relation(A)|is_transitive_in(A,B)|in($f76(A,B),B).
% 4.38/4.51 0 [] -relation(A)|is_transitive_in(A,B)|in(ordered_pair($f78(A,B),$f77(A,B)),A).
% 4.38/4.51 0 [] -relation(A)|is_transitive_in(A,B)|in(ordered_pair($f77(A,B),$f76(A,B)),A).
% 4.38/4.51 0 [] -relation(A)|is_transitive_in(A,B)| -in(ordered_pair($f78(A,B),$f76(A,B)),A).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C!=complements_of_subsets(A,B)| -element(D,powerset(A))| -in(D,C)|in(subset_complement(A,D),B).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C!=complements_of_subsets(A,B)| -element(D,powerset(A))|in(D,C)| -in(subset_complement(A,D),B).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|element($f79(A,B,C),powerset(A)).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|in($f79(A,B,C),C)|in(subset_complement(A,$f79(A,B,C)),B).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)| -in($f79(A,B,C),C)| -in(subset_complement(A,$f79(A,B,C)),B).
% 4.38/4.51 0 [] -proper_subset(A,B)|subset(A,B).
% 4.38/4.51 0 [] -proper_subset(A,B)|A!=B.
% 4.38/4.51 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)|function_inverse(A)=relation_inverse(A).
% 4.38/4.51 0 [] -relation(A)| -reflexive(A)|is_reflexive_in(A,relation_field(A)).
% 4.38/4.51 0 [] -relation(A)|reflexive(A)| -is_reflexive_in(A,relation_field(A)).
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] element(cast_to_subset(A),powerset(A)).
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] -relation(A)|relation(relation_restriction(A,B)).
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] -relation(A)|relation(relation_inverse(A)).
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))|element(union_of_subsets(A,B),powerset(A)).
% 4.38/4.51 0 [] relation(identity_relation(A)).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))|element(meet_of_subsets(A,B),powerset(A)).
% 4.38/4.51 0 [] -element(B,powerset(A))| -element(C,powerset(A))|element(subset_difference(A,B,C),powerset(A)).
% 4.38/4.51 0 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))).
% 4.38/4.51 0 [] -relation(B)|relation(relation_rng_restriction(A,B)).
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] $T.
% 4.38/4.51 0 [] element($f80(A),A).
% 4.38/4.51 0 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 4.38/4.51 0 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 4.38/4.51 0 [] -empty(A)|empty(relation_inverse(A)).
% 4.38/4.51 0 [] -empty(A)|relation(relation_inverse(A)).
% 4.38/4.51 0 [] empty(empty_set).
% 4.38/4.51 0 [] relation(empty_set).
% 4.38/4.51 0 [] relation_empty_yielding(empty_set).
% 4.38/4.51 0 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 4.38/4.51 0 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 4.38/4.51 0 [] -empty(succ(A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|relation(set_intersection2(A,B)).
% 4.38/4.51 0 [] -empty(powerset(A)).
% 4.38/4.51 0 [] empty(empty_set).
% 4.38/4.51 0 [] -empty(ordered_pair(A,B)).
% 4.38/4.51 0 [] relation(identity_relation(A)).
% 4.38/4.51 0 [] function(identity_relation(A)).
% 4.38/4.51 0 [] relation(empty_set).
% 4.38/4.51 0 [] relation_empty_yielding(empty_set).
% 4.38/4.51 0 [] function(empty_set).
% 4.38/4.51 0 [] one_to_one(empty_set).
% 4.38/4.51 0 [] empty(empty_set).
% 4.38/4.51 0 [] epsilon_transitive(empty_set).
% 4.38/4.51 0 [] epsilon_connected(empty_set).
% 4.38/4.51 0 [] ordinal(empty_set).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 4.38/4.51 0 [] -empty(singleton(A)).
% 4.38/4.51 0 [] empty(A)| -empty(set_union2(A,B)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation(relation_inverse(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)|function(relation_inverse(A)).
% 4.38/4.51 0 [] -ordinal(A)| -empty(succ(A)).
% 4.38/4.51 0 [] -ordinal(A)|epsilon_transitive(succ(A)).
% 4.38/4.51 0 [] -ordinal(A)|epsilon_connected(succ(A)).
% 4.38/4.51 0 [] -ordinal(A)|ordinal(succ(A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|relation(set_difference(A,B)).
% 4.38/4.51 0 [] -empty(unordered_pair(A,B)).
% 4.38/4.51 0 [] empty(A)| -empty(set_union2(B,A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 4.38/4.51 0 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 4.38/4.51 0 [] -ordinal(A)|epsilon_transitive(union(A)).
% 4.38/4.51 0 [] -ordinal(A)|epsilon_connected(union(A)).
% 4.38/4.51 0 [] -ordinal(A)|ordinal(union(A)).
% 4.38/4.51 0 [] empty(empty_set).
% 4.38/4.51 0 [] relation(empty_set).
% 4.38/4.51 0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 4.38/4.51 0 [] -relation(B)| -function(B)|relation(relation_rng_restriction(A,B)).
% 4.38/4.51 0 [] -relation(B)| -function(B)|function(relation_rng_restriction(A,B)).
% 4.38/4.51 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 4.38/4.51 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 4.38/4.51 0 [] -empty(A)|empty(relation_dom(A)).
% 4.38/4.51 0 [] -empty(A)|relation(relation_dom(A)).
% 4.38/4.51 0 [] -empty(A)|empty(relation_rng(A)).
% 4.38/4.51 0 [] -empty(A)|relation(relation_rng(A)).
% 4.38/4.51 0 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 4.38/4.51 0 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 4.38/4.51 0 [] set_union2(A,A)=A.
% 4.38/4.51 0 [] set_intersection2(A,A)=A.
% 4.38/4.51 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 4.38/4.51 0 [] -relation(A)|relation_inverse(relation_inverse(A))=A.
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B.
% 4.38/4.51 0 [] -proper_subset(A,A).
% 4.38/4.51 0 [] -relation(A)| -reflexive(A)| -in(B,relation_field(A))|in(ordered_pair(B,B),A).
% 4.38/4.51 0 [] -relation(A)|reflexive(A)|in($f81(A),relation_field(A)).
% 4.38/4.51 0 [] -relation(A)|reflexive(A)| -in(ordered_pair($f81(A),$f81(A)),A).
% 4.38/4.51 0 [] singleton(A)!=empty_set.
% 4.38/4.51 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 4.38/4.51 0 [] -disjoint(singleton(A),B)| -in(A,B).
% 4.38/4.51 0 [] in(A,B)|disjoint(singleton(A),B).
% 4.38/4.51 0 [] -relation(B)|subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)).
% 4.38/4.51 0 [] -relation(A)| -transitive(A)| -in(ordered_pair(B,C),A)| -in(ordered_pair(C,D),A)|in(ordered_pair(B,D),A).
% 4.38/4.51 0 [] -relation(A)|transitive(A)|in(ordered_pair($f84(A),$f83(A)),A).
% 4.38/4.51 0 [] -relation(A)|transitive(A)|in(ordered_pair($f83(A),$f82(A)),A).
% 4.38/4.51 0 [] -relation(A)|transitive(A)| -in(ordered_pair($f84(A),$f82(A)),A).
% 4.38/4.51 0 [] -subset(singleton(A),B)|in(A,B).
% 4.38/4.51 0 [] subset(singleton(A),B)| -in(A,B).
% 4.38/4.51 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 4.38/4.51 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 4.38/4.51 0 [] -element(B,powerset(A))| -in(C,B)|in(C,A).
% 4.38/4.51 0 [] -relation(A)| -antisymmetric(A)| -in(ordered_pair(B,C),A)| -in(ordered_pair(C,B),A)|B=C.
% 4.38/4.51 0 [] -relation(A)|antisymmetric(A)|in(ordered_pair($f86(A),$f85(A)),A).
% 4.38/4.51 0 [] -relation(A)|antisymmetric(A)|in(ordered_pair($f85(A),$f86(A)),A).
% 4.38/4.51 0 [] -relation(A)|antisymmetric(A)|$f86(A)!=$f85(A).
% 4.38/4.51 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 4.38/4.51 0 [] -relation(A)| -connected(A)| -in(B,relation_field(A))| -in(C,relation_field(A))|B=C|in(ordered_pair(B,C),A)|in(ordered_pair(C,B),A).
% 4.38/4.51 0 [] -relation(A)|connected(A)|in($f88(A),relation_field(A)).
% 4.38/4.51 0 [] -relation(A)|connected(A)|in($f87(A),relation_field(A)).
% 4.38/4.51 0 [] -relation(A)|connected(A)|$f88(A)!=$f87(A).
% 4.38/4.51 0 [] -relation(A)|connected(A)| -in(ordered_pair($f88(A),$f87(A)),A).
% 4.38/4.51 0 [] -relation(A)|connected(A)| -in(ordered_pair($f87(A),$f88(A)),A).
% 4.38/4.51 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 4.38/4.51 0 [] subset(A,singleton(B))|A!=empty_set.
% 4.38/4.51 0 [] subset(A,singleton(B))|A!=singleton(B).
% 4.38/4.51 0 [] -in(A,B)|subset(A,union(B)).
% 4.38/4.51 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 4.38/4.51 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 4.38/4.51 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 4.38/4.51 0 [] in($f89(A,B),A)|element(A,powerset(B)).
% 4.38/4.51 0 [] -in($f89(A,B),B)|element(A,powerset(B)).
% 4.38/4.51 0 [] -relation(C)| -function(C)| -in(B,relation_dom(relation_dom_restriction(C,A)))|in(B,relation_dom(C)).
% 4.38/4.51 0 [] -relation(C)| -function(C)| -in(B,relation_dom(relation_dom_restriction(C,A)))|in(B,A).
% 4.38/4.51 0 [] -relation(C)| -function(C)|in(B,relation_dom(relation_dom_restriction(C,A)))| -in(B,relation_dom(C))| -in(B,A).
% 4.38/4.51 0 [] relation($c1).
% 4.38/4.51 0 [] function($c1).
% 4.38/4.51 0 [] epsilon_transitive($c2).
% 4.38/4.51 0 [] epsilon_connected($c2).
% 4.38/4.51 0 [] ordinal($c2).
% 4.38/4.51 0 [] empty($c3).
% 4.38/4.51 0 [] relation($c3).
% 4.38/4.51 0 [] empty(A)|element($f90(A),powerset(A)).
% 4.38/4.51 0 [] empty(A)| -empty($f90(A)).
% 4.38/4.51 0 [] empty($c4).
% 4.38/4.51 0 [] relation($c5).
% 4.38/4.51 0 [] empty($c5).
% 4.38/4.51 0 [] function($c5).
% 4.38/4.51 0 [] relation($c6).
% 4.38/4.51 0 [] function($c6).
% 4.38/4.51 0 [] one_to_one($c6).
% 4.38/4.51 0 [] empty($c6).
% 4.38/4.51 0 [] epsilon_transitive($c6).
% 4.38/4.51 0 [] epsilon_connected($c6).
% 4.38/4.51 0 [] ordinal($c6).
% 4.38/4.51 0 [] -empty($c7).
% 4.38/4.51 0 [] relation($c7).
% 4.38/4.51 0 [] element($f91(A),powerset(A)).
% 4.38/4.51 0 [] empty($f91(A)).
% 4.38/4.51 0 [] -empty($c8).
% 4.38/4.51 0 [] relation($c9).
% 4.38/4.51 0 [] function($c9).
% 4.38/4.51 0 [] one_to_one($c9).
% 4.38/4.51 0 [] -empty($c10).
% 4.38/4.51 0 [] epsilon_transitive($c10).
% 4.38/4.51 0 [] epsilon_connected($c10).
% 4.38/4.51 0 [] ordinal($c10).
% 4.38/4.51 0 [] relation($c11).
% 4.38/4.51 0 [] relation_empty_yielding($c11).
% 4.38/4.51 0 [] relation($c12).
% 4.38/4.51 0 [] relation_empty_yielding($c12).
% 4.38/4.51 0 [] function($c12).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))|union_of_subsets(A,B)=union(B).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))|meet_of_subsets(A,B)=set_meet(B).
% 4.38/4.51 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_difference(A,B,C)=set_difference(B,C).
% 4.38/4.51 0 [] -ordinal(A)| -ordinal(B)| -ordinal_subset(A,B)|subset(A,B).
% 4.38/4.51 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)| -subset(A,B).
% 4.38/4.51 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,A).
% 4.38/4.51 0 [] subset(A,A).
% 4.38/4.51 0 [] -disjoint(A,B)|disjoint(B,A).
% 4.38/4.51 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 4.38/4.51 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 4.38/4.51 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 4.38/4.51 0 [] in(A,succ(A)).
% 4.38/4.51 0 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_rng(relation_rng_restriction(B,C)))|in(A,B).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_rng(relation_rng_restriction(B,C)))|in(A,relation_rng(C)).
% 4.38/4.51 0 [] -relation(C)|in(A,relation_rng(relation_rng_restriction(B,C)))| -in(A,B)| -in(A,relation_rng(C)).
% 4.38/4.51 0 [] -relation(B)|subset(relation_rng(relation_rng_restriction(A,B)),A).
% 4.38/4.51 0 [] -relation(B)|subset(relation_rng_restriction(A,B),B).
% 4.38/4.51 0 [] -relation(B)|subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)).
% 4.38/4.51 0 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 4.38/4.51 0 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 4.38/4.51 0 [] -relation(B)|relation_rng(relation_rng_restriction(A,B))=set_intersection2(relation_rng(B),A).
% 4.38/4.51 0 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 4.38/4.51 0 [] -subset(A,B)|set_union2(A,B)=B.
% 4.38/4.51 0 [] in(A,$f92(A)).
% 4.38/4.51 0 [] -in(C,$f92(A))| -subset(D,C)|in(D,$f92(A)).
% 4.38/4.51 0 [] -in(X12,$f92(A))|in(powerset(X12),$f92(A)).
% 4.38/4.51 0 [] -subset(X13,$f92(A))|are_e_quipotent(X13,$f92(A))|in(X13,$f92(A)).
% 4.38/4.51 0 [] -relation(C)|relation_dom_restriction(relation_rng_restriction(A,C),B)=relation_rng_restriction(A,relation_dom_restriction(C,B)).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_image(C,B))|in($f93(A,B,C),relation_dom(C)).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_image(C,B))|in(ordered_pair($f93(A,B,C),A),C).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_image(C,B))|in($f93(A,B,C),B).
% 4.38/4.51 0 [] -relation(C)|in(A,relation_image(C,B))| -in(D,relation_dom(C))| -in(ordered_pair(D,A),C)| -in(D,B).
% 4.38/4.51 0 [] -relation(B)|subset(relation_image(B,A),relation_rng(B)).
% 4.38/4.51 0 [] -relation(B)| -function(B)|subset(relation_image(B,relation_inverse_image(B,A)),A).
% 4.38/4.51 0 [] -relation(B)|relation_image(B,A)=relation_image(B,set_intersection2(relation_dom(B),A)).
% 4.38/4.51 0 [] -relation(B)| -subset(A,relation_dom(B))|subset(A,relation_inverse_image(B,relation_image(B,A))).
% 4.38/4.51 0 [] -relation(A)|relation_image(A,relation_dom(A))=relation_rng(A).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -subset(A,relation_rng(B))|relation_image(B,relation_inverse_image(B,A))=A.
% 4.38/4.51 0 [] -relation(A)| -relation(B)|relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A)).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in($f94(A,B,C),relation_rng(C)).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in(ordered_pair(A,$f94(A,B,C)),C).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in($f94(A,B,C),B).
% 4.38/4.51 0 [] -relation(C)|in(A,relation_inverse_image(C,B))| -in(D,relation_rng(C))| -in(ordered_pair(A,D),C)| -in(D,B).
% 4.38/4.51 0 [] -relation(B)|subset(relation_inverse_image(B,A),relation_dom(B)).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_restriction(C,B))|in(A,C).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_restriction(C,B))|in(A,cartesian_product2(B,B)).
% 4.38/4.51 0 [] -relation(C)|in(A,relation_restriction(C,B))| -in(A,C)| -in(A,cartesian_product2(B,B)).
% 4.38/4.51 0 [] -relation(B)|A=empty_set| -subset(A,relation_rng(B))|relation_inverse_image(B,A)!=empty_set.
% 4.38/4.51 0 [] -relation(C)| -subset(A,B)|subset(relation_inverse_image(C,A),relation_inverse_image(C,B)).
% 4.38/4.51 0 [] -relation(B)|relation_restriction(B,A)=relation_dom_restriction(relation_rng_restriction(A,B),A).
% 4.38/4.51 0 [] subset(set_intersection2(A,B),A).
% 4.38/4.51 0 [] -relation(B)|relation_restriction(B,A)=relation_rng_restriction(A,relation_dom_restriction(B,A)).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_field(relation_restriction(C,B)))|in(A,relation_field(C)).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_field(relation_restriction(C,B)))|in(A,B).
% 4.38/4.51 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 4.38/4.51 0 [] set_union2(A,empty_set)=A.
% 4.38/4.51 0 [] -in(A,B)|element(A,B).
% 4.38/4.51 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 4.38/4.51 0 [] powerset(empty_set)=singleton(empty_set).
% 4.38/4.51 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(A,relation_dom(C)).
% 4.38/4.51 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(B,relation_rng(C)).
% 4.38/4.51 0 [] -relation(B)|subset(relation_field(relation_restriction(B,A)),relation_field(B)).
% 4.38/4.51 0 [] -relation(B)|subset(relation_field(relation_restriction(B,A)),A).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)| -in(A,relation_dom(relation_composition(C,B)))|in(A,relation_dom(C)).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)| -in(A,relation_dom(relation_composition(C,B)))|in(apply(C,A),relation_dom(B)).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|in(A,relation_dom(relation_composition(C,B)))| -in(A,relation_dom(C))| -in(apply(C,A),relation_dom(B)).
% 4.38/4.51 0 [] -epsilon_transitive(A)| -ordinal(B)| -proper_subset(A,B)|in(A,B).
% 4.38/4.51 0 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 4.38/4.51 0 [] -relation(C)|subset(fiber(relation_restriction(C,A),B),fiber(C,B)).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)| -in(A,relation_dom(relation_composition(C,B)))|apply(relation_composition(C,B),A)=apply(B,apply(C,A)).
% 4.38/4.51 0 [] -relation(B)| -reflexive(B)|reflexive(relation_restriction(B,A)).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)| -in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A)).
% 4.38/4.51 0 [] -ordinal(B)| -in(A,B)|ordinal(A).
% 4.38/4.51 0 [] -relation(B)| -connected(B)|connected(relation_restriction(B,A)).
% 4.38/4.51 0 [] -ordinal(A)| -ordinal(B)|in(A,B)|A=B|in(B,A).
% 4.38/4.51 0 [] -relation(B)| -transitive(B)|transitive(relation_restriction(B,A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_dom(A),relation_dom(B)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_rng(A),relation_rng(B)).
% 4.38/4.51 0 [] -relation(B)| -antisymmetric(B)|antisymmetric(relation_restriction(B,A)).
% 4.38/4.51 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 4.38/4.51 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 4.38/4.51 0 [] set_intersection2(A,empty_set)=empty_set.
% 4.38/4.51 0 [] -element(A,B)|empty(B)|in(A,B).
% 4.38/4.51 0 [] in($f95(A,B),A)|in($f95(A,B),B)|A=B.
% 4.38/4.51 0 [] -in($f95(A,B),A)| -in($f95(A,B),B)|A=B.
% 4.38/4.51 0 [] subset(empty_set,A).
% 4.38/4.51 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(A,relation_field(C)).
% 4.38/4.51 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(B,relation_field(C)).
% 4.38/4.51 0 [] in($f96(A),A)|ordinal(A).
% 4.38/4.51 0 [] -ordinal($f96(A))| -subset($f96(A),A)|ordinal(A).
% 4.38/4.51 0 [] -relation(B)| -well_founded_relation(B)|well_founded_relation(relation_restriction(B,A)).
% 4.38/4.51 0 [] -ordinal(B)| -subset(A,B)|A=empty_set|ordinal($f97(A,B)).
% 4.38/4.51 0 [] -ordinal(B)| -subset(A,B)|A=empty_set|in($f97(A,B),A).
% 4.38/4.51 0 [] -ordinal(B)| -subset(A,B)|A=empty_set| -ordinal(D)| -in(D,A)|ordinal_subset($f97(A,B),D).
% 4.38/4.51 0 [] -relation(B)| -well_ordering(B)|well_ordering(relation_restriction(B,A)).
% 4.38/4.51 0 [] -ordinal(A)| -ordinal(B)| -in(A,B)|ordinal_subset(succ(A),B).
% 4.38/4.51 0 [] -ordinal(A)| -ordinal(B)|in(A,B)| -ordinal_subset(succ(A),B).
% 4.38/4.51 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 4.38/4.51 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 4.38/4.51 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 4.38/4.51 0 [] -relation(B)| -function(B)|B!=identity_relation(A)|relation_dom(B)=A.
% 4.38/4.51 0 [] -relation(B)| -function(B)|B!=identity_relation(A)| -in(C,A)|apply(B,C)=C.
% 4.38/4.51 0 [] -relation(B)| -function(B)|B=identity_relation(A)|relation_dom(B)!=A|in($f98(A,B),A).
% 4.38/4.51 0 [] -relation(B)| -function(B)|B=identity_relation(A)|relation_dom(B)!=A|apply(B,$f98(A,B))!=$f98(A,B).
% 4.38/4.51 0 [] -in(B,A)|apply(identity_relation(A),B)=B.
% 4.38/4.51 0 [] subset(set_difference(A,B),A).
% 4.38/4.51 0 [] -relation(A)|relation_rng(A)=relation_dom(relation_inverse(A)).
% 4.38/4.51 0 [] -relation(A)|relation_dom(A)=relation_rng(relation_inverse(A)).
% 4.38/4.51 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 4.38/4.51 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 4.38/4.51 0 [] -subset(singleton(A),B)|in(A,B).
% 4.38/4.51 0 [] subset(singleton(A),B)| -in(A,B).
% 4.38/4.51 0 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 4.38/4.51 0 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 4.38/4.51 0 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 4.38/4.51 0 [] -relation(B)| -well_ordering(B)| -subset(A,relation_field(B))|relation_field(relation_restriction(B,A))=A.
% 4.38/4.51 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 4.38/4.51 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 4.38/4.51 0 [] subset(A,singleton(B))|A!=empty_set.
% 4.38/4.51 0 [] subset(A,singleton(B))|A!=singleton(B).
% 4.38/4.51 0 [] set_difference(A,empty_set)=A.
% 4.38/4.51 0 [] -in(A,B)| -in(B,C)| -in(C,A).
% 4.38/4.51 0 [] -element(A,powerset(B))|subset(A,B).
% 4.38/4.51 0 [] element(A,powerset(B))| -subset(A,B).
% 4.38/4.51 0 [] disjoint(A,B)|in($f99(A,B),A).
% 4.38/4.51 0 [] disjoint(A,B)|in($f99(A,B),B).
% 4.38/4.51 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 4.38/4.51 0 [] -subset(A,empty_set)|A=empty_set.
% 4.38/4.51 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 4.38/4.51 0 [] -ordinal(A)| -being_limit_ordinal(A)| -ordinal(B)| -in(B,A)|in(succ(B),A).
% 4.38/4.51 0 [] -ordinal(A)|being_limit_ordinal(A)|ordinal($f100(A)).
% 4.38/4.51 0 [] -ordinal(A)|being_limit_ordinal(A)|in($f100(A),A).
% 4.38/4.51 0 [] -ordinal(A)|being_limit_ordinal(A)| -in(succ($f100(A)),A).
% 4.38/4.51 0 [] -ordinal(A)|being_limit_ordinal(A)|ordinal($f101(A)).
% 4.38/4.51 0 [] -ordinal(A)|being_limit_ordinal(A)|A=succ($f101(A)).
% 4.38/4.51 0 [] -ordinal(A)| -ordinal(B)|A!=succ(B)| -being_limit_ordinal(A).
% 4.38/4.51 0 [] -element(B,powerset(A))| -element(C,powerset(A))| -disjoint(B,C)|subset(B,subset_complement(A,C)).
% 4.38/4.51 0 [] -element(B,powerset(A))| -element(C,powerset(A))|disjoint(B,C)| -subset(B,subset_complement(A,C)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|subset(relation_dom(relation_composition(A,B)),relation_dom(A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)|subset(relation_rng(relation_composition(A,B)),relation_rng(B)).
% 4.38/4.51 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -subset(relation_rng(A),relation_dom(B))|relation_dom(relation_composition(A,B))=relation_dom(A).
% 4.38/4.51 0 [] -element(B,powerset(powerset(A)))|B=empty_set|complements_of_subsets(A,B)!=empty_set.
% 4.38/4.51 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -subset(relation_dom(A),relation_rng(B))|relation_rng(relation_composition(B,A))=relation_rng(A).
% 4.38/4.51 0 [] -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)).
% 4.38/4.51 0 [] -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)).
% 4.38/4.51 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|relation_isomorphism(B,A,function_inverse(C)).
% 4.38/4.51 0 [] set_difference(empty_set,A)=empty_set.
% 4.38/4.51 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 4.38/4.51 0 [] disjoint(A,B)|in($f102(A,B),set_intersection2(A,B)).
% 4.38/4.51 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 4.38/4.51 0 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -reflexive(A)|reflexive(B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -transitive(A)|transitive(B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -connected(A)|connected(B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -antisymmetric(A)|antisymmetric(B).
% 4.38/4.51 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -well_founded_relation(A)|well_founded_relation(B).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)|relation_dom(B)=relation_rng(A).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_rng(A))|D!=apply(B,C)|in(D,relation_dom(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_rng(A))|D!=apply(B,C)|C=apply(A,D).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(D,relation_dom(A))|C!=apply(A,D)|in(C,relation_rng(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(D,relation_dom(A))|C!=apply(A,D)|D=apply(B,C).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f104(A,B),relation_rng(A))|in($f103(A,B),relation_dom(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f104(A,B),relation_rng(A))|$f104(A,B)=apply(A,$f103(A,B)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|$f103(A,B)=apply(B,$f104(A,B))|in($f103(A,B),relation_dom(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|$f103(A,B)=apply(B,$f104(A,B))|$f104(A,B)=apply(A,$f103(A,B)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)| -in($f103(A,B),relation_dom(A))|$f104(A,B)!=apply(A,$f103(A,B))| -in($f104(A,B),relation_rng(A))|$f103(A,B)!=apply(B,$f104(A,B)).
% 4.38/4.51 0 [] -element(C,powerset(A))| -in(B,subset_complement(A,C))| -in(B,C).
% 4.38/4.51 0 [] relation($c15).
% 4.38/4.51 0 [] relation($c14).
% 4.38/4.51 0 [] relation($c13).
% 4.38/4.51 0 [] function($c13).
% 4.38/4.51 0 [] well_ordering($c15).
% 4.38/4.51 0 [] relation_isomorphism($c15,$c14,$c13).
% 4.38/4.51 0 [] -well_ordering($c14).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(A)=relation_dom(function_inverse(A)).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation_dom(A)=relation_rng(function_inverse(A)).
% 4.38/4.51 0 [] -relation(A)|in(ordered_pair($f106(A),$f105(A)),A)|A=empty_set.
% 4.38/4.51 0 [] -relation(B)| -function(B)| -one_to_one(B)| -in(A,relation_rng(B))|A=apply(B,apply(function_inverse(B),A)).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -one_to_one(B)| -in(A,relation_rng(B))|A=apply(relation_composition(function_inverse(B),B),A).
% 4.38/4.51 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 4.38/4.51 0 [] -relation(A)| -well_founded_relation(A)|is_well_founded_in(A,relation_field(A)).
% 4.38/4.51 0 [] -relation(A)|well_founded_relation(A)| -is_well_founded_in(A,relation_field(A)).
% 4.38/4.51 0 [] relation_dom(empty_set)=empty_set.
% 4.38/4.51 0 [] relation_rng(empty_set)=empty_set.
% 4.38/4.51 0 [] -subset(A,B)| -proper_subset(B,A).
% 4.38/4.51 0 [] -relation(A)| -function(A)| -one_to_one(A)|one_to_one(function_inverse(A)).
% 4.38/4.51 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 4.38/4.51 0 [] -relation(A)|relation_dom(A)!=empty_set|A=empty_set.
% 4.38/4.51 0 [] -relation(A)|relation_rng(A)!=empty_set|A=empty_set.
% 4.38/4.51 0 [] -relation(A)|relation_dom(A)!=empty_set|relation_rng(A)=empty_set.
% 4.38/4.51 0 [] -relation(A)|relation_dom(A)=empty_set|relation_rng(A)!=empty_set.
% 4.38/4.51 0 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 4.38/4.51 0 [] set_difference(A,singleton(B))=A|in(B,A).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_dom_restriction(C,A)|relation_dom(B)=set_intersection2(relation_dom(C),A).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_dom_restriction(C,A)| -in(D,relation_dom(B))|apply(B,D)=apply(C,D).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_dom_restriction(C,A)|relation_dom(B)!=set_intersection2(relation_dom(C),A)|in($f107(A,B,C),relation_dom(B)).
% 4.38/4.51 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_dom_restriction(C,A)|relation_dom(B)!=set_intersection2(relation_dom(C),A)|apply(B,$f107(A,B,C))!=apply(C,$f107(A,B,C)).
% 4.38/4.51 0 [] unordered_pair(A,A)=singleton(A).
% 4.38/4.51 0 [] -empty(A)|A=empty_set.
% 4.38/4.51 0 [] -subset(singleton(A),singleton(B))|A=B.
% 4.38/4.51 0 [] -relation(C)| -function(C)| -in(B,relation_dom(relation_dom_restriction(C,A)))|apply(relation_dom_restriction(C,A),B)=apply(C,B).
% 4.38/4.51 0 [] relation_dom(identity_relation(A))=A.
% 4.38/4.51 0 [] relation_rng(identity_relation(A))=A.
% 4.38/4.51 0 [] -relation(C)| -function(C)| -in(B,A)|apply(relation_dom_restriction(C,A),B)=apply(C,B).
% 4.38/4.51 0 [] -relation(D)| -in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|in(A,C).
% 4.38/4.51 0 [] -relation(D)| -in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|in(ordered_pair(A,B),D).
% 4.38/4.51 0 [] -relation(D)|in(ordered_pair(A,B),relation_composition(identity_relation(C),D))| -in(A,C)| -in(ordered_pair(A,B),D).
% 4.38/4.51 0 [] -in(A,B)| -empty(B).
% 4.38/4.51 0 [] -in(A,B)|in($f108(A,B),B).
% 4.38/4.51 0 [] -in(A,B)| -in(D,B)| -in(D,$f108(A,B)).
% 4.38/4.51 0 [] subset(A,set_union2(A,B)).
% 4.38/4.51 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 4.38/4.51 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_dom(relation_dom_restriction(C,B)))|in(A,B).
% 4.38/4.51 0 [] -relation(C)| -in(A,relation_dom(relation_dom_restriction(C,B)))|in(A,relation_dom(C)).
% 4.38/4.52 0 [] -relation(C)|in(A,relation_dom(relation_dom_restriction(C,B)))| -in(A,B)| -in(A,relation_dom(C)).
% 4.38/4.52 0 [] -relation(B)|subset(relation_dom_restriction(B,A),B).
% 4.38/4.52 0 [] -empty(A)|A=B| -empty(B).
% 4.38/4.52 0 [] -relation(C)| -function(C)| -in(ordered_pair(A,B),C)|in(A,relation_dom(C)).
% 4.38/4.52 0 [] -relation(C)| -function(C)| -in(ordered_pair(A,B),C)|B=apply(C,A).
% 4.38/4.52 0 [] -relation(C)| -function(C)|in(ordered_pair(A,B),C)| -in(A,relation_dom(C))|B!=apply(C,A).
% 4.38/4.52 0 [] -relation(A)| -well_orders(A,relation_field(A))|well_ordering(A).
% 4.38/4.52 0 [] -relation(A)|well_orders(A,relation_field(A))| -well_ordering(A).
% 4.38/4.52 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 4.38/4.52 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 4.38/4.52 0 [] -relation(B)|relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A).
% 4.38/4.52 0 [] -in(A,B)|subset(A,union(B)).
% 4.38/4.52 0 [] -relation(B)|relation_dom_restriction(B,A)=relation_composition(identity_relation(A),B).
% 4.38/4.52 0 [] -relation(B)|subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)).
% 4.38/4.52 0 [] union(powerset(A))=A.
% 4.38/4.52 0 [] in(A,$f110(A)).
% 4.38/4.52 0 [] -in(C,$f110(A))| -subset(D,C)|in(D,$f110(A)).
% 4.38/4.52 0 [] -in(X14,$f110(A))|in($f109(A,X14),$f110(A)).
% 4.38/4.52 0 [] -in(X14,$f110(A))| -subset(E,X14)|in(E,$f109(A,X14)).
% 4.38/4.52 0 [] -subset(X15,$f110(A))|are_e_quipotent(X15,$f110(A))|in(X15,$f110(A)).
% 4.38/4.52 0 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 4.38/4.52 end_of_list.
% 4.38/4.52
% 4.38/4.52 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=12.
% 4.38/4.52
% 4.38/4.52 This ia a non-Horn set with equality. The strategy will be
% 4.38/4.52 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 4.38/4.52 deletion, with positive clauses in sos and nonpositive
% 4.38/4.52 clauses in usable.
% 4.38/4.52
% 4.38/4.52 dependent: set(knuth_bendix).
% 4.38/4.52 dependent: set(anl_eq).
% 4.38/4.52 dependent: set(para_from).
% 4.38/4.52 dependent: set(para_into).
% 4.38/4.52 dependent: clear(para_from_right).
% 4.38/4.52 dependent: clear(para_into_right).
% 4.38/4.52 dependent: set(para_from_vars).
% 4.38/4.52 dependent: set(eq_units_both_ways).
% 4.38/4.52 dependent: set(dynamic_demod_all).
% 4.38/4.52 dependent: set(dynamic_demod).
% 4.38/4.52 dependent: set(order_eq).
% 4.38/4.52 dependent: set(back_demod).
% 4.38/4.52 dependent: set(lrpo).
% 4.38/4.52 dependent: set(hyper_res).
% 4.38/4.52 dependent: set(unit_deletion).
% 4.38/4.52 dependent: set(factor).
% 4.38/4.52
% 4.38/4.52 ------------> process usable:
% 4.38/4.52 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 4.38/4.52 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 4.38/4.52 ** KEPT (pick-wt=4): 3 [] -empty(A)|function(A).
% 4.38/4.52 ** KEPT (pick-wt=4): 4 [] -ordinal(A)|epsilon_transitive(A).
% 4.38/4.52 ** KEPT (pick-wt=4): 5 [] -ordinal(A)|epsilon_connected(A).
% 4.38/4.52 ** KEPT (pick-wt=4): 6 [] -empty(A)|relation(A).
% 4.38/4.52 ** KEPT (pick-wt=8): 7 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 4.38/4.52 ** KEPT (pick-wt=6): 8 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 4.38/4.52 ** KEPT (pick-wt=4): 9 [] -empty(A)|epsilon_transitive(A).
% 4.38/4.52 ** KEPT (pick-wt=4): 10 [] -empty(A)|epsilon_connected(A).
% 4.38/4.52 ** KEPT (pick-wt=4): 11 [] -empty(A)|ordinal(A).
% 4.38/4.52 ** KEPT (pick-wt=10): 12 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)|ordinal_subset(B,A).
% 4.38/4.52 ** KEPT (pick-wt=14): 13 [] -relation(A)|A!=identity_relation(B)| -in(ordered_pair(C,D),A)|in(C,B).
% 4.38/4.52 ** KEPT (pick-wt=14): 14 [] -relation(A)|A!=identity_relation(B)| -in(ordered_pair(C,D),A)|C=D.
% 4.38/4.52 ** KEPT (pick-wt=17): 15 [] -relation(A)|A!=identity_relation(B)|in(ordered_pair(C,D),A)| -in(C,B)|C!=D.
% 4.38/4.52 ** KEPT (pick-wt=20): 16 [] -relation(A)|A=identity_relation(B)|in(ordered_pair($f2(B,A),$f1(B,A)),A)|in($f2(B,A),B).
% 4.38/4.52 ** KEPT (pick-wt=22): 17 [] -relation(A)|A=identity_relation(B)|in(ordered_pair($f2(B,A),$f1(B,A)),A)|$f2(B,A)=$f1(B,A).
% 4.38/4.52 ** KEPT (pick-wt=27): 18 [] -relation(A)|A=identity_relation(B)| -in(ordered_pair($f2(B,A),$f1(B,A)),A)| -in($f2(B,A),B)|$f2(B,A)!=$f1(B,A).
% 4.38/4.52 ** KEPT (pick-wt=6): 19 [] A!=B|subset(A,B).
% 4.38/4.52 ** KEPT (pick-wt=6): 20 [] A!=B|subset(B,A).
% 4.38/4.52 ** KEPT (pick-wt=9): 21 [] A=B| -subset(A,B)| -subset(B,A).
% 4.38/4.52 ** KEPT (pick-wt=17): 22 [] -relation(A)| -relation(B)|B!=relation_dom_restriction(A,C)| -in(ordered_pair(D,E),B)|in(D,C).
% 4.38/4.52 ** KEPT (pick-wt=19): 23 [] -relation(A)| -relation(B)|B!=relation_dom_restriction(A,C)| -in(ordered_pair(D,E),B)|in(ordered_pair(D,E),A).
% 4.38/4.52 ** KEPT (pick-wt=22): 24 [] -relation(A)| -relation(B)|B!=relation_dom_restriction(A,C)|in(ordered_pair(D,E),B)| -in(D,C)| -in(ordered_pair(D,E),A).
% 4.38/4.52 ** KEPT (pick-wt=26): 25 [] -relation(A)| -relation(B)|B=relation_dom_restriction(A,C)|in(ordered_pair($f4(A,C,B),$f3(A,C,B)),B)|in($f4(A,C,B),C).
% 4.38/4.52 ** KEPT (pick-wt=31): 26 [] -relation(A)| -relation(B)|B=relation_dom_restriction(A,C)|in(ordered_pair($f4(A,C,B),$f3(A,C,B)),B)|in(ordered_pair($f4(A,C,B),$f3(A,C,B)),A).
% 4.38/4.52 ** KEPT (pick-wt=37): 27 [] -relation(A)| -relation(B)|B=relation_dom_restriction(A,C)| -in(ordered_pair($f4(A,C,B),$f3(A,C,B)),B)| -in($f4(A,C,B),C)| -in(ordered_pair($f4(A,C,B),$f3(A,C,B)),A).
% 4.38/4.52 ** KEPT (pick-wt=20): 28 [] -relation(A)| -function(A)|B!=relation_image(A,C)| -in(D,B)|in($f5(A,C,B,D),relation_dom(A)).
% 4.38/4.52 ** KEPT (pick-wt=19): 29 [] -relation(A)| -function(A)|B!=relation_image(A,C)| -in(D,B)|in($f5(A,C,B,D),C).
% 4.38/4.52 ** KEPT (pick-wt=21): 31 [copy,30,flip.5] -relation(A)| -function(A)|B!=relation_image(A,C)| -in(D,B)|apply(A,$f5(A,C,B,D))=D.
% 4.38/4.52 ** KEPT (pick-wt=24): 32 [] -relation(A)| -function(A)|B!=relation_image(A,C)|in(D,B)| -in(E,relation_dom(A))| -in(E,C)|D!=apply(A,E).
% 4.38/4.52 ** KEPT (pick-wt=22): 33 [] -relation(A)| -function(A)|B=relation_image(A,C)|in($f7(A,C,B),B)|in($f6(A,C,B),relation_dom(A)).
% 4.38/4.52 ** KEPT (pick-wt=21): 34 [] -relation(A)| -function(A)|B=relation_image(A,C)|in($f7(A,C,B),B)|in($f6(A,C,B),C).
% 4.38/4.52 ** KEPT (pick-wt=26): 36 [copy,35,flip.5] -relation(A)| -function(A)|B=relation_image(A,C)|in($f7(A,C,B),B)|apply(A,$f6(A,C,B))=$f7(A,C,B).
% 4.38/4.52 ** KEPT (pick-wt=30): 37 [] -relation(A)| -function(A)|B=relation_image(A,C)| -in($f7(A,C,B),B)| -in(D,relation_dom(A))| -in(D,C)|$f7(A,C,B)!=apply(A,D).
% 4.38/4.52 ** KEPT (pick-wt=17): 38 [] -relation(A)| -relation(B)|B!=relation_rng_restriction(C,A)| -in(ordered_pair(D,E),B)|in(E,C).
% 4.38/4.52 ** KEPT (pick-wt=19): 39 [] -relation(A)| -relation(B)|B!=relation_rng_restriction(C,A)| -in(ordered_pair(D,E),B)|in(ordered_pair(D,E),A).
% 4.38/4.52 ** KEPT (pick-wt=22): 40 [] -relation(A)| -relation(B)|B!=relation_rng_restriction(C,A)|in(ordered_pair(D,E),B)| -in(E,C)| -in(ordered_pair(D,E),A).
% 4.38/4.52 ** KEPT (pick-wt=26): 41 [] -relation(A)| -relation(B)|B=relation_rng_restriction(C,A)|in(ordered_pair($f9(C,A,B),$f8(C,A,B)),B)|in($f8(C,A,B),C).
% 4.38/4.52 ** KEPT (pick-wt=31): 42 [] -relation(A)| -relation(B)|B=relation_rng_restriction(C,A)|in(ordered_pair($f9(C,A,B),$f8(C,A,B)),B)|in(ordered_pair($f9(C,A,B),$f8(C,A,B)),A).
% 4.38/4.52 ** KEPT (pick-wt=37): 43 [] -relation(A)| -relation(B)|B=relation_rng_restriction(C,A)| -in(ordered_pair($f9(C,A,B),$f8(C,A,B)),B)| -in($f8(C,A,B),C)| -in(ordered_pair($f9(C,A,B),$f8(C,A,B)),A).
% 4.38/4.52 ** KEPT (pick-wt=8): 44 [] -relation(A)| -antisymmetric(A)|is_antisymmetric_in(A,relation_field(A)).
% 4.38/4.52 ** KEPT (pick-wt=8): 45 [] -relation(A)|antisymmetric(A)| -is_antisymmetric_in(A,relation_field(A)).
% 4.38/4.52 ** KEPT (pick-wt=16): 46 [] -relation(A)| -function(A)|B!=relation_inverse_image(A,C)| -in(D,B)|in(D,relation_dom(A)).
% 4.38/4.52 ** KEPT (pick-wt=17): 47 [] -relation(A)| -function(A)|B!=relation_inverse_image(A,C)| -in(D,B)|in(apply(A,D),C).
% 4.38/4.52 ** KEPT (pick-wt=21): 48 [] -relation(A)| -function(A)|B!=relation_inverse_image(A,C)|in(D,B)| -in(D,relation_dom(A))| -in(apply(A,D),C).
% 4.38/4.52 ** KEPT (pick-wt=22): 49 [] -relation(A)| -function(A)|B=relation_inverse_image(A,C)|in($f10(A,C,B),B)|in($f10(A,C,B),relation_dom(A)).
% 4.38/4.52 ** KEPT (pick-wt=23): 50 [] -relation(A)| -function(A)|B=relation_inverse_image(A,C)|in($f10(A,C,B),B)|in(apply(A,$f10(A,C,B)),C).
% 4.38/4.52 ** KEPT (pick-wt=30): 51 [] -relation(A)| -function(A)|B=relation_inverse_image(A,C)| -in($f10(A,C,B),B)| -in($f10(A,C,B),relation_dom(A))| -in(apply(A,$f10(A,C,B)),C).
% 4.38/4.52 ** KEPT (pick-wt=19): 52 [] -relation(A)|B!=relation_image(A,C)| -in(D,B)|in(ordered_pair($f11(A,C,B,D),D),A).
% 4.38/4.52 ** KEPT (pick-wt=17): 53 [] -relation(A)|B!=relation_image(A,C)| -in(D,B)|in($f11(A,C,B,D),C).
% 4.38/4.52 ** KEPT (pick-wt=18): 54 [] -relation(A)|B!=relation_image(A,C)|in(D,B)| -in(ordered_pair(E,D),A)| -in(E,C).
% 4.38/4.52 ** KEPT (pick-wt=24): 55 [] -relation(A)|B=relation_image(A,C)|in($f13(A,C,B),B)|in(ordered_pair($f12(A,C,B),$f13(A,C,B)),A).
% 4.38/4.52 ** KEPT (pick-wt=19): 56 [] -relation(A)|B=relation_image(A,C)|in($f13(A,C,B),B)|in($f12(A,C,B),C).
% 4.38/4.52 ** KEPT (pick-wt=24): 57 [] -relation(A)|B=relation_image(A,C)| -in($f13(A,C,B),B)| -in(ordered_pair(D,$f13(A,C,B)),A)| -in(D,C).
% 4.38/4.52 ** KEPT (pick-wt=19): 58 [] -relation(A)|B!=relation_inverse_image(A,C)| -in(D,B)|in(ordered_pair(D,$f14(A,C,B,D)),A).
% 4.38/4.52 ** KEPT (pick-wt=17): 59 [] -relation(A)|B!=relation_inverse_image(A,C)| -in(D,B)|in($f14(A,C,B,D),C).
% 4.38/4.52 ** KEPT (pick-wt=18): 60 [] -relation(A)|B!=relation_inverse_image(A,C)|in(D,B)| -in(ordered_pair(D,E),A)| -in(E,C).
% 4.38/4.52 ** KEPT (pick-wt=24): 61 [] -relation(A)|B=relation_inverse_image(A,C)|in($f16(A,C,B),B)|in(ordered_pair($f16(A,C,B),$f15(A,C,B)),A).
% 4.38/4.52 ** KEPT (pick-wt=19): 62 [] -relation(A)|B=relation_inverse_image(A,C)|in($f16(A,C,B),B)|in($f15(A,C,B),C).
% 4.38/4.52 ** KEPT (pick-wt=24): 63 [] -relation(A)|B=relation_inverse_image(A,C)| -in($f16(A,C,B),B)| -in(ordered_pair($f16(A,C,B),D),A)| -in(D,C).
% 4.38/4.52 ** KEPT (pick-wt=8): 64 [] -relation(A)| -connected(A)|is_connected_in(A,relation_field(A)).
% 4.38/4.52 ** KEPT (pick-wt=8): 65 [] -relation(A)|connected(A)| -is_connected_in(A,relation_field(A)).
% 4.38/4.52 ** KEPT (pick-wt=8): 66 [] -relation(A)| -transitive(A)|is_transitive_in(A,relation_field(A)).
% 4.38/4.52 ** KEPT (pick-wt=8): 67 [] -relation(A)|transitive(A)| -is_transitive_in(A,relation_field(A)).
% 4.38/4.52 ** KEPT (pick-wt=18): 68 [] A!=unordered_triple(B,C,D)| -in(E,A)|E=B|E=C|E=D.
% 4.38/4.52 ** KEPT (pick-wt=12): 69 [] A!=unordered_triple(B,C,D)|in(E,A)|E!=B.
% 4.38/4.52 ** KEPT (pick-wt=12): 70 [] A!=unordered_triple(B,C,D)|in(E,A)|E!=C.
% 4.38/4.52 ** KEPT (pick-wt=12): 71 [] A!=unordered_triple(B,C,D)|in(E,A)|E!=D.
% 4.38/4.52 ** KEPT (pick-wt=20): 72 [] A=unordered_triple(B,C,D)| -in($f17(B,C,D,A),A)|$f17(B,C,D,A)!=B.
% 4.38/4.52 ** KEPT (pick-wt=20): 73 [] A=unordered_triple(B,C,D)| -in($f17(B,C,D,A),A)|$f17(B,C,D,A)!=C.
% 4.38/4.52 ** KEPT (pick-wt=20): 74 [] A=unordered_triple(B,C,D)| -in($f17(B,C,D,A),A)|$f17(B,C,D,A)!=D.
% 4.38/4.52 ** KEPT (pick-wt=14): 76 [copy,75,flip.3] -relation(A)| -in(B,A)|ordered_pair($f19(A,B),$f18(A,B))=B.
% 4.38/4.52 ** KEPT (pick-wt=8): 77 [] relation(A)|$f20(A)!=ordered_pair(B,C).
% 4.38/4.52 ** KEPT (pick-wt=13): 78 [] -relation(A)| -is_reflexive_in(A,B)| -in(C,B)|in(ordered_pair(C,C),A).
% 4.38/4.52 ** KEPT (pick-wt=10): 79 [] -relation(A)|is_reflexive_in(A,B)|in($f21(A,B),B).
% 4.38/4.52 ** KEPT (pick-wt=14): 80 [] -relation(A)|is_reflexive_in(A,B)| -in(ordered_pair($f21(A,B),$f21(A,B)),A).
% 4.38/4.52 ** KEPT (pick-wt=16): 81 [] A=empty_set|B!=set_meet(A)| -in(C,B)| -in(D,A)|in(C,D).
% 4.38/4.52 ** KEPT (pick-wt=16): 82 [] A=empty_set|B!=set_meet(A)|in(C,B)|in($f22(A,B,C),A).
% 4.38/4.52 ** KEPT (pick-wt=16): 83 [] A=empty_set|B!=set_meet(A)|in(C,B)| -in(C,$f22(A,B,C)).
% 4.38/4.52 ** KEPT (pick-wt=20): 84 [] A=empty_set|B=set_meet(A)|in($f24(A,B),B)| -in(C,A)|in($f24(A,B),C).
% 4.38/4.52 ** KEPT (pick-wt=17): 85 [] A=empty_set|B=set_meet(A)| -in($f24(A,B),B)|in($f23(A,B),A).
% 4.38/4.52 ** KEPT (pick-wt=19): 86 [] A=empty_set|B=set_meet(A)| -in($f24(A,B),B)| -in($f24(A,B),$f23(A,B)).
% 4.38/4.52 ** KEPT (pick-wt=10): 87 [] A!=empty_set|B!=set_meet(A)|B=empty_set.
% 4.38/4.52 ** KEPT (pick-wt=10): 88 [] A!=empty_set|B=set_meet(A)|B!=empty_set.
% 4.38/4.52 ** KEPT (pick-wt=10): 89 [] A!=singleton(B)| -in(C,A)|C=B.
% 4.38/4.52 ** KEPT (pick-wt=10): 90 [] A!=singleton(B)|in(C,A)|C!=B.
% 4.38/4.52 ** KEPT (pick-wt=14): 91 [] A=singleton(B)| -in($f25(B,A),A)|$f25(B,A)!=B.
% 4.38/4.52 ** KEPT (pick-wt=13): 92 [] -relation(A)|B!=fiber(A,C)| -in(D,B)|D!=C.
% 4.38/4.52 ** KEPT (pick-wt=15): 93 [] -relation(A)|B!=fiber(A,C)| -in(D,B)|in(ordered_pair(D,C),A).
% 4.38/4.52 ** KEPT (pick-wt=18): 94 [] -relation(A)|B!=fiber(A,C)|in(D,B)|D=C| -in(ordered_pair(D,C),A).
% 4.38/4.52 ** KEPT (pick-wt=19): 95 [] -relation(A)|B=fiber(A,C)|in($f26(A,C,B),B)|$f26(A,C,B)!=C.
% 4.38/4.52 ** KEPT (pick-wt=21): 96 [] -relation(A)|B=fiber(A,C)|in($f26(A,C,B),B)|in(ordered_pair($f26(A,C,B),C),A).
% 4.38/4.52 ** KEPT (pick-wt=27): 97 [] -relation(A)|B=fiber(A,C)| -in($f26(A,C,B),B)|$f26(A,C,B)=C| -in(ordered_pair($f26(A,C,B),C),A).
% 4.38/4.52 ** KEPT (pick-wt=6): 98 [] A!=empty_set| -in(B,A).
% 4.38/4.52 ** KEPT (pick-wt=10): 99 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 4.38/4.52 ** KEPT (pick-wt=10): 100 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 4.38/4.52 ** KEPT (pick-wt=14): 101 [] A=powerset(B)| -in($f28(B,A),A)| -subset($f28(B,A),B).
% 4.38/4.52 ** KEPT (pick-wt=8): 102 [] -epsilon_transitive(A)| -in(B,A)|subset(B,A).
% 4.38/4.52 ** KEPT (pick-wt=6): 103 [] epsilon_transitive(A)| -subset($f29(A),A).
% 4.38/4.53 ** KEPT (pick-wt=17): 104 [] -relation(A)| -relation(B)|A!=B| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 4.38/4.53 ** KEPT (pick-wt=17): 105 [] -relation(A)| -relation(B)|A!=B|in(ordered_pair(C,D),A)| -in(ordered_pair(C,D),B).
% 4.38/4.53 ** KEPT (pick-wt=25): 106 [] -relation(A)| -relation(B)|A=B|in(ordered_pair($f31(A,B),$f30(A,B)),A)|in(ordered_pair($f31(A,B),$f30(A,B)),B).
% 4.38/4.53 ** KEPT (pick-wt=25): 107 [] -relation(A)| -relation(B)|A=B| -in(ordered_pair($f31(A,B),$f30(A,B)),A)| -in(ordered_pair($f31(A,B),$f30(A,B)),B).
% 4.38/4.53 ** KEPT (pick-wt=8): 108 [] empty(A)| -element(B,A)|in(B,A).
% 4.38/4.53 ** KEPT (pick-wt=8): 109 [] empty(A)|element(B,A)| -in(B,A).
% 4.38/4.53 ** KEPT (pick-wt=7): 110 [] -empty(A)| -element(B,A)|empty(B).
% 4.38/4.53 ** KEPT (pick-wt=7): 111 [] -empty(A)|element(B,A)| -empty(B).
% 4.38/4.53 ** KEPT (pick-wt=14): 112 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 4.38/4.53 ** KEPT (pick-wt=11): 113 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 4.38/4.53 ** KEPT (pick-wt=11): 114 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 4.38/4.53 ** KEPT (pick-wt=17): 115 [] A=unordered_pair(B,C)| -in($f32(B,C,A),A)|$f32(B,C,A)!=B.
% 4.38/4.53 ** KEPT (pick-wt=17): 116 [] A=unordered_pair(B,C)| -in($f32(B,C,A),A)|$f32(B,C,A)!=C.
% 4.38/4.53 ** KEPT (pick-wt=16): 117 [] -relation(A)| -well_founded_relation(A)| -subset(B,relation_field(A))|B=empty_set|in($f33(A,B),B).
% 4.38/4.53 ** KEPT (pick-wt=18): 118 [] -relation(A)| -well_founded_relation(A)| -subset(B,relation_field(A))|B=empty_set|disjoint(fiber(A,$f33(A,B)),B).
% 4.38/4.53 ** KEPT (pick-wt=9): 119 [] -relation(A)|well_founded_relation(A)|subset($f34(A),relation_field(A)).
% 4.38/4.53 ** KEPT (pick-wt=8): 120 [] -relation(A)|well_founded_relation(A)|$f34(A)!=empty_set.
% 4.38/4.53 ** KEPT (pick-wt=14): 121 [] -relation(A)|well_founded_relation(A)| -in(B,$f34(A))| -disjoint(fiber(A,B),$f34(A)).
% 4.38/4.53 ** KEPT (pick-wt=14): 122 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 4.38/4.53 ** KEPT (pick-wt=11): 123 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 4.38/4.53 ** KEPT (pick-wt=11): 124 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 4.38/4.53 ** KEPT (pick-wt=17): 125 [] A=set_union2(B,C)| -in($f35(B,C,A),A)| -in($f35(B,C,A),B).
% 4.38/4.53 ** KEPT (pick-wt=17): 126 [] A=set_union2(B,C)| -in($f35(B,C,A),A)| -in($f35(B,C,A),C).
% 4.38/4.53 ** KEPT (pick-wt=15): 127 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f37(B,C,A,D),B).
% 4.38/4.53 ** KEPT (pick-wt=15): 128 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f36(B,C,A,D),C).
% 4.38/4.53 ** KEPT (pick-wt=21): 130 [copy,129,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f37(B,C,A,D),$f36(B,C,A,D))=D.
% 4.38/4.53 ** KEPT (pick-wt=19): 131 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 4.38/4.53 ** KEPT (pick-wt=25): 132 [] A=cartesian_product2(B,C)| -in($f40(B,C,A),A)| -in(D,B)| -in(E,C)|$f40(B,C,A)!=ordered_pair(D,E).
% 4.38/4.53 ** KEPT (pick-wt=17): 133 [] -epsilon_connected(A)| -in(B,A)| -in(C,A)|in(B,C)|B=C|in(C,B).
% 4.38/4.53 ** KEPT (pick-wt=7): 134 [] epsilon_connected(A)| -in($f42(A),$f41(A)).
% 4.38/4.53 ** KEPT (pick-wt=7): 135 [] epsilon_connected(A)|$f42(A)!=$f41(A).
% 4.38/4.53 ** KEPT (pick-wt=7): 136 [] epsilon_connected(A)| -in($f41(A),$f42(A)).
% 4.38/4.53 ** KEPT (pick-wt=17): 137 [] -relation(A)| -relation(B)| -subset(A,B)| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 4.38/4.53 ** KEPT (pick-wt=16): 138 [] -relation(A)| -relation(B)|subset(A,B)|in(ordered_pair($f44(A,B),$f43(A,B)),A).
% 4.38/4.53 ** KEPT (pick-wt=16): 139 [] -relation(A)| -relation(B)|subset(A,B)| -in(ordered_pair($f44(A,B),$f43(A,B)),B).
% 4.38/4.53 ** KEPT (pick-wt=9): 140 [] -subset(A,B)| -in(C,A)|in(C,B).
% 4.38/4.53 ** KEPT (pick-wt=8): 141 [] subset(A,B)| -in($f45(A,B),B).
% 4.38/4.53 ** KEPT (pick-wt=17): 142 [] -relation(A)| -is_well_founded_in(A,B)| -subset(C,B)|C=empty_set|in($f46(A,B,C),C).
% 4.38/4.53 ** KEPT (pick-wt=19): 143 [] -relation(A)| -is_well_founded_in(A,B)| -subset(C,B)|C=empty_set|disjoint(fiber(A,$f46(A,B,C)),C).
% 4.38/4.53 ** KEPT (pick-wt=10): 144 [] -relation(A)|is_well_founded_in(A,B)|subset($f47(A,B),B).
% 4.38/4.53 ** KEPT (pick-wt=10): 145 [] -relation(A)|is_well_founded_in(A,B)|$f47(A,B)!=empty_set.
% 4.38/4.53 ** KEPT (pick-wt=17): 146 [] -relation(A)|is_well_founded_in(A,B)| -in(C,$f47(A,B))| -disjoint(fiber(A,C),$f47(A,B)).
% 4.38/4.53 ** KEPT (pick-wt=11): 147 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 4.38/4.53 ** KEPT (pick-wt=11): 148 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 4.38/4.53 ** KEPT (pick-wt=14): 149 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 4.38/4.53 ** KEPT (pick-wt=23): 150 [] A=set_intersection2(B,C)| -in($f48(B,C,A),A)| -in($f48(B,C,A),B)| -in($f48(B,C,A),C).
% 4.38/4.53 ** KEPT (pick-wt=18): 151 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C!=apply(A,B)|in(ordered_pair(B,C),A).
% 4.38/4.53 ** KEPT (pick-wt=18): 152 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C=apply(A,B)| -in(ordered_pair(B,C),A).
% 4.38/4.53 ** KEPT (pick-wt=16): 153 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C!=apply(A,B)|C=empty_set.
% 4.38/4.53 ** KEPT (pick-wt=16): 154 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C=apply(A,B)|C!=empty_set.
% 4.38/4.53 Following clause subsumed by 4 during input processing: 0 [] -ordinal(A)|epsilon_transitive(A).
% 4.38/4.53 Following clause subsumed by 5 during input processing: 0 [] -ordinal(A)|epsilon_connected(A).
% 4.38/4.53 Following clause subsumed by 8 during input processing: 0 [] ordinal(A)| -epsilon_transitive(A)| -epsilon_connected(A).
% 4.38/4.53 ** KEPT (pick-wt=17): 155 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f49(A,B,C)),A).
% 4.38/4.53 ** KEPT (pick-wt=14): 156 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 4.38/4.53 ** KEPT (pick-wt=20): 157 [] -relation(A)|B=relation_dom(A)|in($f51(A,B),B)|in(ordered_pair($f51(A,B),$f50(A,B)),A).
% 4.38/4.53 ** KEPT (pick-wt=18): 158 [] -relation(A)|B=relation_dom(A)| -in($f51(A,B),B)| -in(ordered_pair($f51(A,B),C),A).
% 4.38/4.53 ** KEPT (pick-wt=24): 159 [] -relation(A)| -is_antisymmetric_in(A,B)| -in(C,B)| -in(D,B)| -in(ordered_pair(C,D),A)| -in(ordered_pair(D,C),A)|C=D.
% 4.38/4.53 ** KEPT (pick-wt=10): 160 [] -relation(A)|is_antisymmetric_in(A,B)|in($f53(A,B),B).
% 4.38/4.53 ** KEPT (pick-wt=10): 161 [] -relation(A)|is_antisymmetric_in(A,B)|in($f52(A,B),B).
% 4.38/4.53 ** KEPT (pick-wt=14): 162 [] -relation(A)|is_antisymmetric_in(A,B)|in(ordered_pair($f53(A,B),$f52(A,B)),A).
% 4.38/4.53 ** KEPT (pick-wt=14): 163 [] -relation(A)|is_antisymmetric_in(A,B)|in(ordered_pair($f52(A,B),$f53(A,B)),A).
% 4.38/4.53 ** KEPT (pick-wt=12): 164 [] -relation(A)|is_antisymmetric_in(A,B)|$f53(A,B)!=$f52(A,B).
% 4.38/4.53 ** KEPT (pick-wt=13): 165 [] A!=union(B)| -in(C,A)|in(C,$f54(B,A,C)).
% 4.38/4.53 ** KEPT (pick-wt=13): 166 [] A!=union(B)| -in(C,A)|in($f54(B,A,C),B).
% 4.38/4.53 ** KEPT (pick-wt=13): 167 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 4.38/4.53 ** KEPT (pick-wt=17): 168 [] A=union(B)| -in($f56(B,A),A)| -in($f56(B,A),C)| -in(C,B).
% 4.38/4.53 ** KEPT (pick-wt=6): 169 [] -relation(A)| -well_ordering(A)|reflexive(A).
% 4.38/4.53 ** KEPT (pick-wt=6): 170 [] -relation(A)| -well_ordering(A)|transitive(A).
% 4.38/4.53 ** KEPT (pick-wt=6): 171 [] -relation(A)| -well_ordering(A)|antisymmetric(A).
% 4.38/4.53 ** KEPT (pick-wt=6): 172 [] -relation(A)| -well_ordering(A)|connected(A).
% 4.38/4.53 ** KEPT (pick-wt=6): 173 [] -relation(A)| -well_ordering(A)|well_founded_relation(A).
% 4.38/4.53 ** KEPT (pick-wt=14): 174 [] -relation(A)|well_ordering(A)| -reflexive(A)| -transitive(A)| -antisymmetric(A)| -connected(A)| -well_founded_relation(A).
% 4.38/4.53 ** KEPT (pick-wt=11): 175 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 4.38/4.53 ** KEPT (pick-wt=11): 176 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 4.38/4.53 ** KEPT (pick-wt=14): 177 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 4.38/4.53 ** KEPT (pick-wt=17): 178 [] A=set_difference(B,C)|in($f57(B,C,A),A)| -in($f57(B,C,A),C).
% 4.38/4.53 ** KEPT (pick-wt=23): 179 [] A=set_difference(B,C)| -in($f57(B,C,A),A)| -in($f57(B,C,A),B)|in($f57(B,C,A),C).
% 4.38/4.53 ** KEPT (pick-wt=18): 180 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|in($f58(A,B,C),relation_dom(A)).
% 4.38/4.53 ** KEPT (pick-wt=19): 182 [copy,181,flip.5] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|apply(A,$f58(A,B,C))=C.
% 4.38/4.53 ** KEPT (pick-wt=20): 183 [] -relation(A)| -function(A)|B!=relation_rng(A)|in(C,B)| -in(D,relation_dom(A))|C!=apply(A,D).
% 4.38/4.53 ** KEPT (pick-wt=19): 184 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f60(A,B),B)|in($f59(A,B),relation_dom(A)).
% 4.38/4.53 ** KEPT (pick-wt=22): 186 [copy,185,flip.5] -relation(A)| -function(A)|B=relation_rng(A)|in($f60(A,B),B)|apply(A,$f59(A,B))=$f60(A,B).
% 4.38/4.53 ** KEPT (pick-wt=24): 187 [] -relation(A)| -function(A)|B=relation_rng(A)| -in($f60(A,B),B)| -in(C,relation_dom(A))|$f60(A,B)!=apply(A,C).
% 4.38/4.53 ** KEPT (pick-wt=17): 188 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f61(A,B,C),C),A).
% 4.38/4.54 ** KEPT (pick-wt=14): 189 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 4.38/4.54 ** KEPT (pick-wt=20): 190 [] -relation(A)|B=relation_rng(A)|in($f63(A,B),B)|in(ordered_pair($f62(A,B),$f63(A,B)),A).
% 4.38/4.54 ** KEPT (pick-wt=18): 191 [] -relation(A)|B=relation_rng(A)| -in($f63(A,B),B)| -in(ordered_pair(C,$f63(A,B)),A).
% 4.38/4.54 ** KEPT (pick-wt=11): 192 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 4.38/4.54 ** KEPT (pick-wt=8): 193 [] -relation(A)| -well_orders(A,B)|is_reflexive_in(A,B).
% 4.38/4.54 ** KEPT (pick-wt=8): 194 [] -relation(A)| -well_orders(A,B)|is_transitive_in(A,B).
% 4.38/4.54 ** KEPT (pick-wt=8): 195 [] -relation(A)| -well_orders(A,B)|is_antisymmetric_in(A,B).
% 4.38/4.54 ** KEPT (pick-wt=8): 196 [] -relation(A)| -well_orders(A,B)|is_connected_in(A,B).
% 4.38/4.54 ** KEPT (pick-wt=8): 197 [] -relation(A)| -well_orders(A,B)|is_well_founded_in(A,B).
% 4.38/4.54 ** KEPT (pick-wt=20): 198 [] -relation(A)|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).
% 4.38/4.54 ** KEPT (pick-wt=6): 200 [copy,199,flip.2] -being_limit_ordinal(A)|union(A)=A.
% 4.38/4.54 ** KEPT (pick-wt=6): 202 [copy,201,flip.2] being_limit_ordinal(A)|union(A)!=A.
% 4.38/4.54 ** KEPT (pick-wt=10): 204 [copy,203,flip.2] -relation(A)|set_union2(relation_dom(A),relation_rng(A))=relation_field(A).
% 4.38/4.54 ** KEPT (pick-wt=24): 205 [] -relation(A)| -is_connected_in(A,B)| -in(C,B)| -in(D,B)|C=D|in(ordered_pair(C,D),A)|in(ordered_pair(D,C),A).
% 4.38/4.54 ** KEPT (pick-wt=10): 206 [] -relation(A)|is_connected_in(A,B)|in($f65(A,B),B).
% 4.38/4.54 ** KEPT (pick-wt=10): 207 [] -relation(A)|is_connected_in(A,B)|in($f64(A,B),B).
% 4.38/4.54 ** KEPT (pick-wt=12): 208 [] -relation(A)|is_connected_in(A,B)|$f65(A,B)!=$f64(A,B).
% 4.38/4.54 ** KEPT (pick-wt=14): 209 [] -relation(A)|is_connected_in(A,B)| -in(ordered_pair($f65(A,B),$f64(A,B)),A).
% 4.38/4.54 ** KEPT (pick-wt=14): 210 [] -relation(A)|is_connected_in(A,B)| -in(ordered_pair($f64(A,B),$f65(A,B)),A).
% 4.38/4.54 ** KEPT (pick-wt=11): 212 [copy,211,flip.2] -relation(A)|set_intersection2(A,cartesian_product2(B,B))=relation_restriction(A,B).
% 4.38/4.54 ** KEPT (pick-wt=18): 213 [] -relation(A)| -relation(B)|B!=relation_inverse(A)| -in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A).
% 4.38/4.54 ** KEPT (pick-wt=18): 214 [] -relation(A)| -relation(B)|B!=relation_inverse(A)|in(ordered_pair(C,D),B)| -in(ordered_pair(D,C),A).
% 4.38/4.54 ** KEPT (pick-wt=26): 215 [] -relation(A)| -relation(B)|B=relation_inverse(A)|in(ordered_pair($f67(A,B),$f66(A,B)),B)|in(ordered_pair($f66(A,B),$f67(A,B)),A).
% 4.38/4.54 ** KEPT (pick-wt=26): 216 [] -relation(A)| -relation(B)|B=relation_inverse(A)| -in(ordered_pair($f67(A,B),$f66(A,B)),B)| -in(ordered_pair($f66(A,B),$f67(A,B)),A).
% 4.38/4.54 ** KEPT (pick-wt=17): 217 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|relation_dom(C)=relation_field(A).
% 4.38/4.54 ** KEPT (pick-wt=17): 218 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|relation_rng(C)=relation_field(B).
% 4.38/4.54 ** KEPT (pick-wt=14): 219 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|one_to_one(C).
% 4.38/4.54 ** KEPT (pick-wt=21): 220 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -in(ordered_pair(D,E),A)|in(D,relation_field(A)).
% 4.38/4.54 ** KEPT (pick-wt=21): 221 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -in(ordered_pair(D,E),A)|in(E,relation_field(A)).
% 4.38/4.54 ** KEPT (pick-wt=26): 222 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -in(ordered_pair(D,E),A)|in(ordered_pair(apply(C,D),apply(C,E)),B).
% 4.38/4.54 ** KEPT (pick-wt=34): 223 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|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).
% 4.38/4.54 ** KEPT (pick-wt=42): 224 [] -relation(A)| -relation(B)| -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)|in(ordered_pair($f69(A,B,C),$f68(A,B,C)),A)|in($f69(A,B,C),relation_field(A)).
% 4.44/4.54 ** KEPT (pick-wt=42): 225 [] -relation(A)| -relation(B)| -relation(C)| -function(C)|relation_isomorphism(A,B,C)|relation_dom(C)!=relation_field(A)|relation_rng(C)!=relation_field(B)| -one_to_one(C)|in(ordered_pair($f69(A,B,C),$f68(A,B,C)),A)|in($f68(A,B,C),relation_field(A)).
% 4.44/4.54 ** KEPT (pick-wt=50): 226 [] -relation(A)| -relation(B)| -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)|in(ordered_pair($f69(A,B,C),$f68(A,B,C)),A)|in(ordered_pair(apply(C,$f69(A,B,C)),apply(C,$f68(A,B,C))),B).
% 4.44/4.54 ** KEPT (pick-wt=64): 227 [] -relation(A)| -relation(B)| -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)| -in(ordered_pair($f69(A,B,C),$f68(A,B,C)),A)| -in($f69(A,B,C),relation_field(A))| -in($f68(A,B,C),relation_field(A))| -in(ordered_pair(apply(C,$f69(A,B,C)),apply(C,$f68(A,B,C))),B).
% 4.44/4.54 ** KEPT (pick-wt=8): 228 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 4.44/4.54 ** KEPT (pick-wt=8): 229 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 4.44/4.54 ** KEPT (pick-wt=24): 230 [] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_dom(A))| -in(C,relation_dom(A))|apply(A,B)!=apply(A,C)|B=C.
% 4.44/4.54 ** KEPT (pick-wt=11): 231 [] -relation(A)| -function(A)|one_to_one(A)|in($f71(A),relation_dom(A)).
% 4.44/4.54 ** KEPT (pick-wt=11): 232 [] -relation(A)| -function(A)|one_to_one(A)|in($f70(A),relation_dom(A)).
% 4.44/4.54 ** KEPT (pick-wt=15): 233 [] -relation(A)| -function(A)|one_to_one(A)|apply(A,$f71(A))=apply(A,$f70(A)).
% 4.44/4.54 ** KEPT (pick-wt=11): 234 [] -relation(A)| -function(A)|one_to_one(A)|$f71(A)!=$f70(A).
% 4.44/4.54 ** KEPT (pick-wt=26): 235 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,$f72(A,B,C,D,E)),A).
% 4.44/4.54 ** KEPT (pick-wt=26): 236 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair($f72(A,B,C,D,E),E),B).
% 4.44/4.54 ** KEPT (pick-wt=26): 237 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)|in(ordered_pair(D,E),C)| -in(ordered_pair(D,F),A)| -in(ordered_pair(F,E),B).
% 4.44/4.54 ** KEPT (pick-wt=33): 238 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f75(A,B,C),$f74(A,B,C)),C)|in(ordered_pair($f75(A,B,C),$f73(A,B,C)),A).
% 4.44/4.54 ** KEPT (pick-wt=33): 239 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f75(A,B,C),$f74(A,B,C)),C)|in(ordered_pair($f73(A,B,C),$f74(A,B,C)),B).
% 4.44/4.54 ** KEPT (pick-wt=38): 240 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)| -in(ordered_pair($f75(A,B,C),$f74(A,B,C)),C)| -in(ordered_pair($f75(A,B,C),D),A)| -in(ordered_pair(D,$f74(A,B,C)),B).
% 4.44/4.54 ** KEPT (pick-wt=29): 241 [] -relation(A)| -is_transitive_in(A,B)| -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).
% 4.44/4.54 ** KEPT (pick-wt=10): 242 [] -relation(A)|is_transitive_in(A,B)|in($f78(A,B),B).
% 4.44/4.54 ** KEPT (pick-wt=10): 243 [] -relation(A)|is_transitive_in(A,B)|in($f77(A,B),B).
% 4.44/4.54 ** KEPT (pick-wt=10): 244 [] -relation(A)|is_transitive_in(A,B)|in($f76(A,B),B).
% 4.44/4.54 ** KEPT (pick-wt=14): 245 [] -relation(A)|is_transitive_in(A,B)|in(ordered_pair($f78(A,B),$f77(A,B)),A).
% 4.44/4.54 ** KEPT (pick-wt=14): 246 [] -relation(A)|is_transitive_in(A,B)|in(ordered_pair($f77(A,B),$f76(A,B)),A).
% 4.44/4.54 ** KEPT (pick-wt=14): 247 [] -relation(A)|is_transitive_in(A,B)| -in(ordered_pair($f78(A,B),$f76(A,B)),A).
% 4.44/4.54 ** KEPT (pick-wt=27): 248 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C!=complements_of_subsets(B,A)| -element(D,powerset(B))| -in(D,C)|in(subset_complement(B,D),A).
% 4.44/4.54 ** KEPT (pick-wt=27): 249 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C!=complements_of_subsets(B,A)| -element(D,powerset(B))|in(D,C)| -in(subset_complement(B,D),A).
% 4.44/4.54 ** KEPT (pick-wt=22): 250 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|element($f79(B,A,C),powerset(B)).
% 4.44/4.54 ** KEPT (pick-wt=29): 251 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|in($f79(B,A,C),C)|in(subset_complement(B,$f79(B,A,C)),A).
% 4.44/4.54 ** KEPT (pick-wt=29): 252 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)| -in($f79(B,A,C),C)| -in(subset_complement(B,$f79(B,A,C)),A).
% 4.44/4.54 ** KEPT (pick-wt=6): 253 [] -proper_subset(A,B)|subset(A,B).
% 4.44/4.54 ** KEPT (pick-wt=6): 254 [] -proper_subset(A,B)|A!=B.
% 4.44/4.54 ** KEPT (pick-wt=9): 255 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 4.44/4.54 ** KEPT (pick-wt=11): 257 [copy,256,flip.4] -relation(A)| -function(A)| -one_to_one(A)|relation_inverse(A)=function_inverse(A).
% 4.44/4.54 ** KEPT (pick-wt=8): 258 [] -relation(A)| -reflexive(A)|is_reflexive_in(A,relation_field(A)).
% 4.44/4.54 ** KEPT (pick-wt=8): 259 [] -relation(A)|reflexive(A)| -is_reflexive_in(A,relation_field(A)).
% 4.44/4.54 ** KEPT (pick-wt=7): 260 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 4.44/4.54 ** KEPT (pick-wt=7): 261 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 4.44/4.54 ** KEPT (pick-wt=6): 262 [] -relation(A)|relation(relation_restriction(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=10): 263 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 4.44/4.54 ** KEPT (pick-wt=5): 264 [] -relation(A)|relation(relation_inverse(A)).
% 4.44/4.54 ** KEPT (pick-wt=8): 265 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=11): 266 [] -element(A,powerset(powerset(B)))|element(union_of_subsets(B,A),powerset(B)).
% 4.44/4.54 ** KEPT (pick-wt=11): 267 [] -element(A,powerset(powerset(B)))|element(meet_of_subsets(B,A),powerset(B)).
% 4.44/4.54 ** KEPT (pick-wt=15): 268 [] -element(A,powerset(B))| -element(C,powerset(B))|element(subset_difference(B,A,C),powerset(B)).
% 4.44/4.54 ** KEPT (pick-wt=6): 269 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=12): 270 [] -element(A,powerset(powerset(B)))|element(complements_of_subsets(B,A),powerset(powerset(B))).
% 4.44/4.54 ** KEPT (pick-wt=6): 271 [] -relation(A)|relation(relation_rng_restriction(B,A)).
% 4.44/4.54 ** KEPT (pick-wt=8): 272 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 4.44/4.54 ** KEPT (pick-wt=8): 273 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 4.44/4.54 ** KEPT (pick-wt=5): 274 [] -empty(A)|empty(relation_inverse(A)).
% 4.44/4.54 ** KEPT (pick-wt=5): 275 [] -empty(A)|relation(relation_inverse(A)).
% 4.44/4.54 Following clause subsumed by 269 during input processing: 0 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=8): 276 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 4.44/4.54 Following clause subsumed by 265 during input processing: 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=12): 277 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=3): 278 [] -empty(succ(A)).
% 4.44/4.54 ** KEPT (pick-wt=8): 279 [] -relation(A)| -relation(B)|relation(set_intersection2(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=3): 280 [] -empty(powerset(A)).
% 4.44/4.54 ** KEPT (pick-wt=4): 281 [] -empty(ordered_pair(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=8): 282 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=3): 283 [] -empty(singleton(A)).
% 4.44/4.54 ** KEPT (pick-wt=6): 284 [] empty(A)| -empty(set_union2(A,B)).
% 4.44/4.54 Following clause subsumed by 264 during input processing: 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation(relation_inverse(A)).
% 4.44/4.54 ** KEPT (pick-wt=9): 285 [] -relation(A)| -function(A)| -one_to_one(A)|function(relation_inverse(A)).
% 4.44/4.54 Following clause subsumed by 278 during input processing: 0 [] -ordinal(A)| -empty(succ(A)).
% 4.44/4.54 ** KEPT (pick-wt=5): 286 [] -ordinal(A)|epsilon_transitive(succ(A)).
% 4.44/4.54 ** KEPT (pick-wt=5): 287 [] -ordinal(A)|epsilon_connected(succ(A)).
% 4.44/4.54 ** KEPT (pick-wt=5): 288 [] -ordinal(A)|ordinal(succ(A)).
% 4.44/4.54 ** KEPT (pick-wt=8): 289 [] -relation(A)| -relation(B)|relation(set_difference(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=4): 290 [] -empty(unordered_pair(A,B)).
% 4.44/4.54 ** KEPT (pick-wt=6): 291 [] empty(A)| -empty(set_union2(B,A)).
% 4.44/4.54 Following clause subsumed by 269 during input processing: 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 4.44/4.55 ** KEPT (pick-wt=8): 292 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 4.44/4.55 ** KEPT (pick-wt=5): 293 [] -ordinal(A)|epsilon_transitive(union(A)).
% 4.44/4.55 ** KEPT (pick-wt=5): 294 [] -ordinal(A)|epsilon_connected(union(A)).
% 4.44/4.55 ** KEPT (pick-wt=5): 295 [] -ordinal(A)|ordinal(union(A)).
% 4.44/4.55 ** KEPT (pick-wt=8): 296 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 4.44/4.55 Following clause subsumed by 271 during input processing: 0 [] -relation(A)| -function(A)|relation(relation_rng_restriction(B,A)).
% 4.44/4.55 ** KEPT (pick-wt=8): 297 [] -relation(A)| -function(A)|function(relation_rng_restriction(B,A)).
% 4.44/4.55 ** KEPT (pick-wt=7): 298 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=7): 299 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=5): 300 [] -empty(A)|empty(relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=5): 301 [] -empty(A)|relation(relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=5): 302 [] -empty(A)|empty(relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=5): 303 [] -empty(A)|relation(relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=8): 304 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 4.44/4.55 ** KEPT (pick-wt=8): 305 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 4.44/4.55 ** KEPT (pick-wt=11): 306 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 4.44/4.55 ** KEPT (pick-wt=7): 307 [] -relation(A)|relation_inverse(relation_inverse(A))=A.
% 4.44/4.55 ** KEPT (pick-wt=12): 308 [] -element(A,powerset(powerset(B)))|complements_of_subsets(B,complements_of_subsets(B,A))=A.
% 4.44/4.55 ** KEPT (pick-wt=3): 309 [] -proper_subset(A,A).
% 4.44/4.55 ** KEPT (pick-wt=13): 310 [] -relation(A)| -reflexive(A)| -in(B,relation_field(A))|in(ordered_pair(B,B),A).
% 4.44/4.55 ** KEPT (pick-wt=9): 311 [] -relation(A)|reflexive(A)|in($f81(A),relation_field(A)).
% 4.44/4.55 ** KEPT (pick-wt=11): 312 [] -relation(A)|reflexive(A)| -in(ordered_pair($f81(A),$f81(A)),A).
% 4.44/4.55 ** KEPT (pick-wt=4): 313 [] singleton(A)!=empty_set.
% 4.44/4.55 ** KEPT (pick-wt=9): 314 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 4.44/4.55 ** KEPT (pick-wt=7): 315 [] -disjoint(singleton(A),B)| -in(A,B).
% 4.44/4.55 ** KEPT (pick-wt=9): 316 [] -relation(A)|subset(relation_dom(relation_rng_restriction(B,A)),relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=19): 317 [] -relation(A)| -transitive(A)| -in(ordered_pair(B,C),A)| -in(ordered_pair(C,D),A)|in(ordered_pair(B,D),A).
% 4.44/4.55 ** KEPT (pick-wt=11): 318 [] -relation(A)|transitive(A)|in(ordered_pair($f84(A),$f83(A)),A).
% 4.44/4.55 ** KEPT (pick-wt=11): 319 [] -relation(A)|transitive(A)|in(ordered_pair($f83(A),$f82(A)),A).
% 4.44/4.55 ** KEPT (pick-wt=11): 320 [] -relation(A)|transitive(A)| -in(ordered_pair($f84(A),$f82(A)),A).
% 4.44/4.55 ** KEPT (pick-wt=7): 321 [] -subset(singleton(A),B)|in(A,B).
% 4.44/4.55 ** KEPT (pick-wt=7): 322 [] subset(singleton(A),B)| -in(A,B).
% 4.44/4.55 ** KEPT (pick-wt=8): 323 [] set_difference(A,B)!=empty_set|subset(A,B).
% 4.44/4.55 ** KEPT (pick-wt=8): 324 [] set_difference(A,B)=empty_set| -subset(A,B).
% 4.44/4.55 ** KEPT (pick-wt=10): 325 [] -element(A,powerset(B))| -in(C,A)|in(C,B).
% 4.44/4.55 ** KEPT (pick-wt=17): 326 [] -relation(A)| -antisymmetric(A)| -in(ordered_pair(B,C),A)| -in(ordered_pair(C,B),A)|B=C.
% 4.44/4.55 ** KEPT (pick-wt=11): 327 [] -relation(A)|antisymmetric(A)|in(ordered_pair($f86(A),$f85(A)),A).
% 4.44/4.55 ** KEPT (pick-wt=11): 328 [] -relation(A)|antisymmetric(A)|in(ordered_pair($f85(A),$f86(A)),A).
% 4.44/4.55 ** KEPT (pick-wt=9): 329 [] -relation(A)|antisymmetric(A)|$f86(A)!=$f85(A).
% 4.44/4.55 ** KEPT (pick-wt=12): 330 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 4.44/4.55 ** KEPT (pick-wt=25): 331 [] -relation(A)| -connected(A)| -in(B,relation_field(A))| -in(C,relation_field(A))|B=C|in(ordered_pair(B,C),A)|in(ordered_pair(C,B),A).
% 4.44/4.55 ** KEPT (pick-wt=9): 332 [] -relation(A)|connected(A)|in($f88(A),relation_field(A)).
% 4.44/4.55 ** KEPT (pick-wt=9): 333 [] -relation(A)|connected(A)|in($f87(A),relation_field(A)).
% 4.44/4.55 ** KEPT (pick-wt=9): 334 [] -relation(A)|connected(A)|$f88(A)!=$f87(A).
% 4.44/4.55 ** KEPT (pick-wt=11): 335 [] -relation(A)|connected(A)| -in(ordered_pair($f88(A),$f87(A)),A).
% 4.44/4.55 ** KEPT (pick-wt=11): 336 [] -relation(A)|connected(A)| -in(ordered_pair($f87(A),$f88(A)),A).
% 4.44/4.55 ** KEPT (pick-wt=11): 337 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 4.44/4.55 ** KEPT (pick-wt=7): 338 [] subset(A,singleton(B))|A!=empty_set.
% 4.44/4.55 Following clause subsumed by 19 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 4.44/4.55 ** KEPT (pick-wt=7): 339 [] -in(A,B)|subset(A,union(B)).
% 4.44/4.55 ** KEPT (pick-wt=10): 340 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 4.44/4.55 ** KEPT (pick-wt=10): 341 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 4.44/4.55 ** KEPT (pick-wt=13): 342 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 4.44/4.55 ** KEPT (pick-wt=9): 343 [] -in($f89(A,B),B)|element(A,powerset(B)).
% 4.44/4.55 ** KEPT (pick-wt=14): 344 [] -relation(A)| -function(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|in(B,relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=13): 345 [] -relation(A)| -function(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|in(B,C).
% 4.44/4.55 ** KEPT (pick-wt=17): 346 [] -relation(A)| -function(A)|in(B,relation_dom(relation_dom_restriction(A,C)))| -in(B,relation_dom(A))| -in(B,C).
% 4.44/4.55 ** KEPT (pick-wt=5): 347 [] empty(A)| -empty($f90(A)).
% 4.44/4.55 ** KEPT (pick-wt=2): 348 [] -empty($c7).
% 4.44/4.55 ** KEPT (pick-wt=2): 349 [] -empty($c8).
% 4.44/4.55 ** KEPT (pick-wt=2): 350 [] -empty($c10).
% 4.44/4.55 ** KEPT (pick-wt=11): 351 [] -element(A,powerset(powerset(B)))|union_of_subsets(B,A)=union(A).
% 4.44/4.55 ** KEPT (pick-wt=11): 352 [] -element(A,powerset(powerset(B)))|meet_of_subsets(B,A)=set_meet(A).
% 4.44/4.55 ** KEPT (pick-wt=16): 353 [] -element(A,powerset(B))| -element(C,powerset(B))|subset_difference(B,A,C)=set_difference(A,C).
% 4.44/4.55 ** KEPT (pick-wt=10): 354 [] -ordinal(A)| -ordinal(B)| -ordinal_subset(A,B)|subset(A,B).
% 4.44/4.55 ** KEPT (pick-wt=10): 355 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)| -subset(A,B).
% 4.44/4.55 ** KEPT (pick-wt=5): 357 [copy,356,factor_simp] -ordinal(A)|ordinal_subset(A,A).
% 4.44/4.55 ** KEPT (pick-wt=6): 358 [] -disjoint(A,B)|disjoint(B,A).
% 4.44/4.55 Following clause subsumed by 340 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 4.44/4.55 Following clause subsumed by 341 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 4.44/4.55 Following clause subsumed by 342 during input processing: 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 4.44/4.55 ** KEPT (pick-wt=13): 359 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 4.44/4.55 ** KEPT (pick-wt=11): 360 [] -relation(A)| -in(B,relation_rng(relation_rng_restriction(C,A)))|in(B,C).
% 4.44/4.55 ** KEPT (pick-wt=12): 361 [] -relation(A)| -in(B,relation_rng(relation_rng_restriction(C,A)))|in(B,relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=15): 362 [] -relation(A)|in(B,relation_rng(relation_rng_restriction(C,A)))| -in(B,C)| -in(B,relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=8): 363 [] -relation(A)|subset(relation_rng(relation_rng_restriction(B,A)),B).
% 4.44/4.55 ** KEPT (pick-wt=7): 364 [] -relation(A)|subset(relation_rng_restriction(B,A),A).
% 4.44/4.55 ** KEPT (pick-wt=9): 365 [] -relation(A)|subset(relation_rng(relation_rng_restriction(B,A)),relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=10): 366 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 4.44/4.55 ** KEPT (pick-wt=10): 367 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 4.44/4.55 ** KEPT (pick-wt=11): 368 [] -relation(A)|relation_rng(relation_rng_restriction(B,A))=set_intersection2(relation_rng(A),B).
% 4.44/4.55 ** KEPT (pick-wt=13): 369 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 4.44/4.55 ** KEPT (pick-wt=8): 370 [] -subset(A,B)|set_union2(A,B)=B.
% 4.44/4.55 ** KEPT (pick-wt=11): 371 [] -in(A,$f92(B))| -subset(C,A)|in(C,$f92(B)).
% 4.44/4.55 ** KEPT (pick-wt=9): 372 [] -in(A,$f92(B))|in(powerset(A),$f92(B)).
% 4.44/4.55 ** KEPT (pick-wt=12): 373 [] -subset(A,$f92(B))|are_e_quipotent(A,$f92(B))|in(A,$f92(B)).
% 4.44/4.55 ** KEPT (pick-wt=13): 375 [copy,374,flip.2] -relation(A)|relation_rng_restriction(B,relation_dom_restriction(A,C))=relation_dom_restriction(relation_rng_restriction(B,A),C).
% 4.44/4.55 ** KEPT (pick-wt=14): 376 [] -relation(A)| -in(B,relation_image(A,C))|in($f93(B,C,A),relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=15): 377 [] -relation(A)| -in(B,relation_image(A,C))|in(ordered_pair($f93(B,C,A),B),A).
% 4.44/4.55 ** KEPT (pick-wt=13): 378 [] -relation(A)| -in(B,relation_image(A,C))|in($f93(B,C,A),C).
% 4.44/4.55 ** KEPT (pick-wt=19): 379 [] -relation(A)|in(B,relation_image(A,C))| -in(D,relation_dom(A))| -in(ordered_pair(D,B),A)| -in(D,C).
% 4.44/4.55 ** KEPT (pick-wt=8): 380 [] -relation(A)|subset(relation_image(A,B),relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=11): 381 [] -relation(A)| -function(A)|subset(relation_image(A,relation_inverse_image(A,B)),B).
% 4.44/4.55 ** KEPT (pick-wt=12): 383 [copy,382,flip.2] -relation(A)|relation_image(A,set_intersection2(relation_dom(A),B))=relation_image(A,B).
% 4.44/4.55 ** KEPT (pick-wt=13): 384 [] -relation(A)| -subset(B,relation_dom(A))|subset(B,relation_inverse_image(A,relation_image(A,B))).
% 4.44/4.55 ** KEPT (pick-wt=9): 386 [copy,385,flip.2] -relation(A)|relation_rng(A)=relation_image(A,relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=15): 387 [] -relation(A)| -function(A)| -subset(B,relation_rng(A))|relation_image(A,relation_inverse_image(A,B))=B.
% 4.44/4.55 ** KEPT (pick-wt=13): 388 [] -relation(A)| -relation(B)|relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=14): 389 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in($f94(B,C,A),relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=15): 390 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in(ordered_pair(B,$f94(B,C,A)),A).
% 4.44/4.55 ** KEPT (pick-wt=13): 391 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in($f94(B,C,A),C).
% 4.44/4.55 ** KEPT (pick-wt=19): 392 [] -relation(A)|in(B,relation_inverse_image(A,C))| -in(D,relation_rng(A))| -in(ordered_pair(B,D),A)| -in(D,C).
% 4.44/4.55 ** KEPT (pick-wt=8): 393 [] -relation(A)|subset(relation_inverse_image(A,B),relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=10): 394 [] -relation(A)| -in(B,relation_restriction(A,C))|in(B,A).
% 4.44/4.55 ** KEPT (pick-wt=12): 395 [] -relation(A)| -in(B,relation_restriction(A,C))|in(B,cartesian_product2(C,C)).
% 4.44/4.55 ** KEPT (pick-wt=15): 396 [] -relation(A)|in(B,relation_restriction(A,C))| -in(B,A)| -in(B,cartesian_product2(C,C)).
% 4.44/4.55 ** KEPT (pick-wt=14): 397 [] -relation(A)|B=empty_set| -subset(B,relation_rng(A))|relation_inverse_image(A,B)!=empty_set.
% 4.44/4.55 ** KEPT (pick-wt=12): 398 [] -relation(A)| -subset(B,C)|subset(relation_inverse_image(A,B),relation_inverse_image(A,C)).
% 4.44/4.55 ** KEPT (pick-wt=11): 400 [copy,399,flip.2] -relation(A)|relation_dom_restriction(relation_rng_restriction(B,A),B)=relation_restriction(A,B).
% 4.44/4.55 ** KEPT (pick-wt=11): 402 [copy,401,flip.2] -relation(A)|relation_rng_restriction(B,relation_dom_restriction(A,B))=relation_restriction(A,B).
% 4.44/4.55 ** KEPT (pick-wt=12): 403 [] -relation(A)| -in(B,relation_field(relation_restriction(A,C)))|in(B,relation_field(A)).
% 4.44/4.55 ** KEPT (pick-wt=11): 404 [] -relation(A)| -in(B,relation_field(relation_restriction(A,C)))|in(B,C).
% 4.44/4.55 ** KEPT (pick-wt=11): 405 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 4.44/4.55 ** KEPT (pick-wt=6): 406 [] -in(A,B)|element(A,B).
% 4.44/4.55 ** KEPT (pick-wt=9): 407 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 4.44/4.55 ** KEPT (pick-wt=11): 408 [] -relation(A)| -in(ordered_pair(B,C),A)|in(B,relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=11): 409 [] -relation(A)| -in(ordered_pair(B,C),A)|in(C,relation_rng(A)).
% 4.44/4.55 ** KEPT (pick-wt=9): 410 [] -relation(A)|subset(relation_field(relation_restriction(A,B)),relation_field(A)).
% 4.44/4.55 ** KEPT (pick-wt=8): 411 [] -relation(A)|subset(relation_field(relation_restriction(A,B)),B).
% 4.44/4.55 ** KEPT (pick-wt=18): 412 [] -relation(A)| -function(A)| -relation(B)| -function(B)| -in(C,relation_dom(relation_composition(B,A)))|in(C,relation_dom(B)).
% 4.44/4.55 ** KEPT (pick-wt=20): 413 [] -relation(A)| -function(A)| -relation(B)| -function(B)| -in(C,relation_dom(relation_composition(B,A)))|in(apply(B,C),relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=24): 414 [] -relation(A)| -function(A)| -relation(B)| -function(B)|in(C,relation_dom(relation_composition(B,A)))| -in(C,relation_dom(B))| -in(apply(B,C),relation_dom(A)).
% 4.44/4.55 ** KEPT (pick-wt=10): 415 [] -epsilon_transitive(A)| -ordinal(B)| -proper_subset(A,B)|in(A,B).
% 4.44/4.55 ** KEPT (pick-wt=9): 416 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 4.44/4.55 ** KEPT (pick-wt=11): 417 [] -relation(A)|subset(fiber(relation_restriction(A,B),C),fiber(A,C)).
% 4.44/4.55 ** KEPT (pick-wt=25): 418 [] -relation(A)| -function(A)| -relation(B)| -function(B)| -in(C,relation_dom(relation_composition(B,A)))|apply(relation_composition(B,A),C)=apply(A,apply(B,C)).
% 4.44/4.55 ** KEPT (pick-wt=8): 419 [] -relation(A)| -reflexive(A)|reflexive(relation_restriction(A,B)).
% 4.46/4.56 ** KEPT (pick-wt=23): 420 [] -relation(A)| -function(A)| -relation(B)| -function(B)| -in(C,relation_dom(A))|apply(relation_composition(A,B),C)=apply(B,apply(A,C)).
% 4.46/4.56 ** KEPT (pick-wt=7): 421 [] -ordinal(A)| -in(B,A)|ordinal(B).
% 4.46/4.56 ** KEPT (pick-wt=8): 422 [] -relation(A)| -connected(A)|connected(relation_restriction(A,B)).
% 4.46/4.56 ** KEPT (pick-wt=13): 423 [] -ordinal(A)| -ordinal(B)|in(A,B)|A=B|in(B,A).
% 4.46/4.56 ** KEPT (pick-wt=8): 424 [] -relation(A)| -transitive(A)|transitive(relation_restriction(A,B)).
% 4.46/4.56 ** KEPT (pick-wt=12): 425 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_dom(A),relation_dom(B)).
% 4.46/4.56 ** KEPT (pick-wt=12): 426 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_rng(A),relation_rng(B)).
% 4.46/4.56 ** KEPT (pick-wt=8): 427 [] -relation(A)| -antisymmetric(A)|antisymmetric(relation_restriction(A,B)).
% 4.46/4.56 ** KEPT (pick-wt=10): 428 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 4.46/4.56 ** KEPT (pick-wt=8): 429 [] -subset(A,B)|set_intersection2(A,B)=A.
% 4.46/4.56 Following clause subsumed by 108 during input processing: 0 [] -element(A,B)|empty(B)|in(A,B).
% 4.46/4.56 ** KEPT (pick-wt=13): 430 [] -in($f95(A,B),A)| -in($f95(A,B),B)|A=B.
% 4.46/4.56 ** KEPT (pick-wt=11): 431 [] -relation(A)| -in(ordered_pair(B,C),A)|in(B,relation_field(A)).
% 4.46/4.56 ** KEPT (pick-wt=11): 432 [] -relation(A)| -in(ordered_pair(B,C),A)|in(C,relation_field(A)).
% 4.46/4.56 ** KEPT (pick-wt=9): 433 [] -ordinal($f96(A))| -subset($f96(A),A)|ordinal(A).
% 4.46/4.56 ** KEPT (pick-wt=8): 434 [] -relation(A)| -well_founded_relation(A)|well_founded_relation(relation_restriction(A,B)).
% 4.46/4.56 ** KEPT (pick-wt=12): 435 [] -ordinal(A)| -subset(B,A)|B=empty_set|ordinal($f97(B,A)).
% 4.46/4.56 ** KEPT (pick-wt=13): 436 [] -ordinal(A)| -subset(B,A)|B=empty_set|in($f97(B,A),B).
% 4.46/4.56 ** KEPT (pick-wt=18): 437 [] -ordinal(A)| -subset(B,A)|B=empty_set| -ordinal(C)| -in(C,B)|ordinal_subset($f97(B,A),C).
% 4.46/4.56 ** KEPT (pick-wt=8): 438 [] -relation(A)| -well_ordering(A)|well_ordering(relation_restriction(A,B)).
% 4.46/4.56 ** KEPT (pick-wt=11): 439 [] -ordinal(A)| -ordinal(B)| -in(A,B)|ordinal_subset(succ(A),B).
% 4.46/4.56 ** KEPT (pick-wt=11): 440 [] -ordinal(A)| -ordinal(B)|in(A,B)| -ordinal_subset(succ(A),B).
% 4.46/4.56 ** KEPT (pick-wt=10): 441 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 4.46/4.56 ** KEPT (pick-wt=10): 442 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 4.46/4.56 ** KEPT (pick-wt=10): 443 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 4.46/4.56 ** KEPT (pick-wt=12): 444 [] -relation(A)| -function(A)|A!=identity_relation(B)|relation_dom(A)=B.
% 4.46/4.56 ** KEPT (pick-wt=16): 445 [] -relation(A)| -function(A)|A!=identity_relation(B)| -in(C,B)|apply(A,C)=C.
% 4.46/4.56 ** KEPT (pick-wt=17): 446 [] -relation(A)| -function(A)|A=identity_relation(B)|relation_dom(A)!=B|in($f98(B,A),B).
% 4.46/4.56 ** KEPT (pick-wt=21): 447 [] -relation(A)| -function(A)|A=identity_relation(B)|relation_dom(A)!=B|apply(A,$f98(B,A))!=$f98(B,A).
% 4.46/4.56 ** KEPT (pick-wt=9): 448 [] -in(A,B)|apply(identity_relation(B),A)=A.
% 4.46/4.56 ** KEPT (pick-wt=8): 449 [] -relation(A)|relation_rng(A)=relation_dom(relation_inverse(A)).
% 4.46/4.56 ** KEPT (pick-wt=8): 451 [copy,450,flip.2] -relation(A)|relation_rng(relation_inverse(A))=relation_dom(A).
% 4.46/4.56 Following clause subsumed by 323 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 4.46/4.56 Following clause subsumed by 324 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 4.46/4.56 Following clause subsumed by 321 during input processing: 0 [] -subset(singleton(A),B)|in(A,B).
% 4.46/4.56 Following clause subsumed by 322 during input processing: 0 [] subset(singleton(A),B)| -in(A,B).
% 4.46/4.56 ** KEPT (pick-wt=8): 452 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 4.46/4.56 ** KEPT (pick-wt=8): 453 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 4.46/4.56 ** KEPT (pick-wt=11): 454 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 4.46/4.56 ** KEPT (pick-wt=14): 455 [] -relation(A)| -well_ordering(A)| -subset(B,relation_field(A))|relation_field(relation_restriction(A,B))=B.
% 4.46/4.56 Following clause subsumed by 337 during input processing: 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 4.46/4.56 Following clause subsumed by 338 during input processing: 0 [] subset(A,singleton(B))|A!=empty_set.
% 4.46/4.57 Following clause subsumed by 19 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 4.46/4.57 ** KEPT (pick-wt=9): 456 [] -in(A,B)| -in(B,C)| -in(C,A).
% 4.46/4.57 ** KEPT (pick-wt=7): 457 [] -element(A,powerset(B))|subset(A,B).
% 4.46/4.57 ** KEPT (pick-wt=7): 458 [] element(A,powerset(B))| -subset(A,B).
% 4.46/4.57 ** KEPT (pick-wt=9): 459 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 4.46/4.57 ** KEPT (pick-wt=6): 460 [] -subset(A,empty_set)|A=empty_set.
% 4.46/4.57 ** KEPT (pick-wt=13): 461 [] -ordinal(A)| -being_limit_ordinal(A)| -ordinal(B)| -in(B,A)|in(succ(B),A).
% 4.46/4.57 ** KEPT (pick-wt=7): 462 [] -ordinal(A)|being_limit_ordinal(A)|ordinal($f100(A)).
% 4.46/4.57 ** KEPT (pick-wt=8): 463 [] -ordinal(A)|being_limit_ordinal(A)|in($f100(A),A).
% 4.46/4.57 ** KEPT (pick-wt=9): 464 [] -ordinal(A)|being_limit_ordinal(A)| -in(succ($f100(A)),A).
% 4.46/4.57 ** KEPT (pick-wt=7): 465 [] -ordinal(A)|being_limit_ordinal(A)|ordinal($f101(A)).
% 4.46/4.57 ** KEPT (pick-wt=9): 467 [copy,466,flip.3] -ordinal(A)|being_limit_ordinal(A)|succ($f101(A))=A.
% 4.46/4.57 ** KEPT (pick-wt=10): 468 [] -ordinal(A)| -ordinal(B)|A!=succ(B)| -being_limit_ordinal(A).
% 4.46/4.57 ** KEPT (pick-wt=16): 469 [] -element(A,powerset(B))| -element(C,powerset(B))| -disjoint(A,C)|subset(A,subset_complement(B,C)).
% 4.46/4.57 ** KEPT (pick-wt=16): 470 [] -element(A,powerset(B))| -element(C,powerset(B))|disjoint(A,C)| -subset(A,subset_complement(B,C)).
% 4.46/4.57 ** KEPT (pick-wt=11): 471 [] -relation(A)| -relation(B)|subset(relation_dom(relation_composition(A,B)),relation_dom(A)).
% 4.46/4.57 ** KEPT (pick-wt=11): 472 [] -relation(A)| -relation(B)|subset(relation_rng(relation_composition(A,B)),relation_rng(B)).
% 4.46/4.57 ** KEPT (pick-wt=10): 474 [copy,473,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 4.46/4.57 ** KEPT (pick-wt=16): 475 [] -relation(A)| -relation(B)| -subset(relation_rng(A),relation_dom(B))|relation_dom(relation_composition(A,B))=relation_dom(A).
% 4.46/4.57 ** KEPT (pick-wt=13): 476 [] -element(A,powerset(powerset(B)))|A=empty_set|complements_of_subsets(B,A)!=empty_set.
% 4.46/4.57 Following clause subsumed by 314 during input processing: 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 4.46/4.57 ** KEPT (pick-wt=16): 477 [] -relation(A)| -relation(B)| -subset(relation_dom(A),relation_rng(B))|relation_rng(relation_composition(B,A))=relation_rng(A).
% 4.46/4.57 ** KEPT (pick-wt=21): 478 [] -element(A,powerset(powerset(B)))|A=empty_set|subset_difference(B,cast_to_subset(B),union_of_subsets(B,A))=meet_of_subsets(B,complements_of_subsets(B,A)).
% 4.46/4.57 ** KEPT (pick-wt=21): 479 [] -element(A,powerset(powerset(B)))|A=empty_set|union_of_subsets(B,complements_of_subsets(B,A))=subset_difference(B,cast_to_subset(B),meet_of_subsets(B,A)).
% 4.46/4.57 ** KEPT (pick-wt=17): 480 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)|relation_isomorphism(B,A,function_inverse(C)).
% 4.46/4.57 ** KEPT (pick-wt=10): 481 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 4.46/4.57 ** KEPT (pick-wt=8): 482 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 4.46/4.57 ** KEPT (pick-wt=18): 483 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 4.46/4.57 ** KEPT (pick-wt=16): 484 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -reflexive(A)|reflexive(B).
% 4.46/4.57 ** KEPT (pick-wt=16): 485 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -transitive(A)|transitive(B).
% 4.46/4.57 ** KEPT (pick-wt=16): 486 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -connected(A)|connected(B).
% 4.46/4.57 ** KEPT (pick-wt=16): 487 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -antisymmetric(A)|antisymmetric(B).
% 4.46/4.57 ** KEPT (pick-wt=16): 488 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -well_founded_relation(A)|well_founded_relation(B).
% 4.46/4.57 ** KEPT (pick-wt=19): 489 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)|relation_dom(B)=relation_rng(A).
% 4.46/4.57 ** KEPT (pick-wt=27): 490 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_rng(A))|D!=apply(B,C)|in(D,relation_dom(A)).
% 4.46/4.57 ** KEPT (pick-wt=28): 491 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_rng(A))|D!=apply(B,C)|C=apply(A,D).
% 4.55/4.68 ** KEPT (pick-wt=27): 492 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_dom(A))|D!=apply(A,C)|in(D,relation_rng(A)).
% 4.55/4.68 ** KEPT (pick-wt=28): 493 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_dom(A))|D!=apply(A,C)|C=apply(B,D).
% 4.55/4.68 ** KEPT (pick-wt=31): 494 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f104(A,B),relation_rng(A))|in($f103(A,B),relation_dom(A)).
% 4.55/4.68 ** KEPT (pick-wt=34): 496 [copy,495,flip.9] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f104(A,B),relation_rng(A))|apply(A,$f103(A,B))=$f104(A,B).
% 4.55/4.68 ** KEPT (pick-wt=34): 498 [copy,497,flip.8] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|apply(B,$f104(A,B))=$f103(A,B)|in($f103(A,B),relation_dom(A)).
% 4.55/4.68 ** KEPT (pick-wt=37): 500 [copy,499,flip.8,flip.9] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|apply(B,$f104(A,B))=$f103(A,B)|apply(A,$f103(A,B))=$f104(A,B).
% 4.55/4.68 ** KEPT (pick-wt=49): 502 [copy,501,flip.9,flip.11] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)| -in($f103(A,B),relation_dom(A))|apply(A,$f103(A,B))!=$f104(A,B)| -in($f104(A,B),relation_rng(A))|apply(B,$f104(A,B))!=$f103(A,B).
% 4.55/4.68 ** KEPT (pick-wt=12): 503 [] -element(A,powerset(B))| -in(C,subset_complement(B,A))| -in(C,A).
% 4.55/4.68 ** KEPT (pick-wt=2): 504 [] -well_ordering($c14).
% 4.55/4.68 ** KEPT (pick-wt=12): 505 [] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(A)=relation_dom(function_inverse(A)).
% 4.55/4.68 ** KEPT (pick-wt=12): 507 [copy,506,flip.4] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(function_inverse(A))=relation_dom(A).
% 4.55/4.68 ** KEPT (pick-wt=12): 508 [] -relation(A)|in(ordered_pair($f106(A),$f105(A)),A)|A=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=18): 510 [copy,509,flip.5] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_rng(A))|apply(A,apply(function_inverse(A),B))=B.
% 4.55/4.68 ** KEPT (pick-wt=18): 512 [copy,511,flip.5] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_rng(A))|apply(relation_composition(function_inverse(A),A),B)=B.
% 4.55/4.68 ** KEPT (pick-wt=9): 513 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 4.55/4.68 ** KEPT (pick-wt=8): 514 [] -relation(A)| -well_founded_relation(A)|is_well_founded_in(A,relation_field(A)).
% 4.55/4.68 ** KEPT (pick-wt=8): 515 [] -relation(A)|well_founded_relation(A)| -is_well_founded_in(A,relation_field(A)).
% 4.55/4.68 ** KEPT (pick-wt=6): 516 [] -subset(A,B)| -proper_subset(B,A).
% 4.55/4.68 ** KEPT (pick-wt=9): 517 [] -relation(A)| -function(A)| -one_to_one(A)|one_to_one(function_inverse(A)).
% 4.55/4.68 ** KEPT (pick-wt=9): 518 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 4.55/4.68 ** KEPT (pick-wt=9): 519 [] -relation(A)|relation_dom(A)!=empty_set|A=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=9): 520 [] -relation(A)|relation_rng(A)!=empty_set|A=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=10): 521 [] -relation(A)|relation_dom(A)!=empty_set|relation_rng(A)=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=10): 522 [] -relation(A)|relation_dom(A)=empty_set|relation_rng(A)!=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=9): 523 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 4.55/4.68 ** KEPT (pick-wt=20): 524 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_dom_restriction(B,C)|relation_dom(A)=set_intersection2(relation_dom(B),C).
% 4.55/4.68 ** KEPT (pick-wt=24): 525 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_dom_restriction(B,C)| -in(D,relation_dom(A))|apply(A,D)=apply(B,D).
% 4.55/4.68 ** KEPT (pick-wt=27): 526 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_dom_restriction(B,C)|relation_dom(A)!=set_intersection2(relation_dom(B),C)|in($f107(C,A,B),relation_dom(A)).
% 4.55/4.68 ** KEPT (pick-wt=33): 527 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_dom_restriction(B,C)|relation_dom(A)!=set_intersection2(relation_dom(B),C)|apply(A,$f107(C,A,B))!=apply(B,$f107(C,A,B)).
% 4.55/4.68 ** KEPT (pick-wt=5): 528 [] -empty(A)|A=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=8): 529 [] -subset(singleton(A),singleton(B))|A=B.
% 4.55/4.68 ** KEPT (pick-wt=19): 530 [] -relation(A)| -function(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|apply(relation_dom_restriction(A,C),B)=apply(A,B).
% 4.55/4.68 ** KEPT (pick-wt=16): 531 [] -relation(A)| -function(A)| -in(B,C)|apply(relation_dom_restriction(A,C),B)=apply(A,B).
% 4.55/4.68 ** KEPT (pick-wt=13): 532 [] -relation(A)| -in(ordered_pair(B,C),relation_composition(identity_relation(D),A))|in(B,D).
% 4.55/4.68 ** KEPT (pick-wt=15): 533 [] -relation(A)| -in(ordered_pair(B,C),relation_composition(identity_relation(D),A))|in(ordered_pair(B,C),A).
% 4.55/4.68 ** KEPT (pick-wt=18): 534 [] -relation(A)|in(ordered_pair(B,C),relation_composition(identity_relation(D),A))| -in(B,D)| -in(ordered_pair(B,C),A).
% 4.55/4.68 ** KEPT (pick-wt=5): 535 [] -in(A,B)| -empty(B).
% 4.55/4.68 ** KEPT (pick-wt=8): 536 [] -in(A,B)|in($f108(A,B),B).
% 4.55/4.68 ** KEPT (pick-wt=11): 537 [] -in(A,B)| -in(C,B)| -in(C,$f108(A,B)).
% 4.55/4.68 ** KEPT (pick-wt=8): 538 [] -disjoint(A,B)|set_difference(A,B)=A.
% 4.55/4.68 ** KEPT (pick-wt=8): 539 [] disjoint(A,B)|set_difference(A,B)!=A.
% 4.55/4.68 ** KEPT (pick-wt=11): 540 [] -relation(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|in(B,C).
% 4.55/4.68 ** KEPT (pick-wt=12): 541 [] -relation(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|in(B,relation_dom(A)).
% 4.55/4.68 ** KEPT (pick-wt=15): 542 [] -relation(A)|in(B,relation_dom(relation_dom_restriction(A,C)))| -in(B,C)| -in(B,relation_dom(A)).
% 4.55/4.68 ** KEPT (pick-wt=7): 543 [] -relation(A)|subset(relation_dom_restriction(A,B),A).
% 4.55/4.68 ** KEPT (pick-wt=7): 544 [] -empty(A)|A=B| -empty(B).
% 4.55/4.68 Following clause subsumed by 408 during input processing: 0 [] -relation(A)| -function(A)| -in(ordered_pair(B,C),A)|in(B,relation_dom(A)).
% 4.55/4.68 ** KEPT (pick-wt=14): 545 [] -relation(A)| -function(A)| -in(ordered_pair(B,C),A)|C=apply(A,B).
% 4.55/4.68 Following clause subsumed by 151 during input processing: 0 [] -relation(A)| -function(A)|in(ordered_pair(B,C),A)| -in(B,relation_dom(A))|C!=apply(A,B).
% 4.55/4.68 ** KEPT (pick-wt=8): 546 [] -relation(A)| -well_orders(A,relation_field(A))|well_ordering(A).
% 4.55/4.68 ** KEPT (pick-wt=8): 547 [] -relation(A)|well_orders(A,relation_field(A))| -well_ordering(A).
% 4.55/4.68 ** KEPT (pick-wt=11): 548 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 4.55/4.68 ** KEPT (pick-wt=9): 549 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 4.55/4.68 ** KEPT (pick-wt=11): 550 [] -relation(A)|relation_dom(relation_dom_restriction(A,B))=set_intersection2(relation_dom(A),B).
% 4.55/4.68 Following clause subsumed by 339 during input processing: 0 [] -in(A,B)|subset(A,union(B)).
% 4.55/4.68 ** KEPT (pick-wt=10): 551 [] -relation(A)|relation_dom_restriction(A,B)=relation_composition(identity_relation(B),A).
% 4.55/4.68 ** KEPT (pick-wt=9): 552 [] -relation(A)|subset(relation_rng(relation_dom_restriction(A,B)),relation_rng(A)).
% 4.55/4.68 ** KEPT (pick-wt=11): 553 [] -in(A,$f110(B))| -subset(C,A)|in(C,$f110(B)).
% 4.55/4.68 ** KEPT (pick-wt=10): 554 [] -in(A,$f110(B))|in($f109(B,A),$f110(B)).
% 4.55/4.68 ** KEPT (pick-wt=12): 555 [] -in(A,$f110(B))| -subset(C,A)|in(C,$f109(B,A)).
% 4.55/4.68 ** KEPT (pick-wt=12): 556 [] -subset(A,$f110(B))|are_e_quipotent(A,$f110(B))|in(A,$f110(B)).
% 4.55/4.68 ** KEPT (pick-wt=9): 557 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 4.55/4.68 140 back subsumes 137.
% 4.55/4.68 406 back subsumes 109.
% 4.55/4.68 431 back subsumes 220.
% 4.55/4.68 432 back subsumes 221.
% 4.55/4.68 540 back subsumes 345.
% 4.55/4.68 541 back subsumes 344.
% 4.55/4.68 542 back subsumes 346.
% 4.55/4.68 545 back subsumes 152.
% 4.55/4.68 563 back subsumes 562.
% 4.55/4.68 571 back subsumes 570.
% 4.55/4.68
% 4.55/4.68 ------------> process sos:
% 4.55/4.68 ** KEPT (pick-wt=3): 766 [] A=A.
% 4.55/4.68 ** KEPT (pick-wt=7): 767 [] unordered_pair(A,B)=unordered_pair(B,A).
% 4.55/4.68 ** KEPT (pick-wt=7): 768 [] set_union2(A,B)=set_union2(B,A).
% 4.55/4.68 ** KEPT (pick-wt=7): 769 [] set_intersection2(A,B)=set_intersection2(B,A).
% 4.55/4.68 ** KEPT (pick-wt=34): 770 [] A=unordered_triple(B,C,D)|in($f17(B,C,D,A),A)|$f17(B,C,D,A)=B|$f17(B,C,D,A)=C|$f17(B,C,D,A)=D.
% 4.55/4.68 ** KEPT (pick-wt=7): 771 [] succ(A)=set_union2(A,singleton(A)).
% 4.55/4.68 ---> New Demodulator: 772 [new_demod,771] succ(A)=set_union2(A,singleton(A)).
% 4.55/4.68 ** KEPT (pick-wt=6): 773 [] relation(A)|in($f20(A),A).
% 4.55/4.68 ** KEPT (pick-wt=14): 774 [] A=singleton(B)|in($f25(B,A),A)|$f25(B,A)=B.
% 4.55/4.68 ** KEPT (pick-wt=7): 775 [] A=empty_set|in($f27(A),A).
% 4.55/4.68 ** KEPT (pick-wt=14): 776 [] A=powerset(B)|in($f28(B,A),A)|subset($f28(B,A),B).
% 4.55/4.68 ** KEPT (pick-wt=6): 777 [] epsilon_transitive(A)|in($f29(A),A).
% 4.55/4.68 ** KEPT (pick-wt=23): 778 [] A=unordered_pair(B,C)|in($f32(B,C,A),A)|$f32(B,C,A)=B|$f32(B,C,A)=C.
% 4.55/4.68 ** KEPT (pick-wt=23): 779 [] A=set_union2(B,C)|in($f35(B,C,A),A)|in($f35(B,C,A),B)|in($f35(B,C,A),C).
% 4.55/4.68 ** KEPT (pick-wt=17): 780 [] A=cartesian_product2(B,C)|in($f40(B,C,A),A)|in($f39(B,C,A),B).
% 4.55/4.68 ** KEPT (pick-wt=17): 781 [] A=cartesian_product2(B,C)|in($f40(B,C,A),A)|in($f38(B,C,A),C).
% 4.55/4.68 ** KEPT (pick-wt=25): 783 [copy,782,flip.3] A=cartesian_product2(B,C)|in($f40(B,C,A),A)|ordered_pair($f39(B,C,A),$f38(B,C,A))=$f40(B,C,A).
% 4.55/4.68 ** KEPT (pick-wt=6): 784 [] epsilon_connected(A)|in($f42(A),A).
% 4.55/4.68 ** KEPT (pick-wt=6): 785 [] epsilon_connected(A)|in($f41(A),A).
% 4.55/4.68 ** KEPT (pick-wt=8): 786 [] subset(A,B)|in($f45(A,B),A).
% 4.55/4.68 ** KEPT (pick-wt=17): 787 [] A=set_intersection2(B,C)|in($f48(B,C,A),A)|in($f48(B,C,A),B).
% 4.55/4.68 ** KEPT (pick-wt=17): 788 [] A=set_intersection2(B,C)|in($f48(B,C,A),A)|in($f48(B,C,A),C).
% 4.55/4.68 ** KEPT (pick-wt=4): 789 [] cast_to_subset(A)=A.
% 4.55/4.68 ---> New Demodulator: 790 [new_demod,789] cast_to_subset(A)=A.
% 4.55/4.68 ** KEPT (pick-wt=16): 791 [] A=union(B)|in($f56(B,A),A)|in($f56(B,A),$f55(B,A)).
% 4.55/4.68 ** KEPT (pick-wt=14): 792 [] A=union(B)|in($f56(B,A),A)|in($f55(B,A),B).
% 4.55/4.68 ** KEPT (pick-wt=17): 793 [] A=set_difference(B,C)|in($f57(B,C,A),A)|in($f57(B,C,A),B).
% 4.55/4.68 ** KEPT (pick-wt=10): 795 [copy,794,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 4.55/4.68 ---> New Demodulator: 796 [new_demod,795] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 4.55/4.68 ** KEPT (pick-wt=4): 798 [copy,797,demod,790] element(A,powerset(A)).
% 4.55/4.68 ** KEPT (pick-wt=3): 799 [] relation(identity_relation(A)).
% 4.55/4.68 ** KEPT (pick-wt=4): 800 [] element($f80(A),A).
% 4.55/4.68 ** KEPT (pick-wt=2): 801 [] empty(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=2): 802 [] relation(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=2): 803 [] relation_empty_yielding(empty_set).
% 4.55/4.68 Following clause subsumed by 801 during input processing: 0 [] empty(empty_set).
% 4.55/4.68 Following clause subsumed by 799 during input processing: 0 [] relation(identity_relation(A)).
% 4.55/4.68 ** KEPT (pick-wt=3): 804 [] function(identity_relation(A)).
% 4.55/4.68 Following clause subsumed by 802 during input processing: 0 [] relation(empty_set).
% 4.55/4.68 Following clause subsumed by 803 during input processing: 0 [] relation_empty_yielding(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=2): 805 [] function(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=2): 806 [] one_to_one(empty_set).
% 4.55/4.68 Following clause subsumed by 801 during input processing: 0 [] empty(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=2): 807 [] epsilon_transitive(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=2): 808 [] epsilon_connected(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=2): 809 [] ordinal(empty_set).
% 4.55/4.68 Following clause subsumed by 801 during input processing: 0 [] empty(empty_set).
% 4.55/4.68 Following clause subsumed by 802 during input processing: 0 [] relation(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=5): 810 [] set_union2(A,A)=A.
% 4.55/4.68 ---> New Demodulator: 811 [new_demod,810] set_union2(A,A)=A.
% 4.55/4.68 ** KEPT (pick-wt=5): 812 [] set_intersection2(A,A)=A.
% 4.55/4.68 ---> New Demodulator: 813 [new_demod,812] set_intersection2(A,A)=A.
% 4.55/4.68 ** KEPT (pick-wt=7): 814 [] in(A,B)|disjoint(singleton(A),B).
% 4.55/4.68 ** KEPT (pick-wt=9): 815 [] in($f89(A,B),A)|element(A,powerset(B)).
% 4.55/4.68 ** KEPT (pick-wt=2): 816 [] relation($c1).
% 4.55/4.68 ** KEPT (pick-wt=2): 817 [] function($c1).
% 4.55/4.68 ** KEPT (pick-wt=2): 818 [] epsilon_transitive($c2).
% 4.55/4.68 ** KEPT (pick-wt=2): 819 [] epsilon_connected($c2).
% 4.55/4.68 ** KEPT (pick-wt=2): 820 [] ordinal($c2).
% 4.55/4.68 ** KEPT (pick-wt=2): 821 [] empty($c3).
% 4.55/4.68 ** KEPT (pick-wt=2): 822 [] relation($c3).
% 4.55/4.68 ** KEPT (pick-wt=7): 823 [] empty(A)|element($f90(A),powerset(A)).
% 4.55/4.68 ** KEPT (pick-wt=2): 824 [] empty($c4).
% 4.55/4.68 ** KEPT (pick-wt=2): 825 [] relation($c5).
% 4.55/4.68 ** KEPT (pick-wt=2): 826 [] empty($c5).
% 4.55/4.68 ** KEPT (pick-wt=2): 827 [] function($c5).
% 4.55/4.68 ** KEPT (pick-wt=2): 828 [] relation($c6).
% 4.55/4.68 ** KEPT (pick-wt=2): 829 [] function($c6).
% 4.55/4.68 ** KEPT (pick-wt=2): 830 [] one_to_one($c6).
% 4.55/4.68 ** KEPT (pick-wt=2): 831 [] empty($c6).
% 4.55/4.68 ** KEPT (pick-wt=2): 832 [] epsilon_transitive($c6).
% 4.55/4.68 ** KEPT (pick-wt=2): 833 [] epsilon_connected($c6).
% 4.55/4.68 ** KEPT (pick-wt=2): 834 [] ordinal($c6).
% 4.55/4.68 ** KEPT (pick-wt=2): 835 [] relation($c7).
% 4.55/4.68 ** KEPT (pick-wt=5): 836 [] element($f91(A),powerset(A)).
% 4.55/4.68 ** KEPT (pick-wt=3): 837 [] empty($f91(A)).
% 4.55/4.68 ** KEPT (pick-wt=2): 838 [] relation($c9).
% 4.55/4.68 ** KEPT (pick-wt=2): 839 [] function($c9).
% 4.55/4.68 ** KEPT (pick-wt=2): 840 [] one_to_one($c9).
% 4.55/4.68 ** KEPT (pick-wt=2): 841 [] epsilon_transitive($c10).
% 4.55/4.68 ** KEPT (pick-wt=2): 842 [] epsilon_connected($c10).
% 4.55/4.68 ** KEPT (pick-wt=2): 843 [] ordinal($c10).
% 4.55/4.68 ** KEPT (pick-wt=2): 844 [] relation($c11).
% 4.55/4.68 ** KEPT (pick-wt=2): 845 [] relation_empty_yielding($c11).
% 4.55/4.68 ** KEPT (pick-wt=2): 846 [] relation($c12).
% 4.55/4.68 ** KEPT (pick-wt=2): 847 [] relation_empty_yielding($c12).
% 4.55/4.68 ** KEPT (pick-wt=2): 848 [] function($c12).
% 4.55/4.68 ** KEPT (pick-wt=3): 849 [] subset(A,A).
% 4.55/4.68 ** KEPT (pick-wt=6): 851 [copy,850,demod,772] in(A,set_union2(A,singleton(A))).
% 4.55/4.68 ** KEPT (pick-wt=4): 852 [] in(A,$f92(A)).
% 4.55/4.68 ** KEPT (pick-wt=5): 853 [] subset(set_intersection2(A,B),A).
% 4.55/4.68 ** KEPT (pick-wt=5): 854 [] set_union2(A,empty_set)=A.
% 4.55/4.68 ---> New Demodulator: 855 [new_demod,854] set_union2(A,empty_set)=A.
% 4.55/4.68 ** KEPT (pick-wt=5): 857 [copy,856,flip.1] singleton(empty_set)=powerset(empty_set).
% 4.55/4.68 ---> New Demodulator: 858 [new_demod,857] singleton(empty_set)=powerset(empty_set).
% 4.55/4.68 ** KEPT (pick-wt=5): 859 [] set_intersection2(A,empty_set)=empty_set.
% 4.55/4.68 ---> New Demodulator: 860 [new_demod,859] set_intersection2(A,empty_set)=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=13): 861 [] in($f95(A,B),A)|in($f95(A,B),B)|A=B.
% 4.55/4.68 ** KEPT (pick-wt=3): 862 [] subset(empty_set,A).
% 4.55/4.68 ** KEPT (pick-wt=6): 863 [] in($f96(A),A)|ordinal(A).
% 4.55/4.68 ** KEPT (pick-wt=5): 864 [] subset(set_difference(A,B),A).
% 4.55/4.68 ** KEPT (pick-wt=9): 865 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 4.55/4.68 ---> New Demodulator: 866 [new_demod,865] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 4.55/4.68 ** KEPT (pick-wt=5): 867 [] set_difference(A,empty_set)=A.
% 4.55/4.68 ---> New Demodulator: 868 [new_demod,867] set_difference(A,empty_set)=A.
% 4.55/4.68 ** KEPT (pick-wt=8): 869 [] disjoint(A,B)|in($f99(A,B),A).
% 4.55/4.68 ** KEPT (pick-wt=8): 870 [] disjoint(A,B)|in($f99(A,B),B).
% 4.55/4.68 ** KEPT (pick-wt=9): 871 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 4.55/4.68 ---> New Demodulator: 872 [new_demod,871] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 4.55/4.68 ** KEPT (pick-wt=9): 874 [copy,873,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 4.55/4.68 ---> New Demodulator: 875 [new_demod,874] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 4.55/4.68 ** KEPT (pick-wt=5): 876 [] set_difference(empty_set,A)=empty_set.
% 4.55/4.68 ---> New Demodulator: 877 [new_demod,876] set_difference(empty_set,A)=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=12): 879 [copy,878,demod,875] disjoint(A,B)|in($f102(A,B),set_difference(A,set_difference(A,B))).
% 4.55/4.68 ** KEPT (pick-wt=2): 880 [] relation($c15).
% 4.55/4.68 ** KEPT (pick-wt=2): 881 [] relation($c14).
% 4.55/4.68 ** KEPT (pick-wt=2): 882 [] relation($c13).
% 4.55/4.68 ** KEPT (pick-wt=2): 883 [] function($c13).
% 4.55/4.68 ** KEPT (pick-wt=2): 884 [] well_ordering($c15).
% 4.55/4.68 ** KEPT (pick-wt=4): 885 [] relation_isomorphism($c15,$c14,$c13).
% 4.55/4.68 ** KEPT (pick-wt=4): 886 [] relation_dom(empty_set)=empty_set.
% 4.55/4.68 ---> New Demodulator: 887 [new_demod,886] relation_dom(empty_set)=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=4): 888 [] relation_rng(empty_set)=empty_set.
% 4.55/4.68 ---> New Demodulator: 889 [new_demod,888] relation_rng(empty_set)=empty_set.
% 4.55/4.68 ** KEPT (pick-wt=9): 890 [] set_difference(A,singleton(B))=A|in(B,A).
% 4.55/4.68 ** KEPT (pick-wt=6): 892 [copy,891,flip.1] singleton(A)=unordered_pair(A,A).
% 4.55/4.68 ---> New Demodulator: 893 [new_demod,892] singleton(A)=unordered_pair(A,A).
% 4.55/4.68 ** KEPT (pick-wt=5): 894 [] relation_dom(identity_relation(A))=A.
% 4.55/4.68 ---> New Demodulator: 895 [new_demod,894] relation_dom(identity_relation(A))=A.
% 4.55/4.68 ** KEPT (pick-wt=5): 896 [] relation_rng(identity_relation(A))=A.
% 4.55/4.68 ---> New Demodulator: 897 [new_demod,896] relation_rng(identity_relation(A))=A.
% 4.55/4.68 ** KEPT (pick-wt=5): 898 [] subset(A,set_union2(A,B)).
% 4.55/4.68 ** KEPT (pick-wt=5): 899 [] union(powerset(A))=A.
% 4.55/4.68 ---> New Demodulator: 900 [new_demod,899] union(powerset(A))=A.
% 4.55/4.69 ** KEPT (pick-wt=4): 901 [] in(A,$f110(A)).
% 4.55/4.69 Following clause subsumed by 766 during input processing: 0 [copy,766,flip.1] A=A.
% 4.55/4.69 766 back subsumes 738.
% 4.55/4.69 766 back subsumes 733.
% 4.55/4.69 766 back subsumes 697.
% 4.55/4.69 766 back subsumes 694.
% 4.55/4.69 766 back subsumes 677.
% 4.55/4.69 766 back subsumes 676.
% 4.55/4.69 766 back subsumes 639.
% 4.55/4.69 766 back subsumes 607.
% 4.55/4.69 766 back subsumes 601.
% 4.55/4.69 766 back subsumes 594.
% 4.55/4.69 766 back subsumes 584.
% 4.55/4.69 766 back subsumes 583.
% 4.55/4.69 766 back subsumes 560.
% 4.55/4.69 Following clause subsumed by 767 during input processing: 0 [copy,767,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 4.55/4.69 Following clause subsumed by 768 during input processing: 0 [copy,768,flip.1] set_union2(A,B)=set_union2(B,A).
% 4.55/4.69 ** KEPT (pick-wt=11): 902 [copy,769,flip.1,demod,875,875] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 4.55/4.69 >>>> Starting back demodulation with 772.
% 4.55/4.69 >> back demodulating 702 with 772.
% 4.55/4.69 >> back demodulating 699 with 772.
% 4.55/4.69 >> back demodulating 468 with 772.
% 4.55/4.69 >> back demodulating 467 with 772.
% 4.55/4.69 >> back demodulating 464 with 772.
% 4.55/4.69 >> back demodulating 461 with 772.
% 4.55/4.69 >> back demodulating 440 with 772.
% 4.55/4.69 >> back demodulating 439 with 772.
% 4.55/4.69 >> back demodulating 288 with 772.
% 4.55/4.69 >> back demodulating 287 with 772.
% 4.55/4.69 >> back demodulating 286 with 772.
% 4.55/4.69 >> back demodulating 278 with 772.
% 4.55/4.69 >>>> Starting back demodulation with 790.
% 4.55/4.69 >> back demodulating 479 with 790.
% 4.55/4.69 >> back demodulating 478 with 790.
% 4.55/4.69 >>>> Starting back demodulation with 796.
% 4.55/4.69 >>>> Starting back demodulation with 811.
% 4.55/4.69 >> back demodulating 739 with 811.
% 4.55/4.69 >> back demodulating 673 with 811.
% 4.55/4.69 >> back demodulating 587 with 811.
% 4.55/4.69 >>>> Starting back demodulation with 813.
% 4.55/4.69 >> back demodulating 743 with 813.
% 4.55/4.69 >> back demodulating 688 with 813.
% 4.55/4.69 >> back demodulating 672 with 813.
% 4.55/4.69 >> back demodulating 600 with 813.
% 4.55/4.69 >> back demodulating 597 with 813.
% 4.55/4.69 849 back subsumes 696.
% 4.55/4.69 849 back subsumes 695.
% 4.55/4.69 849 back subsumes 680.
% 4.55/4.69 849 back subsumes 596.
% 4.55/4.69 849 back subsumes 595.
% 4.55/4.69 >>>> Starting back demodulation with 855.
% 4.55/4.69 >>>> Starting back demodulation with 858.
% 4.55/4.69 >>>> Starting back demodulation with 860.
% 4.55/4.69 >>>> Starting back demodulation with 866.
% 4.55/4.69 >> back demodulating 474 with 866.
% 4.55/4.69 >>>> Starting back demodulation with 868.
% 4.55/4.69 >>>> Starting back demodulation with 872.
% 4.55/4.69 >>>> Starting back demodulation with 875.
% 4.55/4.69 >> back demodulating 859 with 875.
% 4.55/4.69 >> back demodulating 853 with 875.
% 4.55/4.69 >> back demodulating 812 with 875.
% 4.55/4.69 >> back demodulating 788 with 875.
% 4.55/4.69 >> back demodulating 787 with 875.
% 4.55/4.69 >> back demodulating 769 with 875.
% 4.55/4.69 >> back demodulating 735 with 875.
% 4.55/4.69 >> back demodulating 734 with 875.
% 4.55/4.69 >> back demodulating 732 with 875.
% 4.55/4.69 >> back demodulating 599 with 875.
% 4.55/4.69 >> back demodulating 598 with 875.
% 4.55/4.69 >> back demodulating 550 with 875.
% 4.55/4.69 >> back demodulating 527 with 875.
% 4.55/4.69 >> back demodulating 526 with 875.
% 4.55/4.69 >> back demodulating 524 with 875.
% 4.55/4.69 >> back demodulating 482 with 875.
% 4.55/4.69 >> back demodulating 429 with 875.
% 4.55/4.69 >> back demodulating 428 with 875.
% 4.55/4.69 >> back demodulating 405 with 875.
% 4.55/4.69 >> back demodulating 383 with 875.
% 4.55/4.69 >> back demodulating 368 with 875.
% 4.55/4.69 >> back demodulating 279 with 875.
% 4.55/4.69 >> back demodulating 229 with 875.
% 4.55/4.69 >> back demodulating 228 with 875.
% 4.55/4.69 >> back demodulating 212 with 875.
% 4.55/4.69 >> back demodulating 150 with 875.
% 4.55/4.69 >> back demodulating 149 with 875.
% 4.55/4.69 >> back demodulating 148 with 875.
% 4.55/4.69 >> back demodulating 147 with 875.
% 4.55/4.69 >>>> Starting back demodulation with 877.
% 4.55/4.69 >>>> Starting back demodulation with 887.
% 4.55/4.69 >>>> Starting back demodulation with 889.
% 4.55/4.69 >>>> Starting back demodulation with 893.
% 4.55/4.69 >> back demodulating 890 with 893.
% 4.55/4.69 >> back demodulating 857 with 893.
% 4.55/4.69 >> back demodulating 851 with 893.
% 4.55/4.69 >> back demodulating 814 with 893.
% 4.55/4.69 >> back demodulating 795 with 893.
% 4.55/4.69 >> back demodulating 774 with 893.
% 4.55/4.69 >> back demodulating 771 with 893.
% 4.55/4.69 >> back demodulating 557 with 893.
% 4.55/4.69 >> back demodulating 549 with 893.
% 4.55/4.69 >> back demodulating 529 with 893.
% 4.55/4.69 >> back demodulating 523 with 893.
% 4.55/4.69 >> back demodulating 338 with 893.
% 4.55/4.69 >> back demodulating 337 with 893.
% 8.41/8.57 >> back demodulating 330 with 893.
% 8.41/8.57 >> back demodulating 322 with 893.
% 8.41/8.57 >> back demodulating 321 with 893.
% 8.41/8.57 >> back demodulating 315 with 893.
% 8.41/8.57 >> back demodulating 314 with 893.
% 8.41/8.57 >> back demodulating 313 with 893.
% 8.41/8.57 >> back demodulating 283 with 893.
% 8.41/8.57 >> back demodulating 91 with 893.
% 8.41/8.57 >> back demodulating 90 with 893.
% 8.41/8.57 >> back demodulating 89 with 893.
% 8.41/8.57 >>>> Starting back demodulation with 895.
% 8.41/8.57 >>>> Starting back demodulation with 897.
% 8.41/8.57 >>>> Starting back demodulation with 900.
% 8.41/8.57 Following clause subsumed by 902 during input processing: 0 [copy,902,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 8.41/8.57 927 back subsumes 104.
% 8.41/8.57 929 back subsumes 105.
% 8.41/8.57 >>>> Starting back demodulation with 931.
% 8.41/8.57 >> back demodulating 679 with 931.
% 8.41/8.57 >> back demodulating 674 with 931.
% 8.41/8.57 >>>> Starting back demodulation with 957.
% 8.41/8.57 >>>> Starting back demodulation with 961.
% 8.41/8.57 >>>> Starting back demodulation with 964.
% 8.41/8.57
% 8.41/8.57 ======= end of input processing =======
% 8.41/8.57
% 8.41/8.57 =========== start of search ===========
% 8.41/8.57
% 8.41/8.57
% 8.41/8.57 Resetting weight limit to 2.
% 8.41/8.57
% 8.41/8.57
% 8.41/8.57 Resetting weight limit to 2.
% 8.41/8.57
% 8.41/8.57 sos_size=167
% 8.41/8.57
% 8.41/8.57 -------- PROOF --------
% 8.41/8.57
% 8.41/8.57 ----> UNIT CONFLICT at 4.09 sec ----> 1005 [binary,1004.1,504.1] $F.
% 8.41/8.57
% 8.41/8.57 Length of proof is 11. Level of proof is 3.
% 8.41/8.57
% 8.41/8.57 ---------------- PROOF ----------------
% 8.41/8.57 % SZS status Theorem
% 8.41/8.57 % SZS output start Refutation
% See solution above
% 8.41/8.57 ------------ end of proof -------------
% 8.41/8.57
% 8.41/8.57
% 8.41/8.57 Search stopped by max_proofs option.
% 8.41/8.57
% 8.41/8.57
% 8.41/8.57 Search stopped by max_proofs option.
% 8.41/8.57
% 8.41/8.57 ============ end of search ============
% 8.41/8.57
% 8.41/8.57 -------------- statistics -------------
% 8.41/8.57 clauses given 97
% 8.41/8.57 clauses generated 113859
% 8.41/8.57 clauses kept 946
% 8.41/8.57 clauses forward subsumed 370
% 8.41/8.57 clauses back subsumed 30
% 8.41/8.57 Kbytes malloced 11718
% 8.41/8.57
% 8.41/8.57 ----------- times (seconds) -----------
% 8.41/8.57 user CPU time 4.09 (0 hr, 0 min, 4 sec)
% 8.41/8.57 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 8.41/8.57 wall-clock time 8 (0 hr, 0 min, 8 sec)
% 8.41/8.57
% 8.41/8.57 That finishes the proof of the theorem.
% 8.41/8.57
% 8.41/8.57 Process 2029 finished Wed Jul 27 08:05:30 2022
% 8.41/8.57 Otter interrupted
% 8.49/8.57 PROOF FOUND
%------------------------------------------------------------------------------