TSTP Solution File: SEU223+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU223+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:15:14 EDT 2022
% Result : Unknown 11.85s 12.03s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU223+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 07:39:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.15/3.33 ----- Otter 3.3f, August 2004 -----
% 3.15/3.33 The process was started by sandbox on n003.cluster.edu,
% 3.15/3.33 Wed Jul 27 07:39:41 2022
% 3.15/3.33 The command was "./otter". The process ID is 8569.
% 3.15/3.33
% 3.15/3.33 set(prolog_style_variables).
% 3.15/3.33 set(auto).
% 3.15/3.33 dependent: set(auto1).
% 3.15/3.33 dependent: set(process_input).
% 3.15/3.33 dependent: clear(print_kept).
% 3.15/3.33 dependent: clear(print_new_demod).
% 3.15/3.33 dependent: clear(print_back_demod).
% 3.15/3.33 dependent: clear(print_back_sub).
% 3.15/3.33 dependent: set(control_memory).
% 3.15/3.33 dependent: assign(max_mem, 12000).
% 3.15/3.33 dependent: assign(pick_given_ratio, 4).
% 3.15/3.33 dependent: assign(stats_level, 1).
% 3.15/3.33 dependent: assign(max_seconds, 10800).
% 3.15/3.33 clear(print_given).
% 3.15/3.33
% 3.15/3.33 formula_list(usable).
% 3.15/3.33 all A (A=A).
% 3.15/3.33 all A B (in(A,B)-> -in(B,A)).
% 3.15/3.33 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 3.15/3.33 all A (empty(A)->function(A)).
% 3.15/3.33 all A (empty(A)->relation(A)).
% 3.15/3.33 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 3.15/3.33 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 3.15/3.33 all A B (set_union2(A,B)=set_union2(B,A)).
% 3.15/3.33 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 3.15/3.33 all A B (relation(B)-> (B=identity_relation(A)<-> (all C D (in(ordered_pair(C,D),B)<->in(C,A)&C=D)))).
% 3.15/3.33 all A B (A=B<->subset(A,B)&subset(B,A)).
% 3.15/3.33 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))))))).
% 3.15/3.33 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))))))).
% 3.15/3.33 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)))))))).
% 3.15/3.33 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)))))))).
% 3.15/3.33 all A (relation(A)<-> (all B (-(in(B,A)& (all C D (B!=ordered_pair(C,D))))))).
% 3.15/3.33 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))).
% 3.15/3.33 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 3.15/3.33 all A (A=empty_set<-> (all B (-in(B,A)))).
% 3.15/3.33 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 3.15/3.33 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))))))).
% 3.15/3.33 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 3.15/3.33 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 3.15/3.33 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 3.15/3.33 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)))))).
% 3.15/3.33 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))))))).
% 3.15/3.33 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 3.15/3.33 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 3.15/3.33 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))))).
% 3.15/3.33 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 3.15/3.33 all A (cast_to_subset(A)=A).
% 3.15/3.33 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 3.15/3.33 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 3.15/3.33 all A (relation(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(D,C),A))))))).
% 3.15/3.33 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 3.15/3.33 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 3.15/3.33 all A (relation(A)->relation_field(A)=set_union2(relation_dom(A),relation_rng(A))).
% 3.15/3.33 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))))))).
% 3.15/3.33 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 3.15/3.33 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)))).
% 3.15/3.33 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))))))))))).
% 3.15/3.33 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)))))))).
% 3.15/3.33 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 3.15/3.33 all A (relation(A)&function(A)-> (one_to_one(A)->function_inverse(A)=relation_inverse(A))).
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 all A (relation(A)&function(A)->relation(function_inverse(A))&function(function_inverse(A))).
% 3.15/3.33 $T.
% 3.15/3.33 all A element(cast_to_subset(A),powerset(A)).
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 all A (relation(A)->relation(relation_inverse(A))).
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 all A B (relation(A)&relation(B)->relation(relation_composition(A,B))).
% 3.15/3.33 all A B (element(B,powerset(powerset(A)))->element(union_of_subsets(A,B),powerset(A))).
% 3.15/3.33 all A relation(identity_relation(A)).
% 3.15/3.33 all A B (element(B,powerset(powerset(A)))->element(meet_of_subsets(A,B),powerset(A))).
% 3.15/3.33 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_difference(A,B,C),powerset(A))).
% 3.15/3.33 all A B (relation(A)->relation(relation_dom_restriction(A,B))).
% 3.15/3.33 all A B (element(B,powerset(powerset(A)))->element(complements_of_subsets(A,B),powerset(powerset(A)))).
% 3.15/3.33 all A B (relation(B)->relation(relation_rng_restriction(A,B))).
% 3.15/3.33 $T.
% 3.15/3.33 $T.
% 3.15/3.33 all A exists B element(B,A).
% 3.15/3.33 all A B (empty(A)&relation(B)->empty(relation_composition(B,A))&relation(relation_composition(B,A))).
% 3.15/3.33 all A (empty(A)->empty(relation_inverse(A))&relation(relation_inverse(A))).
% 3.15/3.33 empty(empty_set).
% 3.15/3.33 relation(empty_set).
% 3.15/3.33 relation_empty_yielding(empty_set).
% 3.15/3.33 all A B (relation(A)&relation_empty_yielding(A)->relation(relation_dom_restriction(A,B))&relation_empty_yielding(relation_dom_restriction(A,B))).
% 3.15/3.33 all A B (relation(A)&function(A)&relation(B)&function(B)->relation(relation_composition(A,B))&function(relation_composition(A,B))).
% 3.15/3.33 all A B (relation(A)&relation(B)->relation(set_intersection2(A,B))).
% 3.15/3.33 all A (-empty(powerset(A))).
% 3.15/3.33 empty(empty_set).
% 3.15/3.33 all A B (-empty(ordered_pair(A,B))).
% 3.15/3.33 all A (relation(identity_relation(A))&function(identity_relation(A))).
% 3.15/3.33 all A B (relation(A)&relation(B)->relation(set_union2(A,B))).
% 3.15/3.33 all A (-empty(singleton(A))).
% 3.15/3.33 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 3.15/3.33 all A (relation(A)&function(A)&one_to_one(A)->relation(relation_inverse(A))&function(relation_inverse(A))).
% 3.15/3.33 all A B (-empty(unordered_pair(A,B))).
% 3.15/3.33 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 3.15/3.33 all A B (relation(A)&function(A)->relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))).
% 3.15/3.33 empty(empty_set).
% 3.15/3.33 relation(empty_set).
% 3.15/3.33 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 3.15/3.33 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 3.15/3.33 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 3.15/3.33 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 3.15/3.33 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 3.15/3.33 all A B (empty(A)&relation(B)->empty(relation_composition(A,B))&relation(relation_composition(A,B))).
% 3.15/3.33 all A B (set_union2(A,A)=A).
% 3.15/3.33 all A B (set_intersection2(A,A)=A).
% 3.15/3.33 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 3.15/3.33 all A (relation(A)->relation_inverse(relation_inverse(A))=A).
% 3.15/3.33 all A B (element(B,powerset(powerset(A)))->complements_of_subsets(A,complements_of_subsets(A,B))=B).
% 3.15/3.33 all A B (-proper_subset(A,A)).
% 3.15/3.33 all A (singleton(A)!=empty_set).
% 3.15/3.33 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 3.15/3.33 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 3.15/3.33 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 3.15/3.33 all A B (subset(singleton(A),B)<->in(A,B)).
% 3.15/3.33 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 3.15/3.33 all A B (element(B,powerset(A))-> (all C (in(C,B)->in(C,A)))).
% 3.15/3.33 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 3.15/3.33 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 3.15/3.33 all A B (in(A,B)->subset(A,union(B))).
% 3.15/3.33 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 3.15/3.33 all A B ((all C (in(C,A)->in(C,B)))->element(A,powerset(B))).
% 3.15/3.33 exists A (relation(A)&function(A)).
% 3.15/3.33 exists A (empty(A)&relation(A)).
% 3.15/3.33 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 3.15/3.33 exists A empty(A).
% 3.15/3.33 exists A (relation(A)&empty(A)&function(A)).
% 3.15/3.33 exists A (-empty(A)&relation(A)).
% 3.15/3.33 all A exists B (element(B,powerset(A))&empty(B)).
% 3.15/3.33 exists A (-empty(A)).
% 3.15/3.33 exists A (relation(A)&function(A)&one_to_one(A)).
% 3.15/3.33 exists A (relation(A)&relation_empty_yielding(A)).
% 3.15/3.33 all A B (element(B,powerset(powerset(A)))->union_of_subsets(A,B)=union(B)).
% 3.15/3.33 all A B (element(B,powerset(powerset(A)))->meet_of_subsets(A,B)=set_meet(B)).
% 3.15/3.33 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_difference(A,B,C)=set_difference(B,C)).
% 3.15/3.33 all A B subset(A,A).
% 3.15/3.33 all A B (disjoint(A,B)->disjoint(B,A)).
% 3.15/3.33 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 3.15/3.33 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 3.15/3.33 all A B C (relation(C)-> (in(A,relation_rng(relation_rng_restriction(B,C)))<->in(A,B)&in(A,relation_rng(C)))).
% 3.15/3.33 all A B (relation(B)->subset(relation_rng(relation_rng_restriction(A,B)),A)).
% 3.15/3.33 all A B (relation(B)->subset(relation_rng_restriction(A,B),B)).
% 3.15/3.33 all A B (relation(B)->subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))).
% 3.15/3.33 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))).
% 3.15/3.33 all A B (relation(B)->relation_rng(relation_rng_restriction(A,B))=set_intersection2(relation_rng(B),A)).
% 3.15/3.33 all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 3.15/3.33 all A B (subset(A,B)->set_union2(A,B)=B).
% 3.15/3.33 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))))).
% 3.15/3.33 all A B C (relation(C)->relation_dom_restriction(relation_rng_restriction(A,C),B)=relation_rng_restriction(A,relation_dom_restriction(C,B))).
% 3.15/3.33 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))))).
% 3.15/3.33 all A B (relation(B)->subset(relation_image(B,A),relation_rng(B))).
% 3.15/3.33 all A B (relation(B)->relation_image(B,A)=relation_image(B,set_intersection2(relation_dom(B),A))).
% 3.15/3.33 all A (relation(A)->relation_image(A,relation_dom(A))=relation_rng(A)).
% 3.15/3.33 all A (relation(A)-> (all B (relation(B)->relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A))))).
% 3.15/3.33 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))))).
% 3.15/3.33 all A B (relation(B)->subset(relation_inverse_image(B,A),relation_dom(B))).
% 3.15/3.33 all A B (relation(B)-> -(A!=empty_set&subset(A,relation_rng(B))&relation_inverse_image(B,A)=empty_set)).
% 3.15/3.33 all A B C (relation(C)-> (subset(A,B)->subset(relation_inverse_image(C,A),relation_inverse_image(C,B)))).
% 3.15/3.33 all A B subset(set_intersection2(A,B),A).
% 3.15/3.33 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 3.15/3.33 all A (set_union2(A,empty_set)=A).
% 3.15/3.33 all A B (in(A,B)->element(A,B)).
% 3.15/3.33 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 3.15/3.33 powerset(empty_set)=singleton(empty_set).
% 3.15/3.33 all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_dom(C))&in(B,relation_rng(C)))).
% 3.15/3.33 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)))))).
% 3.15/3.33 all A (relation(A)->subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))).
% 3.15/3.33 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)))))).
% 3.15/3.33 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)))))).
% 3.15/3.33 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)))))).
% 3.15/3.33 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 3.15/3.33 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 3.15/3.33 all A (set_intersection2(A,empty_set)=empty_set).
% 3.15/3.33 all A B (element(A,B)->empty(B)|in(A,B)).
% 3.15/3.33 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 3.15/3.33 all A subset(empty_set,A).
% 3.15/3.33 all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_field(C))&in(B,relation_field(C)))).
% 3.15/3.33 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 3.15/3.33 all A B C D (ordered_pair(A,B)=ordered_pair(C,D)->A=C&B=D).
% 3.15/3.33 all A B (relation(B)&function(B)-> (B=identity_relation(A)<->relation_dom(B)=A& (all C (in(C,A)->apply(B,C)=C)))).
% 3.15/3.33 all A B (in(B,A)->apply(identity_relation(A),B)=B).
% 3.15/3.33 all A B subset(set_difference(A,B),A).
% 3.15/3.33 all A (relation(A)->relation_rng(A)=relation_dom(relation_inverse(A))&relation_dom(A)=relation_rng(relation_inverse(A))).
% 3.15/3.33 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 3.15/3.33 all A B (subset(singleton(A),B)<->in(A,B)).
% 3.15/3.33 all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C)).
% 3.15/3.33 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 3.15/3.33 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 3.15/3.33 all A (set_difference(A,empty_set)=A).
% 3.15/3.33 all A B (element(A,powerset(B))<->subset(A,B)).
% 3.15/3.33 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))).
% 3.15/3.33 all A (subset(A,empty_set)->A=empty_set).
% 3.15/3.33 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 3.15/3.33 all A B (element(B,powerset(A))-> (all C (element(C,powerset(A))-> (disjoint(B,C)<->subset(B,subset_complement(A,C)))))).
% 3.15/3.33 all A (relation(A)-> (all B (relation(B)->subset(relation_dom(relation_composition(A,B)),relation_dom(A))))).
% 3.15/3.33 all A (relation(A)-> (all B (relation(B)->subset(relation_rng(relation_composition(A,B)),relation_rng(B))))).
% 3.15/3.33 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 3.15/3.33 all A (relation(A)-> (all B (relation(B)-> (subset(relation_rng(A),relation_dom(B))->relation_dom(relation_composition(A,B))=relation_dom(A))))).
% 3.15/3.33 all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set)).
% 3.15/3.33 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 3.15/3.33 all A (relation(A)-> (all B (relation(B)-> (subset(relation_dom(A),relation_rng(B))->relation_rng(relation_composition(B,A))=relation_rng(A))))).
% 3.15/3.33 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)))).
% 3.15/3.33 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)))).
% 3.15/3.33 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 3.15/3.33 all A (set_difference(empty_set,A)=empty_set).
% 3.15/3.33 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 3.15/3.33 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))).
% 3.15/3.33 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)))))))).
% 3.15/3.33 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))))))))).
% 3.15/3.33 all A B C (element(C,powerset(A))-> -(in(B,subset_complement(A,C))&in(B,C))).
% 3.15/3.33 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)))).
% 3.15/3.33 all A (relation(A)-> ((all B C (-in(ordered_pair(B,C),A)))->A=empty_set)).
% 3.15/3.33 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))).
% 3.15/3.33 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 3.15/3.33 relation_dom(empty_set)=empty_set.
% 3.15/3.33 relation_rng(empty_set)=empty_set.
% 3.15/3.33 all A B (-(subset(A,B)&proper_subset(B,A))).
% 3.15/3.33 all A (relation(A)&function(A)-> (one_to_one(A)->one_to_one(function_inverse(A)))).
% 3.15/3.33 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 3.15/3.33 all A (relation(A)-> (relation_dom(A)=empty_set|relation_rng(A)=empty_set->A=empty_set)).
% 3.15/3.33 all A (relation(A)-> (relation_dom(A)=empty_set<->relation_rng(A)=empty_set)).
% 3.15/3.33 all A B (set_difference(A,singleton(B))=A<-> -in(B,A)).
% 3.15/3.33 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))))))).
% 3.15/3.33 all A (unordered_pair(A,A)=singleton(A)).
% 3.15/3.33 all A (empty(A)->A=empty_set).
% 3.15/3.33 all A B (subset(singleton(A),singleton(B))->A=B).
% 3.15/3.33 -(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)))).
% 3.15/3.33 all A (relation_dom(identity_relation(A))=A&relation_rng(identity_relation(A))=A).
% 3.15/3.33 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))).
% 3.15/3.33 all A B (-(in(A,B)&empty(B))).
% 3.15/3.33 all A B subset(A,set_union2(A,B)).
% 3.15/3.33 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 3.15/3.33 all A B C (relation(C)-> (in(A,relation_dom(relation_dom_restriction(C,B)))<->in(A,B)&in(A,relation_dom(C)))).
% 3.15/3.33 all A B (relation(B)->subset(relation_dom_restriction(B,A),B)).
% 3.15/3.33 all A B (-(empty(A)&A!=B&empty(B))).
% 3.15/3.33 all A B C (relation(C)&function(C)-> (in(ordered_pair(A,B),C)<->in(A,relation_dom(C))&B=apply(C,A))).
% 3.15/3.33 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 3.15/3.33 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 3.15/3.33 all A B (relation(B)->relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A)).
% 3.15/3.33 all A B (in(A,B)->subset(A,union(B))).
% 3.15/3.33 all A B (relation(B)->relation_dom_restriction(B,A)=relation_composition(identity_relation(A),B)).
% 3.15/3.33 all A B (relation(B)->subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))).
% 3.15/3.33 all A (union(powerset(A))=A).
% 3.15/3.33 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))))).
% 3.15/3.33 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 3.15/3.33 end_of_list.
% 3.15/3.33
% 3.15/3.33 -------> usable clausifies to:
% 3.15/3.33
% 3.15/3.33 list(usable).
% 3.15/3.33 0 [] A=A.
% 3.15/3.33 0 [] -in(A,B)| -in(B,A).
% 3.15/3.33 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 3.15/3.33 0 [] -empty(A)|function(A).
% 3.15/3.33 0 [] -empty(A)|relation(A).
% 3.15/3.33 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 3.15/3.33 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 3.15/3.33 0 [] set_union2(A,B)=set_union2(B,A).
% 3.15/3.33 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 3.15/3.33 0 [] -relation(B)|B!=identity_relation(A)| -in(ordered_pair(C,D),B)|in(C,A).
% 3.15/3.33 0 [] -relation(B)|B!=identity_relation(A)| -in(ordered_pair(C,D),B)|C=D.
% 3.15/3.33 0 [] -relation(B)|B!=identity_relation(A)|in(ordered_pair(C,D),B)| -in(C,A)|C!=D.
% 3.15/3.33 0 [] -relation(B)|B=identity_relation(A)|in(ordered_pair($f2(A,B),$f1(A,B)),B)|in($f2(A,B),A).
% 3.15/3.33 0 [] -relation(B)|B=identity_relation(A)|in(ordered_pair($f2(A,B),$f1(A,B)),B)|$f2(A,B)=$f1(A,B).
% 3.15/3.33 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)!=$f1(A,B).
% 3.15/3.33 0 [] A!=B|subset(A,B).
% 3.15/3.33 0 [] A!=B|subset(B,A).
% 3.15/3.33 0 [] A=B| -subset(A,B)| -subset(B,A).
% 3.15/3.33 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)| -in(ordered_pair(D,E),C)|in(D,B).
% 3.15/3.33 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,E),A).
% 3.15/3.33 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)|in(ordered_pair(D,E),C)| -in(D,B)| -in(ordered_pair(D,E),A).
% 3.15/3.33 0 [] -relation(A)| -relation(C)|C=relation_dom_restriction(A,B)|in(ordered_pair($f4(A,B,C),$f3(A,B,C)),C)|in($f4(A,B,C),B).
% 3.15/3.33 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).
% 3.15/3.33 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),$f3(A,B,C)),A).
% 3.15/3.33 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)| -in(ordered_pair(D,E),C)|in(E,A).
% 3.15/3.33 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,E),B).
% 3.15/3.33 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)|in(ordered_pair(D,E),C)| -in(E,A)| -in(ordered_pair(D,E),B).
% 3.15/3.33 0 [] -relation(B)| -relation(C)|C=relation_rng_restriction(A,B)|in(ordered_pair($f6(A,B,C),$f5(A,B,C)),C)|in($f5(A,B,C),A).
% 3.15/3.33 0 [] -relation(B)| -relation(C)|C=relation_rng_restriction(A,B)|in(ordered_pair($f6(A,B,C),$f5(A,B,C)),C)|in(ordered_pair($f6(A,B,C),$f5(A,B,C)),B).
% 3.15/3.33 0 [] -relation(B)| -relation(C)|C=relation_rng_restriction(A,B)| -in(ordered_pair($f6(A,B,C),$f5(A,B,C)),C)| -in($f5(A,B,C),A)| -in(ordered_pair($f6(A,B,C),$f5(A,B,C)),B).
% 3.15/3.33 0 [] -relation(A)|C!=relation_image(A,B)| -in(D,C)|in(ordered_pair($f7(A,B,C,D),D),A).
% 3.15/3.33 0 [] -relation(A)|C!=relation_image(A,B)| -in(D,C)|in($f7(A,B,C,D),B).
% 3.15/3.33 0 [] -relation(A)|C!=relation_image(A,B)|in(D,C)| -in(ordered_pair(E,D),A)| -in(E,B).
% 3.15/3.33 0 [] -relation(A)|C=relation_image(A,B)|in($f9(A,B,C),C)|in(ordered_pair($f8(A,B,C),$f9(A,B,C)),A).
% 3.15/3.33 0 [] -relation(A)|C=relation_image(A,B)|in($f9(A,B,C),C)|in($f8(A,B,C),B).
% 3.15/3.33 0 [] -relation(A)|C=relation_image(A,B)| -in($f9(A,B,C),C)| -in(ordered_pair(X1,$f9(A,B,C)),A)| -in(X1,B).
% 3.15/3.33 0 [] -relation(A)|C!=relation_inverse_image(A,B)| -in(D,C)|in(ordered_pair(D,$f10(A,B,C,D)),A).
% 3.15/3.33 0 [] -relation(A)|C!=relation_inverse_image(A,B)| -in(D,C)|in($f10(A,B,C,D),B).
% 3.15/3.33 0 [] -relation(A)|C!=relation_inverse_image(A,B)|in(D,C)| -in(ordered_pair(D,E),A)| -in(E,B).
% 3.15/3.33 0 [] -relation(A)|C=relation_inverse_image(A,B)|in($f12(A,B,C),C)|in(ordered_pair($f12(A,B,C),$f11(A,B,C)),A).
% 3.15/3.33 0 [] -relation(A)|C=relation_inverse_image(A,B)|in($f12(A,B,C),C)|in($f11(A,B,C),B).
% 3.15/3.33 0 [] -relation(A)|C=relation_inverse_image(A,B)| -in($f12(A,B,C),C)| -in(ordered_pair($f12(A,B,C),X2),A)| -in(X2,B).
% 3.15/3.33 0 [] -relation(A)| -in(B,A)|B=ordered_pair($f14(A,B),$f13(A,B)).
% 3.15/3.33 0 [] relation(A)|in($f15(A),A).
% 3.15/3.33 0 [] relation(A)|$f15(A)!=ordered_pair(C,D).
% 3.15/3.33 0 [] A=empty_set|B!=set_meet(A)| -in(C,B)| -in(D,A)|in(C,D).
% 3.15/3.33 0 [] A=empty_set|B!=set_meet(A)|in(C,B)|in($f16(A,B,C),A).
% 3.15/3.33 0 [] A=empty_set|B!=set_meet(A)|in(C,B)| -in(C,$f16(A,B,C)).
% 3.15/3.33 0 [] A=empty_set|B=set_meet(A)|in($f18(A,B),B)| -in(X3,A)|in($f18(A,B),X3).
% 3.15/3.33 0 [] A=empty_set|B=set_meet(A)| -in($f18(A,B),B)|in($f17(A,B),A).
% 3.15/3.33 0 [] A=empty_set|B=set_meet(A)| -in($f18(A,B),B)| -in($f18(A,B),$f17(A,B)).
% 3.15/3.33 0 [] A!=empty_set|B!=set_meet(A)|B=empty_set.
% 3.15/3.33 0 [] A!=empty_set|B=set_meet(A)|B!=empty_set.
% 3.15/3.33 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 3.15/3.33 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 3.15/3.33 0 [] B=singleton(A)|in($f19(A,B),B)|$f19(A,B)=A.
% 3.15/3.33 0 [] B=singleton(A)| -in($f19(A,B),B)|$f19(A,B)!=A.
% 3.15/3.33 0 [] A!=empty_set| -in(B,A).
% 3.15/3.33 0 [] A=empty_set|in($f20(A),A).
% 3.15/3.33 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 3.15/3.33 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 3.15/3.33 0 [] B=powerset(A)|in($f21(A,B),B)|subset($f21(A,B),A).
% 3.15/3.33 0 [] B=powerset(A)| -in($f21(A,B),B)| -subset($f21(A,B),A).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|A!=B| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|A!=B|in(ordered_pair(C,D),A)| -in(ordered_pair(C,D),B).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|A=B|in(ordered_pair($f23(A,B),$f22(A,B)),A)|in(ordered_pair($f23(A,B),$f22(A,B)),B).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|A=B| -in(ordered_pair($f23(A,B),$f22(A,B)),A)| -in(ordered_pair($f23(A,B),$f22(A,B)),B).
% 3.15/3.33 0 [] empty(A)| -element(B,A)|in(B,A).
% 3.15/3.33 0 [] empty(A)|element(B,A)| -in(B,A).
% 3.15/3.33 0 [] -empty(A)| -element(B,A)|empty(B).
% 3.15/3.33 0 [] -empty(A)|element(B,A)| -empty(B).
% 3.15/3.33 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 3.15/3.33 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 3.15/3.33 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 3.15/3.33 0 [] C=unordered_pair(A,B)|in($f24(A,B,C),C)|$f24(A,B,C)=A|$f24(A,B,C)=B.
% 3.15/3.33 0 [] C=unordered_pair(A,B)| -in($f24(A,B,C),C)|$f24(A,B,C)!=A.
% 3.15/3.33 0 [] C=unordered_pair(A,B)| -in($f24(A,B,C),C)|$f24(A,B,C)!=B.
% 3.15/3.33 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 3.15/3.33 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 3.15/3.33 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 3.15/3.33 0 [] C=set_union2(A,B)|in($f25(A,B,C),C)|in($f25(A,B,C),A)|in($f25(A,B,C),B).
% 3.15/3.33 0 [] C=set_union2(A,B)| -in($f25(A,B,C),C)| -in($f25(A,B,C),A).
% 3.15/3.33 0 [] C=set_union2(A,B)| -in($f25(A,B,C),C)| -in($f25(A,B,C),B).
% 3.15/3.33 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f27(A,B,C,D),A).
% 3.15/3.33 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f26(A,B,C,D),B).
% 3.15/3.33 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f27(A,B,C,D),$f26(A,B,C,D)).
% 3.15/3.33 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 3.15/3.33 0 [] C=cartesian_product2(A,B)|in($f30(A,B,C),C)|in($f29(A,B,C),A).
% 3.15/3.33 0 [] C=cartesian_product2(A,B)|in($f30(A,B,C),C)|in($f28(A,B,C),B).
% 3.15/3.33 0 [] C=cartesian_product2(A,B)|in($f30(A,B,C),C)|$f30(A,B,C)=ordered_pair($f29(A,B,C),$f28(A,B,C)).
% 3.15/3.33 0 [] C=cartesian_product2(A,B)| -in($f30(A,B,C),C)| -in(X4,A)| -in(X5,B)|$f30(A,B,C)!=ordered_pair(X4,X5).
% 3.15/3.33 0 [] -relation(A)| -relation(B)| -subset(A,B)| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|subset(A,B)|in(ordered_pair($f32(A,B),$f31(A,B)),A).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|subset(A,B)| -in(ordered_pair($f32(A,B),$f31(A,B)),B).
% 3.15/3.33 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 3.15/3.33 0 [] subset(A,B)|in($f33(A,B),A).
% 3.15/3.33 0 [] subset(A,B)| -in($f33(A,B),B).
% 3.15/3.33 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 3.15/3.33 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 3.15/3.33 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 3.15/3.33 0 [] C=set_intersection2(A,B)|in($f34(A,B,C),C)|in($f34(A,B,C),A).
% 3.15/3.33 0 [] C=set_intersection2(A,B)|in($f34(A,B,C),C)|in($f34(A,B,C),B).
% 3.15/3.33 0 [] C=set_intersection2(A,B)| -in($f34(A,B,C),C)| -in($f34(A,B,C),A)| -in($f34(A,B,C),B).
% 3.15/3.33 0 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C!=apply(A,B)|in(ordered_pair(B,C),A).
% 3.15/3.33 0 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C=apply(A,B)| -in(ordered_pair(B,C),A).
% 3.15/3.33 0 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C!=apply(A,B)|C=empty_set.
% 3.15/3.33 0 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C=apply(A,B)|C!=empty_set.
% 3.15/3.33 0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f35(A,B,C)),A).
% 3.15/3.33 0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 3.15/3.33 0 [] -relation(A)|B=relation_dom(A)|in($f37(A,B),B)|in(ordered_pair($f37(A,B),$f36(A,B)),A).
% 3.15/3.33 0 [] -relation(A)|B=relation_dom(A)| -in($f37(A,B),B)| -in(ordered_pair($f37(A,B),X6),A).
% 3.15/3.33 0 [] cast_to_subset(A)=A.
% 3.15/3.33 0 [] B!=union(A)| -in(C,B)|in(C,$f38(A,B,C)).
% 3.15/3.33 0 [] B!=union(A)| -in(C,B)|in($f38(A,B,C),A).
% 3.15/3.33 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 3.15/3.33 0 [] B=union(A)|in($f40(A,B),B)|in($f40(A,B),$f39(A,B)).
% 3.15/3.33 0 [] B=union(A)|in($f40(A,B),B)|in($f39(A,B),A).
% 3.15/3.33 0 [] B=union(A)| -in($f40(A,B),B)| -in($f40(A,B),X7)| -in(X7,A).
% 3.15/3.33 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 3.15/3.33 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 3.15/3.33 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 3.15/3.33 0 [] C=set_difference(A,B)|in($f41(A,B,C),C)|in($f41(A,B,C),A).
% 3.15/3.33 0 [] C=set_difference(A,B)|in($f41(A,B,C),C)| -in($f41(A,B,C),B).
% 3.15/3.33 0 [] C=set_difference(A,B)| -in($f41(A,B,C),C)| -in($f41(A,B,C),A)|in($f41(A,B,C),B).
% 3.15/3.33 0 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f42(A,B,C),C),A).
% 3.15/3.33 0 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 3.15/3.33 0 [] -relation(A)|B=relation_rng(A)|in($f44(A,B),B)|in(ordered_pair($f43(A,B),$f44(A,B)),A).
% 3.15/3.33 0 [] -relation(A)|B=relation_rng(A)| -in($f44(A,B),B)| -in(ordered_pair(X8,$f44(A,B)),A).
% 3.15/3.33 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 3.15/3.33 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 3.15/3.33 0 [] -relation(A)|relation_field(A)=set_union2(relation_dom(A),relation_rng(A)).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|B!=relation_inverse(A)| -in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|B!=relation_inverse(A)|in(ordered_pair(C,D),B)| -in(ordered_pair(D,C),A).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|B=relation_inverse(A)|in(ordered_pair($f46(A,B),$f45(A,B)),B)|in(ordered_pair($f45(A,B),$f46(A,B)),A).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|B=relation_inverse(A)| -in(ordered_pair($f46(A,B),$f45(A,B)),B)| -in(ordered_pair($f45(A,B),$f46(A,B)),A).
% 3.15/3.33 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 3.15/3.33 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 3.15/3.33 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.
% 3.15/3.33 0 [] -relation(A)| -function(A)|one_to_one(A)|in($f48(A),relation_dom(A)).
% 3.15/3.33 0 [] -relation(A)| -function(A)|one_to_one(A)|in($f47(A),relation_dom(A)).
% 3.15/3.33 0 [] -relation(A)| -function(A)|one_to_one(A)|apply(A,$f48(A))=apply(A,$f47(A)).
% 3.15/3.33 0 [] -relation(A)| -function(A)|one_to_one(A)|$f48(A)!=$f47(A).
% 3.15/3.33 0 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,$f49(A,B,C,D,E)),A).
% 3.15/3.33 0 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair($f49(A,B,C,D,E),E),B).
% 3.15/3.33 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).
% 3.15/3.33 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f52(A,B,C),$f51(A,B,C)),C)|in(ordered_pair($f52(A,B,C),$f50(A,B,C)),A).
% 3.15/3.33 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f52(A,B,C),$f51(A,B,C)),C)|in(ordered_pair($f50(A,B,C),$f51(A,B,C)),B).
% 3.15/3.33 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)| -in(ordered_pair($f52(A,B,C),$f51(A,B,C)),C)| -in(ordered_pair($f52(A,B,C),X9),A)| -in(ordered_pair(X9,$f51(A,B,C)),B).
% 3.15/3.33 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).
% 3.15/3.33 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).
% 3.15/3.33 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|element($f53(A,B,C),powerset(A)).
% 3.15/3.33 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|in($f53(A,B,C),C)|in(subset_complement(A,$f53(A,B,C)),B).
% 3.15/3.33 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)| -in($f53(A,B,C),C)| -in(subset_complement(A,$f53(A,B,C)),B).
% 3.15/3.33 0 [] -proper_subset(A,B)|subset(A,B).
% 3.15/3.33 0 [] -proper_subset(A,B)|A!=B.
% 3.15/3.33 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 3.15/3.33 0 [] -relation(A)| -function(A)| -one_to_one(A)|function_inverse(A)=relation_inverse(A).
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 3.15/3.33 0 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] element(cast_to_subset(A),powerset(A)).
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] -relation(A)|relation(relation_inverse(A)).
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 3.15/3.33 0 [] -element(B,powerset(powerset(A)))|element(union_of_subsets(A,B),powerset(A)).
% 3.15/3.33 0 [] relation(identity_relation(A)).
% 3.15/3.33 0 [] -element(B,powerset(powerset(A)))|element(meet_of_subsets(A,B),powerset(A)).
% 3.15/3.33 0 [] -element(B,powerset(A))| -element(C,powerset(A))|element(subset_difference(A,B,C),powerset(A)).
% 3.15/3.33 0 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 3.15/3.33 0 [] -element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))).
% 3.15/3.33 0 [] -relation(B)|relation(relation_rng_restriction(A,B)).
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] $T.
% 3.15/3.33 0 [] element($f54(A),A).
% 3.15/3.33 0 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 3.15/3.33 0 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 3.15/3.33 0 [] -empty(A)|empty(relation_inverse(A)).
% 3.15/3.33 0 [] -empty(A)|relation(relation_inverse(A)).
% 3.15/3.33 0 [] empty(empty_set).
% 3.15/3.33 0 [] relation(empty_set).
% 3.15/3.33 0 [] relation_empty_yielding(empty_set).
% 3.15/3.33 0 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 3.15/3.33 0 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 3.15/3.33 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 3.15/3.33 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|relation(set_intersection2(A,B)).
% 3.15/3.33 0 [] -empty(powerset(A)).
% 3.15/3.33 0 [] empty(empty_set).
% 3.15/3.33 0 [] -empty(ordered_pair(A,B)).
% 3.15/3.33 0 [] relation(identity_relation(A)).
% 3.15/3.33 0 [] function(identity_relation(A)).
% 3.15/3.33 0 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 3.15/3.33 0 [] -empty(singleton(A)).
% 3.15/3.33 0 [] empty(A)| -empty(set_union2(A,B)).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation(relation_inverse(A)).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)|function(relation_inverse(A)).
% 3.15/3.34 0 [] -empty(unordered_pair(A,B)).
% 3.15/3.34 0 [] empty(A)| -empty(set_union2(B,A)).
% 3.15/3.34 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 3.15/3.34 0 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 3.15/3.34 0 [] empty(empty_set).
% 3.15/3.34 0 [] relation(empty_set).
% 3.15/3.34 0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 3.15/3.34 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 3.15/3.34 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 3.15/3.34 0 [] -empty(A)|empty(relation_dom(A)).
% 3.15/3.34 0 [] -empty(A)|relation(relation_dom(A)).
% 3.15/3.34 0 [] -empty(A)|empty(relation_rng(A)).
% 3.15/3.34 0 [] -empty(A)|relation(relation_rng(A)).
% 3.15/3.34 0 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 3.15/3.34 0 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 3.15/3.34 0 [] set_union2(A,A)=A.
% 3.15/3.34 0 [] set_intersection2(A,A)=A.
% 3.15/3.34 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 3.15/3.34 0 [] -relation(A)|relation_inverse(relation_inverse(A))=A.
% 3.15/3.34 0 [] -element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B.
% 3.15/3.34 0 [] -proper_subset(A,A).
% 3.15/3.34 0 [] singleton(A)!=empty_set.
% 3.15/3.34 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 3.15/3.34 0 [] -disjoint(singleton(A),B)| -in(A,B).
% 3.15/3.34 0 [] in(A,B)|disjoint(singleton(A),B).
% 3.15/3.34 0 [] -subset(singleton(A),B)|in(A,B).
% 3.15/3.34 0 [] subset(singleton(A),B)| -in(A,B).
% 3.15/3.34 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 3.15/3.34 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 3.15/3.34 0 [] -element(B,powerset(A))| -in(C,B)|in(C,A).
% 3.15/3.34 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 3.15/3.34 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 3.15/3.34 0 [] subset(A,singleton(B))|A!=empty_set.
% 3.15/3.34 0 [] subset(A,singleton(B))|A!=singleton(B).
% 3.15/3.34 0 [] -in(A,B)|subset(A,union(B)).
% 3.15/3.34 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 3.15/3.34 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 3.15/3.34 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 3.15/3.34 0 [] in($f55(A,B),A)|element(A,powerset(B)).
% 3.15/3.34 0 [] -in($f55(A,B),B)|element(A,powerset(B)).
% 3.15/3.34 0 [] relation($c1).
% 3.15/3.34 0 [] function($c1).
% 3.15/3.34 0 [] empty($c2).
% 3.15/3.34 0 [] relation($c2).
% 3.15/3.34 0 [] empty(A)|element($f56(A),powerset(A)).
% 3.15/3.34 0 [] empty(A)| -empty($f56(A)).
% 3.15/3.34 0 [] empty($c3).
% 3.15/3.34 0 [] relation($c4).
% 3.15/3.34 0 [] empty($c4).
% 3.15/3.34 0 [] function($c4).
% 3.15/3.34 0 [] -empty($c5).
% 3.15/3.34 0 [] relation($c5).
% 3.15/3.34 0 [] element($f57(A),powerset(A)).
% 3.15/3.34 0 [] empty($f57(A)).
% 3.15/3.34 0 [] -empty($c6).
% 3.15/3.34 0 [] relation($c7).
% 3.15/3.34 0 [] function($c7).
% 3.15/3.34 0 [] one_to_one($c7).
% 3.15/3.34 0 [] relation($c8).
% 3.15/3.34 0 [] relation_empty_yielding($c8).
% 3.15/3.34 0 [] -element(B,powerset(powerset(A)))|union_of_subsets(A,B)=union(B).
% 3.15/3.34 0 [] -element(B,powerset(powerset(A)))|meet_of_subsets(A,B)=set_meet(B).
% 3.15/3.34 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_difference(A,B,C)=set_difference(B,C).
% 3.15/3.34 0 [] subset(A,A).
% 3.15/3.34 0 [] -disjoint(A,B)|disjoint(B,A).
% 3.15/3.34 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 3.15/3.34 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 3.15/3.34 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 3.15/3.34 0 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_rng(relation_rng_restriction(B,C)))|in(A,B).
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_rng(relation_rng_restriction(B,C)))|in(A,relation_rng(C)).
% 3.15/3.34 0 [] -relation(C)|in(A,relation_rng(relation_rng_restriction(B,C)))| -in(A,B)| -in(A,relation_rng(C)).
% 3.15/3.34 0 [] -relation(B)|subset(relation_rng(relation_rng_restriction(A,B)),A).
% 3.15/3.34 0 [] -relation(B)|subset(relation_rng_restriction(A,B),B).
% 3.15/3.34 0 [] -relation(B)|subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)).
% 3.15/3.34 0 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 3.15/3.34 0 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 3.15/3.34 0 [] -relation(B)|relation_rng(relation_rng_restriction(A,B))=set_intersection2(relation_rng(B),A).
% 3.15/3.34 0 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 3.15/3.34 0 [] -subset(A,B)|set_union2(A,B)=B.
% 3.15/3.34 0 [] in(A,$f58(A)).
% 3.15/3.34 0 [] -in(C,$f58(A))| -subset(D,C)|in(D,$f58(A)).
% 3.15/3.34 0 [] -in(X10,$f58(A))|in(powerset(X10),$f58(A)).
% 3.15/3.34 0 [] -subset(X11,$f58(A))|are_e_quipotent(X11,$f58(A))|in(X11,$f58(A)).
% 3.15/3.34 0 [] -relation(C)|relation_dom_restriction(relation_rng_restriction(A,C),B)=relation_rng_restriction(A,relation_dom_restriction(C,B)).
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_image(C,B))|in($f59(A,B,C),relation_dom(C)).
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_image(C,B))|in(ordered_pair($f59(A,B,C),A),C).
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_image(C,B))|in($f59(A,B,C),B).
% 3.15/3.34 0 [] -relation(C)|in(A,relation_image(C,B))| -in(D,relation_dom(C))| -in(ordered_pair(D,A),C)| -in(D,B).
% 3.15/3.34 0 [] -relation(B)|subset(relation_image(B,A),relation_rng(B)).
% 3.15/3.34 0 [] -relation(B)|relation_image(B,A)=relation_image(B,set_intersection2(relation_dom(B),A)).
% 3.15/3.34 0 [] -relation(A)|relation_image(A,relation_dom(A))=relation_rng(A).
% 3.15/3.34 0 [] -relation(A)| -relation(B)|relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A)).
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in($f60(A,B,C),relation_rng(C)).
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in(ordered_pair(A,$f60(A,B,C)),C).
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in($f60(A,B,C),B).
% 3.15/3.34 0 [] -relation(C)|in(A,relation_inverse_image(C,B))| -in(D,relation_rng(C))| -in(ordered_pair(A,D),C)| -in(D,B).
% 3.15/3.34 0 [] -relation(B)|subset(relation_inverse_image(B,A),relation_dom(B)).
% 3.15/3.34 0 [] -relation(B)|A=empty_set| -subset(A,relation_rng(B))|relation_inverse_image(B,A)!=empty_set.
% 3.15/3.34 0 [] -relation(C)| -subset(A,B)|subset(relation_inverse_image(C,A),relation_inverse_image(C,B)).
% 3.15/3.34 0 [] subset(set_intersection2(A,B),A).
% 3.15/3.34 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 3.15/3.34 0 [] set_union2(A,empty_set)=A.
% 3.15/3.34 0 [] -in(A,B)|element(A,B).
% 3.15/3.34 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 3.15/3.34 0 [] powerset(empty_set)=singleton(empty_set).
% 3.15/3.34 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(A,relation_dom(C)).
% 3.15/3.34 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(B,relation_rng(C)).
% 3.15/3.34 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)| -in(A,relation_dom(relation_composition(C,B)))|in(A,relation_dom(C)).
% 3.15/3.34 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)| -in(A,relation_dom(relation_composition(C,B)))|in(apply(C,A),relation_dom(B)).
% 3.15/3.34 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)).
% 3.15/3.34 0 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 3.15/3.34 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)).
% 3.15/3.34 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)).
% 3.15/3.34 0 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_dom(A),relation_dom(B)).
% 3.15/3.34 0 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_rng(A),relation_rng(B)).
% 3.15/3.34 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 3.15/3.34 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 3.15/3.34 0 [] set_intersection2(A,empty_set)=empty_set.
% 3.15/3.34 0 [] -element(A,B)|empty(B)|in(A,B).
% 3.15/3.34 0 [] in($f61(A,B),A)|in($f61(A,B),B)|A=B.
% 3.15/3.34 0 [] -in($f61(A,B),A)| -in($f61(A,B),B)|A=B.
% 3.15/3.34 0 [] subset(empty_set,A).
% 3.15/3.34 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(A,relation_field(C)).
% 3.15/3.34 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(B,relation_field(C)).
% 3.15/3.34 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 3.15/3.34 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 3.15/3.34 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 3.15/3.34 0 [] -relation(B)| -function(B)|B!=identity_relation(A)|relation_dom(B)=A.
% 3.15/3.34 0 [] -relation(B)| -function(B)|B!=identity_relation(A)| -in(C,A)|apply(B,C)=C.
% 3.15/3.34 0 [] -relation(B)| -function(B)|B=identity_relation(A)|relation_dom(B)!=A|in($f62(A,B),A).
% 3.15/3.34 0 [] -relation(B)| -function(B)|B=identity_relation(A)|relation_dom(B)!=A|apply(B,$f62(A,B))!=$f62(A,B).
% 3.15/3.34 0 [] -in(B,A)|apply(identity_relation(A),B)=B.
% 3.15/3.34 0 [] subset(set_difference(A,B),A).
% 3.15/3.34 0 [] -relation(A)|relation_rng(A)=relation_dom(relation_inverse(A)).
% 3.15/3.34 0 [] -relation(A)|relation_dom(A)=relation_rng(relation_inverse(A)).
% 3.15/3.34 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 3.15/3.34 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 3.15/3.34 0 [] -subset(singleton(A),B)|in(A,B).
% 3.15/3.34 0 [] subset(singleton(A),B)| -in(A,B).
% 3.15/3.34 0 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 3.15/3.34 0 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 3.15/3.34 0 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 3.15/3.34 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 3.15/3.34 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 3.15/3.34 0 [] subset(A,singleton(B))|A!=empty_set.
% 3.15/3.34 0 [] subset(A,singleton(B))|A!=singleton(B).
% 3.15/3.34 0 [] set_difference(A,empty_set)=A.
% 3.15/3.34 0 [] -element(A,powerset(B))|subset(A,B).
% 3.15/3.34 0 [] element(A,powerset(B))| -subset(A,B).
% 3.15/3.34 0 [] disjoint(A,B)|in($f63(A,B),A).
% 3.15/3.34 0 [] disjoint(A,B)|in($f63(A,B),B).
% 3.15/3.34 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 3.15/3.34 0 [] -subset(A,empty_set)|A=empty_set.
% 3.15/3.34 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 3.15/3.34 0 [] -element(B,powerset(A))| -element(C,powerset(A))| -disjoint(B,C)|subset(B,subset_complement(A,C)).
% 3.15/3.34 0 [] -element(B,powerset(A))| -element(C,powerset(A))|disjoint(B,C)| -subset(B,subset_complement(A,C)).
% 3.15/3.34 0 [] -relation(A)| -relation(B)|subset(relation_dom(relation_composition(A,B)),relation_dom(A)).
% 3.15/3.34 0 [] -relation(A)| -relation(B)|subset(relation_rng(relation_composition(A,B)),relation_rng(B)).
% 3.15/3.34 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 3.15/3.34 0 [] -relation(A)| -relation(B)| -subset(relation_rng(A),relation_dom(B))|relation_dom(relation_composition(A,B))=relation_dom(A).
% 3.15/3.34 0 [] -element(B,powerset(powerset(A)))|B=empty_set|complements_of_subsets(A,B)!=empty_set.
% 3.15/3.34 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 3.15/3.34 0 [] -relation(A)| -relation(B)| -subset(relation_dom(A),relation_rng(B))|relation_rng(relation_composition(B,A))=relation_rng(A).
% 3.15/3.34 0 [] -element(B,powerset(powerset(A)))|B=empty_set|subset_difference(A,cast_to_subset(A),union_of_subsets(A,B))=meet_of_subsets(A,complements_of_subsets(A,B)).
% 3.15/3.34 0 [] -element(B,powerset(powerset(A)))|B=empty_set|union_of_subsets(A,complements_of_subsets(A,B))=subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)).
% 3.15/3.34 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 3.15/3.34 0 [] set_difference(empty_set,A)=empty_set.
% 3.15/3.34 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 3.15/3.34 0 [] disjoint(A,B)|in($f64(A,B),set_intersection2(A,B)).
% 3.15/3.34 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 3.15/3.34 0 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)|relation_dom(B)=relation_rng(A).
% 3.15/3.34 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)).
% 3.15/3.34 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).
% 3.15/3.34 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)).
% 3.15/3.34 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).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f66(A,B),relation_rng(A))|in($f65(A,B),relation_dom(A)).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f66(A,B),relation_rng(A))|$f66(A,B)=apply(A,$f65(A,B)).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|$f65(A,B)=apply(B,$f66(A,B))|in($f65(A,B),relation_dom(A)).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|$f65(A,B)=apply(B,$f66(A,B))|$f66(A,B)=apply(A,$f65(A,B)).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)| -in($f65(A,B),relation_dom(A))|$f66(A,B)!=apply(A,$f65(A,B))| -in($f66(A,B),relation_rng(A))|$f65(A,B)!=apply(B,$f66(A,B)).
% 3.15/3.34 0 [] -element(C,powerset(A))| -in(B,subset_complement(A,C))| -in(B,C).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(A)=relation_dom(function_inverse(A)).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation_dom(A)=relation_rng(function_inverse(A)).
% 3.15/3.34 0 [] -relation(A)|in(ordered_pair($f68(A),$f67(A)),A)|A=empty_set.
% 3.15/3.34 0 [] -relation(B)| -function(B)| -one_to_one(B)| -in(A,relation_rng(B))|A=apply(B,apply(function_inverse(B),A)).
% 3.15/3.34 0 [] -relation(B)| -function(B)| -one_to_one(B)| -in(A,relation_rng(B))|A=apply(relation_composition(function_inverse(B),B),A).
% 3.15/3.34 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 3.15/3.34 0 [] relation_dom(empty_set)=empty_set.
% 3.15/3.34 0 [] relation_rng(empty_set)=empty_set.
% 3.15/3.34 0 [] -subset(A,B)| -proper_subset(B,A).
% 3.15/3.34 0 [] -relation(A)| -function(A)| -one_to_one(A)|one_to_one(function_inverse(A)).
% 3.15/3.34 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 3.15/3.34 0 [] -relation(A)|relation_dom(A)!=empty_set|A=empty_set.
% 3.15/3.34 0 [] -relation(A)|relation_rng(A)!=empty_set|A=empty_set.
% 3.15/3.34 0 [] -relation(A)|relation_dom(A)!=empty_set|relation_rng(A)=empty_set.
% 3.15/3.34 0 [] -relation(A)|relation_dom(A)=empty_set|relation_rng(A)!=empty_set.
% 3.15/3.34 0 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 3.15/3.34 0 [] set_difference(A,singleton(B))=A|in(B,A).
% 3.15/3.34 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_dom_restriction(C,A)|relation_dom(B)=set_intersection2(relation_dom(C),A).
% 3.15/3.34 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).
% 3.15/3.34 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($f69(A,B,C),relation_dom(B)).
% 3.15/3.34 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_dom_restriction(C,A)|relation_dom(B)!=set_intersection2(relation_dom(C),A)|apply(B,$f69(A,B,C))!=apply(C,$f69(A,B,C)).
% 3.15/3.34 0 [] unordered_pair(A,A)=singleton(A).
% 3.15/3.34 0 [] -empty(A)|A=empty_set.
% 3.15/3.34 0 [] -subset(singleton(A),singleton(B))|A=B.
% 3.15/3.34 0 [] relation($c9).
% 3.15/3.34 0 [] function($c9).
% 3.15/3.34 0 [] in($c10,relation_dom(relation_dom_restriction($c9,$c11))).
% 3.15/3.34 0 [] apply(relation_dom_restriction($c9,$c11),$c10)!=apply($c9,$c10).
% 3.15/3.34 0 [] relation_dom(identity_relation(A))=A.
% 3.15/3.34 0 [] relation_rng(identity_relation(A))=A.
% 3.15/3.34 0 [] -relation(D)| -in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|in(A,C).
% 3.15/3.34 0 [] -relation(D)| -in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|in(ordered_pair(A,B),D).
% 3.15/3.34 0 [] -relation(D)|in(ordered_pair(A,B),relation_composition(identity_relation(C),D))| -in(A,C)| -in(ordered_pair(A,B),D).
% 3.15/3.34 0 [] -in(A,B)| -empty(B).
% 3.15/3.34 0 [] subset(A,set_union2(A,B)).
% 3.15/3.34 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 3.15/3.34 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_dom(relation_dom_restriction(C,B)))|in(A,B).
% 3.15/3.34 0 [] -relation(C)| -in(A,relation_dom(relation_dom_restriction(C,B)))|in(A,relation_dom(C)).
% 3.15/3.34 0 [] -relation(C)|in(A,relation_dom(relation_dom_restriction(C,B)))| -in(A,B)| -in(A,relation_dom(C)).
% 3.15/3.34 0 [] -relation(B)|subset(relation_dom_restriction(B,A),B).
% 3.15/3.34 0 [] -empty(A)|A=B| -empty(B).
% 3.15/3.34 0 [] -relation(C)| -function(C)| -in(ordered_pair(A,B),C)|in(A,relation_dom(C)).
% 3.15/3.34 0 [] -relation(C)| -function(C)| -in(ordered_pair(A,B),C)|B=apply(C,A).
% 3.15/3.34 0 [] -relation(C)| -function(C)|in(ordered_pair(A,B),C)| -in(A,relation_dom(C))|B!=apply(C,A).
% 3.15/3.34 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 3.15/3.34 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 3.15/3.34 0 [] -relation(B)|relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A).
% 3.15/3.34 0 [] -in(A,B)|subset(A,union(B)).
% 3.15/3.34 0 [] -relation(B)|relation_dom_restriction(B,A)=relation_composition(identity_relation(A),B).
% 3.15/3.34 0 [] -relation(B)|subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)).
% 3.15/3.34 0 [] union(powerset(A))=A.
% 3.15/3.34 0 [] in(A,$f71(A)).
% 3.15/3.34 0 [] -in(C,$f71(A))| -subset(D,C)|in(D,$f71(A)).
% 3.15/3.34 0 [] -in(X12,$f71(A))|in($f70(A,X12),$f71(A)).
% 3.15/3.34 0 [] -in(X12,$f71(A))| -subset(E,X12)|in(E,$f70(A,X12)).
% 3.15/3.34 0 [] -subset(X13,$f71(A))|are_e_quipotent(X13,$f71(A))|in(X13,$f71(A)).
% 3.15/3.34 0 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 3.15/3.34 end_of_list.
% 3.15/3.34
% 3.15/3.34 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=11.
% 3.15/3.34
% 3.15/3.34 This ia a non-Horn set with equality. The strategy will be
% 3.15/3.34 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.15/3.34 deletion, with positive clauses in sos and nonpositive
% 3.15/3.34 clauses in usable.
% 3.15/3.34
% 3.15/3.34 dependent: set(knuth_bendix).
% 3.15/3.34 dependent: set(anl_eq).
% 3.15/3.34 dependent: set(para_from).
% 3.15/3.34 dependent: set(para_into).
% 3.15/3.34 dependent: clear(para_from_right).
% 3.15/3.34 dependent: clear(para_into_right).
% 3.15/3.34 dependent: set(para_from_vars).
% 3.15/3.34 dependent: set(eq_units_both_ways).
% 3.15/3.34 dependent: set(dynamic_demod_all).
% 3.15/3.34 dependent: set(dynamic_demod).
% 3.15/3.34 dependent: set(order_eq).
% 3.15/3.34 dependent: set(back_demod).
% 3.15/3.34 dependent: set(lrpo).
% 3.15/3.34 dependent: set(hyper_res).
% 3.15/3.34 dependent: set(unit_deletion).
% 3.15/3.34 dependent: set(factor).
% 3.15/3.34
% 3.15/3.34 ------------> process usable:
% 3.15/3.34 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 3.15/3.34 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 3.15/3.34 ** KEPT (pick-wt=4): 3 [] -empty(A)|function(A).
% 3.15/3.34 ** KEPT (pick-wt=4): 4 [] -empty(A)|relation(A).
% 3.15/3.34 ** KEPT (pick-wt=8): 5 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 3.15/3.34 ** KEPT (pick-wt=14): 6 [] -relation(A)|A!=identity_relation(B)| -in(ordered_pair(C,D),A)|in(C,B).
% 3.15/3.34 ** KEPT (pick-wt=14): 7 [] -relation(A)|A!=identity_relation(B)| -in(ordered_pair(C,D),A)|C=D.
% 3.15/3.34 ** KEPT (pick-wt=17): 8 [] -relation(A)|A!=identity_relation(B)|in(ordered_pair(C,D),A)| -in(C,B)|C!=D.
% 3.15/3.34 ** KEPT (pick-wt=20): 9 [] -relation(A)|A=identity_relation(B)|in(ordered_pair($f2(B,A),$f1(B,A)),A)|in($f2(B,A),B).
% 3.15/3.34 ** KEPT (pick-wt=22): 10 [] -relation(A)|A=identity_relation(B)|in(ordered_pair($f2(B,A),$f1(B,A)),A)|$f2(B,A)=$f1(B,A).
% 3.15/3.34 ** KEPT (pick-wt=27): 11 [] -relation(A)|A=identity_relation(B)| -in(ordered_pair($f2(B,A),$f1(B,A)),A)| -in($f2(B,A),B)|$f2(B,A)!=$f1(B,A).
% 3.15/3.34 ** KEPT (pick-wt=6): 12 [] A!=B|subset(A,B).
% 3.15/3.34 ** KEPT (pick-wt=6): 13 [] A!=B|subset(B,A).
% 3.15/3.34 ** KEPT (pick-wt=9): 14 [] A=B| -subset(A,B)| -subset(B,A).
% 3.15/3.34 ** KEPT (pick-wt=17): 15 [] -relation(A)| -relation(B)|B!=relation_dom_restriction(A,C)| -in(ordered_pair(D,E),B)|in(D,C).
% 3.15/3.34 ** KEPT (pick-wt=19): 16 [] -relation(A)| -relation(B)|B!=relation_dom_restriction(A,C)| -in(ordered_pair(D,E),B)|in(ordered_pair(D,E),A).
% 3.15/3.34 ** KEPT (pick-wt=22): 17 [] -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).
% 3.15/3.34 ** KEPT (pick-wt=26): 18 [] -relation(A)| -relation(B)|B=relation_dom_restriction(A,C)|in(ordered_pair($f4(A,C,B),$f3(A,C,B)),B)|in($f4(A,C,B),C).
% 3.15/3.34 ** KEPT (pick-wt=31): 19 [] -relation(A)| -relation(B)|B=relation_dom_restriction(A,C)|in(ordered_pair($f4(A,C,B),$f3(A,C,B)),B)|in(ordered_pair($f4(A,C,B),$f3(A,C,B)),A).
% 3.15/3.34 ** KEPT (pick-wt=37): 20 [] -relation(A)| -relation(B)|B=relation_dom_restriction(A,C)| -in(ordered_pair($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).
% 3.15/3.34 ** KEPT (pick-wt=17): 21 [] -relation(A)| -relation(B)|B!=relation_rng_restriction(C,A)| -in(ordered_pair(D,E),B)|in(E,C).
% 3.15/3.34 ** KEPT (pick-wt=19): 22 [] -relation(A)| -relation(B)|B!=relation_rng_restriction(C,A)| -in(ordered_pair(D,E),B)|in(ordered_pair(D,E),A).
% 3.15/3.34 ** KEPT (pick-wt=22): 23 [] -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).
% 3.15/3.34 ** KEPT (pick-wt=26): 24 [] -relation(A)| -relation(B)|B=relation_rng_restriction(C,A)|in(ordered_pair($f6(C,A,B),$f5(C,A,B)),B)|in($f5(C,A,B),C).
% 3.15/3.34 ** KEPT (pick-wt=31): 25 [] -relation(A)| -relation(B)|B=relation_rng_restriction(C,A)|in(ordered_pair($f6(C,A,B),$f5(C,A,B)),B)|in(ordered_pair($f6(C,A,B),$f5(C,A,B)),A).
% 3.15/3.34 ** KEPT (pick-wt=37): 26 [] -relation(A)| -relation(B)|B=relation_rng_restriction(C,A)| -in(ordered_pair($f6(C,A,B),$f5(C,A,B)),B)| -in($f5(C,A,B),C)| -in(ordered_pair($f6(C,A,B),$f5(C,A,B)),A).
% 3.15/3.34 ** KEPT (pick-wt=19): 27 [] -relation(A)|B!=relation_image(A,C)| -in(D,B)|in(ordered_pair($f7(A,C,B,D),D),A).
% 3.15/3.34 ** KEPT (pick-wt=17): 28 [] -relation(A)|B!=relation_image(A,C)| -in(D,B)|in($f7(A,C,B,D),C).
% 3.15/3.34 ** KEPT (pick-wt=18): 29 [] -relation(A)|B!=relation_image(A,C)|in(D,B)| -in(ordered_pair(E,D),A)| -in(E,C).
% 3.15/3.35 ** KEPT (pick-wt=24): 30 [] -relation(A)|B=relation_image(A,C)|in($f9(A,C,B),B)|in(ordered_pair($f8(A,C,B),$f9(A,C,B)),A).
% 3.15/3.35 ** KEPT (pick-wt=19): 31 [] -relation(A)|B=relation_image(A,C)|in($f9(A,C,B),B)|in($f8(A,C,B),C).
% 3.15/3.35 ** KEPT (pick-wt=24): 32 [] -relation(A)|B=relation_image(A,C)| -in($f9(A,C,B),B)| -in(ordered_pair(D,$f9(A,C,B)),A)| -in(D,C).
% 3.15/3.35 ** KEPT (pick-wt=19): 33 [] -relation(A)|B!=relation_inverse_image(A,C)| -in(D,B)|in(ordered_pair(D,$f10(A,C,B,D)),A).
% 3.15/3.35 ** KEPT (pick-wt=17): 34 [] -relation(A)|B!=relation_inverse_image(A,C)| -in(D,B)|in($f10(A,C,B,D),C).
% 3.15/3.35 ** KEPT (pick-wt=18): 35 [] -relation(A)|B!=relation_inverse_image(A,C)|in(D,B)| -in(ordered_pair(D,E),A)| -in(E,C).
% 3.15/3.35 ** KEPT (pick-wt=24): 36 [] -relation(A)|B=relation_inverse_image(A,C)|in($f12(A,C,B),B)|in(ordered_pair($f12(A,C,B),$f11(A,C,B)),A).
% 3.15/3.35 ** KEPT (pick-wt=19): 37 [] -relation(A)|B=relation_inverse_image(A,C)|in($f12(A,C,B),B)|in($f11(A,C,B),C).
% 3.15/3.35 ** KEPT (pick-wt=24): 38 [] -relation(A)|B=relation_inverse_image(A,C)| -in($f12(A,C,B),B)| -in(ordered_pair($f12(A,C,B),D),A)| -in(D,C).
% 3.15/3.35 ** KEPT (pick-wt=14): 40 [copy,39,flip.3] -relation(A)| -in(B,A)|ordered_pair($f14(A,B),$f13(A,B))=B.
% 3.15/3.35 ** KEPT (pick-wt=8): 41 [] relation(A)|$f15(A)!=ordered_pair(B,C).
% 3.15/3.35 ** KEPT (pick-wt=16): 42 [] A=empty_set|B!=set_meet(A)| -in(C,B)| -in(D,A)|in(C,D).
% 3.15/3.35 ** KEPT (pick-wt=16): 43 [] A=empty_set|B!=set_meet(A)|in(C,B)|in($f16(A,B,C),A).
% 3.15/3.35 ** KEPT (pick-wt=16): 44 [] A=empty_set|B!=set_meet(A)|in(C,B)| -in(C,$f16(A,B,C)).
% 3.15/3.35 ** KEPT (pick-wt=20): 45 [] A=empty_set|B=set_meet(A)|in($f18(A,B),B)| -in(C,A)|in($f18(A,B),C).
% 3.15/3.35 ** KEPT (pick-wt=17): 46 [] A=empty_set|B=set_meet(A)| -in($f18(A,B),B)|in($f17(A,B),A).
% 3.15/3.35 ** KEPT (pick-wt=19): 47 [] A=empty_set|B=set_meet(A)| -in($f18(A,B),B)| -in($f18(A,B),$f17(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=10): 48 [] A!=empty_set|B!=set_meet(A)|B=empty_set.
% 3.15/3.35 ** KEPT (pick-wt=10): 49 [] A!=empty_set|B=set_meet(A)|B!=empty_set.
% 3.15/3.35 ** KEPT (pick-wt=10): 50 [] A!=singleton(B)| -in(C,A)|C=B.
% 3.15/3.35 ** KEPT (pick-wt=10): 51 [] A!=singleton(B)|in(C,A)|C!=B.
% 3.15/3.35 ** KEPT (pick-wt=14): 52 [] A=singleton(B)| -in($f19(B,A),A)|$f19(B,A)!=B.
% 3.15/3.35 ** KEPT (pick-wt=6): 53 [] A!=empty_set| -in(B,A).
% 3.15/3.35 ** KEPT (pick-wt=10): 54 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 3.15/3.35 ** KEPT (pick-wt=10): 55 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 3.15/3.35 ** KEPT (pick-wt=14): 56 [] A=powerset(B)| -in($f21(B,A),A)| -subset($f21(B,A),B).
% 3.15/3.35 ** KEPT (pick-wt=17): 57 [] -relation(A)| -relation(B)|A!=B| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 3.15/3.35 ** KEPT (pick-wt=17): 58 [] -relation(A)| -relation(B)|A!=B|in(ordered_pair(C,D),A)| -in(ordered_pair(C,D),B).
% 3.15/3.35 ** KEPT (pick-wt=25): 59 [] -relation(A)| -relation(B)|A=B|in(ordered_pair($f23(A,B),$f22(A,B)),A)|in(ordered_pair($f23(A,B),$f22(A,B)),B).
% 3.15/3.35 ** KEPT (pick-wt=25): 60 [] -relation(A)| -relation(B)|A=B| -in(ordered_pair($f23(A,B),$f22(A,B)),A)| -in(ordered_pair($f23(A,B),$f22(A,B)),B).
% 3.15/3.35 ** KEPT (pick-wt=8): 61 [] empty(A)| -element(B,A)|in(B,A).
% 3.15/3.35 ** KEPT (pick-wt=8): 62 [] empty(A)|element(B,A)| -in(B,A).
% 3.15/3.35 ** KEPT (pick-wt=7): 63 [] -empty(A)| -element(B,A)|empty(B).
% 3.15/3.35 ** KEPT (pick-wt=7): 64 [] -empty(A)|element(B,A)| -empty(B).
% 3.15/3.35 ** KEPT (pick-wt=14): 65 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 3.15/3.35 ** KEPT (pick-wt=11): 66 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 3.15/3.35 ** KEPT (pick-wt=11): 67 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 3.15/3.35 ** KEPT (pick-wt=17): 68 [] A=unordered_pair(B,C)| -in($f24(B,C,A),A)|$f24(B,C,A)!=B.
% 3.15/3.35 ** KEPT (pick-wt=17): 69 [] A=unordered_pair(B,C)| -in($f24(B,C,A),A)|$f24(B,C,A)!=C.
% 3.15/3.35 ** KEPT (pick-wt=14): 70 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 3.15/3.35 ** KEPT (pick-wt=11): 71 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 3.15/3.35 ** KEPT (pick-wt=11): 72 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 3.15/3.35 ** KEPT (pick-wt=17): 73 [] A=set_union2(B,C)| -in($f25(B,C,A),A)| -in($f25(B,C,A),B).
% 3.15/3.35 ** KEPT (pick-wt=17): 74 [] A=set_union2(B,C)| -in($f25(B,C,A),A)| -in($f25(B,C,A),C).
% 3.15/3.35 ** KEPT (pick-wt=15): 75 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f27(B,C,A,D),B).
% 3.15/3.35 ** KEPT (pick-wt=15): 76 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f26(B,C,A,D),C).
% 3.15/3.35 ** KEPT (pick-wt=21): 78 [copy,77,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f27(B,C,A,D),$f26(B,C,A,D))=D.
% 3.15/3.35 ** KEPT (pick-wt=19): 79 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 3.15/3.35 ** KEPT (pick-wt=25): 80 [] A=cartesian_product2(B,C)| -in($f30(B,C,A),A)| -in(D,B)| -in(E,C)|$f30(B,C,A)!=ordered_pair(D,E).
% 3.15/3.35 ** KEPT (pick-wt=17): 81 [] -relation(A)| -relation(B)| -subset(A,B)| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 3.15/3.35 ** KEPT (pick-wt=16): 82 [] -relation(A)| -relation(B)|subset(A,B)|in(ordered_pair($f32(A,B),$f31(A,B)),A).
% 3.15/3.35 ** KEPT (pick-wt=16): 83 [] -relation(A)| -relation(B)|subset(A,B)| -in(ordered_pair($f32(A,B),$f31(A,B)),B).
% 3.15/3.35 ** KEPT (pick-wt=9): 84 [] -subset(A,B)| -in(C,A)|in(C,B).
% 3.15/3.35 ** KEPT (pick-wt=8): 85 [] subset(A,B)| -in($f33(A,B),B).
% 3.15/3.35 ** KEPT (pick-wt=11): 86 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 3.15/3.35 ** KEPT (pick-wt=11): 87 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 3.15/3.35 ** KEPT (pick-wt=14): 88 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 3.15/3.35 ** KEPT (pick-wt=23): 89 [] A=set_intersection2(B,C)| -in($f34(B,C,A),A)| -in($f34(B,C,A),B)| -in($f34(B,C,A),C).
% 3.15/3.35 ** KEPT (pick-wt=18): 90 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C!=apply(A,B)|in(ordered_pair(B,C),A).
% 3.15/3.35 ** KEPT (pick-wt=18): 91 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C=apply(A,B)| -in(ordered_pair(B,C),A).
% 3.15/3.35 ** KEPT (pick-wt=16): 92 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C!=apply(A,B)|C=empty_set.
% 3.15/3.35 ** KEPT (pick-wt=16): 93 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C=apply(A,B)|C!=empty_set.
% 3.15/3.35 ** KEPT (pick-wt=17): 94 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f35(A,B,C)),A).
% 3.15/3.35 ** KEPT (pick-wt=14): 95 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 3.15/3.35 ** KEPT (pick-wt=20): 96 [] -relation(A)|B=relation_dom(A)|in($f37(A,B),B)|in(ordered_pair($f37(A,B),$f36(A,B)),A).
% 3.15/3.35 ** KEPT (pick-wt=18): 97 [] -relation(A)|B=relation_dom(A)| -in($f37(A,B),B)| -in(ordered_pair($f37(A,B),C),A).
% 3.15/3.35 ** KEPT (pick-wt=13): 98 [] A!=union(B)| -in(C,A)|in(C,$f38(B,A,C)).
% 3.15/3.35 ** KEPT (pick-wt=13): 99 [] A!=union(B)| -in(C,A)|in($f38(B,A,C),B).
% 3.15/3.35 ** KEPT (pick-wt=13): 100 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 3.15/3.35 ** KEPT (pick-wt=17): 101 [] A=union(B)| -in($f40(B,A),A)| -in($f40(B,A),C)| -in(C,B).
% 3.15/3.35 ** KEPT (pick-wt=11): 102 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 3.15/3.35 ** KEPT (pick-wt=11): 103 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 3.15/3.35 ** KEPT (pick-wt=14): 104 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 3.15/3.35 ** KEPT (pick-wt=17): 105 [] A=set_difference(B,C)|in($f41(B,C,A),A)| -in($f41(B,C,A),C).
% 3.15/3.35 ** KEPT (pick-wt=23): 106 [] A=set_difference(B,C)| -in($f41(B,C,A),A)| -in($f41(B,C,A),B)|in($f41(B,C,A),C).
% 3.15/3.35 ** KEPT (pick-wt=17): 107 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f42(A,B,C),C),A).
% 3.15/3.35 ** KEPT (pick-wt=14): 108 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 3.15/3.35 ** KEPT (pick-wt=20): 109 [] -relation(A)|B=relation_rng(A)|in($f44(A,B),B)|in(ordered_pair($f43(A,B),$f44(A,B)),A).
% 3.15/3.35 ** KEPT (pick-wt=18): 110 [] -relation(A)|B=relation_rng(A)| -in($f44(A,B),B)| -in(ordered_pair(C,$f44(A,B)),A).
% 3.15/3.35 ** KEPT (pick-wt=11): 111 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 3.15/3.35 ** KEPT (pick-wt=10): 113 [copy,112,flip.2] -relation(A)|set_union2(relation_dom(A),relation_rng(A))=relation_field(A).
% 3.15/3.35 ** KEPT (pick-wt=18): 114 [] -relation(A)| -relation(B)|B!=relation_inverse(A)| -in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A).
% 3.15/3.35 ** KEPT (pick-wt=18): 115 [] -relation(A)| -relation(B)|B!=relation_inverse(A)|in(ordered_pair(C,D),B)| -in(ordered_pair(D,C),A).
% 3.15/3.35 ** KEPT (pick-wt=26): 116 [] -relation(A)| -relation(B)|B=relation_inverse(A)|in(ordered_pair($f46(A,B),$f45(A,B)),B)|in(ordered_pair($f45(A,B),$f46(A,B)),A).
% 3.15/3.35 ** KEPT (pick-wt=26): 117 [] -relation(A)| -relation(B)|B=relation_inverse(A)| -in(ordered_pair($f46(A,B),$f45(A,B)),B)| -in(ordered_pair($f45(A,B),$f46(A,B)),A).
% 3.15/3.35 ** KEPT (pick-wt=8): 118 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 3.15/3.35 ** KEPT (pick-wt=8): 119 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 3.15/3.35 ** KEPT (pick-wt=24): 120 [] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_dom(A))| -in(C,relation_dom(A))|apply(A,B)!=apply(A,C)|B=C.
% 3.15/3.35 ** KEPT (pick-wt=11): 121 [] -relation(A)| -function(A)|one_to_one(A)|in($f48(A),relation_dom(A)).
% 3.15/3.35 ** KEPT (pick-wt=11): 122 [] -relation(A)| -function(A)|one_to_one(A)|in($f47(A),relation_dom(A)).
% 3.15/3.35 ** KEPT (pick-wt=15): 123 [] -relation(A)| -function(A)|one_to_one(A)|apply(A,$f48(A))=apply(A,$f47(A)).
% 3.15/3.35 ** KEPT (pick-wt=11): 124 [] -relation(A)| -function(A)|one_to_one(A)|$f48(A)!=$f47(A).
% 3.15/3.35 ** KEPT (pick-wt=26): 125 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,$f49(A,B,C,D,E)),A).
% 3.15/3.35 ** KEPT (pick-wt=26): 126 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair($f49(A,B,C,D,E),E),B).
% 3.15/3.35 ** KEPT (pick-wt=26): 127 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)|in(ordered_pair(D,E),C)| -in(ordered_pair(D,F),A)| -in(ordered_pair(F,E),B).
% 3.15/3.35 ** KEPT (pick-wt=33): 128 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f52(A,B,C),$f51(A,B,C)),C)|in(ordered_pair($f52(A,B,C),$f50(A,B,C)),A).
% 3.15/3.35 ** KEPT (pick-wt=33): 129 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f52(A,B,C),$f51(A,B,C)),C)|in(ordered_pair($f50(A,B,C),$f51(A,B,C)),B).
% 3.15/3.35 ** KEPT (pick-wt=38): 130 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)| -in(ordered_pair($f52(A,B,C),$f51(A,B,C)),C)| -in(ordered_pair($f52(A,B,C),D),A)| -in(ordered_pair(D,$f51(A,B,C)),B).
% 3.15/3.35 ** KEPT (pick-wt=27): 131 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C!=complements_of_subsets(B,A)| -element(D,powerset(B))| -in(D,C)|in(subset_complement(B,D),A).
% 3.15/3.35 ** KEPT (pick-wt=27): 132 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C!=complements_of_subsets(B,A)| -element(D,powerset(B))|in(D,C)| -in(subset_complement(B,D),A).
% 3.15/3.35 ** KEPT (pick-wt=22): 133 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|element($f53(B,A,C),powerset(B)).
% 3.15/3.35 ** KEPT (pick-wt=29): 134 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|in($f53(B,A,C),C)|in(subset_complement(B,$f53(B,A,C)),A).
% 3.15/3.35 ** KEPT (pick-wt=29): 135 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)| -in($f53(B,A,C),C)| -in(subset_complement(B,$f53(B,A,C)),A).
% 3.15/3.35 ** KEPT (pick-wt=6): 136 [] -proper_subset(A,B)|subset(A,B).
% 3.15/3.35 ** KEPT (pick-wt=6): 137 [] -proper_subset(A,B)|A!=B.
% 3.15/3.35 ** KEPT (pick-wt=9): 138 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 3.15/3.35 ** KEPT (pick-wt=11): 140 [copy,139,flip.4] -relation(A)| -function(A)| -one_to_one(A)|relation_inverse(A)=function_inverse(A).
% 3.15/3.35 ** KEPT (pick-wt=7): 141 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 3.15/3.35 ** KEPT (pick-wt=7): 142 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 3.15/3.35 ** KEPT (pick-wt=10): 143 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 3.15/3.35 ** KEPT (pick-wt=5): 144 [] -relation(A)|relation(relation_inverse(A)).
% 3.15/3.35 ** KEPT (pick-wt=8): 145 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=11): 146 [] -element(A,powerset(powerset(B)))|element(union_of_subsets(B,A),powerset(B)).
% 3.15/3.35 ** KEPT (pick-wt=11): 147 [] -element(A,powerset(powerset(B)))|element(meet_of_subsets(B,A),powerset(B)).
% 3.15/3.35 ** KEPT (pick-wt=15): 148 [] -element(A,powerset(B))| -element(C,powerset(B))|element(subset_difference(B,A,C),powerset(B)).
% 3.15/3.35 ** KEPT (pick-wt=6): 149 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=12): 150 [] -element(A,powerset(powerset(B)))|element(complements_of_subsets(B,A),powerset(powerset(B))).
% 3.15/3.35 ** KEPT (pick-wt=6): 151 [] -relation(A)|relation(relation_rng_restriction(B,A)).
% 3.15/3.35 ** KEPT (pick-wt=8): 152 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 3.15/3.35 ** KEPT (pick-wt=8): 153 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 3.15/3.35 ** KEPT (pick-wt=5): 154 [] -empty(A)|empty(relation_inverse(A)).
% 3.15/3.35 ** KEPT (pick-wt=5): 155 [] -empty(A)|relation(relation_inverse(A)).
% 3.15/3.35 Following clause subsumed by 149 during input processing: 0 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=8): 156 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 3.15/3.35 Following clause subsumed by 145 during input processing: 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=12): 157 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=8): 158 [] -relation(A)| -relation(B)|relation(set_intersection2(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=3): 159 [] -empty(powerset(A)).
% 3.15/3.35 ** KEPT (pick-wt=4): 160 [] -empty(ordered_pair(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=8): 161 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=3): 162 [] -empty(singleton(A)).
% 3.15/3.35 ** KEPT (pick-wt=6): 163 [] empty(A)| -empty(set_union2(A,B)).
% 3.15/3.35 Following clause subsumed by 144 during input processing: 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation(relation_inverse(A)).
% 3.15/3.35 ** KEPT (pick-wt=9): 164 [] -relation(A)| -function(A)| -one_to_one(A)|function(relation_inverse(A)).
% 3.15/3.35 ** KEPT (pick-wt=4): 165 [] -empty(unordered_pair(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=6): 166 [] empty(A)| -empty(set_union2(B,A)).
% 3.15/3.35 Following clause subsumed by 149 during input processing: 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=8): 167 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=8): 168 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=7): 169 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 3.15/3.35 ** KEPT (pick-wt=7): 170 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 3.15/3.35 ** KEPT (pick-wt=5): 171 [] -empty(A)|empty(relation_dom(A)).
% 3.15/3.35 ** KEPT (pick-wt=5): 172 [] -empty(A)|relation(relation_dom(A)).
% 3.15/3.35 ** KEPT (pick-wt=5): 173 [] -empty(A)|empty(relation_rng(A)).
% 3.15/3.35 ** KEPT (pick-wt=5): 174 [] -empty(A)|relation(relation_rng(A)).
% 3.15/3.35 ** KEPT (pick-wt=8): 175 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=8): 176 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 3.15/3.35 ** KEPT (pick-wt=11): 177 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 3.15/3.35 ** KEPT (pick-wt=7): 178 [] -relation(A)|relation_inverse(relation_inverse(A))=A.
% 3.15/3.35 ** KEPT (pick-wt=12): 179 [] -element(A,powerset(powerset(B)))|complements_of_subsets(B,complements_of_subsets(B,A))=A.
% 3.15/3.35 ** KEPT (pick-wt=3): 180 [] -proper_subset(A,A).
% 3.15/3.35 ** KEPT (pick-wt=4): 181 [] singleton(A)!=empty_set.
% 3.15/3.35 ** KEPT (pick-wt=9): 182 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 3.15/3.35 ** KEPT (pick-wt=7): 183 [] -disjoint(singleton(A),B)| -in(A,B).
% 3.15/3.35 ** KEPT (pick-wt=7): 184 [] -subset(singleton(A),B)|in(A,B).
% 3.15/3.35 ** KEPT (pick-wt=7): 185 [] subset(singleton(A),B)| -in(A,B).
% 3.15/3.35 ** KEPT (pick-wt=8): 186 [] set_difference(A,B)!=empty_set|subset(A,B).
% 3.15/3.35 ** KEPT (pick-wt=8): 187 [] set_difference(A,B)=empty_set| -subset(A,B).
% 3.15/3.35 ** KEPT (pick-wt=10): 188 [] -element(A,powerset(B))| -in(C,A)|in(C,B).
% 3.15/3.35 ** KEPT (pick-wt=12): 189 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 3.15/3.35 ** KEPT (pick-wt=11): 190 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 3.15/3.35 ** KEPT (pick-wt=7): 191 [] subset(A,singleton(B))|A!=empty_set.
% 3.15/3.35 Following clause subsumed by 12 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 3.15/3.35 ** KEPT (pick-wt=7): 192 [] -in(A,B)|subset(A,union(B)).
% 3.15/3.35 ** KEPT (pick-wt=10): 193 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 3.15/3.35 ** KEPT (pick-wt=10): 194 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 3.15/3.35 ** KEPT (pick-wt=13): 195 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 3.15/3.35 ** KEPT (pick-wt=9): 196 [] -in($f55(A,B),B)|element(A,powerset(B)).
% 3.15/3.35 ** KEPT (pick-wt=5): 197 [] empty(A)| -empty($f56(A)).
% 3.15/3.35 ** KEPT (pick-wt=2): 198 [] -empty($c5).
% 3.15/3.35 ** KEPT (pick-wt=2): 199 [] -empty($c6).
% 3.15/3.36 ** KEPT (pick-wt=11): 200 [] -element(A,powerset(powerset(B)))|union_of_subsets(B,A)=union(A).
% 3.15/3.36 ** KEPT (pick-wt=11): 201 [] -element(A,powerset(powerset(B)))|meet_of_subsets(B,A)=set_meet(A).
% 3.15/3.36 ** KEPT (pick-wt=16): 202 [] -element(A,powerset(B))| -element(C,powerset(B))|subset_difference(B,A,C)=set_difference(A,C).
% 3.15/3.36 ** KEPT (pick-wt=6): 203 [] -disjoint(A,B)|disjoint(B,A).
% 3.15/3.36 Following clause subsumed by 193 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 3.15/3.36 Following clause subsumed by 194 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 3.15/3.36 Following clause subsumed by 195 during input processing: 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 3.15/3.36 ** KEPT (pick-wt=13): 204 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 3.15/3.36 ** KEPT (pick-wt=11): 205 [] -relation(A)| -in(B,relation_rng(relation_rng_restriction(C,A)))|in(B,C).
% 3.15/3.36 ** KEPT (pick-wt=12): 206 [] -relation(A)| -in(B,relation_rng(relation_rng_restriction(C,A)))|in(B,relation_rng(A)).
% 3.15/3.36 ** KEPT (pick-wt=15): 207 [] -relation(A)|in(B,relation_rng(relation_rng_restriction(C,A)))| -in(B,C)| -in(B,relation_rng(A)).
% 3.15/3.36 ** KEPT (pick-wt=8): 208 [] -relation(A)|subset(relation_rng(relation_rng_restriction(B,A)),B).
% 3.15/3.36 ** KEPT (pick-wt=7): 209 [] -relation(A)|subset(relation_rng_restriction(B,A),A).
% 3.15/3.36 ** KEPT (pick-wt=9): 210 [] -relation(A)|subset(relation_rng(relation_rng_restriction(B,A)),relation_rng(A)).
% 3.15/3.36 ** KEPT (pick-wt=10): 211 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 3.15/3.36 ** KEPT (pick-wt=10): 212 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 3.15/3.36 ** KEPT (pick-wt=11): 213 [] -relation(A)|relation_rng(relation_rng_restriction(B,A))=set_intersection2(relation_rng(A),B).
% 3.15/3.36 ** KEPT (pick-wt=13): 214 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 3.15/3.36 ** KEPT (pick-wt=8): 215 [] -subset(A,B)|set_union2(A,B)=B.
% 3.15/3.36 ** KEPT (pick-wt=11): 216 [] -in(A,$f58(B))| -subset(C,A)|in(C,$f58(B)).
% 3.15/3.36 ** KEPT (pick-wt=9): 217 [] -in(A,$f58(B))|in(powerset(A),$f58(B)).
% 3.15/3.36 ** KEPT (pick-wt=12): 218 [] -subset(A,$f58(B))|are_e_quipotent(A,$f58(B))|in(A,$f58(B)).
% 3.15/3.36 ** KEPT (pick-wt=13): 220 [copy,219,flip.2] -relation(A)|relation_rng_restriction(B,relation_dom_restriction(A,C))=relation_dom_restriction(relation_rng_restriction(B,A),C).
% 3.15/3.36 ** KEPT (pick-wt=14): 221 [] -relation(A)| -in(B,relation_image(A,C))|in($f59(B,C,A),relation_dom(A)).
% 3.15/3.36 ** KEPT (pick-wt=15): 222 [] -relation(A)| -in(B,relation_image(A,C))|in(ordered_pair($f59(B,C,A),B),A).
% 3.15/3.36 ** KEPT (pick-wt=13): 223 [] -relation(A)| -in(B,relation_image(A,C))|in($f59(B,C,A),C).
% 3.15/3.36 ** KEPT (pick-wt=19): 224 [] -relation(A)|in(B,relation_image(A,C))| -in(D,relation_dom(A))| -in(ordered_pair(D,B),A)| -in(D,C).
% 3.15/3.36 ** KEPT (pick-wt=8): 225 [] -relation(A)|subset(relation_image(A,B),relation_rng(A)).
% 3.15/3.36 ** KEPT (pick-wt=12): 227 [copy,226,flip.2] -relation(A)|relation_image(A,set_intersection2(relation_dom(A),B))=relation_image(A,B).
% 3.15/3.36 ** KEPT (pick-wt=9): 229 [copy,228,flip.2] -relation(A)|relation_rng(A)=relation_image(A,relation_dom(A)).
% 3.15/3.36 ** KEPT (pick-wt=13): 230 [] -relation(A)| -relation(B)|relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A)).
% 3.15/3.36 ** KEPT (pick-wt=14): 231 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in($f60(B,C,A),relation_rng(A)).
% 3.15/3.36 ** KEPT (pick-wt=15): 232 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in(ordered_pair(B,$f60(B,C,A)),A).
% 3.15/3.36 ** KEPT (pick-wt=13): 233 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in($f60(B,C,A),C).
% 3.15/3.36 ** KEPT (pick-wt=19): 234 [] -relation(A)|in(B,relation_inverse_image(A,C))| -in(D,relation_rng(A))| -in(ordered_pair(B,D),A)| -in(D,C).
% 3.15/3.36 ** KEPT (pick-wt=8): 235 [] -relation(A)|subset(relation_inverse_image(A,B),relation_dom(A)).
% 3.15/3.36 ** KEPT (pick-wt=14): 236 [] -relation(A)|B=empty_set| -subset(B,relation_rng(A))|relation_inverse_image(A,B)!=empty_set.
% 3.15/3.36 ** KEPT (pick-wt=12): 237 [] -relation(A)| -subset(B,C)|subset(relation_inverse_image(A,B),relation_inverse_image(A,C)).
% 3.15/3.36 ** KEPT (pick-wt=11): 238 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 3.15/3.36 ** KEPT (pick-wt=6): 239 [] -in(A,B)|element(A,B).
% 3.15/3.36 ** KEPT (pick-wt=9): 240 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 3.15/3.36 ** KEPT (pick-wt=11): 241 [] -relation(A)| -in(ordered_pair(B,C),A)|in(B,relation_dom(A)).
% 3.15/3.36 ** KEPT (pick-wt=11): 242 [] -relation(A)| -in(ordered_pair(B,C),A)|in(C,relation_rng(A)).
% 3.15/3.36 ** KEPT (pick-wt=18): 243 [] -relation(A)| -function(A)| -relation(B)| -function(B)| -in(C,relation_dom(relation_composition(B,A)))|in(C,relation_dom(B)).
% 3.15/3.36 ** KEPT (pick-wt=20): 244 [] -relation(A)| -function(A)| -relation(B)| -function(B)| -in(C,relation_dom(relation_composition(B,A)))|in(apply(B,C),relation_dom(A)).
% 3.15/3.36 ** KEPT (pick-wt=24): 245 [] -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)).
% 3.15/3.36 ** KEPT (pick-wt=9): 246 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 3.15/3.36 ** KEPT (pick-wt=25): 247 [] -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)).
% 3.15/3.36 ** KEPT (pick-wt=23): 248 [] -relation(A)| -function(A)| -relation(B)| -function(B)| -in(C,relation_dom(A))|apply(relation_composition(A,B),C)=apply(B,apply(A,C)).
% 3.15/3.36 ** KEPT (pick-wt=12): 249 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_dom(A),relation_dom(B)).
% 3.15/3.36 ** KEPT (pick-wt=12): 250 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_rng(A),relation_rng(B)).
% 3.15/3.36 ** KEPT (pick-wt=10): 251 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 3.15/3.36 ** KEPT (pick-wt=8): 252 [] -subset(A,B)|set_intersection2(A,B)=A.
% 3.15/3.36 Following clause subsumed by 61 during input processing: 0 [] -element(A,B)|empty(B)|in(A,B).
% 3.15/3.36 ** KEPT (pick-wt=13): 253 [] -in($f61(A,B),A)| -in($f61(A,B),B)|A=B.
% 3.15/3.36 ** KEPT (pick-wt=11): 254 [] -relation(A)| -in(ordered_pair(B,C),A)|in(B,relation_field(A)).
% 3.15/3.36 ** KEPT (pick-wt=11): 255 [] -relation(A)| -in(ordered_pair(B,C),A)|in(C,relation_field(A)).
% 3.15/3.36 ** KEPT (pick-wt=10): 256 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 3.15/3.36 ** KEPT (pick-wt=10): 257 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 3.15/3.36 ** KEPT (pick-wt=10): 258 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 3.15/3.36 ** KEPT (pick-wt=12): 259 [] -relation(A)| -function(A)|A!=identity_relation(B)|relation_dom(A)=B.
% 3.15/3.36 ** KEPT (pick-wt=16): 260 [] -relation(A)| -function(A)|A!=identity_relation(B)| -in(C,B)|apply(A,C)=C.
% 3.15/3.36 ** KEPT (pick-wt=17): 261 [] -relation(A)| -function(A)|A=identity_relation(B)|relation_dom(A)!=B|in($f62(B,A),B).
% 3.15/3.36 ** KEPT (pick-wt=21): 262 [] -relation(A)| -function(A)|A=identity_relation(B)|relation_dom(A)!=B|apply(A,$f62(B,A))!=$f62(B,A).
% 3.15/3.36 ** KEPT (pick-wt=9): 263 [] -in(A,B)|apply(identity_relation(B),A)=A.
% 3.15/3.36 ** KEPT (pick-wt=8): 264 [] -relation(A)|relation_rng(A)=relation_dom(relation_inverse(A)).
% 3.15/3.36 ** KEPT (pick-wt=8): 266 [copy,265,flip.2] -relation(A)|relation_rng(relation_inverse(A))=relation_dom(A).
% 3.15/3.36 Following clause subsumed by 186 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 3.15/3.36 Following clause subsumed by 187 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 3.15/3.36 Following clause subsumed by 184 during input processing: 0 [] -subset(singleton(A),B)|in(A,B).
% 3.15/3.36 Following clause subsumed by 185 during input processing: 0 [] subset(singleton(A),B)| -in(A,B).
% 3.15/3.36 ** KEPT (pick-wt=8): 267 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 3.15/3.36 ** KEPT (pick-wt=8): 268 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 3.15/3.36 ** KEPT (pick-wt=11): 269 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 3.15/3.36 Following clause subsumed by 190 during input processing: 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 3.15/3.36 Following clause subsumed by 191 during input processing: 0 [] subset(A,singleton(B))|A!=empty_set.
% 3.15/3.36 Following clause subsumed by 12 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 3.15/3.36 ** KEPT (pick-wt=7): 270 [] -element(A,powerset(B))|subset(A,B).
% 3.15/3.36 ** KEPT (pick-wt=7): 271 [] element(A,powerset(B))| -subset(A,B).
% 3.15/3.36 ** KEPT (pick-wt=9): 272 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 3.15/3.36 ** KEPT (pick-wt=6): 273 [] -subset(A,empty_set)|A=empty_set.
% 3.15/3.36 ** KEPT (pick-wt=16): 274 [] -element(A,powerset(B))| -element(C,powerset(B))| -disjoint(A,C)|subset(A,subset_complement(B,C)).
% 3.15/3.36 ** KEPT (pick-wt=16): 275 [] -element(A,powerset(B))| -element(C,powerset(B))|disjoint(A,C)| -subset(A,subset_complement(B,C)).
% 3.15/3.36 ** KEPT (pick-wt=11): 276 [] -relation(A)| -relation(B)|subset(relation_dom(relation_composition(A,B)),relation_dom(A)).
% 3.15/3.36 ** KEPT (pick-wt=11): 277 [] -relation(A)| -relation(B)|subset(relation_rng(relation_composition(A,B)),relation_rng(B)).
% 3.15/3.36 ** KEPT (pick-wt=10): 279 [copy,278,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 3.15/3.36 ** KEPT (pick-wt=16): 280 [] -relation(A)| -relation(B)| -subset(relation_rng(A),relation_dom(B))|relation_dom(relation_composition(A,B))=relation_dom(A).
% 3.15/3.36 ** KEPT (pick-wt=13): 281 [] -element(A,powerset(powerset(B)))|A=empty_set|complements_of_subsets(B,A)!=empty_set.
% 3.15/3.36 Following clause subsumed by 182 during input processing: 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 3.15/3.36 ** KEPT (pick-wt=16): 282 [] -relation(A)| -relation(B)| -subset(relation_dom(A),relation_rng(B))|relation_rng(relation_composition(B,A))=relation_rng(A).
% 3.15/3.36 ** KEPT (pick-wt=21): 283 [] -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)).
% 3.15/3.36 ** KEPT (pick-wt=21): 284 [] -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)).
% 3.15/3.36 ** KEPT (pick-wt=10): 285 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 3.15/3.36 ** KEPT (pick-wt=8): 286 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 3.15/3.36 ** KEPT (pick-wt=18): 287 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 3.15/3.36 ** KEPT (pick-wt=19): 288 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)|relation_dom(B)=relation_rng(A).
% 3.15/3.36 ** KEPT (pick-wt=27): 289 [] -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)).
% 3.15/3.36 ** KEPT (pick-wt=28): 290 [] -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).
% 3.15/3.36 ** KEPT (pick-wt=27): 291 [] -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)).
% 3.15/3.36 ** KEPT (pick-wt=28): 292 [] -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).
% 3.15/3.36 ** KEPT (pick-wt=31): 293 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f66(A,B),relation_rng(A))|in($f65(A,B),relation_dom(A)).
% 3.15/3.36 ** KEPT (pick-wt=34): 295 [copy,294,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($f66(A,B),relation_rng(A))|apply(A,$f65(A,B))=$f66(A,B).
% 3.15/3.36 ** KEPT (pick-wt=34): 297 [copy,296,flip.8] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|apply(B,$f66(A,B))=$f65(A,B)|in($f65(A,B),relation_dom(A)).
% 3.15/3.36 ** KEPT (pick-wt=37): 299 [copy,298,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,$f66(A,B))=$f65(A,B)|apply(A,$f65(A,B))=$f66(A,B).
% 3.15/3.36 ** KEPT (pick-wt=49): 301 [copy,300,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($f65(A,B),relation_dom(A))|apply(A,$f65(A,B))!=$f66(A,B)| -in($f66(A,B),relation_rng(A))|apply(B,$f66(A,B))!=$f65(A,B).
% 3.15/3.36 ** KEPT (pick-wt=12): 302 [] -element(A,powerset(B))| -in(C,subset_complement(B,A))| -in(C,A).
% 3.15/3.36 ** KEPT (pick-wt=12): 303 [] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(A)=relation_dom(function_inverse(A)).
% 3.23/3.41 ** KEPT (pick-wt=12): 305 [copy,304,flip.4] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(function_inverse(A))=relation_dom(A).
% 3.23/3.41 ** KEPT (pick-wt=12): 306 [] -relation(A)|in(ordered_pair($f68(A),$f67(A)),A)|A=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=18): 308 [copy,307,flip.5] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_rng(A))|apply(A,apply(function_inverse(A),B))=B.
% 3.23/3.41 ** KEPT (pick-wt=18): 310 [copy,309,flip.5] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_rng(A))|apply(relation_composition(function_inverse(A),A),B)=B.
% 3.23/3.41 ** KEPT (pick-wt=9): 311 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 3.23/3.41 ** KEPT (pick-wt=6): 312 [] -subset(A,B)| -proper_subset(B,A).
% 3.23/3.41 ** KEPT (pick-wt=9): 313 [] -relation(A)| -function(A)| -one_to_one(A)|one_to_one(function_inverse(A)).
% 3.23/3.41 ** KEPT (pick-wt=9): 314 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 3.23/3.41 ** KEPT (pick-wt=9): 315 [] -relation(A)|relation_dom(A)!=empty_set|A=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=9): 316 [] -relation(A)|relation_rng(A)!=empty_set|A=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=10): 317 [] -relation(A)|relation_dom(A)!=empty_set|relation_rng(A)=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=10): 318 [] -relation(A)|relation_dom(A)=empty_set|relation_rng(A)!=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=9): 319 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 3.23/3.41 ** KEPT (pick-wt=20): 320 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_dom_restriction(B,C)|relation_dom(A)=set_intersection2(relation_dom(B),C).
% 3.23/3.41 ** KEPT (pick-wt=24): 321 [] -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).
% 3.23/3.41 ** KEPT (pick-wt=27): 322 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_dom_restriction(B,C)|relation_dom(A)!=set_intersection2(relation_dom(B),C)|in($f69(C,A,B),relation_dom(A)).
% 3.23/3.41 ** KEPT (pick-wt=33): 323 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_dom_restriction(B,C)|relation_dom(A)!=set_intersection2(relation_dom(B),C)|apply(A,$f69(C,A,B))!=apply(B,$f69(C,A,B)).
% 3.23/3.41 ** KEPT (pick-wt=5): 324 [] -empty(A)|A=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=8): 325 [] -subset(singleton(A),singleton(B))|A=B.
% 3.23/3.41 ** KEPT (pick-wt=9): 326 [] apply(relation_dom_restriction($c9,$c11),$c10)!=apply($c9,$c10).
% 3.23/3.41 ** KEPT (pick-wt=13): 327 [] -relation(A)| -in(ordered_pair(B,C),relation_composition(identity_relation(D),A))|in(B,D).
% 3.23/3.41 ** KEPT (pick-wt=15): 328 [] -relation(A)| -in(ordered_pair(B,C),relation_composition(identity_relation(D),A))|in(ordered_pair(B,C),A).
% 3.23/3.41 ** KEPT (pick-wt=18): 329 [] -relation(A)|in(ordered_pair(B,C),relation_composition(identity_relation(D),A))| -in(B,D)| -in(ordered_pair(B,C),A).
% 3.23/3.41 ** KEPT (pick-wt=5): 330 [] -in(A,B)| -empty(B).
% 3.23/3.41 ** KEPT (pick-wt=8): 331 [] -disjoint(A,B)|set_difference(A,B)=A.
% 3.23/3.41 ** KEPT (pick-wt=8): 332 [] disjoint(A,B)|set_difference(A,B)!=A.
% 3.23/3.41 ** KEPT (pick-wt=11): 333 [] -relation(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|in(B,C).
% 3.23/3.41 ** KEPT (pick-wt=12): 334 [] -relation(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|in(B,relation_dom(A)).
% 3.23/3.41 ** KEPT (pick-wt=15): 335 [] -relation(A)|in(B,relation_dom(relation_dom_restriction(A,C)))| -in(B,C)| -in(B,relation_dom(A)).
% 3.23/3.41 ** KEPT (pick-wt=7): 336 [] -relation(A)|subset(relation_dom_restriction(A,B),A).
% 3.23/3.41 ** KEPT (pick-wt=7): 337 [] -empty(A)|A=B| -empty(B).
% 3.23/3.41 Following clause subsumed by 241 during input processing: 0 [] -relation(A)| -function(A)| -in(ordered_pair(B,C),A)|in(B,relation_dom(A)).
% 3.23/3.41 ** KEPT (pick-wt=14): 338 [] -relation(A)| -function(A)| -in(ordered_pair(B,C),A)|C=apply(A,B).
% 3.23/3.41 Following clause subsumed by 90 during input processing: 0 [] -relation(A)| -function(A)|in(ordered_pair(B,C),A)| -in(B,relation_dom(A))|C!=apply(A,B).
% 3.23/3.41 ** KEPT (pick-wt=11): 339 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 3.23/3.41 ** KEPT (pick-wt=9): 340 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 3.23/3.41 ** KEPT (pick-wt=11): 341 [] -relation(A)|relation_dom(relation_dom_restriction(A,B))=set_intersection2(relation_dom(A),B).
% 3.23/3.41 Following clause subsumed by 192 during input processing: 0 [] -in(A,B)|subset(A,union(B)).
% 3.23/3.41 ** KEPT (pick-wt=10): 342 [] -relation(A)|relation_dom_restriction(A,B)=relation_composition(identity_relation(B),A).
% 3.23/3.41 ** KEPT (pick-wt=9): 343 [] -relation(A)|subset(relation_rng(relation_dom_restriction(A,B)),relation_rng(A)).
% 3.23/3.41 ** KEPT (pick-wt=11): 344 [] -in(A,$f71(B))| -subset(C,A)|in(C,$f71(B)).
% 3.23/3.41 ** KEPT (pick-wt=10): 345 [] -in(A,$f71(B))|in($f70(B,A),$f71(B)).
% 3.23/3.41 ** KEPT (pick-wt=12): 346 [] -in(A,$f71(B))| -subset(C,A)|in(C,$f70(B,A)).
% 3.23/3.41 ** KEPT (pick-wt=12): 347 [] -subset(A,$f71(B))|are_e_quipotent(A,$f71(B))|in(A,$f71(B)).
% 3.23/3.41 ** KEPT (pick-wt=9): 348 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 3.23/3.41 84 back subsumes 81.
% 3.23/3.41 239 back subsumes 62.
% 3.23/3.41 338 back subsumes 91.
% 3.23/3.41 354 back subsumes 353.
% 3.23/3.41 358 back subsumes 357.
% 3.23/3.41
% 3.23/3.41 ------------> process sos:
% 3.23/3.41 ** KEPT (pick-wt=3): 474 [] A=A.
% 3.23/3.41 ** KEPT (pick-wt=7): 475 [] unordered_pair(A,B)=unordered_pair(B,A).
% 3.23/3.41 ** KEPT (pick-wt=7): 476 [] set_union2(A,B)=set_union2(B,A).
% 3.23/3.41 ** KEPT (pick-wt=7): 477 [] set_intersection2(A,B)=set_intersection2(B,A).
% 3.23/3.41 ** KEPT (pick-wt=6): 478 [] relation(A)|in($f15(A),A).
% 3.23/3.41 ** KEPT (pick-wt=14): 479 [] A=singleton(B)|in($f19(B,A),A)|$f19(B,A)=B.
% 3.23/3.41 ** KEPT (pick-wt=7): 480 [] A=empty_set|in($f20(A),A).
% 3.23/3.41 ** KEPT (pick-wt=14): 481 [] A=powerset(B)|in($f21(B,A),A)|subset($f21(B,A),B).
% 3.23/3.41 ** KEPT (pick-wt=23): 482 [] A=unordered_pair(B,C)|in($f24(B,C,A),A)|$f24(B,C,A)=B|$f24(B,C,A)=C.
% 3.23/3.41 ** KEPT (pick-wt=23): 483 [] A=set_union2(B,C)|in($f25(B,C,A),A)|in($f25(B,C,A),B)|in($f25(B,C,A),C).
% 3.23/3.41 ** KEPT (pick-wt=17): 484 [] A=cartesian_product2(B,C)|in($f30(B,C,A),A)|in($f29(B,C,A),B).
% 3.23/3.41 ** KEPT (pick-wt=17): 485 [] A=cartesian_product2(B,C)|in($f30(B,C,A),A)|in($f28(B,C,A),C).
% 3.23/3.41 ** KEPT (pick-wt=25): 487 [copy,486,flip.3] A=cartesian_product2(B,C)|in($f30(B,C,A),A)|ordered_pair($f29(B,C,A),$f28(B,C,A))=$f30(B,C,A).
% 3.23/3.41 ** KEPT (pick-wt=8): 488 [] subset(A,B)|in($f33(A,B),A).
% 3.23/3.41 ** KEPT (pick-wt=17): 489 [] A=set_intersection2(B,C)|in($f34(B,C,A),A)|in($f34(B,C,A),B).
% 3.23/3.41 ** KEPT (pick-wt=17): 490 [] A=set_intersection2(B,C)|in($f34(B,C,A),A)|in($f34(B,C,A),C).
% 3.23/3.41 ** KEPT (pick-wt=4): 491 [] cast_to_subset(A)=A.
% 3.23/3.41 ---> New Demodulator: 492 [new_demod,491] cast_to_subset(A)=A.
% 3.23/3.41 ** KEPT (pick-wt=16): 493 [] A=union(B)|in($f40(B,A),A)|in($f40(B,A),$f39(B,A)).
% 3.23/3.41 ** KEPT (pick-wt=14): 494 [] A=union(B)|in($f40(B,A),A)|in($f39(B,A),B).
% 3.23/3.41 ** KEPT (pick-wt=17): 495 [] A=set_difference(B,C)|in($f41(B,C,A),A)|in($f41(B,C,A),B).
% 3.23/3.41 ** KEPT (pick-wt=10): 497 [copy,496,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 3.23/3.41 ---> New Demodulator: 498 [new_demod,497] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 3.23/3.41 ** KEPT (pick-wt=4): 500 [copy,499,demod,492] element(A,powerset(A)).
% 3.23/3.41 ** KEPT (pick-wt=3): 501 [] relation(identity_relation(A)).
% 3.23/3.41 ** KEPT (pick-wt=4): 502 [] element($f54(A),A).
% 3.23/3.41 ** KEPT (pick-wt=2): 503 [] empty(empty_set).
% 3.23/3.41 ** KEPT (pick-wt=2): 504 [] relation(empty_set).
% 3.23/3.41 ** KEPT (pick-wt=2): 505 [] relation_empty_yielding(empty_set).
% 3.23/3.41 Following clause subsumed by 503 during input processing: 0 [] empty(empty_set).
% 3.23/3.41 Following clause subsumed by 501 during input processing: 0 [] relation(identity_relation(A)).
% 3.23/3.41 ** KEPT (pick-wt=3): 506 [] function(identity_relation(A)).
% 3.23/3.41 Following clause subsumed by 503 during input processing: 0 [] empty(empty_set).
% 3.23/3.41 Following clause subsumed by 504 during input processing: 0 [] relation(empty_set).
% 3.23/3.41 ** KEPT (pick-wt=5): 507 [] set_union2(A,A)=A.
% 3.23/3.41 ---> New Demodulator: 508 [new_demod,507] set_union2(A,A)=A.
% 3.23/3.41 ** KEPT (pick-wt=5): 509 [] set_intersection2(A,A)=A.
% 3.23/3.41 ---> New Demodulator: 510 [new_demod,509] set_intersection2(A,A)=A.
% 3.23/3.41 ** KEPT (pick-wt=7): 511 [] in(A,B)|disjoint(singleton(A),B).
% 3.23/3.41 ** KEPT (pick-wt=9): 512 [] in($f55(A,B),A)|element(A,powerset(B)).
% 3.23/3.41 ** KEPT (pick-wt=2): 513 [] relation($c1).
% 3.23/3.41 ** KEPT (pick-wt=2): 514 [] function($c1).
% 3.23/3.41 ** KEPT (pick-wt=2): 515 [] empty($c2).
% 3.23/3.41 ** KEPT (pick-wt=2): 516 [] relation($c2).
% 3.23/3.41 ** KEPT (pick-wt=7): 517 [] empty(A)|element($f56(A),powerset(A)).
% 3.23/3.41 ** KEPT (pick-wt=2): 518 [] empty($c3).
% 3.23/3.41 ** KEPT (pick-wt=2): 519 [] relation($c4).
% 3.23/3.41 ** KEPT (pick-wt=2): 520 [] empty($c4).
% 3.23/3.41 ** KEPT (pick-wt=2): 521 [] function($c4).
% 3.23/3.41 ** KEPT (pick-wt=2): 522 [] relation($c5).
% 3.23/3.41 ** KEPT (pick-wt=5): 523 [] element($f57(A),powerset(A)).
% 3.23/3.41 ** KEPT (pick-wt=3): 524 [] empty($f57(A)).
% 3.23/3.41 ** KEPT (pick-wt=2): 525 [] relation($c7).
% 3.23/3.41 ** KEPT (pick-wt=2): 526 [] function($c7).
% 3.23/3.41 ** KEPT (pick-wt=2): 527 [] one_to_one($c7).
% 3.23/3.41 ** KEPT (pick-wt=2): 528 [] relation($c8).
% 3.23/3.41 ** KEPT (pick-wt=2): 529 [] relation_empty_yielding($c8).
% 3.23/3.41 ** KEPT (pick-wt=3): 530 [] subset(A,A).
% 3.23/3.41 ** KEPT (pick-wt=4): 531 [] in(A,$f58(A)).
% 3.23/3.41 ** KEPT (pick-wt=5): 532 [] subset(set_intersection2(A,B),A).
% 3.23/3.41 ** KEPT (pick-wt=5): 533 [] set_union2(A,empty_set)=A.
% 3.23/3.41 ---> New Demodulator: 534 [new_demod,533] set_union2(A,empty_set)=A.
% 3.23/3.41 ** KEPT (pick-wt=5): 536 [copy,535,flip.1] singleton(empty_set)=powerset(empty_set).
% 3.23/3.41 ---> New Demodulator: 537 [new_demod,536] singleton(empty_set)=powerset(empty_set).
% 3.23/3.41 ** KEPT (pick-wt=5): 538 [] set_intersection2(A,empty_set)=empty_set.
% 3.23/3.41 ---> New Demodulator: 539 [new_demod,538] set_intersection2(A,empty_set)=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=13): 540 [] in($f61(A,B),A)|in($f61(A,B),B)|A=B.
% 3.23/3.41 ** KEPT (pick-wt=3): 541 [] subset(empty_set,A).
% 3.23/3.41 ** KEPT (pick-wt=5): 542 [] subset(set_difference(A,B),A).
% 3.23/3.41 ** KEPT (pick-wt=9): 543 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 3.23/3.41 ---> New Demodulator: 544 [new_demod,543] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 3.23/3.41 ** KEPT (pick-wt=5): 545 [] set_difference(A,empty_set)=A.
% 3.23/3.41 ---> New Demodulator: 546 [new_demod,545] set_difference(A,empty_set)=A.
% 3.23/3.41 ** KEPT (pick-wt=8): 547 [] disjoint(A,B)|in($f63(A,B),A).
% 3.23/3.41 ** KEPT (pick-wt=8): 548 [] disjoint(A,B)|in($f63(A,B),B).
% 3.23/3.41 ** KEPT (pick-wt=9): 549 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 3.23/3.41 ---> New Demodulator: 550 [new_demod,549] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 3.23/3.41 ** KEPT (pick-wt=9): 552 [copy,551,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 3.23/3.41 ---> New Demodulator: 553 [new_demod,552] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 3.23/3.41 ** KEPT (pick-wt=5): 554 [] set_difference(empty_set,A)=empty_set.
% 3.23/3.41 ---> New Demodulator: 555 [new_demod,554] set_difference(empty_set,A)=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=12): 557 [copy,556,demod,553] disjoint(A,B)|in($f64(A,B),set_difference(A,set_difference(A,B))).
% 3.23/3.41 ** KEPT (pick-wt=4): 558 [] relation_dom(empty_set)=empty_set.
% 3.23/3.41 ---> New Demodulator: 559 [new_demod,558] relation_dom(empty_set)=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=4): 560 [] relation_rng(empty_set)=empty_set.
% 3.23/3.41 ---> New Demodulator: 561 [new_demod,560] relation_rng(empty_set)=empty_set.
% 3.23/3.41 ** KEPT (pick-wt=9): 562 [] set_difference(A,singleton(B))=A|in(B,A).
% 3.23/3.41 ** KEPT (pick-wt=6): 564 [copy,563,flip.1] singleton(A)=unordered_pair(A,A).
% 3.23/3.41 ---> New Demodulator: 565 [new_demod,564] singleton(A)=unordered_pair(A,A).
% 3.23/3.41 ** KEPT (pick-wt=2): 566 [] relation($c9).
% 3.23/3.41 ** KEPT (pick-wt=2): 567 [] function($c9).
% 3.23/3.41 ** KEPT (pick-wt=6): 568 [] in($c10,relation_dom(relation_dom_restriction($c9,$c11))).
% 3.23/3.41 ** KEPT (pick-wt=5): 569 [] relation_dom(identity_relation(A))=A.
% 3.23/3.41 ---> New Demodulator: 570 [new_demod,569] relation_dom(identity_relation(A))=A.
% 3.23/3.41 ** KEPT (pick-wt=5): 571 [] relation_rng(identity_relation(A))=A.
% 3.23/3.41 ---> New Demodulator: 572 [new_demod,571] relation_rng(identity_relation(A))=A.
% 3.23/3.41 ** KEPT (pick-wt=5): 573 [] subset(A,set_union2(A,B)).
% 3.23/3.41 ** KEPT (pick-wt=5): 574 [] union(powerset(A))=A.
% 3.23/3.41 ---> New Demodulator: 575 [new_demod,574] union(powerset(A))=A.
% 3.23/3.41 ** KEPT (pick-wt=4): 576 [] in(A,$f71(A)).
% 3.23/3.41 Following clause subsumed by 474 during input processing: 0 [copy,474,flip.1] A=A.
% 3.23/3.41 474 back subsumes 462.
% 3.23/3.41 474 back subsumes 458.
% 3.23/3.41 474 back subsumes 438.
% 3.23/3.41 474 back subsumes 389.
% 3.23/3.41 474 back subsumes 366.
% 3.23/3.41 474 back subsumes 365.
% 3.23/3.41 474 back subsumes 351.
% 3.23/3.41 Following clause subsumed by 475 during input processing: 0 [copy,475,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 3.23/3.41 Following clause subsumed by 476 during input processing: 0 [copy,476,flip.1] set_union2(A,B)=set_union2(B,A).
% 3.23/3.41 ** KEPT (pick-wt=11): 577 [copy,477,flip.1,demod,553,553] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 3.23/3.41 >>>> Starting back demodulation with 492.
% 11.85/12.03 >> back demodulating 284 with 492.
% 11.85/12.03 >> back demodulating 283 with 492.
% 11.85/12.03 >>>> Starting back demodulation with 498.
% 11.85/12.03 >>>> Starting back demodulation with 508.
% 11.85/12.03 >> back demodulating 463 with 508.
% 11.85/12.03 >> back demodulating 420 with 508.
% 11.85/12.03 >> back demodulating 369 with 508.
% 11.85/12.03 >>>> Starting back demodulation with 510.
% 11.85/12.03 >> back demodulating 465 with 510.
% 11.85/12.03 >> back demodulating 430 with 510.
% 11.85/12.03 >> back demodulating 419 with 510.
% 11.85/12.03 >> back demodulating 381 with 510.
% 11.85/12.03 >> back demodulating 378 with 510.
% 11.85/12.03 530 back subsumes 437.
% 11.85/12.03 530 back subsumes 436.
% 11.85/12.03 530 back subsumes 377.
% 11.85/12.03 530 back subsumes 376.
% 11.85/12.03 >>>> Starting back demodulation with 534.
% 11.85/12.03 >>>> Starting back demodulation with 537.
% 11.85/12.03 >>>> Starting back demodulation with 539.
% 11.85/12.03 >>>> Starting back demodulation with 544.
% 11.85/12.03 >> back demodulating 279 with 544.
% 11.85/12.03 >>>> Starting back demodulation with 546.
% 11.85/12.03 >>>> Starting back demodulation with 550.
% 11.85/12.03 >>>> Starting back demodulation with 553.
% 11.85/12.03 >> back demodulating 538 with 553.
% 11.85/12.03 >> back demodulating 532 with 553.
% 11.85/12.03 >> back demodulating 509 with 553.
% 11.85/12.03 >> back demodulating 490 with 553.
% 11.85/12.03 >> back demodulating 489 with 553.
% 11.85/12.03 >> back demodulating 477 with 553.
% 11.85/12.03 >> back demodulating 460 with 553.
% 11.85/12.03 >> back demodulating 459 with 553.
% 11.85/12.03 >> back demodulating 457 with 553.
% 11.85/12.03 >> back demodulating 380 with 553.
% 11.85/12.03 >> back demodulating 379 with 553.
% 11.85/12.03 >> back demodulating 341 with 553.
% 11.85/12.03 >> back demodulating 323 with 553.
% 11.85/12.03 >> back demodulating 322 with 553.
% 11.85/12.03 >> back demodulating 320 with 553.
% 11.85/12.03 >> back demodulating 286 with 553.
% 11.85/12.03 >> back demodulating 252 with 553.
% 11.85/12.03 >> back demodulating 251 with 553.
% 11.85/12.03 >> back demodulating 238 with 553.
% 11.85/12.03 >> back demodulating 227 with 553.
% 11.85/12.03 >> back demodulating 213 with 553.
% 11.85/12.03 >> back demodulating 158 with 553.
% 11.85/12.03 >> back demodulating 119 with 553.
% 11.85/12.03 >> back demodulating 118 with 553.
% 11.85/12.03 >> back demodulating 89 with 553.
% 11.85/12.03 >> back demodulating 88 with 553.
% 11.85/12.03 >> back demodulating 87 with 553.
% 11.85/12.03 >> back demodulating 86 with 553.
% 11.85/12.03 >>>> Starting back demodulation with 555.
% 11.85/12.03 >>>> Starting back demodulation with 559.
% 11.85/12.03 >>>> Starting back demodulation with 561.
% 11.85/12.03 >>>> Starting back demodulation with 565.
% 11.85/12.03 >> back demodulating 562 with 565.
% 11.85/12.03 >> back demodulating 536 with 565.
% 11.85/12.03 >> back demodulating 511 with 565.
% 11.85/12.03 >> back demodulating 497 with 565.
% 11.85/12.03 >> back demodulating 479 with 565.
% 11.85/12.03 >> back demodulating 348 with 565.
% 11.85/12.03 >> back demodulating 340 with 565.
% 11.85/12.03 >> back demodulating 325 with 565.
% 11.85/12.03 >> back demodulating 319 with 565.
% 11.85/12.03 >> back demodulating 191 with 565.
% 11.85/12.03 >> back demodulating 190 with 565.
% 11.85/12.03 >> back demodulating 189 with 565.
% 11.85/12.03 >> back demodulating 185 with 565.
% 11.85/12.03 >> back demodulating 184 with 565.
% 11.85/12.03 >> back demodulating 183 with 565.
% 11.85/12.03 >> back demodulating 182 with 565.
% 11.85/12.03 >> back demodulating 181 with 565.
% 11.85/12.03 >> back demodulating 162 with 565.
% 11.85/12.03 >> back demodulating 52 with 565.
% 11.85/12.03 >> back demodulating 51 with 565.
% 11.85/12.03 >> back demodulating 50 with 565.
% 11.85/12.03 >>>> Starting back demodulation with 570.
% 11.85/12.03 >>>> Starting back demodulation with 572.
% 11.85/12.03 >>>> Starting back demodulation with 575.
% 11.85/12.03 Following clause subsumed by 577 during input processing: 0 [copy,577,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 11.85/12.03 587 back subsumes 57.
% 11.85/12.03 589 back subsumes 58.
% 11.85/12.03 >>>> Starting back demodulation with 591.
% 11.85/12.03 >> back demodulating 423 with 591.
% 11.85/12.03 >>>> Starting back demodulation with 616.
% 11.85/12.03 >>>> Starting back demodulation with 619.
% 11.85/12.03
% 11.85/12.03 ======= end of input processing =======
% 11.85/12.03
% 11.85/12.03 =========== start of search ===========
% 11.85/12.03
% 11.85/12.03
% 11.85/12.03 Resetting weight limit to 2.
% 11.85/12.03
% 11.85/12.03
% 11.85/12.03 Resetting weight limit to 2.
% 11.85/12.03
% 11.85/12.03 sos_size=119
% 11.85/12.03
% 11.85/12.03 Search stopped because sos empty.
% 11.85/12.03
% 11.85/12.03
% 11.85/12.03 Search stopped because sos empty.
% 11.85/12.03
% 11.85/12.03 ============ end of search ============
% 11.85/12.03
% 11.85/12.03 -------------- statistics -------------
% 11.85/12.03 clauses given 128
% 11.85/12.03 clauses generated 463009
% 11.85/12.03 clauses kept 596
% 11.85/12.03 clauses forward subsumed 219
% 11.85/12.03 clauses back subsumed 18
% 11.85/12.03 Kbytes malloced 7812
% 11.85/12.03
% 11.85/12.03 ----------- times (seconds) -----------
% 11.85/12.03 user CPU time 8.71 (0 hr, 0 min, 8 sec)
% 11.85/12.03 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 11.85/12.03 wall-clock time 12 (0 hr, 0 min, 12 sec)
% 11.85/12.03
% 11.85/12.03 Process 8569 finished Wed Jul 27 07:39:53 2022
% 11.85/12.03 Otter interrupted
% 11.85/12.03 PROOF NOT FOUND
%------------------------------------------------------------------------------