TSTP Solution File: SEU212+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU212+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:15:10 EDT 2022
% Result : Unknown 9.71s 9.84s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU212+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 08:09:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.01/3.21 ----- Otter 3.3f, August 2004 -----
% 3.01/3.21 The process was started by sandbox2 on n027.cluster.edu,
% 3.01/3.21 Wed Jul 27 08:09:52 2022
% 3.01/3.21 The command was "./otter". The process ID is 13964.
% 3.01/3.21
% 3.01/3.21 set(prolog_style_variables).
% 3.01/3.21 set(auto).
% 3.01/3.21 dependent: set(auto1).
% 3.01/3.21 dependent: set(process_input).
% 3.01/3.21 dependent: clear(print_kept).
% 3.01/3.21 dependent: clear(print_new_demod).
% 3.01/3.21 dependent: clear(print_back_demod).
% 3.01/3.21 dependent: clear(print_back_sub).
% 3.01/3.21 dependent: set(control_memory).
% 3.01/3.21 dependent: assign(max_mem, 12000).
% 3.01/3.21 dependent: assign(pick_given_ratio, 4).
% 3.01/3.21 dependent: assign(stats_level, 1).
% 3.01/3.21 dependent: assign(max_seconds, 10800).
% 3.01/3.21 clear(print_given).
% 3.01/3.21
% 3.01/3.21 formula_list(usable).
% 3.01/3.21 all A (A=A).
% 3.01/3.21 all A B (in(A,B)-> -in(B,A)).
% 3.01/3.21 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 3.01/3.21 all A (empty(A)->function(A)).
% 3.01/3.21 all A (empty(A)->relation(A)).
% 3.01/3.21 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 3.01/3.21 all A B (set_union2(A,B)=set_union2(B,A)).
% 3.01/3.21 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 3.01/3.21 all A B (relation(B)-> (B=identity_relation(A)<-> (all C D (in(ordered_pair(C,D),B)<->in(C,A)&C=D)))).
% 3.01/3.21 all A B (A=B<->subset(A,B)&subset(B,A)).
% 3.01/3.21 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))))))).
% 3.01/3.21 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))))))).
% 3.01/3.21 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)))))))).
% 3.01/3.21 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)))))))).
% 3.01/3.21 all A (relation(A)<-> (all B (-(in(B,A)& (all C D (B!=ordered_pair(C,D))))))).
% 3.01/3.21 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))).
% 3.01/3.21 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 3.01/3.21 all A (A=empty_set<-> (all B (-in(B,A)))).
% 3.01/3.21 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 3.01/3.21 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))))))).
% 3.01/3.21 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 3.01/3.21 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 3.01/3.21 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 3.01/3.21 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)))))).
% 3.01/3.21 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))))))).
% 3.01/3.21 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 3.01/3.21 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 3.01/3.21 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))))).
% 3.01/3.21 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 3.01/3.21 all A (cast_to_subset(A)=A).
% 3.01/3.21 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 3.01/3.21 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 3.01/3.21 all A (relation(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(D,C),A))))))).
% 3.01/3.21 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 3.01/3.21 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 3.01/3.21 all A (relation(A)->relation_field(A)=set_union2(relation_dom(A),relation_rng(A))).
% 3.01/3.21 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))))))).
% 3.01/3.21 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 3.01/3.21 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))))))))))).
% 3.01/3.21 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)))))))).
% 3.01/3.21 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 all A element(cast_to_subset(A),powerset(A)).
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 all A (relation(A)->relation(relation_inverse(A))).
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 all A B (relation(A)&relation(B)->relation(relation_composition(A,B))).
% 3.01/3.21 all A B (element(B,powerset(powerset(A)))->element(union_of_subsets(A,B),powerset(A))).
% 3.01/3.21 all A relation(identity_relation(A)).
% 3.01/3.21 all A B (element(B,powerset(powerset(A)))->element(meet_of_subsets(A,B),powerset(A))).
% 3.01/3.21 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_difference(A,B,C),powerset(A))).
% 3.01/3.21 all A B (relation(A)->relation(relation_dom_restriction(A,B))).
% 3.01/3.21 all A B (element(B,powerset(powerset(A)))->element(complements_of_subsets(A,B),powerset(powerset(A)))).
% 3.01/3.21 all A B (relation(B)->relation(relation_rng_restriction(A,B))).
% 3.01/3.21 $T.
% 3.01/3.21 $T.
% 3.01/3.21 all A exists B element(B,A).
% 3.01/3.21 all A B (empty(A)&relation(B)->empty(relation_composition(B,A))&relation(relation_composition(B,A))).
% 3.01/3.21 empty(empty_set).
% 3.01/3.21 relation(empty_set).
% 3.01/3.21 relation_empty_yielding(empty_set).
% 3.01/3.21 all A B (relation(A)&relation(B)->relation(set_intersection2(A,B))).
% 3.01/3.21 all A (-empty(powerset(A))).
% 3.01/3.21 empty(empty_set).
% 3.01/3.21 all A B (-empty(ordered_pair(A,B))).
% 3.01/3.21 all A B (relation(A)&relation(B)->relation(set_union2(A,B))).
% 3.01/3.21 all A (-empty(singleton(A))).
% 3.01/3.21 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 3.01/3.21 all A B (-empty(unordered_pair(A,B))).
% 3.01/3.21 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 3.01/3.21 empty(empty_set).
% 3.01/3.21 relation(empty_set).
% 3.01/3.21 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 3.01/3.21 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 3.01/3.21 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 3.01/3.21 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 3.01/3.21 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 3.01/3.21 all A B (empty(A)&relation(B)->empty(relation_composition(A,B))&relation(relation_composition(A,B))).
% 3.01/3.21 all A B (set_union2(A,A)=A).
% 3.01/3.21 all A B (set_intersection2(A,A)=A).
% 3.01/3.21 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 3.01/3.21 all A (relation(A)->relation_inverse(relation_inverse(A))=A).
% 3.01/3.21 all A B (element(B,powerset(powerset(A)))->complements_of_subsets(A,complements_of_subsets(A,B))=B).
% 3.01/3.21 all A B (-proper_subset(A,A)).
% 3.01/3.21 all A (singleton(A)!=empty_set).
% 3.01/3.21 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 3.01/3.21 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 3.01/3.21 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 3.01/3.21 all A B (subset(singleton(A),B)<->in(A,B)).
% 3.01/3.21 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 3.01/3.21 all A B (element(B,powerset(A))-> (all C (in(C,B)->in(C,A)))).
% 3.01/3.21 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 3.01/3.21 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 3.01/3.21 all A B (in(A,B)->subset(A,union(B))).
% 3.01/3.21 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 3.01/3.21 all A B ((all C (in(C,A)->in(C,B)))->element(A,powerset(B))).
% 3.01/3.21 exists A (relation(A)&function(A)).
% 3.01/3.21 exists A (empty(A)&relation(A)).
% 3.01/3.21 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 3.01/3.21 exists A empty(A).
% 3.01/3.21 exists A (-empty(A)&relation(A)).
% 3.01/3.21 all A exists B (element(B,powerset(A))&empty(B)).
% 3.01/3.21 exists A (-empty(A)).
% 3.01/3.21 exists A (relation(A)&relation_empty_yielding(A)).
% 3.01/3.21 all A B (element(B,powerset(powerset(A)))->union_of_subsets(A,B)=union(B)).
% 3.01/3.21 all A B (element(B,powerset(powerset(A)))->meet_of_subsets(A,B)=set_meet(B)).
% 3.01/3.21 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_difference(A,B,C)=set_difference(B,C)).
% 3.01/3.21 all A B subset(A,A).
% 3.01/3.21 all A B (disjoint(A,B)->disjoint(B,A)).
% 3.01/3.21 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 3.01/3.21 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 3.01/3.21 all A B C (relation(C)-> (in(A,relation_rng(relation_rng_restriction(B,C)))<->in(A,B)&in(A,relation_rng(C)))).
% 3.01/3.21 all A B (relation(B)->subset(relation_rng(relation_rng_restriction(A,B)),A)).
% 3.01/3.21 all A B (relation(B)->subset(relation_rng_restriction(A,B),B)).
% 3.01/3.21 all A B (relation(B)->subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))).
% 3.01/3.22 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))).
% 3.01/3.22 all A B (relation(B)->relation_rng(relation_rng_restriction(A,B))=set_intersection2(relation_rng(B),A)).
% 3.01/3.22 all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 3.01/3.22 all A B (subset(A,B)->set_union2(A,B)=B).
% 3.01/3.22 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))))).
% 3.01/3.22 all A B C (relation(C)->relation_dom_restriction(relation_rng_restriction(A,C),B)=relation_rng_restriction(A,relation_dom_restriction(C,B))).
% 3.01/3.22 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))))).
% 3.01/3.22 all A B (relation(B)->subset(relation_image(B,A),relation_rng(B))).
% 3.01/3.22 all A B (relation(B)->relation_image(B,A)=relation_image(B,set_intersection2(relation_dom(B),A))).
% 3.01/3.22 all A (relation(A)->relation_image(A,relation_dom(A))=relation_rng(A)).
% 3.01/3.22 all A (relation(A)-> (all B (relation(B)->relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A))))).
% 3.01/3.22 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))))).
% 3.01/3.22 all A B (relation(B)->subset(relation_inverse_image(B,A),relation_dom(B))).
% 3.01/3.22 all A B (relation(B)-> -(A!=empty_set&subset(A,relation_rng(B))&relation_inverse_image(B,A)=empty_set)).
% 3.01/3.22 all A B C (relation(C)-> (subset(A,B)->subset(relation_inverse_image(C,A),relation_inverse_image(C,B)))).
% 3.01/3.22 all A B subset(set_intersection2(A,B),A).
% 3.01/3.22 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 3.01/3.22 all A (set_union2(A,empty_set)=A).
% 3.01/3.22 all A B (in(A,B)->element(A,B)).
% 3.01/3.22 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 3.01/3.22 powerset(empty_set)=singleton(empty_set).
% 3.01/3.22 all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_dom(C))&in(B,relation_rng(C)))).
% 3.01/3.22 all A (relation(A)->subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))).
% 3.01/3.22 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)))))).
% 3.01/3.22 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 3.01/3.22 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 3.01/3.22 all A (set_intersection2(A,empty_set)=empty_set).
% 3.01/3.22 all A B (element(A,B)->empty(B)|in(A,B)).
% 3.01/3.22 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 3.01/3.22 all A subset(empty_set,A).
% 3.01/3.22 all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_field(C))&in(B,relation_field(C)))).
% 3.01/3.22 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 3.01/3.22 all A B C D (ordered_pair(A,B)=ordered_pair(C,D)->A=C&B=D).
% 3.01/3.22 all A B subset(set_difference(A,B),A).
% 3.01/3.22 all A (relation(A)->relation_rng(A)=relation_dom(relation_inverse(A))&relation_dom(A)=relation_rng(relation_inverse(A))).
% 3.01/3.22 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 3.01/3.22 all A B (subset(singleton(A),B)<->in(A,B)).
% 3.01/3.22 all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C)).
% 3.01/3.22 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 3.01/3.22 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 3.01/3.22 all A (set_difference(A,empty_set)=A).
% 3.01/3.22 all A B (element(A,powerset(B))<->subset(A,B)).
% 3.01/3.22 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))).
% 3.01/3.22 all A (subset(A,empty_set)->A=empty_set).
% 3.01/3.22 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 3.01/3.22 all A B (element(B,powerset(A))-> (all C (element(C,powerset(A))-> (disjoint(B,C)<->subset(B,subset_complement(A,C)))))).
% 3.01/3.22 all A (relation(A)-> (all B (relation(B)->subset(relation_dom(relation_composition(A,B)),relation_dom(A))))).
% 3.01/3.22 all A (relation(A)-> (all B (relation(B)->subset(relation_rng(relation_composition(A,B)),relation_rng(B))))).
% 3.01/3.22 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 3.01/3.22 all A (relation(A)-> (all B (relation(B)-> (subset(relation_rng(A),relation_dom(B))->relation_dom(relation_composition(A,B))=relation_dom(A))))).
% 3.01/3.22 all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set)).
% 3.01/3.22 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 3.01/3.22 all A (relation(A)-> (all B (relation(B)-> (subset(relation_dom(A),relation_rng(B))->relation_rng(relation_composition(B,A))=relation_rng(A))))).
% 3.01/3.22 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)))).
% 3.01/3.22 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)))).
% 3.01/3.22 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 3.01/3.22 all A (set_difference(empty_set,A)=empty_set).
% 3.01/3.22 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 3.01/3.22 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))).
% 3.01/3.22 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)))))))).
% 3.01/3.22 all A B C (element(C,powerset(A))-> -(in(B,subset_complement(A,C))&in(B,C))).
% 3.01/3.22 all A (relation(A)-> ((all B C (-in(ordered_pair(B,C),A)))->A=empty_set)).
% 3.01/3.22 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 3.01/3.22 relation_dom(empty_set)=empty_set.
% 3.01/3.22 relation_rng(empty_set)=empty_set.
% 3.01/3.22 all A B (-(subset(A,B)&proper_subset(B,A))).
% 3.01/3.22 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 3.01/3.22 all A (relation(A)-> (relation_dom(A)=empty_set|relation_rng(A)=empty_set->A=empty_set)).
% 3.01/3.22 all A (relation(A)-> (relation_dom(A)=empty_set<->relation_rng(A)=empty_set)).
% 3.01/3.22 all A B (set_difference(A,singleton(B))=A<-> -in(B,A)).
% 3.01/3.22 all A (unordered_pair(A,A)=singleton(A)).
% 3.01/3.22 all A (empty(A)->A=empty_set).
% 3.01/3.22 all A B (subset(singleton(A),singleton(B))->A=B).
% 3.01/3.22 all A (relation_dom(identity_relation(A))=A&relation_rng(identity_relation(A))=A).
% 3.01/3.22 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))).
% 3.01/3.22 all A B (-(in(A,B)&empty(B))).
% 3.01/3.22 all A B subset(A,set_union2(A,B)).
% 3.01/3.22 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 3.01/3.22 all A B C (relation(C)-> (in(A,relation_dom(relation_dom_restriction(C,B)))<->in(A,B)&in(A,relation_dom(C)))).
% 3.01/3.22 all A B (relation(B)->subset(relation_dom_restriction(B,A),B)).
% 3.01/3.22 all A B (-(empty(A)&A!=B&empty(B))).
% 3.01/3.22 -(all A B C (relation(C)&function(C)-> (in(ordered_pair(A,B),C)<->in(A,relation_dom(C))&B=apply(C,A)))).
% 3.01/3.22 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 3.01/3.22 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 3.01/3.22 all A B (relation(B)->relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A)).
% 3.01/3.22 all A B (in(A,B)->subset(A,union(B))).
% 3.01/3.22 all A B (relation(B)->relation_dom_restriction(B,A)=relation_composition(identity_relation(A),B)).
% 3.01/3.22 all A B (relation(B)->subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))).
% 3.01/3.22 all A (union(powerset(A))=A).
% 3.01/3.22 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))))).
% 3.01/3.22 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 3.01/3.22 end_of_list.
% 3.01/3.22
% 3.01/3.22 -------> usable clausifies to:
% 3.01/3.22
% 3.01/3.22 list(usable).
% 3.01/3.22 0 [] A=A.
% 3.01/3.22 0 [] -in(A,B)| -in(B,A).
% 3.01/3.22 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 3.01/3.22 0 [] -empty(A)|function(A).
% 3.01/3.22 0 [] -empty(A)|relation(A).
% 3.01/3.22 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 3.01/3.22 0 [] set_union2(A,B)=set_union2(B,A).
% 3.01/3.22 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 3.01/3.22 0 [] -relation(B)|B!=identity_relation(A)| -in(ordered_pair(C,D),B)|in(C,A).
% 3.01/3.22 0 [] -relation(B)|B!=identity_relation(A)| -in(ordered_pair(C,D),B)|C=D.
% 3.01/3.22 0 [] -relation(B)|B!=identity_relation(A)|in(ordered_pair(C,D),B)| -in(C,A)|C!=D.
% 3.01/3.22 0 [] -relation(B)|B=identity_relation(A)|in(ordered_pair($f2(A,B),$f1(A,B)),B)|in($f2(A,B),A).
% 3.01/3.22 0 [] -relation(B)|B=identity_relation(A)|in(ordered_pair($f2(A,B),$f1(A,B)),B)|$f2(A,B)=$f1(A,B).
% 3.01/3.22 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)!=$f1(A,B).
% 3.01/3.22 0 [] A!=B|subset(A,B).
% 3.01/3.22 0 [] A!=B|subset(B,A).
% 3.01/3.22 0 [] A=B| -subset(A,B)| -subset(B,A).
% 3.01/3.22 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)| -in(ordered_pair(D,E),C)|in(D,B).
% 3.01/3.22 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,E),A).
% 3.01/3.22 0 [] -relation(A)| -relation(C)|C!=relation_dom_restriction(A,B)|in(ordered_pair(D,E),C)| -in(D,B)| -in(ordered_pair(D,E),A).
% 3.01/3.22 0 [] -relation(A)| -relation(C)|C=relation_dom_restriction(A,B)|in(ordered_pair($f4(A,B,C),$f3(A,B,C)),C)|in($f4(A,B,C),B).
% 3.01/3.22 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).
% 3.01/3.22 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),$f3(A,B,C)),A).
% 3.01/3.22 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)| -in(ordered_pair(D,E),C)|in(E,A).
% 3.01/3.22 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,E),B).
% 3.01/3.22 0 [] -relation(B)| -relation(C)|C!=relation_rng_restriction(A,B)|in(ordered_pair(D,E),C)| -in(E,A)| -in(ordered_pair(D,E),B).
% 3.01/3.22 0 [] -relation(B)| -relation(C)|C=relation_rng_restriction(A,B)|in(ordered_pair($f6(A,B,C),$f5(A,B,C)),C)|in($f5(A,B,C),A).
% 3.01/3.22 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).
% 3.01/3.22 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),$f5(A,B,C)),B).
% 3.01/3.22 0 [] -relation(A)|C!=relation_image(A,B)| -in(D,C)|in(ordered_pair($f7(A,B,C,D),D),A).
% 3.01/3.22 0 [] -relation(A)|C!=relation_image(A,B)| -in(D,C)|in($f7(A,B,C,D),B).
% 3.01/3.22 0 [] -relation(A)|C!=relation_image(A,B)|in(D,C)| -in(ordered_pair(E,D),A)| -in(E,B).
% 3.01/3.22 0 [] -relation(A)|C=relation_image(A,B)|in($f9(A,B,C),C)|in(ordered_pair($f8(A,B,C),$f9(A,B,C)),A).
% 3.01/3.22 0 [] -relation(A)|C=relation_image(A,B)|in($f9(A,B,C),C)|in($f8(A,B,C),B).
% 3.01/3.22 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).
% 3.01/3.22 0 [] -relation(A)|C!=relation_inverse_image(A,B)| -in(D,C)|in(ordered_pair(D,$f10(A,B,C,D)),A).
% 3.01/3.22 0 [] -relation(A)|C!=relation_inverse_image(A,B)| -in(D,C)|in($f10(A,B,C,D),B).
% 3.01/3.22 0 [] -relation(A)|C!=relation_inverse_image(A,B)|in(D,C)| -in(ordered_pair(D,E),A)| -in(E,B).
% 3.01/3.22 0 [] -relation(A)|C=relation_inverse_image(A,B)|in($f12(A,B,C),C)|in(ordered_pair($f12(A,B,C),$f11(A,B,C)),A).
% 3.01/3.22 0 [] -relation(A)|C=relation_inverse_image(A,B)|in($f12(A,B,C),C)|in($f11(A,B,C),B).
% 3.01/3.22 0 [] -relation(A)|C=relation_inverse_image(A,B)| -in($f12(A,B,C),C)| -in(ordered_pair($f12(A,B,C),X2),A)| -in(X2,B).
% 3.01/3.22 0 [] -relation(A)| -in(B,A)|B=ordered_pair($f14(A,B),$f13(A,B)).
% 3.01/3.22 0 [] relation(A)|in($f15(A),A).
% 3.01/3.22 0 [] relation(A)|$f15(A)!=ordered_pair(C,D).
% 3.01/3.22 0 [] A=empty_set|B!=set_meet(A)| -in(C,B)| -in(D,A)|in(C,D).
% 3.01/3.22 0 [] A=empty_set|B!=set_meet(A)|in(C,B)|in($f16(A,B,C),A).
% 3.01/3.22 0 [] A=empty_set|B!=set_meet(A)|in(C,B)| -in(C,$f16(A,B,C)).
% 3.01/3.22 0 [] A=empty_set|B=set_meet(A)|in($f18(A,B),B)| -in(X3,A)|in($f18(A,B),X3).
% 3.01/3.22 0 [] A=empty_set|B=set_meet(A)| -in($f18(A,B),B)|in($f17(A,B),A).
% 3.01/3.22 0 [] A=empty_set|B=set_meet(A)| -in($f18(A,B),B)| -in($f18(A,B),$f17(A,B)).
% 3.01/3.22 0 [] A!=empty_set|B!=set_meet(A)|B=empty_set.
% 3.01/3.22 0 [] A!=empty_set|B=set_meet(A)|B!=empty_set.
% 3.01/3.22 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 3.01/3.22 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 3.01/3.22 0 [] B=singleton(A)|in($f19(A,B),B)|$f19(A,B)=A.
% 3.01/3.22 0 [] B=singleton(A)| -in($f19(A,B),B)|$f19(A,B)!=A.
% 3.01/3.22 0 [] A!=empty_set| -in(B,A).
% 3.01/3.22 0 [] A=empty_set|in($f20(A),A).
% 3.01/3.22 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 3.01/3.22 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 3.01/3.22 0 [] B=powerset(A)|in($f21(A,B),B)|subset($f21(A,B),A).
% 3.01/3.22 0 [] B=powerset(A)| -in($f21(A,B),B)| -subset($f21(A,B),A).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|A!=B| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|A!=B|in(ordered_pair(C,D),A)| -in(ordered_pair(C,D),B).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|A=B|in(ordered_pair($f23(A,B),$f22(A,B)),A)|in(ordered_pair($f23(A,B),$f22(A,B)),B).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|A=B| -in(ordered_pair($f23(A,B),$f22(A,B)),A)| -in(ordered_pair($f23(A,B),$f22(A,B)),B).
% 3.01/3.22 0 [] empty(A)| -element(B,A)|in(B,A).
% 3.01/3.22 0 [] empty(A)|element(B,A)| -in(B,A).
% 3.01/3.22 0 [] -empty(A)| -element(B,A)|empty(B).
% 3.01/3.22 0 [] -empty(A)|element(B,A)| -empty(B).
% 3.01/3.22 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 3.01/3.22 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 3.01/3.22 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 3.01/3.22 0 [] C=unordered_pair(A,B)|in($f24(A,B,C),C)|$f24(A,B,C)=A|$f24(A,B,C)=B.
% 3.01/3.22 0 [] C=unordered_pair(A,B)| -in($f24(A,B,C),C)|$f24(A,B,C)!=A.
% 3.01/3.22 0 [] C=unordered_pair(A,B)| -in($f24(A,B,C),C)|$f24(A,B,C)!=B.
% 3.01/3.22 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 3.01/3.22 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 3.01/3.22 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 3.01/3.22 0 [] C=set_union2(A,B)|in($f25(A,B,C),C)|in($f25(A,B,C),A)|in($f25(A,B,C),B).
% 3.01/3.22 0 [] C=set_union2(A,B)| -in($f25(A,B,C),C)| -in($f25(A,B,C),A).
% 3.01/3.22 0 [] C=set_union2(A,B)| -in($f25(A,B,C),C)| -in($f25(A,B,C),B).
% 3.01/3.22 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f27(A,B,C,D),A).
% 3.01/3.22 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f26(A,B,C,D),B).
% 3.01/3.22 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f27(A,B,C,D),$f26(A,B,C,D)).
% 3.01/3.22 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 3.01/3.22 0 [] C=cartesian_product2(A,B)|in($f30(A,B,C),C)|in($f29(A,B,C),A).
% 3.01/3.22 0 [] C=cartesian_product2(A,B)|in($f30(A,B,C),C)|in($f28(A,B,C),B).
% 3.01/3.22 0 [] C=cartesian_product2(A,B)|in($f30(A,B,C),C)|$f30(A,B,C)=ordered_pair($f29(A,B,C),$f28(A,B,C)).
% 3.01/3.22 0 [] C=cartesian_product2(A,B)| -in($f30(A,B,C),C)| -in(X4,A)| -in(X5,B)|$f30(A,B,C)!=ordered_pair(X4,X5).
% 3.01/3.22 0 [] -relation(A)| -relation(B)| -subset(A,B)| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|subset(A,B)|in(ordered_pair($f32(A,B),$f31(A,B)),A).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|subset(A,B)| -in(ordered_pair($f32(A,B),$f31(A,B)),B).
% 3.01/3.22 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 3.01/3.22 0 [] subset(A,B)|in($f33(A,B),A).
% 3.01/3.22 0 [] subset(A,B)| -in($f33(A,B),B).
% 3.01/3.22 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 3.01/3.22 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 3.01/3.22 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 3.01/3.22 0 [] C=set_intersection2(A,B)|in($f34(A,B,C),C)|in($f34(A,B,C),A).
% 3.01/3.22 0 [] C=set_intersection2(A,B)|in($f34(A,B,C),C)|in($f34(A,B,C),B).
% 3.01/3.22 0 [] C=set_intersection2(A,B)| -in($f34(A,B,C),C)| -in($f34(A,B,C),A)| -in($f34(A,B,C),B).
% 3.01/3.22 0 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C!=apply(A,B)|in(ordered_pair(B,C),A).
% 3.01/3.22 0 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C=apply(A,B)| -in(ordered_pair(B,C),A).
% 3.01/3.22 0 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C!=apply(A,B)|C=empty_set.
% 3.01/3.22 0 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C=apply(A,B)|C!=empty_set.
% 3.01/3.22 0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f35(A,B,C)),A).
% 3.01/3.22 0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 3.01/3.22 0 [] -relation(A)|B=relation_dom(A)|in($f37(A,B),B)|in(ordered_pair($f37(A,B),$f36(A,B)),A).
% 3.01/3.22 0 [] -relation(A)|B=relation_dom(A)| -in($f37(A,B),B)| -in(ordered_pair($f37(A,B),X6),A).
% 3.01/3.22 0 [] cast_to_subset(A)=A.
% 3.01/3.22 0 [] B!=union(A)| -in(C,B)|in(C,$f38(A,B,C)).
% 3.01/3.22 0 [] B!=union(A)| -in(C,B)|in($f38(A,B,C),A).
% 3.01/3.22 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 3.01/3.22 0 [] B=union(A)|in($f40(A,B),B)|in($f40(A,B),$f39(A,B)).
% 3.01/3.22 0 [] B=union(A)|in($f40(A,B),B)|in($f39(A,B),A).
% 3.01/3.22 0 [] B=union(A)| -in($f40(A,B),B)| -in($f40(A,B),X7)| -in(X7,A).
% 3.01/3.22 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 3.01/3.22 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 3.01/3.22 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 3.01/3.22 0 [] C=set_difference(A,B)|in($f41(A,B,C),C)|in($f41(A,B,C),A).
% 3.01/3.22 0 [] C=set_difference(A,B)|in($f41(A,B,C),C)| -in($f41(A,B,C),B).
% 3.01/3.22 0 [] C=set_difference(A,B)| -in($f41(A,B,C),C)| -in($f41(A,B,C),A)|in($f41(A,B,C),B).
% 3.01/3.22 0 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f42(A,B,C),C),A).
% 3.01/3.22 0 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 3.01/3.22 0 [] -relation(A)|B=relation_rng(A)|in($f44(A,B),B)|in(ordered_pair($f43(A,B),$f44(A,B)),A).
% 3.01/3.22 0 [] -relation(A)|B=relation_rng(A)| -in($f44(A,B),B)| -in(ordered_pair(X8,$f44(A,B)),A).
% 3.01/3.22 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 3.01/3.22 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 3.01/3.22 0 [] -relation(A)|relation_field(A)=set_union2(relation_dom(A),relation_rng(A)).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|B!=relation_inverse(A)| -in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|B!=relation_inverse(A)|in(ordered_pair(C,D),B)| -in(ordered_pair(D,C),A).
% 3.01/3.22 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).
% 3.01/3.22 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).
% 3.01/3.22 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 3.01/3.22 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 3.01/3.22 0 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,$f47(A,B,C,D,E)),A).
% 3.01/3.22 0 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair($f47(A,B,C,D,E),E),B).
% 3.01/3.22 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).
% 3.01/3.22 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f50(A,B,C),$f49(A,B,C)),C)|in(ordered_pair($f50(A,B,C),$f48(A,B,C)),A).
% 3.01/3.22 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f50(A,B,C),$f49(A,B,C)),C)|in(ordered_pair($f48(A,B,C),$f49(A,B,C)),B).
% 3.01/3.22 0 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)| -in(ordered_pair($f50(A,B,C),$f49(A,B,C)),C)| -in(ordered_pair($f50(A,B,C),X9),A)| -in(ordered_pair(X9,$f49(A,B,C)),B).
% 3.01/3.22 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).
% 3.01/3.22 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).
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|element($f51(A,B,C),powerset(A)).
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|in($f51(A,B,C),C)|in(subset_complement(A,$f51(A,B,C)),B).
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)| -in($f51(A,B,C),C)| -in(subset_complement(A,$f51(A,B,C)),B).
% 3.01/3.22 0 [] -proper_subset(A,B)|subset(A,B).
% 3.01/3.22 0 [] -proper_subset(A,B)|A!=B.
% 3.01/3.22 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] element(cast_to_subset(A),powerset(A)).
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] -relation(A)|relation(relation_inverse(A)).
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))|element(union_of_subsets(A,B),powerset(A)).
% 3.01/3.22 0 [] relation(identity_relation(A)).
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))|element(meet_of_subsets(A,B),powerset(A)).
% 3.01/3.22 0 [] -element(B,powerset(A))| -element(C,powerset(A))|element(subset_difference(A,B,C),powerset(A)).
% 3.01/3.22 0 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))).
% 3.01/3.22 0 [] -relation(B)|relation(relation_rng_restriction(A,B)).
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] $T.
% 3.01/3.22 0 [] element($f52(A),A).
% 3.01/3.22 0 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 3.01/3.22 0 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 3.01/3.22 0 [] empty(empty_set).
% 3.01/3.22 0 [] relation(empty_set).
% 3.01/3.22 0 [] relation_empty_yielding(empty_set).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|relation(set_intersection2(A,B)).
% 3.01/3.22 0 [] -empty(powerset(A)).
% 3.01/3.22 0 [] empty(empty_set).
% 3.01/3.22 0 [] -empty(ordered_pair(A,B)).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 3.01/3.22 0 [] -empty(singleton(A)).
% 3.01/3.22 0 [] empty(A)| -empty(set_union2(A,B)).
% 3.01/3.22 0 [] -empty(unordered_pair(A,B)).
% 3.01/3.22 0 [] empty(A)| -empty(set_union2(B,A)).
% 3.01/3.22 0 [] empty(empty_set).
% 3.01/3.22 0 [] relation(empty_set).
% 3.01/3.22 0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 3.01/3.22 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 3.01/3.22 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 3.01/3.22 0 [] -empty(A)|empty(relation_dom(A)).
% 3.01/3.22 0 [] -empty(A)|relation(relation_dom(A)).
% 3.01/3.22 0 [] -empty(A)|empty(relation_rng(A)).
% 3.01/3.22 0 [] -empty(A)|relation(relation_rng(A)).
% 3.01/3.22 0 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 3.01/3.22 0 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 3.01/3.22 0 [] set_union2(A,A)=A.
% 3.01/3.22 0 [] set_intersection2(A,A)=A.
% 3.01/3.22 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 3.01/3.22 0 [] -relation(A)|relation_inverse(relation_inverse(A))=A.
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B.
% 3.01/3.22 0 [] -proper_subset(A,A).
% 3.01/3.22 0 [] singleton(A)!=empty_set.
% 3.01/3.22 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 3.01/3.22 0 [] -disjoint(singleton(A),B)| -in(A,B).
% 3.01/3.22 0 [] in(A,B)|disjoint(singleton(A),B).
% 3.01/3.22 0 [] -subset(singleton(A),B)|in(A,B).
% 3.01/3.22 0 [] subset(singleton(A),B)| -in(A,B).
% 3.01/3.22 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 3.01/3.22 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 3.01/3.22 0 [] -element(B,powerset(A))| -in(C,B)|in(C,A).
% 3.01/3.22 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 3.01/3.22 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 3.01/3.22 0 [] subset(A,singleton(B))|A!=empty_set.
% 3.01/3.22 0 [] subset(A,singleton(B))|A!=singleton(B).
% 3.01/3.22 0 [] -in(A,B)|subset(A,union(B)).
% 3.01/3.22 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 3.01/3.22 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 3.01/3.22 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 3.01/3.22 0 [] in($f53(A,B),A)|element(A,powerset(B)).
% 3.01/3.22 0 [] -in($f53(A,B),B)|element(A,powerset(B)).
% 3.01/3.22 0 [] relation($c1).
% 3.01/3.22 0 [] function($c1).
% 3.01/3.22 0 [] empty($c2).
% 3.01/3.22 0 [] relation($c2).
% 3.01/3.22 0 [] empty(A)|element($f54(A),powerset(A)).
% 3.01/3.22 0 [] empty(A)| -empty($f54(A)).
% 3.01/3.22 0 [] empty($c3).
% 3.01/3.22 0 [] -empty($c4).
% 3.01/3.22 0 [] relation($c4).
% 3.01/3.22 0 [] element($f55(A),powerset(A)).
% 3.01/3.22 0 [] empty($f55(A)).
% 3.01/3.22 0 [] -empty($c5).
% 3.01/3.22 0 [] relation($c6).
% 3.01/3.22 0 [] relation_empty_yielding($c6).
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))|union_of_subsets(A,B)=union(B).
% 3.01/3.22 0 [] -element(B,powerset(powerset(A)))|meet_of_subsets(A,B)=set_meet(B).
% 3.01/3.22 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_difference(A,B,C)=set_difference(B,C).
% 3.01/3.22 0 [] subset(A,A).
% 3.01/3.22 0 [] -disjoint(A,B)|disjoint(B,A).
% 3.01/3.22 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 3.01/3.22 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 3.01/3.22 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 3.01/3.22 0 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 3.01/3.22 0 [] -relation(C)| -in(A,relation_rng(relation_rng_restriction(B,C)))|in(A,B).
% 3.01/3.22 0 [] -relation(C)| -in(A,relation_rng(relation_rng_restriction(B,C)))|in(A,relation_rng(C)).
% 3.01/3.22 0 [] -relation(C)|in(A,relation_rng(relation_rng_restriction(B,C)))| -in(A,B)| -in(A,relation_rng(C)).
% 3.01/3.22 0 [] -relation(B)|subset(relation_rng(relation_rng_restriction(A,B)),A).
% 3.01/3.22 0 [] -relation(B)|subset(relation_rng_restriction(A,B),B).
% 3.01/3.22 0 [] -relation(B)|subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)).
% 3.01/3.22 0 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 3.01/3.22 0 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 3.01/3.22 0 [] -relation(B)|relation_rng(relation_rng_restriction(A,B))=set_intersection2(relation_rng(B),A).
% 3.01/3.22 0 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 3.01/3.22 0 [] -subset(A,B)|set_union2(A,B)=B.
% 3.01/3.22 0 [] in(A,$f56(A)).
% 3.01/3.22 0 [] -in(C,$f56(A))| -subset(D,C)|in(D,$f56(A)).
% 3.01/3.22 0 [] -in(X10,$f56(A))|in(powerset(X10),$f56(A)).
% 3.01/3.22 0 [] -subset(X11,$f56(A))|are_e_quipotent(X11,$f56(A))|in(X11,$f56(A)).
% 3.01/3.22 0 [] -relation(C)|relation_dom_restriction(relation_rng_restriction(A,C),B)=relation_rng_restriction(A,relation_dom_restriction(C,B)).
% 3.01/3.22 0 [] -relation(C)| -in(A,relation_image(C,B))|in($f57(A,B,C),relation_dom(C)).
% 3.01/3.22 0 [] -relation(C)| -in(A,relation_image(C,B))|in(ordered_pair($f57(A,B,C),A),C).
% 3.01/3.22 0 [] -relation(C)| -in(A,relation_image(C,B))|in($f57(A,B,C),B).
% 3.01/3.22 0 [] -relation(C)|in(A,relation_image(C,B))| -in(D,relation_dom(C))| -in(ordered_pair(D,A),C)| -in(D,B).
% 3.01/3.22 0 [] -relation(B)|subset(relation_image(B,A),relation_rng(B)).
% 3.01/3.22 0 [] -relation(B)|relation_image(B,A)=relation_image(B,set_intersection2(relation_dom(B),A)).
% 3.01/3.22 0 [] -relation(A)|relation_image(A,relation_dom(A))=relation_rng(A).
% 3.01/3.22 0 [] -relation(A)| -relation(B)|relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A)).
% 3.01/3.22 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in($f58(A,B,C),relation_rng(C)).
% 3.01/3.22 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in(ordered_pair(A,$f58(A,B,C)),C).
% 3.01/3.22 0 [] -relation(C)| -in(A,relation_inverse_image(C,B))|in($f58(A,B,C),B).
% 3.01/3.22 0 [] -relation(C)|in(A,relation_inverse_image(C,B))| -in(D,relation_rng(C))| -in(ordered_pair(A,D),C)| -in(D,B).
% 3.01/3.22 0 [] -relation(B)|subset(relation_inverse_image(B,A),relation_dom(B)).
% 3.01/3.22 0 [] -relation(B)|A=empty_set| -subset(A,relation_rng(B))|relation_inverse_image(B,A)!=empty_set.
% 3.01/3.22 0 [] -relation(C)| -subset(A,B)|subset(relation_inverse_image(C,A),relation_inverse_image(C,B)).
% 3.01/3.22 0 [] subset(set_intersection2(A,B),A).
% 3.01/3.22 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 3.01/3.22 0 [] set_union2(A,empty_set)=A.
% 3.01/3.22 0 [] -in(A,B)|element(A,B).
% 3.01/3.22 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 3.01/3.22 0 [] powerset(empty_set)=singleton(empty_set).
% 3.01/3.22 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(A,relation_dom(C)).
% 3.01/3.22 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(B,relation_rng(C)).
% 3.01/3.22 0 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 3.01/3.22 0 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_dom(A),relation_dom(B)).
% 3.01/3.22 0 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_rng(A),relation_rng(B)).
% 3.01/3.22 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 3.01/3.22 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 3.01/3.22 0 [] set_intersection2(A,empty_set)=empty_set.
% 3.01/3.22 0 [] -element(A,B)|empty(B)|in(A,B).
% 3.01/3.22 0 [] in($f59(A,B),A)|in($f59(A,B),B)|A=B.
% 3.01/3.22 0 [] -in($f59(A,B),A)| -in($f59(A,B),B)|A=B.
% 3.01/3.22 0 [] subset(empty_set,A).
% 3.01/3.22 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(A,relation_field(C)).
% 3.09/3.22 0 [] -relation(C)| -in(ordered_pair(A,B),C)|in(B,relation_field(C)).
% 3.09/3.22 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 3.09/3.22 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 3.09/3.22 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 3.09/3.22 0 [] subset(set_difference(A,B),A).
% 3.09/3.22 0 [] -relation(A)|relation_rng(A)=relation_dom(relation_inverse(A)).
% 3.09/3.22 0 [] -relation(A)|relation_dom(A)=relation_rng(relation_inverse(A)).
% 3.09/3.22 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 3.09/3.22 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 3.09/3.22 0 [] -subset(singleton(A),B)|in(A,B).
% 3.09/3.22 0 [] subset(singleton(A),B)| -in(A,B).
% 3.09/3.22 0 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 3.09/3.22 0 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 3.09/3.22 0 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 3.09/3.22 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 3.09/3.22 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 3.09/3.22 0 [] subset(A,singleton(B))|A!=empty_set.
% 3.09/3.22 0 [] subset(A,singleton(B))|A!=singleton(B).
% 3.09/3.22 0 [] set_difference(A,empty_set)=A.
% 3.09/3.22 0 [] -element(A,powerset(B))|subset(A,B).
% 3.09/3.22 0 [] element(A,powerset(B))| -subset(A,B).
% 3.09/3.22 0 [] disjoint(A,B)|in($f60(A,B),A).
% 3.09/3.22 0 [] disjoint(A,B)|in($f60(A,B),B).
% 3.09/3.22 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 3.09/3.22 0 [] -subset(A,empty_set)|A=empty_set.
% 3.09/3.22 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 3.09/3.22 0 [] -element(B,powerset(A))| -element(C,powerset(A))| -disjoint(B,C)|subset(B,subset_complement(A,C)).
% 3.09/3.22 0 [] -element(B,powerset(A))| -element(C,powerset(A))|disjoint(B,C)| -subset(B,subset_complement(A,C)).
% 3.09/3.22 0 [] -relation(A)| -relation(B)|subset(relation_dom(relation_composition(A,B)),relation_dom(A)).
% 3.09/3.22 0 [] -relation(A)| -relation(B)|subset(relation_rng(relation_composition(A,B)),relation_rng(B)).
% 3.09/3.22 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 3.09/3.22 0 [] -relation(A)| -relation(B)| -subset(relation_rng(A),relation_dom(B))|relation_dom(relation_composition(A,B))=relation_dom(A).
% 3.09/3.22 0 [] -element(B,powerset(powerset(A)))|B=empty_set|complements_of_subsets(A,B)!=empty_set.
% 3.09/3.22 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 3.09/3.22 0 [] -relation(A)| -relation(B)| -subset(relation_dom(A),relation_rng(B))|relation_rng(relation_composition(B,A))=relation_rng(A).
% 3.09/3.22 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)).
% 3.09/3.22 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)).
% 3.09/3.22 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 3.09/3.22 0 [] set_difference(empty_set,A)=empty_set.
% 3.09/3.22 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 3.09/3.22 0 [] disjoint(A,B)|in($f61(A,B),set_intersection2(A,B)).
% 3.09/3.22 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 3.09/3.22 0 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 3.09/3.22 0 [] -element(C,powerset(A))| -in(B,subset_complement(A,C))| -in(B,C).
% 3.09/3.22 0 [] -relation(A)|in(ordered_pair($f63(A),$f62(A)),A)|A=empty_set.
% 3.09/3.22 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 3.09/3.22 0 [] relation_dom(empty_set)=empty_set.
% 3.09/3.22 0 [] relation_rng(empty_set)=empty_set.
% 3.09/3.22 0 [] -subset(A,B)| -proper_subset(B,A).
% 3.09/3.22 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 3.09/3.22 0 [] -relation(A)|relation_dom(A)!=empty_set|A=empty_set.
% 3.09/3.22 0 [] -relation(A)|relation_rng(A)!=empty_set|A=empty_set.
% 3.09/3.22 0 [] -relation(A)|relation_dom(A)!=empty_set|relation_rng(A)=empty_set.
% 3.09/3.22 0 [] -relation(A)|relation_dom(A)=empty_set|relation_rng(A)!=empty_set.
% 3.09/3.22 0 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 3.09/3.22 0 [] set_difference(A,singleton(B))=A|in(B,A).
% 3.09/3.22 0 [] unordered_pair(A,A)=singleton(A).
% 3.09/3.22 0 [] -empty(A)|A=empty_set.
% 3.09/3.22 0 [] -subset(singleton(A),singleton(B))|A=B.
% 3.09/3.22 0 [] relation_dom(identity_relation(A))=A.
% 3.09/3.22 0 [] relation_rng(identity_relation(A))=A.
% 3.09/3.22 0 [] -relation(D)| -in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|in(A,C).
% 3.09/3.22 0 [] -relation(D)| -in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|in(ordered_pair(A,B),D).
% 3.09/3.22 0 [] -relation(D)|in(ordered_pair(A,B),relation_composition(identity_relation(C),D))| -in(A,C)| -in(ordered_pair(A,B),D).
% 3.09/3.22 0 [] -in(A,B)| -empty(B).
% 3.09/3.22 0 [] subset(A,set_union2(A,B)).
% 3.09/3.22 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 3.09/3.22 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 3.09/3.22 0 [] -relation(C)| -in(A,relation_dom(relation_dom_restriction(C,B)))|in(A,B).
% 3.09/3.22 0 [] -relation(C)| -in(A,relation_dom(relation_dom_restriction(C,B)))|in(A,relation_dom(C)).
% 3.09/3.22 0 [] -relation(C)|in(A,relation_dom(relation_dom_restriction(C,B)))| -in(A,B)| -in(A,relation_dom(C)).
% 3.09/3.22 0 [] -relation(B)|subset(relation_dom_restriction(B,A),B).
% 3.09/3.22 0 [] -empty(A)|A=B| -empty(B).
% 3.09/3.22 0 [] relation($c7).
% 3.09/3.22 0 [] function($c7).
% 3.09/3.22 0 [] in(ordered_pair($c9,$c8),$c7)|in($c9,relation_dom($c7)).
% 3.09/3.22 0 [] in(ordered_pair($c9,$c8),$c7)|$c8=apply($c7,$c9).
% 3.09/3.22 0 [] -in(ordered_pair($c9,$c8),$c7)| -in($c9,relation_dom($c7))|$c8!=apply($c7,$c9).
% 3.09/3.22 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 3.09/3.22 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 3.09/3.22 0 [] -relation(B)|relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A).
% 3.09/3.22 0 [] -in(A,B)|subset(A,union(B)).
% 3.09/3.22 0 [] -relation(B)|relation_dom_restriction(B,A)=relation_composition(identity_relation(A),B).
% 3.09/3.22 0 [] -relation(B)|subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)).
% 3.09/3.22 0 [] union(powerset(A))=A.
% 3.09/3.22 0 [] in(A,$f65(A)).
% 3.09/3.22 0 [] -in(C,$f65(A))| -subset(D,C)|in(D,$f65(A)).
% 3.09/3.22 0 [] -in(X12,$f65(A))|in($f64(A,X12),$f65(A)).
% 3.09/3.22 0 [] -in(X12,$f65(A))| -subset(E,X12)|in(E,$f64(A,X12)).
% 3.09/3.22 0 [] -subset(X13,$f65(A))|are_e_quipotent(X13,$f65(A))|in(X13,$f65(A)).
% 3.09/3.22 0 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 3.09/3.22 end_of_list.
% 3.09/3.22
% 3.09/3.22 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 3.09/3.22
% 3.09/3.22 This ia a non-Horn set with equality. The strategy will be
% 3.09/3.22 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.09/3.22 deletion, with positive clauses in sos and nonpositive
% 3.09/3.22 clauses in usable.
% 3.09/3.22
% 3.09/3.22 dependent: set(knuth_bendix).
% 3.09/3.22 dependent: set(anl_eq).
% 3.09/3.22 dependent: set(para_from).
% 3.09/3.22 dependent: set(para_into).
% 3.09/3.22 dependent: clear(para_from_right).
% 3.09/3.22 dependent: clear(para_into_right).
% 3.09/3.22 dependent: set(para_from_vars).
% 3.09/3.22 dependent: set(eq_units_both_ways).
% 3.09/3.22 dependent: set(dynamic_demod_all).
% 3.09/3.23 dependent: set(dynamic_demod).
% 3.09/3.23 dependent: set(order_eq).
% 3.09/3.23 dependent: set(back_demod).
% 3.09/3.23 dependent: set(lrpo).
% 3.09/3.23 dependent: set(hyper_res).
% 3.09/3.23 dependent: set(unit_deletion).
% 3.09/3.23 dependent: set(factor).
% 3.09/3.23
% 3.09/3.23 ------------> process usable:
% 3.09/3.23 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 3.09/3.23 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 3.09/3.23 ** KEPT (pick-wt=4): 3 [] -empty(A)|function(A).
% 3.09/3.23 ** KEPT (pick-wt=4): 4 [] -empty(A)|relation(A).
% 3.09/3.23 ** KEPT (pick-wt=14): 5 [] -relation(A)|A!=identity_relation(B)| -in(ordered_pair(C,D),A)|in(C,B).
% 3.09/3.23 ** KEPT (pick-wt=14): 6 [] -relation(A)|A!=identity_relation(B)| -in(ordered_pair(C,D),A)|C=D.
% 3.09/3.23 ** KEPT (pick-wt=17): 7 [] -relation(A)|A!=identity_relation(B)|in(ordered_pair(C,D),A)| -in(C,B)|C!=D.
% 3.09/3.23 ** KEPT (pick-wt=20): 8 [] -relation(A)|A=identity_relation(B)|in(ordered_pair($f2(B,A),$f1(B,A)),A)|in($f2(B,A),B).
% 3.09/3.23 ** KEPT (pick-wt=22): 9 [] -relation(A)|A=identity_relation(B)|in(ordered_pair($f2(B,A),$f1(B,A)),A)|$f2(B,A)=$f1(B,A).
% 3.09/3.23 ** KEPT (pick-wt=27): 10 [] -relation(A)|A=identity_relation(B)| -in(ordered_pair($f2(B,A),$f1(B,A)),A)| -in($f2(B,A),B)|$f2(B,A)!=$f1(B,A).
% 3.09/3.23 ** KEPT (pick-wt=6): 11 [] A!=B|subset(A,B).
% 3.09/3.23 ** KEPT (pick-wt=6): 12 [] A!=B|subset(B,A).
% 3.09/3.23 ** KEPT (pick-wt=9): 13 [] A=B| -subset(A,B)| -subset(B,A).
% 3.09/3.23 ** KEPT (pick-wt=17): 14 [] -relation(A)| -relation(B)|B!=relation_dom_restriction(A,C)| -in(ordered_pair(D,E),B)|in(D,C).
% 3.09/3.23 ** KEPT (pick-wt=19): 15 [] -relation(A)| -relation(B)|B!=relation_dom_restriction(A,C)| -in(ordered_pair(D,E),B)|in(ordered_pair(D,E),A).
% 3.09/3.23 ** KEPT (pick-wt=22): 16 [] -relation(A)| -relation(B)|B!=relation_dom_restriction(A,C)|in(ordered_pair(D,E),B)| -in(D,C)| -in(ordered_pair(D,E),A).
% 3.09/3.23 ** KEPT (pick-wt=26): 17 [] -relation(A)| -relation(B)|B=relation_dom_restriction(A,C)|in(ordered_pair($f4(A,C,B),$f3(A,C,B)),B)|in($f4(A,C,B),C).
% 3.09/3.23 ** KEPT (pick-wt=31): 18 [] -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).
% 3.09/3.23 ** KEPT (pick-wt=37): 19 [] -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),$f3(A,C,B)),A).
% 3.09/3.23 ** KEPT (pick-wt=17): 20 [] -relation(A)| -relation(B)|B!=relation_rng_restriction(C,A)| -in(ordered_pair(D,E),B)|in(E,C).
% 3.09/3.23 ** KEPT (pick-wt=19): 21 [] -relation(A)| -relation(B)|B!=relation_rng_restriction(C,A)| -in(ordered_pair(D,E),B)|in(ordered_pair(D,E),A).
% 3.09/3.23 ** KEPT (pick-wt=22): 22 [] -relation(A)| -relation(B)|B!=relation_rng_restriction(C,A)|in(ordered_pair(D,E),B)| -in(E,C)| -in(ordered_pair(D,E),A).
% 3.09/3.23 ** KEPT (pick-wt=26): 23 [] -relation(A)| -relation(B)|B=relation_rng_restriction(C,A)|in(ordered_pair($f6(C,A,B),$f5(C,A,B)),B)|in($f5(C,A,B),C).
% 3.09/3.23 ** KEPT (pick-wt=31): 24 [] -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).
% 3.09/3.23 ** KEPT (pick-wt=37): 25 [] -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),$f5(C,A,B)),A).
% 3.09/3.23 ** KEPT (pick-wt=19): 26 [] -relation(A)|B!=relation_image(A,C)| -in(D,B)|in(ordered_pair($f7(A,C,B,D),D),A).
% 3.09/3.23 ** KEPT (pick-wt=17): 27 [] -relation(A)|B!=relation_image(A,C)| -in(D,B)|in($f7(A,C,B,D),C).
% 3.09/3.23 ** KEPT (pick-wt=18): 28 [] -relation(A)|B!=relation_image(A,C)|in(D,B)| -in(ordered_pair(E,D),A)| -in(E,C).
% 3.09/3.23 ** KEPT (pick-wt=24): 29 [] -relation(A)|B=relation_image(A,C)|in($f9(A,C,B),B)|in(ordered_pair($f8(A,C,B),$f9(A,C,B)),A).
% 3.09/3.23 ** KEPT (pick-wt=19): 30 [] -relation(A)|B=relation_image(A,C)|in($f9(A,C,B),B)|in($f8(A,C,B),C).
% 3.09/3.23 ** KEPT (pick-wt=24): 31 [] -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).
% 3.09/3.23 ** KEPT (pick-wt=19): 32 [] -relation(A)|B!=relation_inverse_image(A,C)| -in(D,B)|in(ordered_pair(D,$f10(A,C,B,D)),A).
% 3.09/3.23 ** KEPT (pick-wt=17): 33 [] -relation(A)|B!=relation_inverse_image(A,C)| -in(D,B)|in($f10(A,C,B,D),C).
% 3.09/3.23 ** KEPT (pick-wt=18): 34 [] -relation(A)|B!=relation_inverse_image(A,C)|in(D,B)| -in(ordered_pair(D,E),A)| -in(E,C).
% 3.09/3.23 ** KEPT (pick-wt=24): 35 [] -relation(A)|B=relation_inverse_image(A,C)|in($f12(A,C,B),B)|in(ordered_pair($f12(A,C,B),$f11(A,C,B)),A).
% 3.09/3.23 ** KEPT (pick-wt=19): 36 [] -relation(A)|B=relation_inverse_image(A,C)|in($f12(A,C,B),B)|in($f11(A,C,B),C).
% 3.09/3.23 ** KEPT (pick-wt=24): 37 [] -relation(A)|B=relation_inverse_image(A,C)| -in($f12(A,C,B),B)| -in(ordered_pair($f12(A,C,B),D),A)| -in(D,C).
% 3.09/3.23 ** KEPT (pick-wt=14): 39 [copy,38,flip.3] -relation(A)| -in(B,A)|ordered_pair($f14(A,B),$f13(A,B))=B.
% 3.09/3.23 ** KEPT (pick-wt=8): 40 [] relation(A)|$f15(A)!=ordered_pair(B,C).
% 3.09/3.23 ** KEPT (pick-wt=16): 41 [] A=empty_set|B!=set_meet(A)| -in(C,B)| -in(D,A)|in(C,D).
% 3.09/3.23 ** KEPT (pick-wt=16): 42 [] A=empty_set|B!=set_meet(A)|in(C,B)|in($f16(A,B,C),A).
% 3.09/3.23 ** KEPT (pick-wt=16): 43 [] A=empty_set|B!=set_meet(A)|in(C,B)| -in(C,$f16(A,B,C)).
% 3.09/3.23 ** KEPT (pick-wt=20): 44 [] A=empty_set|B=set_meet(A)|in($f18(A,B),B)| -in(C,A)|in($f18(A,B),C).
% 3.09/3.23 ** KEPT (pick-wt=17): 45 [] A=empty_set|B=set_meet(A)| -in($f18(A,B),B)|in($f17(A,B),A).
% 3.09/3.23 ** KEPT (pick-wt=19): 46 [] A=empty_set|B=set_meet(A)| -in($f18(A,B),B)| -in($f18(A,B),$f17(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=10): 47 [] A!=empty_set|B!=set_meet(A)|B=empty_set.
% 3.09/3.23 ** KEPT (pick-wt=10): 48 [] A!=empty_set|B=set_meet(A)|B!=empty_set.
% 3.09/3.23 ** KEPT (pick-wt=10): 49 [] A!=singleton(B)| -in(C,A)|C=B.
% 3.09/3.23 ** KEPT (pick-wt=10): 50 [] A!=singleton(B)|in(C,A)|C!=B.
% 3.09/3.23 ** KEPT (pick-wt=14): 51 [] A=singleton(B)| -in($f19(B,A),A)|$f19(B,A)!=B.
% 3.09/3.23 ** KEPT (pick-wt=6): 52 [] A!=empty_set| -in(B,A).
% 3.09/3.23 ** KEPT (pick-wt=10): 53 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 3.09/3.23 ** KEPT (pick-wt=10): 54 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 3.09/3.23 ** KEPT (pick-wt=14): 55 [] A=powerset(B)| -in($f21(B,A),A)| -subset($f21(B,A),B).
% 3.09/3.23 ** KEPT (pick-wt=17): 56 [] -relation(A)| -relation(B)|A!=B| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 3.09/3.23 ** KEPT (pick-wt=17): 57 [] -relation(A)| -relation(B)|A!=B|in(ordered_pair(C,D),A)| -in(ordered_pair(C,D),B).
% 3.09/3.23 ** KEPT (pick-wt=25): 58 [] -relation(A)| -relation(B)|A=B|in(ordered_pair($f23(A,B),$f22(A,B)),A)|in(ordered_pair($f23(A,B),$f22(A,B)),B).
% 3.09/3.23 ** KEPT (pick-wt=25): 59 [] -relation(A)| -relation(B)|A=B| -in(ordered_pair($f23(A,B),$f22(A,B)),A)| -in(ordered_pair($f23(A,B),$f22(A,B)),B).
% 3.09/3.23 ** KEPT (pick-wt=8): 60 [] empty(A)| -element(B,A)|in(B,A).
% 3.09/3.23 ** KEPT (pick-wt=8): 61 [] empty(A)|element(B,A)| -in(B,A).
% 3.09/3.23 ** KEPT (pick-wt=7): 62 [] -empty(A)| -element(B,A)|empty(B).
% 3.09/3.23 ** KEPT (pick-wt=7): 63 [] -empty(A)|element(B,A)| -empty(B).
% 3.09/3.23 ** KEPT (pick-wt=14): 64 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 3.09/3.23 ** KEPT (pick-wt=11): 65 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 3.09/3.23 ** KEPT (pick-wt=11): 66 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 3.09/3.23 ** KEPT (pick-wt=17): 67 [] A=unordered_pair(B,C)| -in($f24(B,C,A),A)|$f24(B,C,A)!=B.
% 3.09/3.23 ** KEPT (pick-wt=17): 68 [] A=unordered_pair(B,C)| -in($f24(B,C,A),A)|$f24(B,C,A)!=C.
% 3.09/3.23 ** KEPT (pick-wt=14): 69 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 3.09/3.23 ** KEPT (pick-wt=11): 70 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 3.09/3.23 ** KEPT (pick-wt=11): 71 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 3.09/3.23 ** KEPT (pick-wt=17): 72 [] A=set_union2(B,C)| -in($f25(B,C,A),A)| -in($f25(B,C,A),B).
% 3.09/3.23 ** KEPT (pick-wt=17): 73 [] A=set_union2(B,C)| -in($f25(B,C,A),A)| -in($f25(B,C,A),C).
% 3.09/3.23 ** KEPT (pick-wt=15): 74 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f27(B,C,A,D),B).
% 3.09/3.23 ** KEPT (pick-wt=15): 75 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f26(B,C,A,D),C).
% 3.09/3.23 ** KEPT (pick-wt=21): 77 [copy,76,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f27(B,C,A,D),$f26(B,C,A,D))=D.
% 3.09/3.23 ** KEPT (pick-wt=19): 78 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 3.09/3.23 ** KEPT (pick-wt=25): 79 [] A=cartesian_product2(B,C)| -in($f30(B,C,A),A)| -in(D,B)| -in(E,C)|$f30(B,C,A)!=ordered_pair(D,E).
% 3.09/3.23 ** KEPT (pick-wt=17): 80 [] -relation(A)| -relation(B)| -subset(A,B)| -in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B).
% 3.09/3.23 ** KEPT (pick-wt=16): 81 [] -relation(A)| -relation(B)|subset(A,B)|in(ordered_pair($f32(A,B),$f31(A,B)),A).
% 3.09/3.23 ** KEPT (pick-wt=16): 82 [] -relation(A)| -relation(B)|subset(A,B)| -in(ordered_pair($f32(A,B),$f31(A,B)),B).
% 3.09/3.23 ** KEPT (pick-wt=9): 83 [] -subset(A,B)| -in(C,A)|in(C,B).
% 3.09/3.23 ** KEPT (pick-wt=8): 84 [] subset(A,B)| -in($f33(A,B),B).
% 3.09/3.23 ** KEPT (pick-wt=11): 85 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 3.09/3.23 ** KEPT (pick-wt=11): 86 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 3.09/3.23 ** KEPT (pick-wt=14): 87 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 3.09/3.23 ** KEPT (pick-wt=23): 88 [] A=set_intersection2(B,C)| -in($f34(B,C,A),A)| -in($f34(B,C,A),B)| -in($f34(B,C,A),C).
% 3.09/3.23 ** KEPT (pick-wt=18): 89 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C!=apply(A,B)|in(ordered_pair(B,C),A).
% 3.09/3.23 ** KEPT (pick-wt=18): 90 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C=apply(A,B)| -in(ordered_pair(B,C),A).
% 3.09/3.23 ** KEPT (pick-wt=16): 91 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C!=apply(A,B)|C=empty_set.
% 3.09/3.23 ** KEPT (pick-wt=16): 92 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C=apply(A,B)|C!=empty_set.
% 3.09/3.23 ** KEPT (pick-wt=17): 93 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f35(A,B,C)),A).
% 3.09/3.23 ** KEPT (pick-wt=14): 94 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 3.09/3.23 ** KEPT (pick-wt=20): 95 [] -relation(A)|B=relation_dom(A)|in($f37(A,B),B)|in(ordered_pair($f37(A,B),$f36(A,B)),A).
% 3.09/3.23 ** KEPT (pick-wt=18): 96 [] -relation(A)|B=relation_dom(A)| -in($f37(A,B),B)| -in(ordered_pair($f37(A,B),C),A).
% 3.09/3.23 ** KEPT (pick-wt=13): 97 [] A!=union(B)| -in(C,A)|in(C,$f38(B,A,C)).
% 3.09/3.23 ** KEPT (pick-wt=13): 98 [] A!=union(B)| -in(C,A)|in($f38(B,A,C),B).
% 3.09/3.23 ** KEPT (pick-wt=13): 99 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 3.09/3.23 ** KEPT (pick-wt=17): 100 [] A=union(B)| -in($f40(B,A),A)| -in($f40(B,A),C)| -in(C,B).
% 3.09/3.23 ** KEPT (pick-wt=11): 101 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 3.09/3.23 ** KEPT (pick-wt=11): 102 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 3.09/3.23 ** KEPT (pick-wt=14): 103 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 3.09/3.23 ** KEPT (pick-wt=17): 104 [] A=set_difference(B,C)|in($f41(B,C,A),A)| -in($f41(B,C,A),C).
% 3.09/3.23 ** KEPT (pick-wt=23): 105 [] A=set_difference(B,C)| -in($f41(B,C,A),A)| -in($f41(B,C,A),B)|in($f41(B,C,A),C).
% 3.09/3.23 ** KEPT (pick-wt=17): 106 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f42(A,B,C),C),A).
% 3.09/3.23 ** KEPT (pick-wt=14): 107 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 3.09/3.23 ** KEPT (pick-wt=20): 108 [] -relation(A)|B=relation_rng(A)|in($f44(A,B),B)|in(ordered_pair($f43(A,B),$f44(A,B)),A).
% 3.09/3.23 ** KEPT (pick-wt=18): 109 [] -relation(A)|B=relation_rng(A)| -in($f44(A,B),B)| -in(ordered_pair(C,$f44(A,B)),A).
% 3.09/3.23 ** KEPT (pick-wt=11): 110 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 3.09/3.23 ** KEPT (pick-wt=10): 112 [copy,111,flip.2] -relation(A)|set_union2(relation_dom(A),relation_rng(A))=relation_field(A).
% 3.09/3.23 ** KEPT (pick-wt=18): 113 [] -relation(A)| -relation(B)|B!=relation_inverse(A)| -in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A).
% 3.09/3.23 ** 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).
% 3.09/3.23 ** KEPT (pick-wt=26): 115 [] -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).
% 3.09/3.23 ** 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).
% 3.09/3.23 ** KEPT (pick-wt=8): 117 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 3.09/3.23 ** KEPT (pick-wt=8): 118 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 3.09/3.23 ** KEPT (pick-wt=26): 119 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair(D,$f47(A,B,C,D,E)),A).
% 3.09/3.23 ** KEPT (pick-wt=26): 120 [] -relation(A)| -relation(B)| -relation(C)|C!=relation_composition(A,B)| -in(ordered_pair(D,E),C)|in(ordered_pair($f47(A,B,C,D,E),E),B).
% 3.09/3.23 ** KEPT (pick-wt=26): 121 [] -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).
% 3.09/3.23 ** KEPT (pick-wt=33): 122 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f50(A,B,C),$f49(A,B,C)),C)|in(ordered_pair($f50(A,B,C),$f48(A,B,C)),A).
% 3.09/3.23 ** KEPT (pick-wt=33): 123 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)|in(ordered_pair($f50(A,B,C),$f49(A,B,C)),C)|in(ordered_pair($f48(A,B,C),$f49(A,B,C)),B).
% 3.09/3.23 ** KEPT (pick-wt=38): 124 [] -relation(A)| -relation(B)| -relation(C)|C=relation_composition(A,B)| -in(ordered_pair($f50(A,B,C),$f49(A,B,C)),C)| -in(ordered_pair($f50(A,B,C),D),A)| -in(ordered_pair(D,$f49(A,B,C)),B).
% 3.09/3.23 ** KEPT (pick-wt=27): 125 [] -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).
% 3.09/3.23 ** KEPT (pick-wt=27): 126 [] -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).
% 3.09/3.23 ** KEPT (pick-wt=22): 127 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|element($f51(B,A,C),powerset(B)).
% 3.09/3.23 ** KEPT (pick-wt=29): 128 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|in($f51(B,A,C),C)|in(subset_complement(B,$f51(B,A,C)),A).
% 3.09/3.23 ** KEPT (pick-wt=29): 129 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)| -in($f51(B,A,C),C)| -in(subset_complement(B,$f51(B,A,C)),A).
% 3.09/3.23 ** KEPT (pick-wt=6): 130 [] -proper_subset(A,B)|subset(A,B).
% 3.09/3.23 ** KEPT (pick-wt=6): 131 [] -proper_subset(A,B)|A!=B.
% 3.09/3.23 ** KEPT (pick-wt=9): 132 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 3.09/3.23 ** KEPT (pick-wt=10): 133 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 3.09/3.23 ** KEPT (pick-wt=5): 134 [] -relation(A)|relation(relation_inverse(A)).
% 3.09/3.23 ** KEPT (pick-wt=8): 135 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=11): 136 [] -element(A,powerset(powerset(B)))|element(union_of_subsets(B,A),powerset(B)).
% 3.09/3.23 ** KEPT (pick-wt=11): 137 [] -element(A,powerset(powerset(B)))|element(meet_of_subsets(B,A),powerset(B)).
% 3.09/3.23 ** KEPT (pick-wt=15): 138 [] -element(A,powerset(B))| -element(C,powerset(B))|element(subset_difference(B,A,C),powerset(B)).
% 3.09/3.23 ** KEPT (pick-wt=6): 139 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=12): 140 [] -element(A,powerset(powerset(B)))|element(complements_of_subsets(B,A),powerset(powerset(B))).
% 3.09/3.23 ** KEPT (pick-wt=6): 141 [] -relation(A)|relation(relation_rng_restriction(B,A)).
% 3.09/3.23 ** KEPT (pick-wt=8): 142 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 3.09/3.23 ** KEPT (pick-wt=8): 143 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 3.09/3.23 ** KEPT (pick-wt=8): 144 [] -relation(A)| -relation(B)|relation(set_intersection2(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=3): 145 [] -empty(powerset(A)).
% 3.09/3.23 ** KEPT (pick-wt=4): 146 [] -empty(ordered_pair(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=8): 147 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=3): 148 [] -empty(singleton(A)).
% 3.09/3.23 ** KEPT (pick-wt=6): 149 [] empty(A)| -empty(set_union2(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=4): 150 [] -empty(unordered_pair(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=6): 151 [] empty(A)| -empty(set_union2(B,A)).
% 3.09/3.23 ** KEPT (pick-wt=8): 152 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=7): 153 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 3.09/3.23 ** KEPT (pick-wt=7): 154 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 3.09/3.23 ** KEPT (pick-wt=5): 155 [] -empty(A)|empty(relation_dom(A)).
% 3.09/3.23 ** KEPT (pick-wt=5): 156 [] -empty(A)|relation(relation_dom(A)).
% 3.09/3.23 ** KEPT (pick-wt=5): 157 [] -empty(A)|empty(relation_rng(A)).
% 3.09/3.23 ** KEPT (pick-wt=5): 158 [] -empty(A)|relation(relation_rng(A)).
% 3.09/3.23 ** KEPT (pick-wt=8): 159 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=8): 160 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 3.09/3.23 ** KEPT (pick-wt=11): 161 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 3.09/3.23 ** KEPT (pick-wt=7): 162 [] -relation(A)|relation_inverse(relation_inverse(A))=A.
% 3.09/3.23 ** KEPT (pick-wt=12): 163 [] -element(A,powerset(powerset(B)))|complements_of_subsets(B,complements_of_subsets(B,A))=A.
% 3.09/3.23 ** KEPT (pick-wt=3): 164 [] -proper_subset(A,A).
% 3.09/3.24 ** KEPT (pick-wt=4): 165 [] singleton(A)!=empty_set.
% 3.09/3.24 ** KEPT (pick-wt=9): 166 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 3.09/3.24 ** KEPT (pick-wt=7): 167 [] -disjoint(singleton(A),B)| -in(A,B).
% 3.09/3.24 ** KEPT (pick-wt=7): 168 [] -subset(singleton(A),B)|in(A,B).
% 3.09/3.24 ** KEPT (pick-wt=7): 169 [] subset(singleton(A),B)| -in(A,B).
% 3.09/3.24 ** KEPT (pick-wt=8): 170 [] set_difference(A,B)!=empty_set|subset(A,B).
% 3.09/3.24 ** KEPT (pick-wt=8): 171 [] set_difference(A,B)=empty_set| -subset(A,B).
% 3.09/3.24 ** KEPT (pick-wt=10): 172 [] -element(A,powerset(B))| -in(C,A)|in(C,B).
% 3.09/3.24 ** KEPT (pick-wt=12): 173 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 3.09/3.24 ** KEPT (pick-wt=11): 174 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 3.09/3.24 ** KEPT (pick-wt=7): 175 [] subset(A,singleton(B))|A!=empty_set.
% 3.09/3.24 Following clause subsumed by 11 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 3.09/3.24 ** KEPT (pick-wt=7): 176 [] -in(A,B)|subset(A,union(B)).
% 3.09/3.24 ** KEPT (pick-wt=10): 177 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 3.09/3.24 ** KEPT (pick-wt=10): 178 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 3.09/3.24 ** KEPT (pick-wt=13): 179 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 3.09/3.24 ** KEPT (pick-wt=9): 180 [] -in($f53(A,B),B)|element(A,powerset(B)).
% 3.09/3.24 ** KEPT (pick-wt=5): 181 [] empty(A)| -empty($f54(A)).
% 3.09/3.24 ** KEPT (pick-wt=2): 182 [] -empty($c4).
% 3.09/3.24 ** KEPT (pick-wt=2): 183 [] -empty($c5).
% 3.09/3.24 ** KEPT (pick-wt=11): 184 [] -element(A,powerset(powerset(B)))|union_of_subsets(B,A)=union(A).
% 3.09/3.24 ** KEPT (pick-wt=11): 185 [] -element(A,powerset(powerset(B)))|meet_of_subsets(B,A)=set_meet(A).
% 3.09/3.24 ** KEPT (pick-wt=16): 186 [] -element(A,powerset(B))| -element(C,powerset(B))|subset_difference(B,A,C)=set_difference(A,C).
% 3.09/3.24 ** KEPT (pick-wt=6): 187 [] -disjoint(A,B)|disjoint(B,A).
% 3.09/3.24 Following clause subsumed by 177 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 3.09/3.24 Following clause subsumed by 178 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 3.09/3.24 Following clause subsumed by 179 during input processing: 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 3.09/3.24 ** KEPT (pick-wt=13): 188 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 3.09/3.24 ** KEPT (pick-wt=11): 189 [] -relation(A)| -in(B,relation_rng(relation_rng_restriction(C,A)))|in(B,C).
% 3.09/3.24 ** KEPT (pick-wt=12): 190 [] -relation(A)| -in(B,relation_rng(relation_rng_restriction(C,A)))|in(B,relation_rng(A)).
% 3.09/3.24 ** KEPT (pick-wt=15): 191 [] -relation(A)|in(B,relation_rng(relation_rng_restriction(C,A)))| -in(B,C)| -in(B,relation_rng(A)).
% 3.09/3.24 ** KEPT (pick-wt=8): 192 [] -relation(A)|subset(relation_rng(relation_rng_restriction(B,A)),B).
% 3.09/3.24 ** KEPT (pick-wt=7): 193 [] -relation(A)|subset(relation_rng_restriction(B,A),A).
% 3.09/3.24 ** KEPT (pick-wt=9): 194 [] -relation(A)|subset(relation_rng(relation_rng_restriction(B,A)),relation_rng(A)).
% 3.09/3.24 ** KEPT (pick-wt=10): 195 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 3.09/3.24 ** KEPT (pick-wt=10): 196 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 3.09/3.24 ** KEPT (pick-wt=11): 197 [] -relation(A)|relation_rng(relation_rng_restriction(B,A))=set_intersection2(relation_rng(A),B).
% 3.09/3.24 ** KEPT (pick-wt=13): 198 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 3.09/3.24 ** KEPT (pick-wt=8): 199 [] -subset(A,B)|set_union2(A,B)=B.
% 3.09/3.24 ** KEPT (pick-wt=11): 200 [] -in(A,$f56(B))| -subset(C,A)|in(C,$f56(B)).
% 3.09/3.24 ** KEPT (pick-wt=9): 201 [] -in(A,$f56(B))|in(powerset(A),$f56(B)).
% 3.09/3.24 ** KEPT (pick-wt=12): 202 [] -subset(A,$f56(B))|are_e_quipotent(A,$f56(B))|in(A,$f56(B)).
% 3.09/3.24 ** KEPT (pick-wt=13): 204 [copy,203,flip.2] -relation(A)|relation_rng_restriction(B,relation_dom_restriction(A,C))=relation_dom_restriction(relation_rng_restriction(B,A),C).
% 3.09/3.24 ** KEPT (pick-wt=14): 205 [] -relation(A)| -in(B,relation_image(A,C))|in($f57(B,C,A),relation_dom(A)).
% 3.09/3.24 ** KEPT (pick-wt=15): 206 [] -relation(A)| -in(B,relation_image(A,C))|in(ordered_pair($f57(B,C,A),B),A).
% 3.09/3.24 ** KEPT (pick-wt=13): 207 [] -relation(A)| -in(B,relation_image(A,C))|in($f57(B,C,A),C).
% 3.09/3.24 ** KEPT (pick-wt=19): 208 [] -relation(A)|in(B,relation_image(A,C))| -in(D,relation_dom(A))| -in(ordered_pair(D,B),A)| -in(D,C).
% 3.09/3.24 ** KEPT (pick-wt=8): 209 [] -relation(A)|subset(relation_image(A,B),relation_rng(A)).
% 3.09/3.24 ** KEPT (pick-wt=12): 211 [copy,210,flip.2] -relation(A)|relation_image(A,set_intersection2(relation_dom(A),B))=relation_image(A,B).
% 3.09/3.24 ** KEPT (pick-wt=9): 213 [copy,212,flip.2] -relation(A)|relation_rng(A)=relation_image(A,relation_dom(A)).
% 3.09/3.24 ** KEPT (pick-wt=13): 214 [] -relation(A)| -relation(B)|relation_rng(relation_composition(A,B))=relation_image(B,relation_rng(A)).
% 3.09/3.24 ** KEPT (pick-wt=14): 215 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in($f58(B,C,A),relation_rng(A)).
% 3.09/3.24 ** KEPT (pick-wt=15): 216 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in(ordered_pair(B,$f58(B,C,A)),A).
% 3.09/3.24 ** KEPT (pick-wt=13): 217 [] -relation(A)| -in(B,relation_inverse_image(A,C))|in($f58(B,C,A),C).
% 3.09/3.24 ** KEPT (pick-wt=19): 218 [] -relation(A)|in(B,relation_inverse_image(A,C))| -in(D,relation_rng(A))| -in(ordered_pair(B,D),A)| -in(D,C).
% 3.09/3.24 ** KEPT (pick-wt=8): 219 [] -relation(A)|subset(relation_inverse_image(A,B),relation_dom(A)).
% 3.09/3.24 ** KEPT (pick-wt=14): 220 [] -relation(A)|B=empty_set| -subset(B,relation_rng(A))|relation_inverse_image(A,B)!=empty_set.
% 3.09/3.24 ** KEPT (pick-wt=12): 221 [] -relation(A)| -subset(B,C)|subset(relation_inverse_image(A,B),relation_inverse_image(A,C)).
% 3.09/3.24 ** KEPT (pick-wt=11): 222 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 3.09/3.24 ** KEPT (pick-wt=6): 223 [] -in(A,B)|element(A,B).
% 3.09/3.24 ** KEPT (pick-wt=9): 224 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 3.09/3.24 ** KEPT (pick-wt=11): 225 [] -relation(A)| -in(ordered_pair(B,C),A)|in(B,relation_dom(A)).
% 3.09/3.24 ** KEPT (pick-wt=11): 226 [] -relation(A)| -in(ordered_pair(B,C),A)|in(C,relation_rng(A)).
% 3.09/3.24 ** KEPT (pick-wt=9): 227 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 3.09/3.24 ** KEPT (pick-wt=12): 228 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_dom(A),relation_dom(B)).
% 3.09/3.24 ** KEPT (pick-wt=12): 229 [] -relation(A)| -relation(B)| -subset(A,B)|subset(relation_rng(A),relation_rng(B)).
% 3.09/3.24 ** KEPT (pick-wt=10): 230 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 3.09/3.24 ** KEPT (pick-wt=8): 231 [] -subset(A,B)|set_intersection2(A,B)=A.
% 3.09/3.24 Following clause subsumed by 60 during input processing: 0 [] -element(A,B)|empty(B)|in(A,B).
% 3.09/3.24 ** KEPT (pick-wt=13): 232 [] -in($f59(A,B),A)| -in($f59(A,B),B)|A=B.
% 3.09/3.24 ** KEPT (pick-wt=11): 233 [] -relation(A)| -in(ordered_pair(B,C),A)|in(B,relation_field(A)).
% 3.09/3.24 ** KEPT (pick-wt=11): 234 [] -relation(A)| -in(ordered_pair(B,C),A)|in(C,relation_field(A)).
% 3.09/3.24 ** KEPT (pick-wt=10): 235 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 3.09/3.24 ** KEPT (pick-wt=10): 236 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 3.09/3.24 ** KEPT (pick-wt=10): 237 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 3.09/3.24 ** KEPT (pick-wt=8): 238 [] -relation(A)|relation_rng(A)=relation_dom(relation_inverse(A)).
% 3.09/3.24 ** KEPT (pick-wt=8): 240 [copy,239,flip.2] -relation(A)|relation_rng(relation_inverse(A))=relation_dom(A).
% 3.09/3.24 Following clause subsumed by 170 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 3.09/3.24 Following clause subsumed by 171 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 3.09/3.24 Following clause subsumed by 168 during input processing: 0 [] -subset(singleton(A),B)|in(A,B).
% 3.09/3.24 Following clause subsumed by 169 during input processing: 0 [] subset(singleton(A),B)| -in(A,B).
% 3.09/3.24 ** KEPT (pick-wt=8): 241 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 3.09/3.24 ** KEPT (pick-wt=8): 242 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 3.09/3.24 ** KEPT (pick-wt=11): 243 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 3.09/3.24 Following clause subsumed by 174 during input processing: 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 3.09/3.24 Following clause subsumed by 175 during input processing: 0 [] subset(A,singleton(B))|A!=empty_set.
% 3.09/3.24 Following clause subsumed by 11 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 3.09/3.24 ** KEPT (pick-wt=7): 244 [] -element(A,powerset(B))|subset(A,B).
% 3.09/3.24 ** KEPT (pick-wt=7): 245 [] element(A,powerset(B))| -subset(A,B).
% 3.11/3.27 ** KEPT (pick-wt=9): 246 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 3.11/3.27 ** KEPT (pick-wt=6): 247 [] -subset(A,empty_set)|A=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=16): 248 [] -element(A,powerset(B))| -element(C,powerset(B))| -disjoint(A,C)|subset(A,subset_complement(B,C)).
% 3.11/3.27 ** KEPT (pick-wt=16): 249 [] -element(A,powerset(B))| -element(C,powerset(B))|disjoint(A,C)| -subset(A,subset_complement(B,C)).
% 3.11/3.27 ** KEPT (pick-wt=11): 250 [] -relation(A)| -relation(B)|subset(relation_dom(relation_composition(A,B)),relation_dom(A)).
% 3.11/3.27 ** KEPT (pick-wt=11): 251 [] -relation(A)| -relation(B)|subset(relation_rng(relation_composition(A,B)),relation_rng(B)).
% 3.11/3.27 ** KEPT (pick-wt=10): 253 [copy,252,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 3.11/3.27 ** KEPT (pick-wt=16): 254 [] -relation(A)| -relation(B)| -subset(relation_rng(A),relation_dom(B))|relation_dom(relation_composition(A,B))=relation_dom(A).
% 3.11/3.27 ** KEPT (pick-wt=13): 255 [] -element(A,powerset(powerset(B)))|A=empty_set|complements_of_subsets(B,A)!=empty_set.
% 3.11/3.27 Following clause subsumed by 166 during input processing: 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 3.11/3.27 ** KEPT (pick-wt=16): 256 [] -relation(A)| -relation(B)| -subset(relation_dom(A),relation_rng(B))|relation_rng(relation_composition(B,A))=relation_rng(A).
% 3.11/3.27 ** KEPT (pick-wt=21): 257 [] -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)).
% 3.11/3.27 ** KEPT (pick-wt=21): 258 [] -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)).
% 3.11/3.27 ** KEPT (pick-wt=10): 259 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 3.11/3.27 ** KEPT (pick-wt=8): 260 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 3.11/3.27 ** KEPT (pick-wt=18): 261 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 3.11/3.27 ** KEPT (pick-wt=12): 262 [] -element(A,powerset(B))| -in(C,subset_complement(B,A))| -in(C,A).
% 3.11/3.27 ** KEPT (pick-wt=12): 263 [] -relation(A)|in(ordered_pair($f63(A),$f62(A)),A)|A=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=9): 264 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 3.11/3.27 ** KEPT (pick-wt=6): 265 [] -subset(A,B)| -proper_subset(B,A).
% 3.11/3.27 ** KEPT (pick-wt=9): 266 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 3.11/3.27 ** KEPT (pick-wt=9): 267 [] -relation(A)|relation_dom(A)!=empty_set|A=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=9): 268 [] -relation(A)|relation_rng(A)!=empty_set|A=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=10): 269 [] -relation(A)|relation_dom(A)!=empty_set|relation_rng(A)=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=10): 270 [] -relation(A)|relation_dom(A)=empty_set|relation_rng(A)!=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=9): 271 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 3.11/3.27 ** KEPT (pick-wt=5): 272 [] -empty(A)|A=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=8): 273 [] -subset(singleton(A),singleton(B))|A=B.
% 3.11/3.27 ** KEPT (pick-wt=13): 274 [] -relation(A)| -in(ordered_pair(B,C),relation_composition(identity_relation(D),A))|in(B,D).
% 3.11/3.27 ** KEPT (pick-wt=15): 275 [] -relation(A)| -in(ordered_pair(B,C),relation_composition(identity_relation(D),A))|in(ordered_pair(B,C),A).
% 3.11/3.27 ** KEPT (pick-wt=18): 276 [] -relation(A)|in(ordered_pair(B,C),relation_composition(identity_relation(D),A))| -in(B,D)| -in(ordered_pair(B,C),A).
% 3.11/3.27 ** KEPT (pick-wt=5): 277 [] -in(A,B)| -empty(B).
% 3.11/3.27 ** KEPT (pick-wt=8): 278 [] -disjoint(A,B)|set_difference(A,B)=A.
% 3.11/3.27 ** KEPT (pick-wt=8): 279 [] disjoint(A,B)|set_difference(A,B)!=A.
% 3.11/3.27 ** KEPT (pick-wt=11): 280 [] -relation(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|in(B,C).
% 3.11/3.27 ** KEPT (pick-wt=12): 281 [] -relation(A)| -in(B,relation_dom(relation_dom_restriction(A,C)))|in(B,relation_dom(A)).
% 3.11/3.27 ** KEPT (pick-wt=15): 282 [] -relation(A)|in(B,relation_dom(relation_dom_restriction(A,C)))| -in(B,C)| -in(B,relation_dom(A)).
% 3.11/3.27 ** KEPT (pick-wt=7): 283 [] -relation(A)|subset(relation_dom_restriction(A,B),A).
% 3.11/3.27 ** KEPT (pick-wt=7): 284 [] -empty(A)|A=B| -empty(B).
% 3.11/3.27 ** KEPT (pick-wt=14): 286 [copy,285,flip.3] -in(ordered_pair($c9,$c8),$c7)| -in($c9,relation_dom($c7))|apply($c7,$c9)!=$c8.
% 3.11/3.27 ** KEPT (pick-wt=11): 287 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 3.11/3.27 ** KEPT (pick-wt=9): 288 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 3.11/3.27 ** KEPT (pick-wt=11): 289 [] -relation(A)|relation_dom(relation_dom_restriction(A,B))=set_intersection2(relation_dom(A),B).
% 3.11/3.27 Following clause subsumed by 176 during input processing: 0 [] -in(A,B)|subset(A,union(B)).
% 3.11/3.27 ** KEPT (pick-wt=10): 290 [] -relation(A)|relation_dom_restriction(A,B)=relation_composition(identity_relation(B),A).
% 3.11/3.27 ** KEPT (pick-wt=9): 291 [] -relation(A)|subset(relation_rng(relation_dom_restriction(A,B)),relation_rng(A)).
% 3.11/3.27 ** KEPT (pick-wt=11): 292 [] -in(A,$f65(B))| -subset(C,A)|in(C,$f65(B)).
% 3.11/3.27 ** KEPT (pick-wt=10): 293 [] -in(A,$f65(B))|in($f64(B,A),$f65(B)).
% 3.11/3.27 ** KEPT (pick-wt=12): 294 [] -in(A,$f65(B))| -subset(C,A)|in(C,$f64(B,A)).
% 3.11/3.27 ** KEPT (pick-wt=12): 295 [] -subset(A,$f65(B))|are_e_quipotent(A,$f65(B))|in(A,$f65(B)).
% 3.11/3.27 ** KEPT (pick-wt=9): 296 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 3.11/3.27 83 back subsumes 80.
% 3.11/3.27 223 back subsumes 61.
% 3.11/3.27 302 back subsumes 301.
% 3.11/3.27 306 back subsumes 305.
% 3.11/3.27
% 3.11/3.27 ------------> process sos:
% 3.11/3.27 ** KEPT (pick-wt=3): 401 [] A=A.
% 3.11/3.27 ** KEPT (pick-wt=7): 402 [] unordered_pair(A,B)=unordered_pair(B,A).
% 3.11/3.27 ** KEPT (pick-wt=7): 403 [] set_union2(A,B)=set_union2(B,A).
% 3.11/3.27 ** KEPT (pick-wt=7): 404 [] set_intersection2(A,B)=set_intersection2(B,A).
% 3.11/3.27 ** KEPT (pick-wt=6): 405 [] relation(A)|in($f15(A),A).
% 3.11/3.27 ** KEPT (pick-wt=14): 406 [] A=singleton(B)|in($f19(B,A),A)|$f19(B,A)=B.
% 3.11/3.27 ** KEPT (pick-wt=7): 407 [] A=empty_set|in($f20(A),A).
% 3.11/3.27 ** KEPT (pick-wt=14): 408 [] A=powerset(B)|in($f21(B,A),A)|subset($f21(B,A),B).
% 3.11/3.27 ** KEPT (pick-wt=23): 409 [] A=unordered_pair(B,C)|in($f24(B,C,A),A)|$f24(B,C,A)=B|$f24(B,C,A)=C.
% 3.11/3.27 ** KEPT (pick-wt=23): 410 [] A=set_union2(B,C)|in($f25(B,C,A),A)|in($f25(B,C,A),B)|in($f25(B,C,A),C).
% 3.11/3.27 ** KEPT (pick-wt=17): 411 [] A=cartesian_product2(B,C)|in($f30(B,C,A),A)|in($f29(B,C,A),B).
% 3.11/3.27 ** KEPT (pick-wt=17): 412 [] A=cartesian_product2(B,C)|in($f30(B,C,A),A)|in($f28(B,C,A),C).
% 3.11/3.27 ** KEPT (pick-wt=25): 414 [copy,413,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).
% 3.11/3.27 ** KEPT (pick-wt=8): 415 [] subset(A,B)|in($f33(A,B),A).
% 3.11/3.27 ** KEPT (pick-wt=17): 416 [] A=set_intersection2(B,C)|in($f34(B,C,A),A)|in($f34(B,C,A),B).
% 3.11/3.27 ** KEPT (pick-wt=17): 417 [] A=set_intersection2(B,C)|in($f34(B,C,A),A)|in($f34(B,C,A),C).
% 3.11/3.27 ** KEPT (pick-wt=4): 418 [] cast_to_subset(A)=A.
% 3.11/3.27 ---> New Demodulator: 419 [new_demod,418] cast_to_subset(A)=A.
% 3.11/3.27 ** KEPT (pick-wt=16): 420 [] A=union(B)|in($f40(B,A),A)|in($f40(B,A),$f39(B,A)).
% 3.11/3.27 ** KEPT (pick-wt=14): 421 [] A=union(B)|in($f40(B,A),A)|in($f39(B,A),B).
% 3.11/3.27 ** KEPT (pick-wt=17): 422 [] A=set_difference(B,C)|in($f41(B,C,A),A)|in($f41(B,C,A),B).
% 3.11/3.27 ** KEPT (pick-wt=10): 424 [copy,423,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 3.11/3.27 ---> New Demodulator: 425 [new_demod,424] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 3.11/3.27 ** KEPT (pick-wt=4): 427 [copy,426,demod,419] element(A,powerset(A)).
% 3.11/3.27 ** KEPT (pick-wt=3): 428 [] relation(identity_relation(A)).
% 3.11/3.27 ** KEPT (pick-wt=4): 429 [] element($f52(A),A).
% 3.11/3.27 ** KEPT (pick-wt=2): 430 [] empty(empty_set).
% 3.11/3.27 ** KEPT (pick-wt=2): 431 [] relation(empty_set).
% 3.11/3.27 ** KEPT (pick-wt=2): 432 [] relation_empty_yielding(empty_set).
% 3.11/3.27 Following clause subsumed by 430 during input processing: 0 [] empty(empty_set).
% 3.11/3.27 Following clause subsumed by 430 during input processing: 0 [] empty(empty_set).
% 3.11/3.27 Following clause subsumed by 431 during input processing: 0 [] relation(empty_set).
% 3.11/3.27 ** KEPT (pick-wt=5): 433 [] set_union2(A,A)=A.
% 3.11/3.27 ---> New Demodulator: 434 [new_demod,433] set_union2(A,A)=A.
% 3.11/3.27 ** KEPT (pick-wt=5): 435 [] set_intersection2(A,A)=A.
% 3.11/3.27 ---> New Demodulator: 436 [new_demod,435] set_intersection2(A,A)=A.
% 3.11/3.27 ** KEPT (pick-wt=7): 437 [] in(A,B)|disjoint(singleton(A),B).
% 3.11/3.27 ** KEPT (pick-wt=9): 438 [] in($f53(A,B),A)|element(A,powerset(B)).
% 3.11/3.27 ** KEPT (pick-wt=2): 439 [] relation($c1).
% 3.11/3.27 ** KEPT (pick-wt=2): 440 [] function($c1).
% 3.11/3.27 ** KEPT (pick-wt=2): 441 [] empty($c2).
% 3.11/3.27 ** KEPT (pick-wt=2): 442 [] relation($c2).
% 3.11/3.27 ** KEPT (pick-wt=7): 443 [] empty(A)|element($f54(A),powerset(A)).
% 3.11/3.27 ** KEPT (pick-wt=2): 444 [] empty($c3).
% 3.11/3.27 ** KEPT (pick-wt=2): 445 [] relation($c4).
% 3.11/3.27 ** KEPT (pick-wt=5): 446 [] element($f55(A),powerset(A)).
% 3.11/3.27 ** KEPT (pick-wt=3): 447 [] empty($f55(A)).
% 3.11/3.27 ** KEPT (pick-wt=2): 448 [] relation($c6).
% 3.11/3.27 ** KEPT (pick-wt=2): 449 [] relation_empty_yielding($c6).
% 3.11/3.27 ** KEPT (pick-wt=3): 450 [] subset(A,A).
% 3.11/3.27 ** KEPT (pick-wt=4): 451 [] in(A,$f56(A)).
% 3.11/3.27 ** KEPT (pick-wt=5): 452 [] subset(set_intersection2(A,B),A).
% 3.11/3.27 ** KEPT (pick-wt=5): 453 [] set_union2(A,empty_set)=A.
% 3.11/3.27 ---> New Demodulator: 454 [new_demod,453] set_union2(A,empty_set)=A.
% 3.11/3.27 ** KEPT (pick-wt=5): 456 [copy,455,flip.1] singleton(empty_set)=powerset(empty_set).
% 3.11/3.27 ---> New Demodulator: 457 [new_demod,456] singleton(empty_set)=powerset(empty_set).
% 3.11/3.27 ** KEPT (pick-wt=5): 458 [] set_intersection2(A,empty_set)=empty_set.
% 3.11/3.27 ---> New Demodulator: 459 [new_demod,458] set_intersection2(A,empty_set)=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=13): 460 [] in($f59(A,B),A)|in($f59(A,B),B)|A=B.
% 3.11/3.27 ** KEPT (pick-wt=3): 461 [] subset(empty_set,A).
% 3.11/3.27 ** KEPT (pick-wt=5): 462 [] subset(set_difference(A,B),A).
% 3.11/3.27 ** KEPT (pick-wt=9): 463 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 3.11/3.27 ---> New Demodulator: 464 [new_demod,463] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 3.11/3.27 ** KEPT (pick-wt=5): 465 [] set_difference(A,empty_set)=A.
% 3.11/3.27 ---> New Demodulator: 466 [new_demod,465] set_difference(A,empty_set)=A.
% 3.11/3.27 ** KEPT (pick-wt=8): 467 [] disjoint(A,B)|in($f60(A,B),A).
% 3.11/3.27 ** KEPT (pick-wt=8): 468 [] disjoint(A,B)|in($f60(A,B),B).
% 3.11/3.27 ** KEPT (pick-wt=9): 469 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 3.11/3.27 ---> New Demodulator: 470 [new_demod,469] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 3.11/3.27 ** KEPT (pick-wt=9): 472 [copy,471,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 3.11/3.27 ---> New Demodulator: 473 [new_demod,472] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 3.11/3.27 ** KEPT (pick-wt=5): 474 [] set_difference(empty_set,A)=empty_set.
% 3.11/3.27 ---> New Demodulator: 475 [new_demod,474] set_difference(empty_set,A)=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=12): 477 [copy,476,demod,473] disjoint(A,B)|in($f61(A,B),set_difference(A,set_difference(A,B))).
% 3.11/3.27 ** KEPT (pick-wt=4): 478 [] relation_dom(empty_set)=empty_set.
% 3.11/3.27 ---> New Demodulator: 479 [new_demod,478] relation_dom(empty_set)=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=4): 480 [] relation_rng(empty_set)=empty_set.
% 3.11/3.27 ---> New Demodulator: 481 [new_demod,480] relation_rng(empty_set)=empty_set.
% 3.11/3.27 ** KEPT (pick-wt=9): 482 [] set_difference(A,singleton(B))=A|in(B,A).
% 3.11/3.27 ** KEPT (pick-wt=6): 484 [copy,483,flip.1] singleton(A)=unordered_pair(A,A).
% 3.11/3.27 ---> New Demodulator: 485 [new_demod,484] singleton(A)=unordered_pair(A,A).
% 3.11/3.27 ** KEPT (pick-wt=5): 486 [] relation_dom(identity_relation(A))=A.
% 3.11/3.27 ---> New Demodulator: 487 [new_demod,486] relation_dom(identity_relation(A))=A.
% 3.11/3.27 ** KEPT (pick-wt=5): 488 [] relation_rng(identity_relation(A))=A.
% 3.11/3.27 ---> New Demodulator: 489 [new_demod,488] relation_rng(identity_relation(A))=A.
% 3.11/3.27 ** KEPT (pick-wt=5): 490 [] subset(A,set_union2(A,B)).
% 3.11/3.27 ** KEPT (pick-wt=2): 491 [] relation($c7).
% 3.11/3.27 ** KEPT (pick-wt=2): 492 [] function($c7).
% 3.11/3.27 ** KEPT (pick-wt=9): 493 [] in(ordered_pair($c9,$c8),$c7)|in($c9,relation_dom($c7)).
% 3.11/3.27 ** KEPT (pick-wt=10): 495 [copy,494,flip.2] in(ordered_pair($c9,$c8),$c7)|apply($c7,$c9)=$c8.
% 3.11/3.27 ** KEPT (pick-wt=5): 496 [] union(powerset(A))=A.
% 3.11/3.27 ---> New Demodulator: 497 [new_demod,496] union(powerset(A))=A.
% 3.11/3.27 ** KEPT (pick-wt=4): 498 [] in(A,$f65(A)).
% 3.11/3.27 Following clause subsumed by 401 during input processing: 0 [copy,401,flip.1] A=A.
% 3.11/3.27 401 back subsumes 389.
% 3.11/3.27 401 back subsumes 379.
% 3.11/3.27 401 back subsumes 314.
% 3.11/3.27 401 back subsumes 313.
% 3.11/3.27 401 back subsumes 299.
% 3.11/3.27 Following clause subsumed by 402 during input processing: 0 [copy,402,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 3.11/3.27 Following clause subsumed by 403 during input processing: 0 [copy,403,flip.1] set_union2(A,B)=set_union2(B,A).
% 3.11/3.27 ** KEPT (pick-wt=11): 499 [copy,404,flip.1,demod,473,473] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 3.11/3.27 >>>> Starting back demodulation with 419.
% 3.11/3.27 >> back demodulating 258 with 419.
% 3.11/3.27 >> back demodulating 257 with 419.
% 3.11/3.27 >>>> Starting back demodulation with 425.
% 3.11/3.27 >>>> Starting back demodulation with 434.
% 9.71/9.84 >> back demodulating 390 with 434.
% 9.71/9.84 >> back demodulating 366 with 434.
% 9.71/9.84 >> back demodulating 317 with 434.
% 9.71/9.84 >>>> Starting back demodulation with 436.
% 9.71/9.84 >> back demodulating 392 with 436.
% 9.71/9.84 >> back demodulating 376 with 436.
% 9.71/9.84 >> back demodulating 365 with 436.
% 9.71/9.84 >> back demodulating 329 with 436.
% 9.71/9.84 >> back demodulating 326 with 436.
% 9.71/9.84 450 back subsumes 378.
% 9.71/9.84 450 back subsumes 377.
% 9.71/9.84 450 back subsumes 325.
% 9.71/9.84 450 back subsumes 324.
% 9.71/9.84 >>>> Starting back demodulation with 454.
% 9.71/9.84 >>>> Starting back demodulation with 457.
% 9.71/9.84 >>>> Starting back demodulation with 459.
% 9.71/9.84 >>>> Starting back demodulation with 464.
% 9.71/9.84 >> back demodulating 253 with 464.
% 9.71/9.84 >>>> Starting back demodulation with 466.
% 9.71/9.84 >>>> Starting back demodulation with 470.
% 9.71/9.84 >>>> Starting back demodulation with 473.
% 9.71/9.84 >> back demodulating 458 with 473.
% 9.71/9.84 >> back demodulating 452 with 473.
% 9.71/9.84 >> back demodulating 435 with 473.
% 9.71/9.84 >> back demodulating 417 with 473.
% 9.71/9.84 >> back demodulating 416 with 473.
% 9.71/9.84 >> back demodulating 404 with 473.
% 9.71/9.84 >> back demodulating 328 with 473.
% 9.71/9.84 >> back demodulating 327 with 473.
% 9.71/9.84 >> back demodulating 289 with 473.
% 9.71/9.84 >> back demodulating 260 with 473.
% 9.71/9.84 >> back demodulating 231 with 473.
% 9.71/9.84 >> back demodulating 230 with 473.
% 9.71/9.84 >> back demodulating 222 with 473.
% 9.71/9.84 >> back demodulating 211 with 473.
% 9.71/9.84 >> back demodulating 197 with 473.
% 9.71/9.84 >> back demodulating 144 with 473.
% 9.71/9.84 >> back demodulating 118 with 473.
% 9.71/9.84 >> back demodulating 117 with 473.
% 9.71/9.84 >> back demodulating 88 with 473.
% 9.71/9.84 >> back demodulating 87 with 473.
% 9.71/9.84 >> back demodulating 86 with 473.
% 9.71/9.84 >> back demodulating 85 with 473.
% 9.71/9.84 >>>> Starting back demodulation with 475.
% 9.71/9.84 >>>> Starting back demodulation with 479.
% 9.71/9.84 >>>> Starting back demodulation with 481.
% 9.71/9.84 >>>> Starting back demodulation with 485.
% 9.71/9.84 >> back demodulating 482 with 485.
% 9.71/9.84 >> back demodulating 456 with 485.
% 9.71/9.84 >> back demodulating 437 with 485.
% 9.71/9.84 >> back demodulating 424 with 485.
% 9.71/9.84 >> back demodulating 406 with 485.
% 9.71/9.84 >> back demodulating 296 with 485.
% 9.71/9.84 >> back demodulating 288 with 485.
% 9.71/9.84 >> back demodulating 273 with 485.
% 9.71/9.84 >> back demodulating 271 with 485.
% 9.71/9.84 >> back demodulating 175 with 485.
% 9.71/9.84 >> back demodulating 174 with 485.
% 9.71/9.84 >> back demodulating 173 with 485.
% 9.71/9.84 >> back demodulating 169 with 485.
% 9.71/9.84 >> back demodulating 168 with 485.
% 9.71/9.84 >> back demodulating 167 with 485.
% 9.71/9.84 >> back demodulating 166 with 485.
% 9.71/9.84 >> back demodulating 165 with 485.
% 9.71/9.84 >> back demodulating 148 with 485.
% 9.71/9.84 >> back demodulating 51 with 485.
% 9.71/9.84 >> back demodulating 50 with 485.
% 9.71/9.84 >> back demodulating 49 with 485.
% 9.71/9.84 >>>> Starting back demodulation with 487.
% 9.71/9.84 >>>> Starting back demodulation with 489.
% 9.71/9.84 >>>> Starting back demodulation with 497.
% 9.71/9.84 Following clause subsumed by 499 during input processing: 0 [copy,499,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 9.71/9.84 509 back subsumes 56.
% 9.71/9.84 511 back subsumes 57.
% 9.71/9.84 >>>> Starting back demodulation with 513.
% 9.71/9.84 >> back demodulating 369 with 513.
% 9.71/9.84 >>>> Starting back demodulation with 533.
% 9.71/9.84 >>>> Starting back demodulation with 536.
% 9.71/9.84
% 9.71/9.84 ======= end of input processing =======
% 9.71/9.84
% 9.71/9.84 =========== start of search ===========
% 9.71/9.84
% 9.71/9.84
% 9.71/9.84 Resetting weight limit to 2.
% 9.71/9.84
% 9.71/9.84
% 9.71/9.84 Resetting weight limit to 2.
% 9.71/9.84
% 9.71/9.84 sos_size=108
% 9.71/9.84
% 9.71/9.84 Search stopped because sos empty.
% 9.71/9.84
% 9.71/9.84
% 9.71/9.84 Search stopped because sos empty.
% 9.71/9.84
% 9.71/9.84 ============ end of search ============
% 9.71/9.84
% 9.71/9.84 -------------- statistics -------------
% 9.71/9.84 clauses given 113
% 9.71/9.84 clauses generated 366290
% 9.71/9.84 clauses kept 515
% 9.71/9.84 clauses forward subsumed 160
% 9.71/9.84 clauses back subsumed 15
% 9.71/9.84 Kbytes malloced 6835
% 9.71/9.84
% 9.71/9.84 ----------- times (seconds) -----------
% 9.71/9.84 user CPU time 6.63 (0 hr, 0 min, 6 sec)
% 9.71/9.84 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 9.71/9.84 wall-clock time 9 (0 hr, 0 min, 9 sec)
% 9.71/9.84
% 9.71/9.84 Process 13964 finished Wed Jul 27 08:10:01 2022
% 9.71/9.84 Otter interrupted
% 9.71/9.84 PROOF NOT FOUND
%------------------------------------------------------------------------------