TSTP Solution File: SEU177+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU177+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:15:04 EDT 2022
% Result : Theorem 2.27s 2.49s
% Output : Refutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 8 RR)
% Number of literals : 16 ( 3 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(48,axiom,
( ~ relation(A)
| B != relation_dom(A)
| in(C,B)
| ~ in(ordered_pair(C,D),A) ),
file('SEU177+2.p',unknown),
[] ).
cnf(61,axiom,
( ~ relation(A)
| B != relation_rng(A)
| in(C,B)
| ~ in(ordered_pair(D,C),A) ),
file('SEU177+2.p',unknown),
[] ).
cnf(122,axiom,
( ~ in(dollar_c6,relation_dom(dollar_c4))
| ~ in(dollar_c5,relation_rng(dollar_c4)) ),
file('SEU177+2.p',unknown),
[] ).
cnf(235,axiom,
set_union2(A,A) = A,
file('SEU177+2.p',unknown),
[] ).
cnf(254,axiom,
relation(dollar_c4),
file('SEU177+2.p',unknown),
[] ).
cnf(255,axiom,
in(ordered_pair(dollar_c6,dollar_c5),dollar_c4),
file('SEU177+2.p',unknown),
[] ).
cnf(635,plain,
in(dollar_c5,relation_rng(dollar_c4)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[255,61,254,235]),235]),
[iquote('hyper,255,61,254,234,demod,235')] ).
cnf(636,plain,
in(dollar_c6,relation_dom(dollar_c4)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[255,48,254,235]),235]),
[iquote('hyper,255,48,254,234,demod,235')] ).
cnf(640,plain,
$false,
inference(hyper,[status(thm)],[636,122,635]),
[iquote('hyper,636,122,635')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU177+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 08:07:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.03/2.23 ----- Otter 3.3f, August 2004 -----
% 2.03/2.23 The process was started by sandbox on n019.cluster.edu,
% 2.03/2.23 Wed Jul 27 08:07:37 2022
% 2.03/2.23 The command was "./otter". The process ID is 14949.
% 2.03/2.23
% 2.03/2.23 set(prolog_style_variables).
% 2.03/2.23 set(auto).
% 2.03/2.23 dependent: set(auto1).
% 2.03/2.23 dependent: set(process_input).
% 2.03/2.23 dependent: clear(print_kept).
% 2.03/2.23 dependent: clear(print_new_demod).
% 2.03/2.23 dependent: clear(print_back_demod).
% 2.03/2.23 dependent: clear(print_back_sub).
% 2.03/2.23 dependent: set(control_memory).
% 2.03/2.23 dependent: assign(max_mem, 12000).
% 2.03/2.23 dependent: assign(pick_given_ratio, 4).
% 2.03/2.23 dependent: assign(stats_level, 1).
% 2.03/2.23 dependent: assign(max_seconds, 10800).
% 2.03/2.23 clear(print_given).
% 2.03/2.23
% 2.03/2.23 formula_list(usable).
% 2.03/2.23 all A (A=A).
% 2.03/2.23 all A B (in(A,B)-> -in(B,A)).
% 2.03/2.23 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 2.03/2.23 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.03/2.23 all A B (set_union2(A,B)=set_union2(B,A)).
% 2.03/2.23 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.03/2.23 all A B (A=B<->subset(A,B)&subset(B,A)).
% 2.03/2.23 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))).
% 2.03/2.23 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 2.03/2.23 all A (A=empty_set<-> (all B (-in(B,A)))).
% 2.03/2.23 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 2.03/2.23 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 2.03/2.23 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 2.03/2.23 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 2.03/2.23 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)))))).
% 2.03/2.23 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.03/2.23 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 2.03/2.23 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 2.03/2.23 all A (cast_to_subset(A)=A).
% 2.03/2.23 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 2.03/2.23 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 2.03/2.23 all A (relation(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(D,C),A))))))).
% 2.03/2.23 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 2.03/2.23 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 2.03/2.23 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 2.03/2.23 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)))))))).
% 2.03/2.23 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 all A element(cast_to_subset(A),powerset(A)).
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 $T.
% 2.03/2.23 all A B (element(B,powerset(powerset(A)))->element(union_of_subsets(A,B),powerset(A))).
% 2.03/2.23 all A B (element(B,powerset(powerset(A)))->element(meet_of_subsets(A,B),powerset(A))).
% 2.03/2.23 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_difference(A,B,C),powerset(A))).
% 2.03/2.23 all A B (element(B,powerset(powerset(A)))->element(complements_of_subsets(A,B),powerset(powerset(A)))).
% 2.03/2.23 $T.
% 2.03/2.23 all A exists B element(B,A).
% 2.03/2.23 all A (-empty(powerset(A))).
% 2.03/2.23 empty(empty_set).
% 2.03/2.23 all A B (-empty(ordered_pair(A,B))).
% 2.03/2.23 all A (-empty(singleton(A))).
% 2.03/2.23 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 2.03/2.23 all A B (-empty(unordered_pair(A,B))).
% 2.03/2.23 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 2.03/2.23 all A B (set_union2(A,A)=A).
% 2.03/2.23 all A B (set_intersection2(A,A)=A).
% 2.03/2.23 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 2.03/2.23 all A B (element(B,powerset(powerset(A)))->complements_of_subsets(A,complements_of_subsets(A,B))=B).
% 2.03/2.23 all A B (-proper_subset(A,A)).
% 2.03/2.23 all A (singleton(A)!=empty_set).
% 2.03/2.23 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 2.03/2.23 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 2.03/2.23 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 2.03/2.23 all A B (subset(singleton(A),B)<->in(A,B)).
% 2.03/2.23 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.03/2.23 all A B (element(B,powerset(A))-> (all C (in(C,B)->in(C,A)))).
% 2.03/2.23 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 2.03/2.23 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 2.03/2.23 all A B (in(A,B)->subset(A,union(B))).
% 2.03/2.23 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 2.03/2.23 all A B ((all C (in(C,A)->in(C,B)))->element(A,powerset(B))).
% 2.03/2.23 exists A (empty(A)&relation(A)).
% 2.03/2.23 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.03/2.23 exists A empty(A).
% 2.03/2.23 all A exists B (element(B,powerset(A))&empty(B)).
% 2.03/2.23 exists A (-empty(A)).
% 2.03/2.23 all A B (element(B,powerset(powerset(A)))->union_of_subsets(A,B)=union(B)).
% 2.03/2.23 all A B (element(B,powerset(powerset(A)))->meet_of_subsets(A,B)=set_meet(B)).
% 2.03/2.23 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_difference(A,B,C)=set_difference(B,C)).
% 2.03/2.23 all A B subset(A,A).
% 2.03/2.23 all A B (disjoint(A,B)->disjoint(B,A)).
% 2.03/2.23 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 2.03/2.23 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 2.03/2.23 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))).
% 2.03/2.23 all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 2.03/2.23 all A B (subset(A,B)->set_union2(A,B)=B).
% 2.03/2.23 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))))).
% 2.03/2.23 all A B subset(set_intersection2(A,B),A).
% 2.03/2.23 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 2.03/2.23 all A (set_union2(A,empty_set)=A).
% 2.03/2.23 all A B (in(A,B)->element(A,B)).
% 2.03/2.23 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 2.03/2.23 powerset(empty_set)=singleton(empty_set).
% 2.03/2.23 -(all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_dom(C))&in(B,relation_rng(C))))).
% 2.03/2.23 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 2.03/2.23 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 2.03/2.23 all A (set_intersection2(A,empty_set)=empty_set).
% 2.03/2.23 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.03/2.23 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.03/2.23 all A subset(empty_set,A).
% 2.03/2.23 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 2.03/2.23 all A B C D (ordered_pair(A,B)=ordered_pair(C,D)->A=C&B=D).
% 2.03/2.23 all A B subset(set_difference(A,B),A).
% 2.03/2.23 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.03/2.23 all A B (subset(singleton(A),B)<->in(A,B)).
% 2.03/2.23 all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C)).
% 2.03/2.23 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 2.03/2.23 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 2.03/2.23 all A (set_difference(A,empty_set)=A).
% 2.03/2.23 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.03/2.23 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))).
% 2.03/2.23 all A (subset(A,empty_set)->A=empty_set).
% 2.03/2.23 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 2.03/2.23 all A B (element(B,powerset(A))-> (all C (element(C,powerset(A))-> (disjoint(B,C)<->subset(B,subset_complement(A,C)))))).
% 2.03/2.23 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 2.03/2.23 all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set)).
% 2.03/2.23 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 2.03/2.23 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)))).
% 2.03/2.23 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)))).
% 2.03/2.23 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 2.03/2.23 all A (set_difference(empty_set,A)=empty_set).
% 2.03/2.23 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.03/2.23 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))).
% 2.03/2.23 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)))))))).
% 2.03/2.23 all A B C (element(C,powerset(A))-> -(in(B,subset_complement(A,C))&in(B,C))).
% 2.03/2.23 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.03/2.23 all A B (-(subset(A,B)&proper_subset(B,A))).
% 2.03/2.23 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 2.03/2.23 all A B (set_difference(A,singleton(B))=A<-> -in(B,A)).
% 2.03/2.23 all A (unordered_pair(A,A)=singleton(A)).
% 2.03/2.23 all A (empty(A)->A=empty_set).
% 2.03/2.23 all A B (subset(singleton(A),singleton(B))->A=B).
% 2.03/2.23 all A B (-(in(A,B)&empty(B))).
% 2.03/2.23 all A B subset(A,set_union2(A,B)).
% 2.03/2.23 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 2.03/2.23 all A B (-(empty(A)&A!=B&empty(B))).
% 2.03/2.23 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 2.03/2.23 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 2.03/2.23 all A B (in(A,B)->subset(A,union(B))).
% 2.03/2.23 all A (union(powerset(A))=A).
% 2.03/2.23 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))))).
% 2.03/2.23 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 2.03/2.23 end_of_list.
% 2.03/2.23
% 2.03/2.23 -------> usable clausifies to:
% 2.03/2.23
% 2.03/2.23 list(usable).
% 2.03/2.23 0 [] A=A.
% 2.03/2.23 0 [] -in(A,B)| -in(B,A).
% 2.03/2.23 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.03/2.23 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.03/2.23 0 [] set_union2(A,B)=set_union2(B,A).
% 2.03/2.23 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.03/2.23 0 [] A!=B|subset(A,B).
% 2.03/2.23 0 [] A!=B|subset(B,A).
% 2.03/2.23 0 [] A=B| -subset(A,B)| -subset(B,A).
% 2.03/2.23 0 [] A=empty_set|B!=set_meet(A)| -in(C,B)| -in(D,A)|in(C,D).
% 2.03/2.23 0 [] A=empty_set|B!=set_meet(A)|in(C,B)|in($f1(A,B,C),A).
% 2.03/2.23 0 [] A=empty_set|B!=set_meet(A)|in(C,B)| -in(C,$f1(A,B,C)).
% 2.03/2.23 0 [] A=empty_set|B=set_meet(A)|in($f3(A,B),B)| -in(X1,A)|in($f3(A,B),X1).
% 2.03/2.23 0 [] A=empty_set|B=set_meet(A)| -in($f3(A,B),B)|in($f2(A,B),A).
% 2.03/2.23 0 [] A=empty_set|B=set_meet(A)| -in($f3(A,B),B)| -in($f3(A,B),$f2(A,B)).
% 2.03/2.23 0 [] A!=empty_set|B!=set_meet(A)|B=empty_set.
% 2.03/2.23 0 [] A!=empty_set|B=set_meet(A)|B!=empty_set.
% 2.03/2.23 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 2.03/2.23 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 2.03/2.23 0 [] B=singleton(A)|in($f4(A,B),B)|$f4(A,B)=A.
% 2.03/2.23 0 [] B=singleton(A)| -in($f4(A,B),B)|$f4(A,B)!=A.
% 2.03/2.23 0 [] A!=empty_set| -in(B,A).
% 2.03/2.23 0 [] A=empty_set|in($f5(A),A).
% 2.03/2.23 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 2.03/2.23 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 2.03/2.23 0 [] B=powerset(A)|in($f6(A,B),B)|subset($f6(A,B),A).
% 2.03/2.23 0 [] B=powerset(A)| -in($f6(A,B),B)| -subset($f6(A,B),A).
% 2.03/2.23 0 [] empty(A)| -element(B,A)|in(B,A).
% 2.03/2.23 0 [] empty(A)|element(B,A)| -in(B,A).
% 2.03/2.23 0 [] -empty(A)| -element(B,A)|empty(B).
% 2.03/2.23 0 [] -empty(A)|element(B,A)| -empty(B).
% 2.03/2.23 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 2.03/2.23 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 2.03/2.23 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 2.03/2.23 0 [] C=unordered_pair(A,B)|in($f7(A,B,C),C)|$f7(A,B,C)=A|$f7(A,B,C)=B.
% 2.03/2.23 0 [] C=unordered_pair(A,B)| -in($f7(A,B,C),C)|$f7(A,B,C)!=A.
% 2.03/2.23 0 [] C=unordered_pair(A,B)| -in($f7(A,B,C),C)|$f7(A,B,C)!=B.
% 2.03/2.23 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 2.03/2.23 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 2.03/2.23 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 2.03/2.23 0 [] C=set_union2(A,B)|in($f8(A,B,C),C)|in($f8(A,B,C),A)|in($f8(A,B,C),B).
% 2.03/2.23 0 [] C=set_union2(A,B)| -in($f8(A,B,C),C)| -in($f8(A,B,C),A).
% 2.03/2.23 0 [] C=set_union2(A,B)| -in($f8(A,B,C),C)| -in($f8(A,B,C),B).
% 2.03/2.23 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f10(A,B,C,D),A).
% 2.03/2.23 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f9(A,B,C,D),B).
% 2.03/2.23 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f10(A,B,C,D),$f9(A,B,C,D)).
% 2.03/2.23 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 2.03/2.23 0 [] C=cartesian_product2(A,B)|in($f13(A,B,C),C)|in($f12(A,B,C),A).
% 2.03/2.23 0 [] C=cartesian_product2(A,B)|in($f13(A,B,C),C)|in($f11(A,B,C),B).
% 2.03/2.23 0 [] C=cartesian_product2(A,B)|in($f13(A,B,C),C)|$f13(A,B,C)=ordered_pair($f12(A,B,C),$f11(A,B,C)).
% 2.03/2.23 0 [] C=cartesian_product2(A,B)| -in($f13(A,B,C),C)| -in(X2,A)| -in(X3,B)|$f13(A,B,C)!=ordered_pair(X2,X3).
% 2.03/2.23 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.03/2.23 0 [] subset(A,B)|in($f14(A,B),A).
% 2.03/2.23 0 [] subset(A,B)| -in($f14(A,B),B).
% 2.03/2.23 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 2.03/2.23 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 2.03/2.23 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 2.03/2.23 0 [] C=set_intersection2(A,B)|in($f15(A,B,C),C)|in($f15(A,B,C),A).
% 2.03/2.23 0 [] C=set_intersection2(A,B)|in($f15(A,B,C),C)|in($f15(A,B,C),B).
% 2.03/2.23 0 [] C=set_intersection2(A,B)| -in($f15(A,B,C),C)| -in($f15(A,B,C),A)| -in($f15(A,B,C),B).
% 2.03/2.23 0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f16(A,B,C)),A).
% 2.03/2.23 0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 2.03/2.23 0 [] -relation(A)|B=relation_dom(A)|in($f18(A,B),B)|in(ordered_pair($f18(A,B),$f17(A,B)),A).
% 2.03/2.23 0 [] -relation(A)|B=relation_dom(A)| -in($f18(A,B),B)| -in(ordered_pair($f18(A,B),X4),A).
% 2.03/2.23 0 [] cast_to_subset(A)=A.
% 2.03/2.23 0 [] B!=union(A)| -in(C,B)|in(C,$f19(A,B,C)).
% 2.03/2.23 0 [] B!=union(A)| -in(C,B)|in($f19(A,B,C),A).
% 2.03/2.23 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 2.03/2.23 0 [] B=union(A)|in($f21(A,B),B)|in($f21(A,B),$f20(A,B)).
% 2.03/2.23 0 [] B=union(A)|in($f21(A,B),B)|in($f20(A,B),A).
% 2.03/2.23 0 [] B=union(A)| -in($f21(A,B),B)| -in($f21(A,B),X5)| -in(X5,A).
% 2.03/2.23 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 2.03/2.23 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 2.03/2.23 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 2.03/2.23 0 [] C=set_difference(A,B)|in($f22(A,B,C),C)|in($f22(A,B,C),A).
% 2.03/2.23 0 [] C=set_difference(A,B)|in($f22(A,B,C),C)| -in($f22(A,B,C),B).
% 2.03/2.23 0 [] C=set_difference(A,B)| -in($f22(A,B,C),C)| -in($f22(A,B,C),A)|in($f22(A,B,C),B).
% 2.03/2.23 0 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f23(A,B,C),C),A).
% 2.03/2.23 0 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 2.03/2.23 0 [] -relation(A)|B=relation_rng(A)|in($f25(A,B),B)|in(ordered_pair($f24(A,B),$f25(A,B)),A).
% 2.03/2.23 0 [] -relation(A)|B=relation_rng(A)| -in($f25(A,B),B)| -in(ordered_pair(X6,$f25(A,B)),A).
% 2.03/2.23 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 2.03/2.23 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.03/2.23 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.03/2.23 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.03/2.23 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).
% 2.03/2.23 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).
% 2.03/2.23 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|element($f26(A,B,C),powerset(A)).
% 2.03/2.23 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|in($f26(A,B,C),C)|in(subset_complement(A,$f26(A,B,C)),B).
% 2.03/2.23 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)| -in($f26(A,B,C),C)| -in(subset_complement(A,$f26(A,B,C)),B).
% 2.03/2.23 0 [] -proper_subset(A,B)|subset(A,B).
% 2.03/2.23 0 [] -proper_subset(A,B)|A!=B.
% 2.03/2.23 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] element(cast_to_subset(A),powerset(A)).
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] -element(B,powerset(powerset(A)))|element(union_of_subsets(A,B),powerset(A)).
% 2.03/2.23 0 [] -element(B,powerset(powerset(A)))|element(meet_of_subsets(A,B),powerset(A)).
% 2.03/2.23 0 [] -element(B,powerset(A))| -element(C,powerset(A))|element(subset_difference(A,B,C),powerset(A)).
% 2.03/2.23 0 [] -element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))).
% 2.03/2.23 0 [] $T.
% 2.03/2.23 0 [] element($f27(A),A).
% 2.03/2.23 0 [] -empty(powerset(A)).
% 2.03/2.23 0 [] empty(empty_set).
% 2.03/2.23 0 [] -empty(ordered_pair(A,B)).
% 2.03/2.23 0 [] -empty(singleton(A)).
% 2.03/2.23 0 [] empty(A)| -empty(set_union2(A,B)).
% 2.03/2.23 0 [] -empty(unordered_pair(A,B)).
% 2.03/2.23 0 [] empty(A)| -empty(set_union2(B,A)).
% 2.03/2.23 0 [] set_union2(A,A)=A.
% 2.03/2.23 0 [] set_intersection2(A,A)=A.
% 2.03/2.23 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 2.03/2.23 0 [] -element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B.
% 2.03/2.23 0 [] -proper_subset(A,A).
% 2.03/2.23 0 [] singleton(A)!=empty_set.
% 2.03/2.23 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.03/2.23 0 [] -disjoint(singleton(A),B)| -in(A,B).
% 2.03/2.23 0 [] in(A,B)|disjoint(singleton(A),B).
% 2.03/2.23 0 [] -subset(singleton(A),B)|in(A,B).
% 2.03/2.23 0 [] subset(singleton(A),B)| -in(A,B).
% 2.03/2.23 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.03/2.23 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.03/2.23 0 [] -element(B,powerset(A))| -in(C,B)|in(C,A).
% 2.03/2.23 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 2.03/2.23 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.03/2.23 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.03/2.24 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.03/2.24 0 [] -in(A,B)|subset(A,union(B)).
% 2.03/2.24 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.03/2.24 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.03/2.24 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.03/2.24 0 [] in($f28(A,B),A)|element(A,powerset(B)).
% 2.03/2.24 0 [] -in($f28(A,B),B)|element(A,powerset(B)).
% 2.03/2.24 0 [] empty($c1).
% 2.03/2.24 0 [] relation($c1).
% 2.03/2.24 0 [] empty(A)|element($f29(A),powerset(A)).
% 2.03/2.24 0 [] empty(A)| -empty($f29(A)).
% 2.03/2.24 0 [] empty($c2).
% 2.03/2.24 0 [] element($f30(A),powerset(A)).
% 2.03/2.24 0 [] empty($f30(A)).
% 2.03/2.24 0 [] -empty($c3).
% 2.03/2.24 0 [] -element(B,powerset(powerset(A)))|union_of_subsets(A,B)=union(B).
% 2.03/2.24 0 [] -element(B,powerset(powerset(A)))|meet_of_subsets(A,B)=set_meet(B).
% 2.03/2.24 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_difference(A,B,C)=set_difference(B,C).
% 2.03/2.24 0 [] subset(A,A).
% 2.03/2.24 0 [] -disjoint(A,B)|disjoint(B,A).
% 2.03/2.24 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.03/2.24 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.03/2.24 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.03/2.24 0 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 2.03/2.24 0 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 2.03/2.24 0 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 2.03/2.24 0 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 2.03/2.24 0 [] -subset(A,B)|set_union2(A,B)=B.
% 2.03/2.24 0 [] in(A,$f31(A)).
% 2.03/2.24 0 [] -in(C,$f31(A))| -subset(D,C)|in(D,$f31(A)).
% 2.03/2.24 0 [] -in(X7,$f31(A))|in(powerset(X7),$f31(A)).
% 2.03/2.24 0 [] -subset(X8,$f31(A))|are_e_quipotent(X8,$f31(A))|in(X8,$f31(A)).
% 2.03/2.24 0 [] subset(set_intersection2(A,B),A).
% 2.03/2.24 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.03/2.24 0 [] set_union2(A,empty_set)=A.
% 2.03/2.24 0 [] -in(A,B)|element(A,B).
% 2.03/2.24 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.03/2.24 0 [] powerset(empty_set)=singleton(empty_set).
% 2.03/2.24 0 [] relation($c4).
% 2.03/2.24 0 [] in(ordered_pair($c6,$c5),$c4).
% 2.03/2.24 0 [] -in($c6,relation_dom($c4))| -in($c5,relation_rng($c4)).
% 2.03/2.24 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.03/2.24 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.03/2.24 0 [] set_intersection2(A,empty_set)=empty_set.
% 2.03/2.24 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.03/2.24 0 [] in($f32(A,B),A)|in($f32(A,B),B)|A=B.
% 2.03/2.24 0 [] -in($f32(A,B),A)| -in($f32(A,B),B)|A=B.
% 2.03/2.24 0 [] subset(empty_set,A).
% 2.03/2.24 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.03/2.24 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 2.03/2.24 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 2.03/2.24 0 [] subset(set_difference(A,B),A).
% 2.03/2.24 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.03/2.24 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.03/2.24 0 [] -subset(singleton(A),B)|in(A,B).
% 2.03/2.24 0 [] subset(singleton(A),B)| -in(A,B).
% 2.03/2.24 0 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 2.03/2.24 0 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 2.03/2.24 0 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 2.03/2.24 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.03/2.24 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.03/2.24 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.03/2.24 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.03/2.24 0 [] set_difference(A,empty_set)=A.
% 2.03/2.24 0 [] -element(A,powerset(B))|subset(A,B).
% 2.03/2.24 0 [] element(A,powerset(B))| -subset(A,B).
% 2.03/2.24 0 [] disjoint(A,B)|in($f33(A,B),A).
% 2.03/2.24 0 [] disjoint(A,B)|in($f33(A,B),B).
% 2.03/2.24 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 2.03/2.24 0 [] -subset(A,empty_set)|A=empty_set.
% 2.03/2.24 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.03/2.24 0 [] -element(B,powerset(A))| -element(C,powerset(A))| -disjoint(B,C)|subset(B,subset_complement(A,C)).
% 2.03/2.24 0 [] -element(B,powerset(A))| -element(C,powerset(A))|disjoint(B,C)| -subset(B,subset_complement(A,C)).
% 2.03/2.24 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 2.03/2.24 0 [] -element(B,powerset(powerset(A)))|B=empty_set|complements_of_subsets(A,B)!=empty_set.
% 2.03/2.24 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.03/2.24 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)).
% 2.03/2.24 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)).
% 2.03/2.24 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 2.03/2.24 0 [] set_difference(empty_set,A)=empty_set.
% 2.03/2.24 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.03/2.24 0 [] disjoint(A,B)|in($f34(A,B),set_intersection2(A,B)).
% 2.03/2.24 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 2.03/2.24 0 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 2.03/2.24 0 [] -element(C,powerset(A))| -in(B,subset_complement(A,C))| -in(B,C).
% 2.03/2.24 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.03/2.24 0 [] -subset(A,B)| -proper_subset(B,A).
% 2.03/2.24 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 2.03/2.24 0 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 2.03/2.24 0 [] set_difference(A,singleton(B))=A|in(B,A).
% 2.03/2.24 0 [] unordered_pair(A,A)=singleton(A).
% 2.03/2.24 0 [] -empty(A)|A=empty_set.
% 2.03/2.24 0 [] -subset(singleton(A),singleton(B))|A=B.
% 2.03/2.24 0 [] -in(A,B)| -empty(B).
% 2.03/2.24 0 [] subset(A,set_union2(A,B)).
% 2.03/2.24 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 2.03/2.24 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 2.03/2.24 0 [] -empty(A)|A=B| -empty(B).
% 2.03/2.24 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.03/2.24 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 2.03/2.24 0 [] -in(A,B)|subset(A,union(B)).
% 2.03/2.24 0 [] union(powerset(A))=A.
% 2.03/2.24 0 [] in(A,$f36(A)).
% 2.03/2.24 0 [] -in(C,$f36(A))| -subset(D,C)|in(D,$f36(A)).
% 2.03/2.24 0 [] -in(X9,$f36(A))|in($f35(A,X9),$f36(A)).
% 2.03/2.24 0 [] -in(X9,$f36(A))| -subset(E,X9)|in(E,$f35(A,X9)).
% 2.03/2.24 0 [] -subset(X10,$f36(A))|are_e_quipotent(X10,$f36(A))|in(X10,$f36(A)).
% 2.03/2.24 0 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 2.03/2.24 end_of_list.
% 2.03/2.24
% 2.03/2.24 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 2.03/2.24
% 2.03/2.24 This ia a non-Horn set with equality. The strategy will be
% 2.03/2.24 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.03/2.24 deletion, with positive clauses in sos and nonpositive
% 2.03/2.24 clauses in usable.
% 2.03/2.24
% 2.03/2.24 dependent: set(knuth_bendix).
% 2.03/2.24 dependent: set(anl_eq).
% 2.03/2.24 dependent: set(para_from).
% 2.03/2.24 dependent: set(para_into).
% 2.03/2.24 dependent: clear(para_from_right).
% 2.03/2.24 dependent: clear(para_into_right).
% 2.03/2.24 dependent: set(para_from_vars).
% 2.03/2.24 dependent: set(eq_units_both_ways).
% 2.03/2.24 dependent: set(dynamic_demod_all).
% 2.03/2.24 dependent: set(dynamic_demod).
% 2.03/2.24 dependent: set(order_eq).
% 2.03/2.24 dependent: set(back_demod).
% 2.03/2.24 dependent: set(lrpo).
% 2.03/2.24 dependent: set(hyper_res).
% 2.03/2.24 dependent: set(unit_deletion).
% 2.03/2.24 dependent: set(factor).
% 2.03/2.24
% 2.03/2.24 ------------> process usable:
% 2.03/2.24 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.03/2.24 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.03/2.24 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 2.03/2.24 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 2.03/2.24 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 2.03/2.24 ** KEPT (pick-wt=16): 6 [] A=empty_set|B!=set_meet(A)| -in(C,B)| -in(D,A)|in(C,D).
% 2.03/2.24 ** KEPT (pick-wt=16): 7 [] A=empty_set|B!=set_meet(A)|in(C,B)|in($f1(A,B,C),A).
% 2.03/2.24 ** KEPT (pick-wt=16): 8 [] A=empty_set|B!=set_meet(A)|in(C,B)| -in(C,$f1(A,B,C)).
% 2.03/2.24 ** KEPT (pick-wt=20): 9 [] A=empty_set|B=set_meet(A)|in($f3(A,B),B)| -in(C,A)|in($f3(A,B),C).
% 2.03/2.24 ** KEPT (pick-wt=17): 10 [] A=empty_set|B=set_meet(A)| -in($f3(A,B),B)|in($f2(A,B),A).
% 2.03/2.24 ** KEPT (pick-wt=19): 11 [] A=empty_set|B=set_meet(A)| -in($f3(A,B),B)| -in($f3(A,B),$f2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=10): 12 [] A!=empty_set|B!=set_meet(A)|B=empty_set.
% 2.03/2.24 ** KEPT (pick-wt=10): 13 [] A!=empty_set|B=set_meet(A)|B!=empty_set.
% 2.03/2.24 ** KEPT (pick-wt=10): 14 [] A!=singleton(B)| -in(C,A)|C=B.
% 2.03/2.24 ** KEPT (pick-wt=10): 15 [] A!=singleton(B)|in(C,A)|C!=B.
% 2.03/2.24 ** KEPT (pick-wt=14): 16 [] A=singleton(B)| -in($f4(B,A),A)|$f4(B,A)!=B.
% 2.03/2.24 ** KEPT (pick-wt=6): 17 [] A!=empty_set| -in(B,A).
% 2.03/2.24 ** KEPT (pick-wt=10): 18 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 2.03/2.24 ** KEPT (pick-wt=10): 19 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 2.03/2.24 ** KEPT (pick-wt=14): 20 [] A=powerset(B)| -in($f6(B,A),A)| -subset($f6(B,A),B).
% 2.03/2.24 ** KEPT (pick-wt=8): 21 [] empty(A)| -element(B,A)|in(B,A).
% 2.03/2.24 ** KEPT (pick-wt=8): 22 [] empty(A)|element(B,A)| -in(B,A).
% 2.03/2.24 ** KEPT (pick-wt=7): 23 [] -empty(A)| -element(B,A)|empty(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 24 [] -empty(A)|element(B,A)| -empty(B).
% 2.03/2.24 ** KEPT (pick-wt=14): 25 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 2.03/2.24 ** KEPT (pick-wt=11): 26 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 2.03/2.24 ** KEPT (pick-wt=11): 27 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 2.03/2.24 ** KEPT (pick-wt=17): 28 [] A=unordered_pair(B,C)| -in($f7(B,C,A),A)|$f7(B,C,A)!=B.
% 2.03/2.24 ** KEPT (pick-wt=17): 29 [] A=unordered_pair(B,C)| -in($f7(B,C,A),A)|$f7(B,C,A)!=C.
% 2.03/2.24 ** KEPT (pick-wt=14): 30 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 2.03/2.24 ** KEPT (pick-wt=11): 31 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 2.03/2.24 ** KEPT (pick-wt=11): 32 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 2.03/2.24 ** KEPT (pick-wt=17): 33 [] A=set_union2(B,C)| -in($f8(B,C,A),A)| -in($f8(B,C,A),B).
% 2.03/2.24 ** KEPT (pick-wt=17): 34 [] A=set_union2(B,C)| -in($f8(B,C,A),A)| -in($f8(B,C,A),C).
% 2.03/2.24 ** KEPT (pick-wt=15): 35 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f10(B,C,A,D),B).
% 2.03/2.24 ** KEPT (pick-wt=15): 36 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f9(B,C,A,D),C).
% 2.03/2.24 ** KEPT (pick-wt=21): 38 [copy,37,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f10(B,C,A,D),$f9(B,C,A,D))=D.
% 2.03/2.24 ** KEPT (pick-wt=19): 39 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 2.03/2.24 ** KEPT (pick-wt=25): 40 [] A=cartesian_product2(B,C)| -in($f13(B,C,A),A)| -in(D,B)| -in(E,C)|$f13(B,C,A)!=ordered_pair(D,E).
% 2.03/2.24 ** KEPT (pick-wt=9): 41 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.03/2.24 ** KEPT (pick-wt=8): 42 [] subset(A,B)| -in($f14(A,B),B).
% 2.03/2.24 ** KEPT (pick-wt=11): 43 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 2.03/2.24 ** KEPT (pick-wt=11): 44 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 2.03/2.24 ** KEPT (pick-wt=14): 45 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 2.03/2.24 ** KEPT (pick-wt=23): 46 [] A=set_intersection2(B,C)| -in($f15(B,C,A),A)| -in($f15(B,C,A),B)| -in($f15(B,C,A),C).
% 2.03/2.24 ** KEPT (pick-wt=17): 47 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f16(A,B,C)),A).
% 2.03/2.24 ** KEPT (pick-wt=14): 48 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 2.03/2.24 ** KEPT (pick-wt=20): 49 [] -relation(A)|B=relation_dom(A)|in($f18(A,B),B)|in(ordered_pair($f18(A,B),$f17(A,B)),A).
% 2.03/2.24 ** KEPT (pick-wt=18): 50 [] -relation(A)|B=relation_dom(A)| -in($f18(A,B),B)| -in(ordered_pair($f18(A,B),C),A).
% 2.03/2.24 ** KEPT (pick-wt=13): 51 [] A!=union(B)| -in(C,A)|in(C,$f19(B,A,C)).
% 2.03/2.24 ** KEPT (pick-wt=13): 52 [] A!=union(B)| -in(C,A)|in($f19(B,A,C),B).
% 2.03/2.24 ** KEPT (pick-wt=13): 53 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 2.03/2.24 ** KEPT (pick-wt=17): 54 [] A=union(B)| -in($f21(B,A),A)| -in($f21(B,A),C)| -in(C,B).
% 2.03/2.24 ** KEPT (pick-wt=11): 55 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 2.03/2.24 ** KEPT (pick-wt=11): 56 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 2.03/2.24 ** KEPT (pick-wt=14): 57 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 2.03/2.24 ** KEPT (pick-wt=17): 58 [] A=set_difference(B,C)|in($f22(B,C,A),A)| -in($f22(B,C,A),C).
% 2.03/2.24 ** KEPT (pick-wt=23): 59 [] A=set_difference(B,C)| -in($f22(B,C,A),A)| -in($f22(B,C,A),B)|in($f22(B,C,A),C).
% 2.03/2.24 ** KEPT (pick-wt=17): 60 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f23(A,B,C),C),A).
% 2.03/2.24 ** KEPT (pick-wt=14): 61 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 2.03/2.24 ** KEPT (pick-wt=20): 62 [] -relation(A)|B=relation_rng(A)|in($f25(A,B),B)|in(ordered_pair($f24(A,B),$f25(A,B)),A).
% 2.03/2.24 ** KEPT (pick-wt=18): 63 [] -relation(A)|B=relation_rng(A)| -in($f25(A,B),B)| -in(ordered_pair(C,$f25(A,B)),A).
% 2.03/2.24 ** KEPT (pick-wt=11): 64 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 2.03/2.24 ** KEPT (pick-wt=8): 65 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.03/2.24 ** KEPT (pick-wt=8): 66 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.03/2.24 ** KEPT (pick-wt=27): 67 [] -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).
% 2.03/2.24 ** KEPT (pick-wt=27): 68 [] -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).
% 2.03/2.24 ** KEPT (pick-wt=22): 69 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|element($f26(B,A,C),powerset(B)).
% 2.03/2.24 ** KEPT (pick-wt=29): 70 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|in($f26(B,A,C),C)|in(subset_complement(B,$f26(B,A,C)),A).
% 2.03/2.24 ** KEPT (pick-wt=29): 71 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)| -in($f26(B,A,C),C)| -in(subset_complement(B,$f26(B,A,C)),A).
% 2.03/2.25 ** KEPT (pick-wt=6): 72 [] -proper_subset(A,B)|subset(A,B).
% 2.03/2.25 ** KEPT (pick-wt=6): 73 [] -proper_subset(A,B)|A!=B.
% 2.03/2.25 ** KEPT (pick-wt=9): 74 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.03/2.25 ** KEPT (pick-wt=10): 75 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 2.03/2.25 ** KEPT (pick-wt=11): 76 [] -element(A,powerset(powerset(B)))|element(union_of_subsets(B,A),powerset(B)).
% 2.03/2.25 ** KEPT (pick-wt=11): 77 [] -element(A,powerset(powerset(B)))|element(meet_of_subsets(B,A),powerset(B)).
% 2.03/2.25 ** KEPT (pick-wt=15): 78 [] -element(A,powerset(B))| -element(C,powerset(B))|element(subset_difference(B,A,C),powerset(B)).
% 2.03/2.25 ** KEPT (pick-wt=12): 79 [] -element(A,powerset(powerset(B)))|element(complements_of_subsets(B,A),powerset(powerset(B))).
% 2.03/2.25 ** KEPT (pick-wt=3): 80 [] -empty(powerset(A)).
% 2.03/2.25 ** KEPT (pick-wt=4): 81 [] -empty(ordered_pair(A,B)).
% 2.03/2.25 ** KEPT (pick-wt=3): 82 [] -empty(singleton(A)).
% 2.03/2.25 ** KEPT (pick-wt=6): 83 [] empty(A)| -empty(set_union2(A,B)).
% 2.03/2.25 ** KEPT (pick-wt=4): 84 [] -empty(unordered_pair(A,B)).
% 2.03/2.25 ** KEPT (pick-wt=6): 85 [] empty(A)| -empty(set_union2(B,A)).
% 2.03/2.25 ** KEPT (pick-wt=11): 86 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 2.03/2.25 ** KEPT (pick-wt=12): 87 [] -element(A,powerset(powerset(B)))|complements_of_subsets(B,complements_of_subsets(B,A))=A.
% 2.03/2.25 ** KEPT (pick-wt=3): 88 [] -proper_subset(A,A).
% 2.03/2.25 ** KEPT (pick-wt=4): 89 [] singleton(A)!=empty_set.
% 2.03/2.25 ** KEPT (pick-wt=9): 90 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.03/2.25 ** KEPT (pick-wt=7): 91 [] -disjoint(singleton(A),B)| -in(A,B).
% 2.03/2.25 ** KEPT (pick-wt=7): 92 [] -subset(singleton(A),B)|in(A,B).
% 2.03/2.25 ** KEPT (pick-wt=7): 93 [] subset(singleton(A),B)| -in(A,B).
% 2.03/2.25 ** KEPT (pick-wt=8): 94 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.03/2.25 ** KEPT (pick-wt=8): 95 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.03/2.25 ** KEPT (pick-wt=10): 96 [] -element(A,powerset(B))| -in(C,A)|in(C,B).
% 2.03/2.25 ** KEPT (pick-wt=12): 97 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 2.03/2.25 ** KEPT (pick-wt=11): 98 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.03/2.25 ** KEPT (pick-wt=7): 99 [] subset(A,singleton(B))|A!=empty_set.
% 2.03/2.25 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.03/2.25 ** KEPT (pick-wt=7): 100 [] -in(A,B)|subset(A,union(B)).
% 2.03/2.25 ** KEPT (pick-wt=10): 101 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.03/2.25 ** KEPT (pick-wt=10): 102 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.03/2.25 ** KEPT (pick-wt=13): 103 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.03/2.25 ** KEPT (pick-wt=9): 104 [] -in($f28(A,B),B)|element(A,powerset(B)).
% 2.03/2.25 ** KEPT (pick-wt=5): 105 [] empty(A)| -empty($f29(A)).
% 2.03/2.25 ** KEPT (pick-wt=2): 106 [] -empty($c3).
% 2.03/2.25 ** KEPT (pick-wt=11): 107 [] -element(A,powerset(powerset(B)))|union_of_subsets(B,A)=union(A).
% 2.03/2.25 ** KEPT (pick-wt=11): 108 [] -element(A,powerset(powerset(B)))|meet_of_subsets(B,A)=set_meet(A).
% 2.03/2.25 ** KEPT (pick-wt=16): 109 [] -element(A,powerset(B))| -element(C,powerset(B))|subset_difference(B,A,C)=set_difference(A,C).
% 2.03/2.25 ** KEPT (pick-wt=6): 110 [] -disjoint(A,B)|disjoint(B,A).
% 2.03/2.25 Following clause subsumed by 101 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.03/2.25 Following clause subsumed by 102 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.03/2.25 Following clause subsumed by 103 during input processing: 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.03/2.25 ** KEPT (pick-wt=13): 111 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 2.03/2.25 ** KEPT (pick-wt=10): 112 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 2.03/2.25 ** KEPT (pick-wt=10): 113 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 2.03/2.25 ** KEPT (pick-wt=13): 114 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 2.03/2.25 ** KEPT (pick-wt=8): 115 [] -subset(A,B)|set_union2(A,B)=B.
% 2.03/2.25 ** KEPT (pick-wt=11): 116 [] -in(A,$f31(B))| -subset(C,A)|in(C,$f31(B)).
% 2.03/2.25 ** KEPT (pick-wt=9): 117 [] -in(A,$f31(B))|in(powerset(A),$f31(B)).
% 2.03/2.25 ** KEPT (pick-wt=12): 118 [] -subset(A,$f31(B))|are_e_quipotent(A,$f31(B))|in(A,$f31(B)).
% 2.03/2.25 ** KEPT (pick-wt=11): 119 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.03/2.25 ** KEPT (pick-wt=6): 120 [] -in(A,B)|element(A,B).
% 2.03/2.25 ** KEPT (pick-wt=9): 121 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.03/2.25 ** KEPT (pick-wt=8): 122 [] -in($c6,relation_dom($c4))| -in($c5,relation_rng($c4)).
% 2.03/2.25 ** KEPT (pick-wt=10): 123 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.03/2.25 ** KEPT (pick-wt=8): 124 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.03/2.25 Following clause subsumed by 21 during input processing: 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.03/2.25 ** KEPT (pick-wt=13): 125 [] -in($f32(A,B),A)| -in($f32(A,B),B)|A=B.
% 2.03/2.25 ** KEPT (pick-wt=10): 126 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.03/2.25 ** KEPT (pick-wt=10): 127 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 2.03/2.25 ** KEPT (pick-wt=10): 128 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 2.03/2.25 Following clause subsumed by 94 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.03/2.25 Following clause subsumed by 95 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.03/2.25 Following clause subsumed by 92 during input processing: 0 [] -subset(singleton(A),B)|in(A,B).
% 2.03/2.25 Following clause subsumed by 93 during input processing: 0 [] subset(singleton(A),B)| -in(A,B).
% 2.03/2.25 ** KEPT (pick-wt=8): 129 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 2.03/2.25 ** KEPT (pick-wt=8): 130 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 2.03/2.25 ** KEPT (pick-wt=11): 131 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 2.03/2.25 Following clause subsumed by 98 during input processing: 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.03/2.25 Following clause subsumed by 99 during input processing: 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.03/2.25 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.03/2.25 ** KEPT (pick-wt=7): 132 [] -element(A,powerset(B))|subset(A,B).
% 2.03/2.25 ** KEPT (pick-wt=7): 133 [] element(A,powerset(B))| -subset(A,B).
% 2.03/2.25 ** KEPT (pick-wt=9): 134 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 2.03/2.25 ** KEPT (pick-wt=6): 135 [] -subset(A,empty_set)|A=empty_set.
% 2.03/2.25 ** KEPT (pick-wt=16): 136 [] -element(A,powerset(B))| -element(C,powerset(B))| -disjoint(A,C)|subset(A,subset_complement(B,C)).
% 2.03/2.25 ** KEPT (pick-wt=16): 137 [] -element(A,powerset(B))| -element(C,powerset(B))|disjoint(A,C)| -subset(A,subset_complement(B,C)).
% 2.03/2.25 ** KEPT (pick-wt=10): 139 [copy,138,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 2.03/2.25 ** KEPT (pick-wt=13): 140 [] -element(A,powerset(powerset(B)))|A=empty_set|complements_of_subsets(B,A)!=empty_set.
% 2.03/2.25 Following clause subsumed by 90 during input processing: 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.03/2.25 ** KEPT (pick-wt=21): 141 [] -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)).
% 2.03/2.25 ** KEPT (pick-wt=21): 142 [] -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)).
% 2.03/2.25 ** KEPT (pick-wt=10): 143 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.03/2.25 ** KEPT (pick-wt=8): 144 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 2.03/2.25 ** KEPT (pick-wt=18): 145 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 2.03/2.25 ** KEPT (pick-wt=12): 146 [] -element(A,powerset(B))| -in(C,subset_complement(B,A))| -in(C,A).
% 2.03/2.25 ** KEPT (pick-wt=9): 147 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.03/2.25 ** KEPT (pick-wt=6): 148 [] -subset(A,B)| -proper_subset(B,A).
% 2.03/2.25 ** KEPT (pick-wt=9): 149 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 2.03/2.25 ** KEPT (pick-wt=9): 150 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 2.03/2.25 ** KEPT (pick-wt=5): 151 [] -empty(A)|A=empty_set.
% 2.03/2.25 ** KEPT (pick-wt=8): 152 [] -subset(singleton(A),singleton(B))|A=B.
% 2.03/2.25 ** KEPT (pick-wt=5): 153 [] -in(A,B)| -empty(B).
% 2.03/2.25 ** KEPT (pick-wt=8): 154 [] -disjoint(A,B)|set_difference(A,B)=A.
% 2.03/2.25 ** KEPT (pick-wt=8): 155 [] disjoint(A,B)|set_difference(A,B)!=A.
% 2.03/2.25 ** KEPT (pick-wt=7): 156 [] -empty(A)|A=B| -empty(B).
% 2.03/2.25 ** KEPT (pick-wt=11): 157 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.03/2.25 ** KEPT (pick-wt=9): 158 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 2.03/2.25 Following clause subsumed by 100 during input processing: 0 [] -in(A,B)|subset(A,union(B)).
% 2.03/2.25 ** KEPT (pick-wt=11): 159 [] -in(A,$f36(B))| -subset(C,A)|in(C,$f36(B)).
% 2.03/2.25 ** KEPT (pick-wt=10): 160 [] -in(A,$f36(B))|in($f35(B,A),$f36(B)).
% 2.03/2.25 ** KEPT (pick-wt=12): 161 [] -in(A,$f36(B))| -subset(C,A)|in(C,$f35(B,A)).
% 2.03/2.25 ** KEPT (pick-wt=12): 162 [] -subset(A,$f36(B))|are_e_quipotent(A,$f36(B))|in(A,$f36(B)).
% 2.03/2.25 ** KEPT (pick-wt=9): 163 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 2.03/2.25 120 back subsumes 22.
% 2.03/2.25
% 2.03/2.25 ------------> process sos:
% 2.03/2.25 ** KEPT (pick-wt=3): 206 [] A=A.
% 2.03/2.25 ** KEPT (pick-wt=7): 207 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.03/2.25 ** KEPT (pick-wt=7): 208 [] set_union2(A,B)=set_union2(B,A).
% 2.03/2.25 ** KEPT (pick-wt=7): 209 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.03/2.25 ** KEPT (pick-wt=14): 210 [] A=singleton(B)|in($f4(B,A),A)|$f4(B,A)=B.
% 2.03/2.25 ** KEPT (pick-wt=7): 211 [] A=empty_set|in($f5(A),A).
% 2.03/2.25 ** KEPT (pick-wt=14): 212 [] A=powerset(B)|in($f6(B,A),A)|subset($f6(B,A),B).
% 2.03/2.25 ** KEPT (pick-wt=23): 213 [] A=unordered_pair(B,C)|in($f7(B,C,A),A)|$f7(B,C,A)=B|$f7(B,C,A)=C.
% 2.03/2.25 ** KEPT (pick-wt=23): 214 [] A=set_union2(B,C)|in($f8(B,C,A),A)|in($f8(B,C,A),B)|in($f8(B,C,A),C).
% 2.03/2.25 ** KEPT (pick-wt=17): 215 [] A=cartesian_product2(B,C)|in($f13(B,C,A),A)|in($f12(B,C,A),B).
% 2.03/2.25 ** KEPT (pick-wt=17): 216 [] A=cartesian_product2(B,C)|in($f13(B,C,A),A)|in($f11(B,C,A),C).
% 2.03/2.25 ** KEPT (pick-wt=25): 218 [copy,217,flip.3] A=cartesian_product2(B,C)|in($f13(B,C,A),A)|ordered_pair($f12(B,C,A),$f11(B,C,A))=$f13(B,C,A).
% 2.03/2.25 ** KEPT (pick-wt=8): 219 [] subset(A,B)|in($f14(A,B),A).
% 2.03/2.25 ** KEPT (pick-wt=17): 220 [] A=set_intersection2(B,C)|in($f15(B,C,A),A)|in($f15(B,C,A),B).
% 2.03/2.25 ** KEPT (pick-wt=17): 221 [] A=set_intersection2(B,C)|in($f15(B,C,A),A)|in($f15(B,C,A),C).
% 2.03/2.25 ** KEPT (pick-wt=4): 222 [] cast_to_subset(A)=A.
% 2.03/2.25 ---> New Demodulator: 223 [new_demod,222] cast_to_subset(A)=A.
% 2.03/2.25 ** KEPT (pick-wt=16): 224 [] A=union(B)|in($f21(B,A),A)|in($f21(B,A),$f20(B,A)).
% 2.03/2.25 ** KEPT (pick-wt=14): 225 [] A=union(B)|in($f21(B,A),A)|in($f20(B,A),B).
% 2.03/2.25 ** KEPT (pick-wt=17): 226 [] A=set_difference(B,C)|in($f22(B,C,A),A)|in($f22(B,C,A),B).
% 2.03/2.25 ** KEPT (pick-wt=10): 228 [copy,227,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.03/2.25 ---> New Demodulator: 229 [new_demod,228] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.03/2.25 ** KEPT (pick-wt=4): 231 [copy,230,demod,223] element(A,powerset(A)).
% 2.03/2.25 ** KEPT (pick-wt=4): 232 [] element($f27(A),A).
% 2.03/2.25 ** KEPT (pick-wt=2): 233 [] empty(empty_set).
% 2.03/2.25 ** KEPT (pick-wt=5): 234 [] set_union2(A,A)=A.
% 2.03/2.25 ---> New Demodulator: 235 [new_demod,234] set_union2(A,A)=A.
% 2.03/2.25 ** KEPT (pick-wt=5): 236 [] set_intersection2(A,A)=A.
% 2.03/2.25 ---> New Demodulator: 237 [new_demod,236] set_intersection2(A,A)=A.
% 2.03/2.25 ** KEPT (pick-wt=7): 238 [] in(A,B)|disjoint(singleton(A),B).
% 2.03/2.25 ** KEPT (pick-wt=9): 239 [] in($f28(A,B),A)|element(A,powerset(B)).
% 2.03/2.25 ** KEPT (pick-wt=2): 240 [] empty($c1).
% 2.03/2.25 ** KEPT (pick-wt=2): 241 [] relation($c1).
% 2.03/2.25 ** KEPT (pick-wt=7): 242 [] empty(A)|element($f29(A),powerset(A)).
% 2.03/2.25 ** KEPT (pick-wt=2): 243 [] empty($c2).
% 2.03/2.25 ** KEPT (pick-wt=5): 244 [] element($f30(A),powerset(A)).
% 2.03/2.25 ** KEPT (pick-wt=3): 245 [] empty($f30(A)).
% 2.03/2.25 ** KEPT (pick-wt=3): 246 [] subset(A,A).
% 2.03/2.25 ** KEPT (pick-wt=4): 247 [] in(A,$f31(A)).
% 2.03/2.25 ** KEPT (pick-wt=5): 248 [] subset(set_intersection2(A,B),A).
% 2.03/2.25 ** KEPT (pick-wt=5): 249 [] set_union2(A,empty_set)=A.
% 2.03/2.25 ---> New Demodulator: 250 [new_demod,249] set_union2(A,empty_set)=A.
% 2.03/2.25 ** KEPT (pick-wt=5): 252 [copy,251,flip.1] singleton(empty_set)=powerset(empty_set).
% 2.03/2.25 ---> New Demodulator: 253 [new_demod,252] singleton(empty_set)=powerset(empty_set).
% 2.03/2.25 ** KEPT (pick-wt=2): 254 [] relation($c4).
% 2.03/2.25 ** KEPT (pick-wt=5): 255 [] in(ordered_pair($c6,$c5),$c4).
% 2.03/2.25 ** KEPT (pick-wt=5): 256 [] set_intersection2(A,empty_set)=empty_set.
% 2.03/2.25 ---> New Demodulator: 257 [new_demod,256] set_intersection2(A,empty_set)=empty_set.
% 2.03/2.25 ** KEPT (pick-wt=13): 258 [] in($f32(A,B),A)|in($f32(A,B),B)|A=B.
% 2.03/2.25 ** KEPT (pick-wt=3): 259 [] subset(empty_set,A).
% 2.03/2.25 ** KEPT (pick-wt=5): 260 [] subset(set_difference(A,B),A).
% 2.03/2.26 ** KEPT (pick-wt=9): 261 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.03/2.26 ---> New Demodulator: 262 [new_demod,261] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.03/2.26 ** KEPT (pick-wt=5): 263 [] set_difference(A,empty_set)=A.
% 2.03/2.26 ---> New Demodulator: 264 [new_demod,263] set_difference(A,empty_set)=A.
% 2.03/2.26 ** KEPT (pick-wt=8): 265 [] disjoint(A,B)|in($f33(A,B),A).
% 2.03/2.26 ** KEPT (pick-wt=8): 266 [] disjoint(A,B)|in($f33(A,B),B).
% 2.03/2.26 ** KEPT (pick-wt=9): 267 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.03/2.26 ---> New Demodulator: 268 [new_demod,267] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.03/2.26 ** KEPT (pick-wt=9): 270 [copy,269,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 2.03/2.26 ---> New Demodulator: 271 [new_demod,270] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 2.03/2.26 ** KEPT (pick-wt=5): 272 [] set_difference(empty_set,A)=empty_set.
% 2.03/2.26 ---> New Demodulator: 273 [new_demod,272] set_difference(empty_set,A)=empty_set.
% 2.03/2.26 ** KEPT (pick-wt=12): 275 [copy,274,demod,271] disjoint(A,B)|in($f34(A,B),set_difference(A,set_difference(A,B))).
% 2.03/2.26 ** KEPT (pick-wt=9): 276 [] set_difference(A,singleton(B))=A|in(B,A).
% 2.03/2.26 ** KEPT (pick-wt=6): 278 [copy,277,flip.1] singleton(A)=unordered_pair(A,A).
% 2.03/2.26 ---> New Demodulator: 279 [new_demod,278] singleton(A)=unordered_pair(A,A).
% 2.03/2.26 ** KEPT (pick-wt=5): 280 [] subset(A,set_union2(A,B)).
% 2.03/2.26 ** KEPT (pick-wt=5): 281 [] union(powerset(A))=A.
% 2.03/2.26 ---> New Demodulator: 282 [new_demod,281] union(powerset(A))=A.
% 2.03/2.26 ** KEPT (pick-wt=4): 283 [] in(A,$f36(A)).
% 2.03/2.26 Following clause subsumed by 206 during input processing: 0 [copy,206,flip.1] A=A.
% 2.03/2.26 206 back subsumes 202.
% 2.03/2.26 206 back subsumes 197.
% 2.03/2.26 206 back subsumes 165.
% 2.03/2.26 Following clause subsumed by 207 during input processing: 0 [copy,207,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.03/2.26 Following clause subsumed by 208 during input processing: 0 [copy,208,flip.1] set_union2(A,B)=set_union2(B,A).
% 2.03/2.26 ** KEPT (pick-wt=11): 284 [copy,209,flip.1,demod,271,271] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 2.03/2.26 >>>> Starting back demodulation with 223.
% 2.03/2.26 >> back demodulating 142 with 223.
% 2.03/2.26 >> back demodulating 141 with 223.
% 2.03/2.26 >>>> Starting back demodulation with 229.
% 2.03/2.26 >>>> Starting back demodulation with 235.
% 2.03/2.26 >> back demodulating 203 with 235.
% 2.03/2.26 >> back demodulating 171 with 235.
% 2.03/2.26 >>>> Starting back demodulation with 237.
% 2.03/2.26 >> back demodulating 205 with 237.
% 2.03/2.26 >> back demodulating 196 with 237.
% 2.03/2.26 >> back demodulating 181 with 237.
% 2.03/2.26 >> back demodulating 178 with 237.
% 2.03/2.26 >>>> Starting back demodulation with 250.
% 2.03/2.26 >>>> Starting back demodulation with 253.
% 2.03/2.26 >>>> Starting back demodulation with 257.
% 2.03/2.26 >>>> Starting back demodulation with 262.
% 2.03/2.26 >> back demodulating 139 with 262.
% 2.03/2.26 >>>> Starting back demodulation with 264.
% 2.03/2.26 >>>> Starting back demodulation with 268.
% 2.03/2.26 >>>> Starting back demodulation with 271.
% 2.03/2.26 >> back demodulating 256 with 271.
% 2.03/2.26 >> back demodulating 248 with 271.
% 2.03/2.26 >> back demodulating 236 with 271.
% 2.03/2.26 >> back demodulating 221 with 271.
% 2.03/2.26 >> back demodulating 220 with 271.
% 2.03/2.26 >> back demodulating 209 with 271.
% 2.03/2.26 >> back demodulating 180 with 271.
% 2.03/2.26 >> back demodulating 179 with 271.
% 2.03/2.26 >> back demodulating 144 with 271.
% 2.03/2.26 >> back demodulating 124 with 271.
% 2.03/2.26 >> back demodulating 123 with 271.
% 2.03/2.26 >> back demodulating 119 with 271.
% 2.03/2.26 >> back demodulating 66 with 271.
% 2.03/2.26 >> back demodulating 65 with 271.
% 2.03/2.26 >> back demodulating 46 with 271.
% 2.03/2.26 >> back demodulating 45 with 271.
% 2.03/2.26 >> back demodulating 44 with 271.
% 2.03/2.26 >> back demodulating 43 with 271.
% 2.03/2.26 >>>> Starting back demodulation with 273.
% 2.03/2.26 >>>> Starting back demodulation with 279.
% 2.03/2.26 >> back demodulating 276 with 279.
% 2.03/2.26 >> back demodulating 252 with 279.
% 2.03/2.26 >> back demodulating 238 with 279.
% 2.03/2.26 >> back demodulating 228 with 279.
% 2.03/2.26 >> back demodulating 210 with 279.
% 2.03/2.26 >> back demodulating 163 with 279.
% 2.03/2.26 >> back demodulating 158 with 279.
% 2.03/2.26 >> back demodulating 152 with 279.
% 2.03/2.26 >> back demodulating 150 with 279.
% 2.03/2.26 >> back demodulating 99 with 279.
% 2.03/2.26 >> back demodulating 98 with 279.
% 2.03/2.26 >> back demodulating 97 with 279.
% 2.03/2.26 >> back demodulating 93 with 279.
% 2.27/2.49 >> back demodulating 92 with 279.
% 2.27/2.49 >> back demodulating 91 with 279.
% 2.27/2.49 >> back demodulating 90 with 279.
% 2.27/2.49 >> back demodulating 89 with 279.
% 2.27/2.49 >> back demodulating 82 with 279.
% 2.27/2.49 >> back demodulating 16 with 279.
% 2.27/2.49 >> back demodulating 15 with 279.
% 2.27/2.49 >> back demodulating 14 with 279.
% 2.27/2.49 >>>> Starting back demodulation with 282.
% 2.27/2.49 Following clause subsumed by 284 during input processing: 0 [copy,284,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 2.27/2.49 >>>> Starting back demodulation with 298.
% 2.27/2.49 >> back demodulating 193 with 298.
% 2.27/2.49 >>>> Starting back demodulation with 314.
% 2.27/2.49 >>>> Starting back demodulation with 317.
% 2.27/2.49
% 2.27/2.49 ======= end of input processing =======
% 2.27/2.49
% 2.27/2.49 =========== start of search ===========
% 2.27/2.49
% 2.27/2.49
% 2.27/2.49 Resetting weight limit to 5.
% 2.27/2.49
% 2.27/2.49
% 2.27/2.49 Resetting weight limit to 5.
% 2.27/2.49
% 2.27/2.49 sos_size=269
% 2.27/2.49
% 2.27/2.49 -------- PROOF --------
% 2.27/2.49
% 2.27/2.49 -----> EMPTY CLAUSE at 0.27 sec ----> 640 [hyper,636,122,635] $F.
% 2.27/2.49
% 2.27/2.49 Length of proof is 2. Level of proof is 1.
% 2.27/2.49
% 2.27/2.49 ---------------- PROOF ----------------
% 2.27/2.49 % SZS status Theorem
% 2.27/2.49 % SZS output start Refutation
% See solution above
% 2.27/2.49 ------------ end of proof -------------
% 2.27/2.49
% 2.27/2.49
% 2.27/2.49 Search stopped by max_proofs option.
% 2.27/2.49
% 2.27/2.49
% 2.27/2.49 Search stopped by max_proofs option.
% 2.27/2.49
% 2.27/2.49 ============ end of search ============
% 2.27/2.49
% 2.27/2.49 -------------- statistics -------------
% 2.27/2.49 clauses given 47
% 2.27/2.49 clauses generated 10115
% 2.27/2.49 clauses kept 598
% 2.27/2.49 clauses forward subsumed 466
% 2.27/2.49 clauses back subsumed 8
% 2.27/2.49 Kbytes malloced 4882
% 2.27/2.49
% 2.27/2.49 ----------- times (seconds) -----------
% 2.27/2.49 user CPU time 0.27 (0 hr, 0 min, 0 sec)
% 2.27/2.49 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.27/2.49 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.27/2.49
% 2.27/2.49 That finishes the proof of the theorem.
% 2.27/2.49
% 2.27/2.49 Process 14949 finished Wed Jul 27 08:07:39 2022
% 2.27/2.49 Otter interrupted
% 2.27/2.49 PROOF FOUND
%------------------------------------------------------------------------------