TSTP Solution File: SEU174+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU174+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:15:03 EDT 2022
% Result : Theorem 3.38s 3.53s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of clauses : 25 ( 19 unt; 2 nHn; 18 RR)
% Number of literals : 38 ( 16 equ; 14 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(48,axiom,
( ~ element(A,powerset(B))
| subset_complement(B,A) = set_difference(B,A) ),
file('SEU174+2.p',unknown),
[] ).
cnf(54,axiom,
( ~ element(A,powerset(powerset(B)))
| ~ element(C,powerset(powerset(B)))
| C = complements_of_subsets(B,A)
| in(dollar_f17(B,A,C),C)
| in(subset_complement(B,dollar_f17(B,A,C)),A) ),
file('SEU174+2.p',unknown),
[] ).
cnf(66,axiom,
( ~ element(A,powerset(powerset(B)))
| complements_of_subsets(B,complements_of_subsets(B,A)) = A ),
file('SEU174+2.p',unknown),
[] ).
cnf(115,axiom,
dollar_c3 != empty_set,
file('SEU174+2.p',unknown),
[] ).
cnf(116,plain,
empty_set != dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[115])]),
[iquote('copy,115,flip.1')] ).
cnf(120,axiom,
( ~ element(A,powerset(B))
| ~ in(C,subset_complement(B,A))
| ~ in(C,A) ),
file('SEU174+2.p',unknown),
[] ).
cnf(130,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU174+2.p',unknown),
[] ).
cnf(160,plain,
( ~ element(A,powerset(powerset(B)))
| complements_of_subsets(B,A) = A
| in(dollar_f17(B,A,A),A)
| in(subset_complement(B,dollar_f17(B,A,A)),A) ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[54])]),
[iquote('factor,54.1.2,flip.2')] ).
cnf(198,axiom,
empty(empty_set),
file('SEU174+2.p',unknown),
[] ).
cnf(206,axiom,
empty(dollar_c1),
file('SEU174+2.p',unknown),
[] ).
cnf(207,axiom,
element(dollar_f21(A),powerset(A)),
file('SEU174+2.p',unknown),
[] ).
cnf(208,axiom,
empty(dollar_f21(A)),
file('SEU174+2.p',unknown),
[] ).
cnf(224,axiom,
set_difference(A,empty_set) = A,
file('SEU174+2.p',unknown),
[] ).
cnf(230,axiom,
element(dollar_c3,powerset(powerset(dollar_c4))),
file('SEU174+2.p',unknown),
[] ).
cnf(231,axiom,
complements_of_subsets(dollar_c4,dollar_c3) = empty_set,
file('SEU174+2.p',unknown),
[] ).
cnf(330,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[206,130,198]),
[iquote('hyper,206,130,198')] ).
cnf(376,plain,
complements_of_subsets(dollar_c4,dollar_c3) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[231]),330]),
[iquote('back_demod,231,demod,330')] ).
cnf(378,plain,
set_difference(A,dollar_c1) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[224]),330]),
[iquote('back_demod,224,demod,330')] ).
cnf(385,plain,
dollar_c3 != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[116]),330])]),
[iquote('back_demod,116,demod,330,flip.1')] ).
cnf(393,plain,
dollar_f21(A) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[208,130,206])]),
[iquote('hyper,208,130,206,flip.1')] ).
cnf(394,plain,
element(dollar_c1,powerset(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[207]),393]),
[iquote('back_demod,207,demod,393')] ).
cnf(707,plain,
subset_complement(A,dollar_c1) = A,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[394,48]),378]),
[iquote('hyper,394,48,demod,378')] ).
cnf(721,plain,
complements_of_subsets(dollar_c4,dollar_c1) = dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[230,66]),376]),
[iquote('hyper,230,66,demod,376')] ).
cnf(759,plain,
~ in(A,dollar_c1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[707,120]),394])]),
[iquote('para_from,707.1.1,120.2.2,unit_del,394,factor_simp')] ).
cnf(765,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[721,160]),385,394,759,759]),
[iquote('para_into,721.1.1,160.2.1,unit_del,385,394,759,759')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU174+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 07:53:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.13/2.31 ----- Otter 3.3f, August 2004 -----
% 2.13/2.31 The process was started by sandbox on n003.cluster.edu,
% 2.13/2.31 Wed Jul 27 07:53:56 2022
% 2.13/2.31 The command was "./otter". The process ID is 350.
% 2.13/2.31
% 2.13/2.31 set(prolog_style_variables).
% 2.13/2.31 set(auto).
% 2.13/2.31 dependent: set(auto1).
% 2.13/2.31 dependent: set(process_input).
% 2.13/2.31 dependent: clear(print_kept).
% 2.13/2.31 dependent: clear(print_new_demod).
% 2.13/2.31 dependent: clear(print_back_demod).
% 2.13/2.31 dependent: clear(print_back_sub).
% 2.13/2.31 dependent: set(control_memory).
% 2.13/2.31 dependent: assign(max_mem, 12000).
% 2.13/2.31 dependent: assign(pick_given_ratio, 4).
% 2.13/2.31 dependent: assign(stats_level, 1).
% 2.13/2.31 dependent: assign(max_seconds, 10800).
% 2.13/2.31 clear(print_given).
% 2.13/2.31
% 2.13/2.31 formula_list(usable).
% 2.13/2.31 all A (A=A).
% 2.13/2.31 all A B (in(A,B)-> -in(B,A)).
% 2.13/2.31 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 2.13/2.31 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.13/2.31 all A B (set_union2(A,B)=set_union2(B,A)).
% 2.13/2.31 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.13/2.31 all A B (A=B<->subset(A,B)&subset(B,A)).
% 2.13/2.31 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 2.13/2.31 all A (A=empty_set<-> (all B (-in(B,A)))).
% 2.13/2.31 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 2.13/2.31 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 2.13/2.31 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 2.13/2.31 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 2.13/2.31 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)))))).
% 2.13/2.31 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.13/2.31 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 2.13/2.31 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 2.13/2.31 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 2.13/2.31 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 2.13/2.31 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 2.13/2.31 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 2.13/2.31 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)))))))).
% 2.13/2.31 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 2.13/2.31 $T.
% 2.13/2.31 $T.
% 2.13/2.31 $T.
% 2.13/2.31 $T.
% 2.13/2.31 $T.
% 2.13/2.31 $T.
% 2.13/2.31 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 2.13/2.31 $T.
% 2.13/2.31 $T.
% 2.13/2.31 $T.
% 2.13/2.31 $T.
% 2.13/2.31 all A B (element(B,powerset(powerset(A)))->element(complements_of_subsets(A,B),powerset(powerset(A)))).
% 2.13/2.31 $T.
% 2.13/2.31 all A exists B element(B,A).
% 2.13/2.31 all A (-empty(powerset(A))).
% 2.13/2.31 empty(empty_set).
% 2.13/2.31 all A B (-empty(ordered_pair(A,B))).
% 2.13/2.31 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 2.13/2.31 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 2.13/2.31 all A B (set_union2(A,A)=A).
% 2.13/2.31 all A B (set_intersection2(A,A)=A).
% 2.13/2.31 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 2.13/2.31 all A B (element(B,powerset(powerset(A)))->complements_of_subsets(A,complements_of_subsets(A,B))=B).
% 2.13/2.31 all A B (-proper_subset(A,A)).
% 2.13/2.31 all A (singleton(A)!=empty_set).
% 2.13/2.31 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 2.13/2.31 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 2.13/2.31 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 2.13/2.31 all A B (subset(singleton(A),B)<->in(A,B)).
% 2.13/2.31 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.13/2.31 all A B (element(B,powerset(A))-> (all C (in(C,B)->in(C,A)))).
% 2.13/2.31 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 2.13/2.31 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 2.13/2.31 all A B (in(A,B)->subset(A,union(B))).
% 2.13/2.31 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 2.13/2.31 all A B ((all C (in(C,A)->in(C,B)))->element(A,powerset(B))).
% 2.13/2.31 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.13/2.31 exists A empty(A).
% 2.13/2.31 all A exists B (element(B,powerset(A))&empty(B)).
% 2.13/2.31 exists A (-empty(A)).
% 2.13/2.31 all A B subset(A,A).
% 2.13/2.31 all A B (disjoint(A,B)->disjoint(B,A)).
% 2.13/2.31 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 2.13/2.31 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 2.13/2.31 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))).
% 2.13/2.31 all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 2.13/2.31 all A B (subset(A,B)->set_union2(A,B)=B).
% 2.13/2.31 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))))).
% 2.13/2.31 all A B subset(set_intersection2(A,B),A).
% 2.13/2.31 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 2.13/2.31 all A (set_union2(A,empty_set)=A).
% 2.13/2.31 all A B (in(A,B)->element(A,B)).
% 2.13/2.31 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 2.13/2.31 powerset(empty_set)=singleton(empty_set).
% 2.13/2.31 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 2.13/2.31 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 2.13/2.31 all A (set_intersection2(A,empty_set)=empty_set).
% 2.13/2.31 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.13/2.31 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.13/2.31 all A subset(empty_set,A).
% 2.13/2.31 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 2.13/2.31 all A B C D (ordered_pair(A,B)=ordered_pair(C,D)->A=C&B=D).
% 2.13/2.31 all A B subset(set_difference(A,B),A).
% 2.13/2.31 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.13/2.31 all A B (subset(singleton(A),B)<->in(A,B)).
% 2.13/2.31 all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C)).
% 2.13/2.31 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 2.13/2.31 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 2.13/2.31 all A (set_difference(A,empty_set)=A).
% 2.13/2.31 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.13/2.31 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))).
% 2.13/2.31 all A (subset(A,empty_set)->A=empty_set).
% 2.13/2.31 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 2.13/2.31 all A B (element(B,powerset(A))-> (all C (element(C,powerset(A))-> (disjoint(B,C)<->subset(B,subset_complement(A,C)))))).
% 2.13/2.31 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 2.13/2.31 -(all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set))).
% 2.13/2.31 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 2.13/2.31 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 2.13/2.31 all A (set_difference(empty_set,A)=empty_set).
% 2.13/2.31 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.13/2.31 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))).
% 2.13/2.31 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)))))))).
% 2.13/2.31 all A B C (element(C,powerset(A))-> -(in(B,subset_complement(A,C))&in(B,C))).
% 2.13/2.31 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.13/2.31 all A B (-(subset(A,B)&proper_subset(B,A))).
% 2.13/2.31 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 2.13/2.31 all A B (set_difference(A,singleton(B))=A<-> -in(B,A)).
% 2.13/2.31 all A (unordered_pair(A,A)=singleton(A)).
% 2.13/2.31 all A (empty(A)->A=empty_set).
% 2.13/2.31 all A B (subset(singleton(A),singleton(B))->A=B).
% 2.13/2.31 all A B (-(in(A,B)&empty(B))).
% 2.13/2.31 all A B subset(A,set_union2(A,B)).
% 2.13/2.31 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 2.13/2.31 all A B (-(empty(A)&A!=B&empty(B))).
% 2.13/2.31 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 2.13/2.31 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 2.13/2.31 all A B (in(A,B)->subset(A,union(B))).
% 2.13/2.31 all A (union(powerset(A))=A).
% 2.13/2.31 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))))).
% 2.13/2.31 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 2.13/2.31 end_of_list.
% 2.13/2.31
% 2.13/2.31 -------> usable clausifies to:
% 2.13/2.31
% 2.13/2.31 list(usable).
% 2.13/2.31 0 [] A=A.
% 2.13/2.31 0 [] -in(A,B)| -in(B,A).
% 2.13/2.31 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.13/2.31 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.13/2.31 0 [] set_union2(A,B)=set_union2(B,A).
% 2.13/2.31 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.13/2.31 0 [] A!=B|subset(A,B).
% 2.13/2.31 0 [] A!=B|subset(B,A).
% 2.13/2.31 0 [] A=B| -subset(A,B)| -subset(B,A).
% 2.13/2.31 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 2.13/2.31 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 2.13/2.31 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 2.13/2.31 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 2.13/2.31 0 [] A!=empty_set| -in(B,A).
% 2.13/2.31 0 [] A=empty_set|in($f2(A),A).
% 2.13/2.31 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 2.13/2.31 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 2.13/2.31 0 [] B=powerset(A)|in($f3(A,B),B)|subset($f3(A,B),A).
% 2.13/2.31 0 [] B=powerset(A)| -in($f3(A,B),B)| -subset($f3(A,B),A).
% 2.13/2.31 0 [] empty(A)| -element(B,A)|in(B,A).
% 2.13/2.31 0 [] empty(A)|element(B,A)| -in(B,A).
% 2.13/2.31 0 [] -empty(A)| -element(B,A)|empty(B).
% 2.13/2.31 0 [] -empty(A)|element(B,A)| -empty(B).
% 2.13/2.31 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 2.13/2.31 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 2.13/2.31 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 2.13/2.31 0 [] C=unordered_pair(A,B)|in($f4(A,B,C),C)|$f4(A,B,C)=A|$f4(A,B,C)=B.
% 2.13/2.31 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=A.
% 2.13/2.31 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=B.
% 2.13/2.31 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 2.13/2.31 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 2.13/2.31 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 2.13/2.31 0 [] C=set_union2(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 2.13/2.31 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A).
% 2.13/2.31 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 2.13/2.31 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f7(A,B,C,D),A).
% 2.13/2.31 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f6(A,B,C,D),B).
% 2.13/2.31 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f7(A,B,C,D),$f6(A,B,C,D)).
% 2.13/2.31 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 2.13/2.31 0 [] C=cartesian_product2(A,B)|in($f10(A,B,C),C)|in($f9(A,B,C),A).
% 2.13/2.31 0 [] C=cartesian_product2(A,B)|in($f10(A,B,C),C)|in($f8(A,B,C),B).
% 2.13/2.31 0 [] C=cartesian_product2(A,B)|in($f10(A,B,C),C)|$f10(A,B,C)=ordered_pair($f9(A,B,C),$f8(A,B,C)).
% 2.13/2.31 0 [] C=cartesian_product2(A,B)| -in($f10(A,B,C),C)| -in(X1,A)| -in(X2,B)|$f10(A,B,C)!=ordered_pair(X1,X2).
% 2.13/2.31 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.13/2.31 0 [] subset(A,B)|in($f11(A,B),A).
% 2.13/2.31 0 [] subset(A,B)| -in($f11(A,B),B).
% 2.13/2.31 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 2.13/2.31 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 2.13/2.31 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 2.13/2.31 0 [] C=set_intersection2(A,B)|in($f12(A,B,C),C)|in($f12(A,B,C),A).
% 2.13/2.31 0 [] C=set_intersection2(A,B)|in($f12(A,B,C),C)|in($f12(A,B,C),B).
% 2.13/2.31 0 [] C=set_intersection2(A,B)| -in($f12(A,B,C),C)| -in($f12(A,B,C),A)| -in($f12(A,B,C),B).
% 2.13/2.31 0 [] B!=union(A)| -in(C,B)|in(C,$f13(A,B,C)).
% 2.13/2.31 0 [] B!=union(A)| -in(C,B)|in($f13(A,B,C),A).
% 2.13/2.31 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 2.13/2.31 0 [] B=union(A)|in($f15(A,B),B)|in($f15(A,B),$f14(A,B)).
% 2.13/2.31 0 [] B=union(A)|in($f15(A,B),B)|in($f14(A,B),A).
% 2.13/2.31 0 [] B=union(A)| -in($f15(A,B),B)| -in($f15(A,B),X3)| -in(X3,A).
% 2.13/2.31 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 2.13/2.31 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 2.13/2.31 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 2.13/2.31 0 [] C=set_difference(A,B)|in($f16(A,B,C),C)|in($f16(A,B,C),A).
% 2.13/2.31 0 [] C=set_difference(A,B)|in($f16(A,B,C),C)| -in($f16(A,B,C),B).
% 2.13/2.31 0 [] C=set_difference(A,B)| -in($f16(A,B,C),C)| -in($f16(A,B,C),A)|in($f16(A,B,C),B).
% 2.13/2.31 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 2.13/2.31 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.13/2.31 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.13/2.31 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.13/2.31 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C!=complements_of_subsets(A,B)| -element(D,powerset(A))| -in(D,C)|in(subset_complement(A,D),B).
% 2.13/2.31 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C!=complements_of_subsets(A,B)| -element(D,powerset(A))|in(D,C)| -in(subset_complement(A,D),B).
% 2.13/2.31 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|element($f17(A,B,C),powerset(A)).
% 2.13/2.31 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|in($f17(A,B,C),C)|in(subset_complement(A,$f17(A,B,C)),B).
% 2.13/2.31 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)| -in($f17(A,B,C),C)| -in(subset_complement(A,$f17(A,B,C)),B).
% 2.13/2.31 0 [] -proper_subset(A,B)|subset(A,B).
% 2.13/2.31 0 [] -proper_subset(A,B)|A!=B.
% 2.13/2.31 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] $T.
% 2.13/2.31 0 [] -element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))).
% 2.13/2.31 0 [] $T.
% 2.13/2.32 0 [] element($f18(A),A).
% 2.13/2.32 0 [] -empty(powerset(A)).
% 2.13/2.32 0 [] empty(empty_set).
% 2.13/2.32 0 [] -empty(ordered_pair(A,B)).
% 2.13/2.32 0 [] empty(A)| -empty(set_union2(A,B)).
% 2.13/2.32 0 [] empty(A)| -empty(set_union2(B,A)).
% 2.13/2.32 0 [] set_union2(A,A)=A.
% 2.13/2.32 0 [] set_intersection2(A,A)=A.
% 2.13/2.32 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 2.13/2.32 0 [] -element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B.
% 2.13/2.32 0 [] -proper_subset(A,A).
% 2.13/2.32 0 [] singleton(A)!=empty_set.
% 2.13/2.32 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.13/2.32 0 [] -disjoint(singleton(A),B)| -in(A,B).
% 2.13/2.32 0 [] in(A,B)|disjoint(singleton(A),B).
% 2.13/2.32 0 [] -subset(singleton(A),B)|in(A,B).
% 2.13/2.32 0 [] subset(singleton(A),B)| -in(A,B).
% 2.13/2.32 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.13/2.32 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.13/2.32 0 [] -element(B,powerset(A))| -in(C,B)|in(C,A).
% 2.13/2.32 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 2.13/2.32 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.13/2.32 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.13/2.32 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.13/2.32 0 [] -in(A,B)|subset(A,union(B)).
% 2.13/2.32 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.13/2.32 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.13/2.32 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.13/2.32 0 [] in($f19(A,B),A)|element(A,powerset(B)).
% 2.13/2.32 0 [] -in($f19(A,B),B)|element(A,powerset(B)).
% 2.13/2.32 0 [] empty(A)|element($f20(A),powerset(A)).
% 2.13/2.32 0 [] empty(A)| -empty($f20(A)).
% 2.13/2.32 0 [] empty($c1).
% 2.13/2.32 0 [] element($f21(A),powerset(A)).
% 2.13/2.32 0 [] empty($f21(A)).
% 2.13/2.32 0 [] -empty($c2).
% 2.13/2.32 0 [] subset(A,A).
% 2.13/2.32 0 [] -disjoint(A,B)|disjoint(B,A).
% 2.13/2.32 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.13/2.32 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.13/2.32 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.13/2.32 0 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 2.13/2.32 0 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 2.13/2.32 0 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 2.13/2.32 0 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 2.13/2.32 0 [] -subset(A,B)|set_union2(A,B)=B.
% 2.13/2.32 0 [] in(A,$f22(A)).
% 2.13/2.32 0 [] -in(C,$f22(A))| -subset(D,C)|in(D,$f22(A)).
% 2.13/2.32 0 [] -in(X4,$f22(A))|in(powerset(X4),$f22(A)).
% 2.13/2.32 0 [] -subset(X5,$f22(A))|are_e_quipotent(X5,$f22(A))|in(X5,$f22(A)).
% 2.13/2.32 0 [] subset(set_intersection2(A,B),A).
% 2.13/2.32 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.13/2.32 0 [] set_union2(A,empty_set)=A.
% 2.13/2.32 0 [] -in(A,B)|element(A,B).
% 2.13/2.32 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.13/2.32 0 [] powerset(empty_set)=singleton(empty_set).
% 2.13/2.32 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.13/2.32 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.13/2.32 0 [] set_intersection2(A,empty_set)=empty_set.
% 2.13/2.32 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.13/2.32 0 [] in($f23(A,B),A)|in($f23(A,B),B)|A=B.
% 2.13/2.32 0 [] -in($f23(A,B),A)| -in($f23(A,B),B)|A=B.
% 2.13/2.32 0 [] subset(empty_set,A).
% 2.13/2.32 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.13/2.32 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 2.13/2.32 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 2.13/2.32 0 [] subset(set_difference(A,B),A).
% 2.13/2.32 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.13/2.32 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.13/2.32 0 [] -subset(singleton(A),B)|in(A,B).
% 2.13/2.32 0 [] subset(singleton(A),B)| -in(A,B).
% 2.13/2.32 0 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 2.13/2.32 0 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 2.13/2.32 0 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 2.13/2.32 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.13/2.32 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.13/2.32 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.13/2.32 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.13/2.32 0 [] set_difference(A,empty_set)=A.
% 2.13/2.32 0 [] -element(A,powerset(B))|subset(A,B).
% 2.13/2.32 0 [] element(A,powerset(B))| -subset(A,B).
% 2.13/2.32 0 [] disjoint(A,B)|in($f24(A,B),A).
% 2.13/2.32 0 [] disjoint(A,B)|in($f24(A,B),B).
% 2.13/2.32 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 2.13/2.32 0 [] -subset(A,empty_set)|A=empty_set.
% 2.13/2.32 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.13/2.32 0 [] -element(B,powerset(A))| -element(C,powerset(A))| -disjoint(B,C)|subset(B,subset_complement(A,C)).
% 2.13/2.32 0 [] -element(B,powerset(A))| -element(C,powerset(A))|disjoint(B,C)| -subset(B,subset_complement(A,C)).
% 2.13/2.32 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 2.13/2.32 0 [] element($c3,powerset(powerset($c4))).
% 2.13/2.32 0 [] $c3!=empty_set.
% 2.13/2.32 0 [] complements_of_subsets($c4,$c3)=empty_set.
% 2.13/2.32 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.13/2.32 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 2.13/2.32 0 [] set_difference(empty_set,A)=empty_set.
% 2.13/2.32 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.13/2.32 0 [] disjoint(A,B)|in($f25(A,B),set_intersection2(A,B)).
% 2.13/2.32 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 2.13/2.32 0 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 2.13/2.32 0 [] -element(C,powerset(A))| -in(B,subset_complement(A,C))| -in(B,C).
% 2.13/2.32 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.13/2.32 0 [] -subset(A,B)| -proper_subset(B,A).
% 2.13/2.32 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 2.13/2.32 0 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 2.13/2.32 0 [] set_difference(A,singleton(B))=A|in(B,A).
% 2.13/2.32 0 [] unordered_pair(A,A)=singleton(A).
% 2.13/2.32 0 [] -empty(A)|A=empty_set.
% 2.13/2.32 0 [] -subset(singleton(A),singleton(B))|A=B.
% 2.13/2.32 0 [] -in(A,B)| -empty(B).
% 2.13/2.32 0 [] subset(A,set_union2(A,B)).
% 2.13/2.32 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 2.13/2.32 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 2.13/2.32 0 [] -empty(A)|A=B| -empty(B).
% 2.13/2.32 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.13/2.32 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 2.13/2.32 0 [] -in(A,B)|subset(A,union(B)).
% 2.13/2.32 0 [] union(powerset(A))=A.
% 2.13/2.32 0 [] in(A,$f27(A)).
% 2.13/2.32 0 [] -in(C,$f27(A))| -subset(D,C)|in(D,$f27(A)).
% 2.13/2.32 0 [] -in(X6,$f27(A))|in($f26(A,X6),$f27(A)).
% 2.13/2.32 0 [] -in(X6,$f27(A))| -subset(E,X6)|in(E,$f26(A,X6)).
% 2.13/2.32 0 [] -subset(X7,$f27(A))|are_e_quipotent(X7,$f27(A))|in(X7,$f27(A)).
% 2.13/2.32 0 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 2.13/2.32 end_of_list.
% 2.13/2.32
% 2.13/2.32 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 2.13/2.32
% 2.13/2.32 This ia a non-Horn set with equality. The strategy will be
% 2.13/2.32 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.13/2.32 deletion, with positive clauses in sos and nonpositive
% 2.13/2.32 clauses in usable.
% 2.13/2.32
% 2.13/2.32 dependent: set(knuth_bendix).
% 2.13/2.32 dependent: set(anl_eq).
% 2.13/2.32 dependent: set(para_from).
% 2.13/2.32 dependent: set(para_into).
% 2.13/2.32 dependent: clear(para_from_right).
% 2.13/2.32 dependent: clear(para_into_right).
% 2.13/2.32 dependent: set(para_from_vars).
% 2.13/2.32 dependent: set(eq_units_both_ways).
% 2.13/2.32 dependent: set(dynamic_demod_all).
% 2.13/2.32 dependent: set(dynamic_demod).
% 2.13/2.32 dependent: set(order_eq).
% 2.13/2.32 dependent: set(back_demod).
% 2.13/2.32 dependent: set(lrpo).
% 2.13/2.32 dependent: set(hyper_res).
% 2.13/2.32 dependent: set(unit_deletion).
% 2.13/2.32 dependent: set(factor).
% 2.13/2.32
% 2.13/2.32 ------------> process usable:
% 2.13/2.32 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.13/2.32 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.13/2.32 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 2.13/2.32 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 2.13/2.32 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 2.13/2.32 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)| -in(C,A)|C=B.
% 2.13/2.32 ** KEPT (pick-wt=10): 7 [] A!=singleton(B)|in(C,A)|C!=B.
% 2.13/2.32 ** KEPT (pick-wt=14): 8 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 2.13/2.32 ** KEPT (pick-wt=6): 9 [] A!=empty_set| -in(B,A).
% 2.13/2.32 ** KEPT (pick-wt=10): 10 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 2.13/2.32 ** KEPT (pick-wt=10): 11 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 2.13/2.32 ** KEPT (pick-wt=14): 12 [] A=powerset(B)| -in($f3(B,A),A)| -subset($f3(B,A),B).
% 2.13/2.32 ** KEPT (pick-wt=8): 13 [] empty(A)| -element(B,A)|in(B,A).
% 2.13/2.32 ** KEPT (pick-wt=8): 14 [] empty(A)|element(B,A)| -in(B,A).
% 2.13/2.32 ** KEPT (pick-wt=7): 15 [] -empty(A)| -element(B,A)|empty(B).
% 2.13/2.32 ** KEPT (pick-wt=7): 16 [] -empty(A)|element(B,A)| -empty(B).
% 2.13/2.32 ** KEPT (pick-wt=14): 17 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 2.13/2.32 ** KEPT (pick-wt=11): 18 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 2.13/2.32 ** KEPT (pick-wt=11): 19 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 2.13/2.32 ** KEPT (pick-wt=17): 20 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=B.
% 2.13/2.32 ** KEPT (pick-wt=17): 21 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=C.
% 2.13/2.32 ** KEPT (pick-wt=14): 22 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 2.13/2.32 ** KEPT (pick-wt=11): 23 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 2.13/2.32 ** KEPT (pick-wt=11): 24 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 2.13/2.32 ** KEPT (pick-wt=17): 25 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B).
% 2.13/2.32 ** KEPT (pick-wt=17): 26 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 2.13/2.32 ** KEPT (pick-wt=15): 27 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f7(B,C,A,D),B).
% 2.13/2.32 ** KEPT (pick-wt=15): 28 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f6(B,C,A,D),C).
% 2.13/2.32 ** KEPT (pick-wt=21): 30 [copy,29,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f7(B,C,A,D),$f6(B,C,A,D))=D.
% 2.13/2.32 ** KEPT (pick-wt=19): 31 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 2.13/2.32 ** KEPT (pick-wt=25): 32 [] A=cartesian_product2(B,C)| -in($f10(B,C,A),A)| -in(D,B)| -in(E,C)|$f10(B,C,A)!=ordered_pair(D,E).
% 2.13/2.32 ** KEPT (pick-wt=9): 33 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.13/2.32 ** KEPT (pick-wt=8): 34 [] subset(A,B)| -in($f11(A,B),B).
% 2.13/2.32 ** KEPT (pick-wt=11): 35 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 2.13/2.32 ** KEPT (pick-wt=11): 36 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 2.13/2.32 ** KEPT (pick-wt=14): 37 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 2.13/2.32 ** KEPT (pick-wt=23): 38 [] A=set_intersection2(B,C)| -in($f12(B,C,A),A)| -in($f12(B,C,A),B)| -in($f12(B,C,A),C).
% 2.13/2.32 ** KEPT (pick-wt=13): 39 [] A!=union(B)| -in(C,A)|in(C,$f13(B,A,C)).
% 2.13/2.32 ** KEPT (pick-wt=13): 40 [] A!=union(B)| -in(C,A)|in($f13(B,A,C),B).
% 2.13/2.32 ** KEPT (pick-wt=13): 41 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 2.13/2.32 ** KEPT (pick-wt=17): 42 [] A=union(B)| -in($f15(B,A),A)| -in($f15(B,A),C)| -in(C,B).
% 2.13/2.32 ** KEPT (pick-wt=11): 43 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 2.13/2.32 ** KEPT (pick-wt=11): 44 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 2.13/2.32 ** KEPT (pick-wt=14): 45 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 2.13/2.32 ** KEPT (pick-wt=17): 46 [] A=set_difference(B,C)|in($f16(B,C,A),A)| -in($f16(B,C,A),C).
% 2.13/2.32 ** KEPT (pick-wt=23): 47 [] A=set_difference(B,C)| -in($f16(B,C,A),A)| -in($f16(B,C,A),B)|in($f16(B,C,A),C).
% 2.13/2.32 ** KEPT (pick-wt=11): 48 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 2.13/2.32 ** KEPT (pick-wt=8): 49 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.13/2.32 ** KEPT (pick-wt=8): 50 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.13/2.32 ** KEPT (pick-wt=27): 51 [] -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).
% 2.13/2.32 ** KEPT (pick-wt=27): 52 [] -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).
% 2.13/2.32 ** KEPT (pick-wt=22): 53 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|element($f17(B,A,C),powerset(B)).
% 2.13/2.32 ** KEPT (pick-wt=29): 54 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|in($f17(B,A,C),C)|in(subset_complement(B,$f17(B,A,C)),A).
% 2.13/2.32 ** KEPT (pick-wt=29): 55 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)| -in($f17(B,A,C),C)| -in(subset_complement(B,$f17(B,A,C)),A).
% 2.13/2.32 ** KEPT (pick-wt=6): 56 [] -proper_subset(A,B)|subset(A,B).
% 2.13/2.32 ** KEPT (pick-wt=6): 57 [] -proper_subset(A,B)|A!=B.
% 2.13/2.32 ** KEPT (pick-wt=9): 58 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.13/2.32 ** KEPT (pick-wt=10): 59 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 2.13/2.32 ** KEPT (pick-wt=12): 60 [] -element(A,powerset(powerset(B)))|element(complements_of_subsets(B,A),powerset(powerset(B))).
% 2.13/2.32 ** KEPT (pick-wt=3): 61 [] -empty(powerset(A)).
% 2.13/2.32 ** KEPT (pick-wt=4): 62 [] -empty(ordered_pair(A,B)).
% 2.13/2.32 ** KEPT (pick-wt=6): 63 [] empty(A)| -empty(set_union2(A,B)).
% 2.13/2.32 ** KEPT (pick-wt=6): 64 [] empty(A)| -empty(set_union2(B,A)).
% 2.13/2.32 ** KEPT (pick-wt=11): 65 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 2.13/2.32 ** KEPT (pick-wt=12): 66 [] -element(A,powerset(powerset(B)))|complements_of_subsets(B,complements_of_subsets(B,A))=A.
% 2.13/2.32 ** KEPT (pick-wt=3): 67 [] -proper_subset(A,A).
% 2.13/2.32 ** KEPT (pick-wt=4): 68 [] singleton(A)!=empty_set.
% 2.13/2.32 ** KEPT (pick-wt=9): 69 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.13/2.32 ** KEPT (pick-wt=7): 70 [] -disjoint(singleton(A),B)| -in(A,B).
% 2.13/2.32 ** KEPT (pick-wt=7): 71 [] -subset(singleton(A),B)|in(A,B).
% 2.13/2.32 ** KEPT (pick-wt=7): 72 [] subset(singleton(A),B)| -in(A,B).
% 2.13/2.32 ** KEPT (pick-wt=8): 73 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.13/2.32 ** KEPT (pick-wt=8): 74 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.13/2.32 ** KEPT (pick-wt=10): 75 [] -element(A,powerset(B))| -in(C,A)|in(C,B).
% 2.13/2.32 ** KEPT (pick-wt=12): 76 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 2.13/2.32 ** KEPT (pick-wt=11): 77 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.13/2.32 ** KEPT (pick-wt=7): 78 [] subset(A,singleton(B))|A!=empty_set.
% 2.13/2.32 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.13/2.32 ** KEPT (pick-wt=7): 79 [] -in(A,B)|subset(A,union(B)).
% 2.13/2.32 ** KEPT (pick-wt=10): 80 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.13/2.32 ** KEPT (pick-wt=10): 81 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.13/2.32 ** KEPT (pick-wt=13): 82 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.13/2.32 ** KEPT (pick-wt=9): 83 [] -in($f19(A,B),B)|element(A,powerset(B)).
% 2.13/2.32 ** KEPT (pick-wt=5): 84 [] empty(A)| -empty($f20(A)).
% 2.13/2.32 ** KEPT (pick-wt=2): 85 [] -empty($c2).
% 2.13/2.32 ** KEPT (pick-wt=6): 86 [] -disjoint(A,B)|disjoint(B,A).
% 2.13/2.32 Following clause subsumed by 80 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.13/2.32 Following clause subsumed by 81 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.13/2.32 Following clause subsumed by 82 during input processing: 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.13/2.32 ** KEPT (pick-wt=13): 87 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 2.13/2.32 ** KEPT (pick-wt=10): 88 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 2.13/2.32 ** KEPT (pick-wt=10): 89 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 2.13/2.32 ** KEPT (pick-wt=13): 90 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 2.13/2.32 ** KEPT (pick-wt=8): 91 [] -subset(A,B)|set_union2(A,B)=B.
% 2.13/2.32 ** KEPT (pick-wt=11): 92 [] -in(A,$f22(B))| -subset(C,A)|in(C,$f22(B)).
% 2.13/2.32 ** KEPT (pick-wt=9): 93 [] -in(A,$f22(B))|in(powerset(A),$f22(B)).
% 2.13/2.32 ** KEPT (pick-wt=12): 94 [] -subset(A,$f22(B))|are_e_quipotent(A,$f22(B))|in(A,$f22(B)).
% 2.13/2.32 ** KEPT (pick-wt=11): 95 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.13/2.32 ** KEPT (pick-wt=6): 96 [] -in(A,B)|element(A,B).
% 2.13/2.32 ** KEPT (pick-wt=9): 97 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.13/2.32 ** KEPT (pick-wt=10): 98 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.13/2.32 ** KEPT (pick-wt=8): 99 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.13/2.32 Following clause subsumed by 13 during input processing: 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.13/2.32 ** KEPT (pick-wt=13): 100 [] -in($f23(A,B),A)| -in($f23(A,B),B)|A=B.
% 2.13/2.32 ** KEPT (pick-wt=10): 101 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.13/2.32 ** KEPT (pick-wt=10): 102 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 2.13/2.32 ** KEPT (pick-wt=10): 103 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 2.13/2.32 Following clause subsumed by 73 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.13/2.32 Following clause subsumed by 74 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.13/2.32 Following clause subsumed by 71 during input processing: 0 [] -subset(singleton(A),B)|in(A,B).
% 2.13/2.32 Following clause subsumed by 72 during input processing: 0 [] subset(singleton(A),B)| -in(A,B).
% 2.13/2.32 ** KEPT (pick-wt=8): 104 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 2.13/2.32 ** KEPT (pick-wt=8): 105 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 2.13/2.32 ** KEPT (pick-wt=11): 106 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 2.13/2.32 Following clause subsumed by 77 during input processing: 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.13/2.32 Following clause subsumed by 78 during input processing: 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.13/2.32 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.13/2.32 ** KEPT (pick-wt=7): 107 [] -element(A,powerset(B))|subset(A,B).
% 2.13/2.32 ** KEPT (pick-wt=7): 108 [] element(A,powerset(B))| -subset(A,B).
% 2.13/2.32 ** KEPT (pick-wt=9): 109 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 2.13/2.32 ** KEPT (pick-wt=6): 110 [] -subset(A,empty_set)|A=empty_set.
% 2.13/2.33 ** KEPT (pick-wt=16): 111 [] -element(A,powerset(B))| -element(C,powerset(B))| -disjoint(A,C)|subset(A,subset_complement(B,C)).
% 2.13/2.33 ** KEPT (pick-wt=16): 112 [] -element(A,powerset(B))| -element(C,powerset(B))|disjoint(A,C)| -subset(A,subset_complement(B,C)).
% 2.13/2.33 ** KEPT (pick-wt=10): 114 [copy,113,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 2.13/2.33 ** KEPT (pick-wt=3): 116 [copy,115,flip.1] empty_set!=$c3.
% 2.13/2.33 Following clause subsumed by 69 during input processing: 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.13/2.33 ** KEPT (pick-wt=10): 117 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.13/2.33 ** KEPT (pick-wt=8): 118 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 2.13/2.33 ** KEPT (pick-wt=18): 119 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 2.13/2.33 ** KEPT (pick-wt=12): 120 [] -element(A,powerset(B))| -in(C,subset_complement(B,A))| -in(C,A).
% 2.13/2.33 ** KEPT (pick-wt=9): 121 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.13/2.33 ** KEPT (pick-wt=6): 122 [] -subset(A,B)| -proper_subset(B,A).
% 2.13/2.33 ** KEPT (pick-wt=9): 123 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 2.13/2.33 ** KEPT (pick-wt=9): 124 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 2.13/2.33 ** KEPT (pick-wt=5): 125 [] -empty(A)|A=empty_set.
% 2.13/2.33 ** KEPT (pick-wt=8): 126 [] -subset(singleton(A),singleton(B))|A=B.
% 2.13/2.33 ** KEPT (pick-wt=5): 127 [] -in(A,B)| -empty(B).
% 2.13/2.33 ** KEPT (pick-wt=8): 128 [] -disjoint(A,B)|set_difference(A,B)=A.
% 2.13/2.33 ** KEPT (pick-wt=8): 129 [] disjoint(A,B)|set_difference(A,B)!=A.
% 2.13/2.33 ** KEPT (pick-wt=7): 130 [] -empty(A)|A=B| -empty(B).
% 2.13/2.33 ** KEPT (pick-wt=11): 131 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.13/2.33 ** KEPT (pick-wt=9): 132 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 2.13/2.33 Following clause subsumed by 79 during input processing: 0 [] -in(A,B)|subset(A,union(B)).
% 2.13/2.33 ** KEPT (pick-wt=11): 133 [] -in(A,$f27(B))| -subset(C,A)|in(C,$f27(B)).
% 2.13/2.33 ** KEPT (pick-wt=10): 134 [] -in(A,$f27(B))|in($f26(B,A),$f27(B)).
% 2.13/2.33 ** KEPT (pick-wt=12): 135 [] -in(A,$f27(B))| -subset(C,A)|in(C,$f26(B,A)).
% 2.13/2.33 ** KEPT (pick-wt=12): 136 [] -subset(A,$f27(B))|are_e_quipotent(A,$f27(B))|in(A,$f27(B)).
% 2.13/2.33 ** KEPT (pick-wt=9): 137 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 2.13/2.33 96 back subsumes 14.
% 2.13/2.33
% 2.13/2.33 ------------> process sos:
% 2.13/2.33 ** KEPT (pick-wt=3): 175 [] A=A.
% 2.13/2.33 ** KEPT (pick-wt=7): 176 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.13/2.33 ** KEPT (pick-wt=7): 177 [] set_union2(A,B)=set_union2(B,A).
% 2.13/2.33 ** KEPT (pick-wt=7): 178 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.13/2.33 ** KEPT (pick-wt=14): 179 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 2.13/2.33 ** KEPT (pick-wt=7): 180 [] A=empty_set|in($f2(A),A).
% 2.13/2.33 ** KEPT (pick-wt=14): 181 [] A=powerset(B)|in($f3(B,A),A)|subset($f3(B,A),B).
% 2.13/2.33 ** KEPT (pick-wt=23): 182 [] A=unordered_pair(B,C)|in($f4(B,C,A),A)|$f4(B,C,A)=B|$f4(B,C,A)=C.
% 2.13/2.33 ** KEPT (pick-wt=23): 183 [] A=set_union2(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 2.13/2.33 ** KEPT (pick-wt=17): 184 [] A=cartesian_product2(B,C)|in($f10(B,C,A),A)|in($f9(B,C,A),B).
% 2.13/2.33 ** KEPT (pick-wt=17): 185 [] A=cartesian_product2(B,C)|in($f10(B,C,A),A)|in($f8(B,C,A),C).
% 2.13/2.33 ** KEPT (pick-wt=25): 187 [copy,186,flip.3] A=cartesian_product2(B,C)|in($f10(B,C,A),A)|ordered_pair($f9(B,C,A),$f8(B,C,A))=$f10(B,C,A).
% 2.13/2.33 ** KEPT (pick-wt=8): 188 [] subset(A,B)|in($f11(A,B),A).
% 2.13/2.33 ** KEPT (pick-wt=17): 189 [] A=set_intersection2(B,C)|in($f12(B,C,A),A)|in($f12(B,C,A),B).
% 2.13/2.33 ** KEPT (pick-wt=17): 190 [] A=set_intersection2(B,C)|in($f12(B,C,A),A)|in($f12(B,C,A),C).
% 2.13/2.33 ** KEPT (pick-wt=16): 191 [] A=union(B)|in($f15(B,A),A)|in($f15(B,A),$f14(B,A)).
% 2.13/2.33 ** KEPT (pick-wt=14): 192 [] A=union(B)|in($f15(B,A),A)|in($f14(B,A),B).
% 2.13/2.33 ** KEPT (pick-wt=17): 193 [] A=set_difference(B,C)|in($f16(B,C,A),A)|in($f16(B,C,A),B).
% 2.13/2.33 ** KEPT (pick-wt=10): 195 [copy,194,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.13/2.33 ---> New Demodulator: 196 [new_demod,195] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.13/2.33 ** KEPT (pick-wt=4): 197 [] element($f18(A),A).
% 2.13/2.33 ** KEPT (pick-wt=2): 198 [] empty(empty_set).
% 2.13/2.33 ** KEPT (pick-wt=5): 199 [] set_union2(A,A)=A.
% 2.13/2.33 ---> New Demodulator: 200 [new_demod,199] set_union2(A,A)=A.
% 2.13/2.33 ** KEPT (pick-wt=5): 201 [] set_intersection2(A,A)=A.
% 2.13/2.33 ---> New Demodulator: 202 [new_demod,201] set_intersection2(A,A)=A.
% 2.13/2.33 ** KEPT (pick-wt=7): 203 [] in(A,B)|disjoint(singleton(A),B).
% 2.13/2.33 ** KEPT (pick-wt=9): 204 [] in($f19(A,B),A)|element(A,powerset(B)).
% 2.13/2.33 ** KEPT (pick-wt=7): 205 [] empty(A)|element($f20(A),powerset(A)).
% 2.13/2.33 ** KEPT (pick-wt=2): 206 [] empty($c1).
% 2.13/2.33 ** KEPT (pick-wt=5): 207 [] element($f21(A),powerset(A)).
% 2.13/2.33 ** KEPT (pick-wt=3): 208 [] empty($f21(A)).
% 2.13/2.33 ** KEPT (pick-wt=3): 209 [] subset(A,A).
% 2.13/2.33 ** KEPT (pick-wt=4): 210 [] in(A,$f22(A)).
% 2.13/2.33 ** KEPT (pick-wt=5): 211 [] subset(set_intersection2(A,B),A).
% 2.13/2.33 ** KEPT (pick-wt=5): 212 [] set_union2(A,empty_set)=A.
% 2.13/2.33 ---> New Demodulator: 213 [new_demod,212] set_union2(A,empty_set)=A.
% 2.13/2.33 ** KEPT (pick-wt=5): 215 [copy,214,flip.1] singleton(empty_set)=powerset(empty_set).
% 2.13/2.33 ---> New Demodulator: 216 [new_demod,215] singleton(empty_set)=powerset(empty_set).
% 2.13/2.33 ** KEPT (pick-wt=5): 217 [] set_intersection2(A,empty_set)=empty_set.
% 2.13/2.33 ---> New Demodulator: 218 [new_demod,217] set_intersection2(A,empty_set)=empty_set.
% 2.13/2.33 ** KEPT (pick-wt=13): 219 [] in($f23(A,B),A)|in($f23(A,B),B)|A=B.
% 2.13/2.33 ** KEPT (pick-wt=3): 220 [] subset(empty_set,A).
% 2.13/2.33 ** KEPT (pick-wt=5): 221 [] subset(set_difference(A,B),A).
% 2.13/2.33 ** KEPT (pick-wt=9): 222 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.13/2.33 ---> New Demodulator: 223 [new_demod,222] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.13/2.33 ** KEPT (pick-wt=5): 224 [] set_difference(A,empty_set)=A.
% 2.13/2.33 ---> New Demodulator: 225 [new_demod,224] set_difference(A,empty_set)=A.
% 2.13/2.33 ** KEPT (pick-wt=8): 226 [] disjoint(A,B)|in($f24(A,B),A).
% 2.13/2.33 ** KEPT (pick-wt=8): 227 [] disjoint(A,B)|in($f24(A,B),B).
% 2.13/2.33 ** KEPT (pick-wt=9): 228 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.13/2.33 ---> New Demodulator: 229 [new_demod,228] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.13/2.33 ** KEPT (pick-wt=5): 230 [] element($c3,powerset(powerset($c4))).
% 2.13/2.33 ** KEPT (pick-wt=5): 231 [] complements_of_subsets($c4,$c3)=empty_set.
% 2.13/2.33 ---> New Demodulator: 232 [new_demod,231] complements_of_subsets($c4,$c3)=empty_set.
% 2.13/2.33 ** KEPT (pick-wt=9): 234 [copy,233,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 2.13/2.33 ---> New Demodulator: 235 [new_demod,234] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 2.13/2.33 ** KEPT (pick-wt=5): 236 [] set_difference(empty_set,A)=empty_set.
% 2.13/2.33 ---> New Demodulator: 237 [new_demod,236] set_difference(empty_set,A)=empty_set.
% 2.13/2.33 ** KEPT (pick-wt=12): 239 [copy,238,demod,235] disjoint(A,B)|in($f25(A,B),set_difference(A,set_difference(A,B))).
% 2.13/2.33 ** KEPT (pick-wt=9): 240 [] set_difference(A,singleton(B))=A|in(B,A).
% 2.13/2.33 ** KEPT (pick-wt=6): 242 [copy,241,flip.1] singleton(A)=unordered_pair(A,A).
% 2.13/2.33 ---> New Demodulator: 243 [new_demod,242] singleton(A)=unordered_pair(A,A).
% 2.13/2.33 ** KEPT (pick-wt=5): 244 [] subset(A,set_union2(A,B)).
% 2.13/2.33 ** KEPT (pick-wt=5): 245 [] union(powerset(A))=A.
% 2.13/2.33 ---> New Demodulator: 246 [new_demod,245] union(powerset(A))=A.
% 2.13/2.33 ** KEPT (pick-wt=4): 247 [] in(A,$f27(A)).
% 2.13/2.33 Following clause subsumed by 175 during input processing: 0 [copy,175,flip.1] A=A.
% 2.13/2.33 175 back subsumes 171.
% 2.13/2.33 175 back subsumes 166.
% 2.13/2.33 175 back subsumes 139.
% 2.13/2.33 Following clause subsumed by 176 during input processing: 0 [copy,176,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.13/2.33 Following clause subsumed by 177 during input processing: 0 [copy,177,flip.1] set_union2(A,B)=set_union2(B,A).
% 2.13/2.33 ** KEPT (pick-wt=11): 248 [copy,178,flip.1,demod,235,235] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 2.13/2.33 >>>> Starting back demodulation with 196.
% 2.13/2.33 >>>> Starting back demodulation with 200.
% 2.13/2.33 >> back demodulating 172 with 200.
% 2.13/2.33 >> back demodulating 142 with 200.
% 2.13/2.33 >>>> Starting back demodulation with 202.
% 2.13/2.33 >> back demodulating 174 with 202.
% 2.13/2.33 >> back demodulating 165 with 202.
% 2.13/2.33 >> back demodulating 152 with 202.
% 2.13/2.33 >> back demodulating 149 with 202.
% 2.13/2.33 >>>> Starting back demodulation with 213.
% 2.13/2.33 >>>> Starting back demodulation with 216.
% 2.13/2.33 >>>> Starting back demodulation with 218.
% 2.13/2.33 >>>> Starting back demodulation with 223.
% 2.13/2.33 >> back demodulating 114 with 223.
% 2.13/2.33 >>>> Starting back demodulation with 225.
% 2.13/2.33 >>>> Starting back demodulation with 229.
% 3.38/3.53 >>>> Starting back demodulation with 232.
% 3.38/3.53 >>>> Starting back demodulation with 235.
% 3.38/3.53 >> back demodulating 217 with 235.
% 3.38/3.53 >> back demodulating 211 with 235.
% 3.38/3.53 >> back demodulating 201 with 235.
% 3.38/3.53 >> back demodulating 190 with 235.
% 3.38/3.53 >> back demodulating 189 with 235.
% 3.38/3.53 >> back demodulating 178 with 235.
% 3.38/3.53 >> back demodulating 151 with 235.
% 3.38/3.53 >> back demodulating 150 with 235.
% 3.38/3.53 >> back demodulating 118 with 235.
% 3.38/3.53 >> back demodulating 99 with 235.
% 3.38/3.53 >> back demodulating 98 with 235.
% 3.38/3.53 >> back demodulating 95 with 235.
% 3.38/3.53 >> back demodulating 50 with 235.
% 3.38/3.53 >> back demodulating 49 with 235.
% 3.38/3.53 >> back demodulating 38 with 235.
% 3.38/3.53 >> back demodulating 37 with 235.
% 3.38/3.53 >> back demodulating 36 with 235.
% 3.38/3.53 >> back demodulating 35 with 235.
% 3.38/3.53 >>>> Starting back demodulation with 237.
% 3.38/3.53 >>>> Starting back demodulation with 243.
% 3.38/3.53 >> back demodulating 240 with 243.
% 3.38/3.53 >> back demodulating 215 with 243.
% 3.38/3.53 >> back demodulating 203 with 243.
% 3.38/3.53 >> back demodulating 195 with 243.
% 3.38/3.53 >> back demodulating 179 with 243.
% 3.38/3.53 >> back demodulating 137 with 243.
% 3.38/3.53 >> back demodulating 132 with 243.
% 3.38/3.53 >> back demodulating 126 with 243.
% 3.38/3.53 >> back demodulating 124 with 243.
% 3.38/3.53 >> back demodulating 78 with 243.
% 3.38/3.53 >> back demodulating 77 with 243.
% 3.38/3.53 >> back demodulating 76 with 243.
% 3.38/3.53 >> back demodulating 72 with 243.
% 3.38/3.53 >> back demodulating 71 with 243.
% 3.38/3.53 >> back demodulating 70 with 243.
% 3.38/3.53 >> back demodulating 69 with 243.
% 3.38/3.53 >> back demodulating 68 with 243.
% 3.38/3.53 >> back demodulating 8 with 243.
% 3.38/3.53 >> back demodulating 7 with 243.
% 3.38/3.53 >> back demodulating 6 with 243.
% 3.38/3.53 >>>> Starting back demodulation with 246.
% 3.38/3.53 Following clause subsumed by 248 during input processing: 0 [copy,248,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 3.38/3.53 >>>> Starting back demodulation with 260.
% 3.38/3.53 >>>> Starting back demodulation with 276.
% 3.38/3.53 >>>> Starting back demodulation with 279.
% 3.38/3.53
% 3.38/3.53 ======= end of input processing =======
% 3.38/3.53
% 3.38/3.53 =========== start of search ===========
% 3.38/3.53
% 3.38/3.53
% 3.38/3.53 Resetting weight limit to 5.
% 3.38/3.53
% 3.38/3.53
% 3.38/3.53 Resetting weight limit to 5.
% 3.38/3.53
% 3.38/3.53 sos_size=401
% 3.38/3.53
% 3.38/3.53 -------- PROOF --------
% 3.38/3.53
% 3.38/3.53 -----> EMPTY CLAUSE at 1.23 sec ----> 765 [para_into,721.1.1,160.2.1,unit_del,385,394,759,759] $F.
% 3.38/3.53
% 3.38/3.53 Length of proof is 11. Level of proof is 4.
% 3.38/3.53
% 3.38/3.53 ---------------- PROOF ----------------
% 3.38/3.53 % SZS status Theorem
% 3.38/3.53 % SZS output start Refutation
% See solution above
% 3.38/3.53 ------------ end of proof -------------
% 3.38/3.53
% 3.38/3.53
% 3.38/3.53 Search stopped by max_proofs option.
% 3.38/3.53
% 3.38/3.53
% 3.38/3.53 Search stopped by max_proofs option.
% 3.38/3.53
% 3.38/3.53 ============ end of search ============
% 3.38/3.53
% 3.38/3.53 -------------- statistics -------------
% 3.38/3.53 clauses given 95
% 3.38/3.53 clauses generated 79716
% 3.38/3.53 clauses kept 721
% 3.38/3.53 clauses forward subsumed 1161
% 3.38/3.53 clauses back subsumed 90
% 3.38/3.53 Kbytes malloced 4882
% 3.38/3.53
% 3.38/3.53 ----------- times (seconds) -----------
% 3.38/3.53 user CPU time 1.23 (0 hr, 0 min, 1 sec)
% 3.38/3.53 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.38/3.53 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.38/3.53
% 3.38/3.53 That finishes the proof of the theorem.
% 3.38/3.53
% 3.38/3.53 Process 350 finished Wed Jul 27 07:53:59 2022
% 3.38/3.53 Otter interrupted
% 3.38/3.53 PROOF FOUND
%------------------------------------------------------------------------------