%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU172+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:15:02 EDT 2022
% Result : Theorem 3.24s 3.46s
% Output : Refutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 12 ( 4 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(44,axiom,
( A != set_difference(B,C)
| ~ in(D,A)
| ~ in(D,C) ),
file('SEU172+2.p',unknown),
[] ).
cnf(48,axiom,
( ~ element(A,powerset(B))
| subset_complement(B,A) = set_difference(B,A) ),
file('SEU172+2.p',unknown),
[] ).
cnf(154,axiom,
A = A,
file('SEU172+2.p',unknown),
[] ).
cnf(215,axiom,
element(dollar_c3,powerset(dollar_c5)),
file('SEU172+2.p',unknown),
[] ).
cnf(216,axiom,
in(dollar_c4,subset_complement(dollar_c5,dollar_c3)),
file('SEU172+2.p',unknown),
[] ).
cnf(217,axiom,
in(dollar_c4,dollar_c3),
file('SEU172+2.p',unknown),
[] ).
cnf(697,plain,
subset_complement(dollar_c5,dollar_c3) = set_difference(dollar_c5,dollar_c3),
inference(hyper,[status(thm)],[215,48]),
[iquote('hyper,215,48')] ).
cnf(702,plain,
in(dollar_c4,set_difference(dollar_c5,dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[216]),697]),
[iquote('back_demod,216,demod,697')] ).
cnf(882,plain,
$false,
inference(hyper,[status(thm)],[702,44,154,217]),
[iquote('hyper,702,44,154,217')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU172+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:42:01 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.14/2.29 ----- Otter 3.3f, August 2004 -----
% 2.14/2.29 The process was started by sandbox on n018.cluster.edu,
% 2.14/2.29 Wed Jul 27 07:42:01 2022
% 2.14/2.29 The command was "./otter". The process ID is 8508.
% 2.14/2.29
% 2.14/2.29 set(prolog_style_variables).
% 2.14/2.29 set(auto).
% 2.14/2.29 dependent: set(auto1).
% 2.14/2.29 dependent: set(process_input).
% 2.14/2.29 dependent: clear(print_kept).
% 2.14/2.29 dependent: clear(print_new_demod).
% 2.14/2.29 dependent: clear(print_back_demod).
% 2.14/2.29 dependent: clear(print_back_sub).
% 2.14/2.29 dependent: set(control_memory).
% 2.14/2.29 dependent: assign(max_mem, 12000).
% 2.14/2.29 dependent: assign(pick_given_ratio, 4).
% 2.14/2.29 dependent: assign(stats_level, 1).
% 2.14/2.29 dependent: assign(max_seconds, 10800).
% 2.14/2.29 clear(print_given).
% 2.14/2.29
% 2.14/2.29 formula_list(usable).
% 2.14/2.29 all A (A=A).
% 2.14/2.29 all A B (in(A,B)-> -in(B,A)).
% 2.14/2.29 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 2.14/2.29 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.14/2.29 all A B (set_union2(A,B)=set_union2(B,A)).
% 2.14/2.29 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.14/2.29 all A B (A=B<->subset(A,B)&subset(B,A)).
% 2.14/2.29 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 2.14/2.29 all A (A=empty_set<-> (all B (-in(B,A)))).
% 2.14/2.29 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 2.14/2.29 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 2.14/2.29 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 2.14/2.29 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 2.14/2.29 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)))))).
% 2.14/2.29 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.14/2.29 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 2.14/2.29 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 2.14/2.29 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 2.14/2.29 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 2.14/2.29 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 2.14/2.29 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 2.14/2.29 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 $T.
% 2.14/2.29 all A exists B element(B,A).
% 2.14/2.29 all A (-empty(powerset(A))).
% 2.14/2.29 empty(empty_set).
% 2.14/2.29 all A B (-empty(ordered_pair(A,B))).
% 2.14/2.29 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 2.14/2.29 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 2.14/2.29 all A B (set_union2(A,A)=A).
% 2.14/2.29 all A B (set_intersection2(A,A)=A).
% 2.14/2.29 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 2.14/2.29 all A B (-proper_subset(A,A)).
% 2.14/2.29 all A (singleton(A)!=empty_set).
% 2.14/2.29 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 2.14/2.29 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 2.14/2.29 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 2.14/2.29 all A B (subset(singleton(A),B)<->in(A,B)).
% 2.14/2.29 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.14/2.29 all A B (element(B,powerset(A))-> (all C (in(C,B)->in(C,A)))).
% 2.14/2.29 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 2.14/2.29 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 2.14/2.29 all A B (in(A,B)->subset(A,union(B))).
% 2.14/2.29 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 2.14/2.29 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.14/2.29 exists A empty(A).
% 2.14/2.29 all A exists B (element(B,powerset(A))&empty(B)).
% 2.14/2.29 exists A (-empty(A)).
% 2.14/2.29 all A B subset(A,A).
% 2.14/2.29 all A B (disjoint(A,B)->disjoint(B,A)).
% 2.14/2.29 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 2.14/2.29 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 2.14/2.29 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))).
% 2.14/2.29 all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 2.14/2.29 all A B (subset(A,B)->set_union2(A,B)=B).
% 2.14/2.29 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))))).
% 2.14/2.29 all A B subset(set_intersection2(A,B),A).
% 2.14/2.29 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 2.14/2.29 all A (set_union2(A,empty_set)=A).
% 2.14/2.29 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 2.14/2.29 powerset(empty_set)=singleton(empty_set).
% 2.14/2.29 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 2.14/2.29 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 2.14/2.29 all A (set_intersection2(A,empty_set)=empty_set).
% 2.14/2.29 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.14/2.29 all A subset(empty_set,A).
% 2.14/2.29 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 2.14/2.29 all A B C D (ordered_pair(A,B)=ordered_pair(C,D)->A=C&B=D).
% 2.14/2.29 all A B subset(set_difference(A,B),A).
% 2.14/2.29 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.14/2.29 all A B (subset(singleton(A),B)<->in(A,B)).
% 2.14/2.29 all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C)).
% 2.14/2.29 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 2.14/2.29 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 2.14/2.29 all A (set_difference(A,empty_set)=A).
% 2.14/2.29 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))).
% 2.14/2.29 all A (subset(A,empty_set)->A=empty_set).
% 2.14/2.29 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 2.14/2.29 all A B (element(B,powerset(A))-> (all C (element(C,powerset(A))-> (disjoint(B,C)<->subset(B,subset_complement(A,C)))))).
% 2.14/2.29 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 2.14/2.29 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 2.14/2.29 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 2.14/2.29 all A (set_difference(empty_set,A)=empty_set).
% 2.14/2.29 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))).
% 2.14/2.29 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)))))))).
% 2.14/2.29 -(all A B C (element(C,powerset(A))-> -(in(B,subset_complement(A,C))&in(B,C)))).
% 2.14/2.29 all A B (-(subset(A,B)&proper_subset(B,A))).
% 2.14/2.29 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 2.14/2.29 all A B (set_difference(A,singleton(B))=A<-> -in(B,A)).
% 2.14/2.29 all A (unordered_pair(A,A)=singleton(A)).
% 2.14/2.29 all A (empty(A)->A=empty_set).
% 2.14/2.29 all A B (subset(singleton(A),singleton(B))->A=B).
% 2.14/2.29 all A B (-(in(A,B)&empty(B))).
% 2.14/2.29 all A B subset(A,set_union2(A,B)).
% 2.14/2.29 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 2.14/2.29 all A B (-(empty(A)&A!=B&empty(B))).
% 2.14/2.29 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 2.14/2.29 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 2.14/2.29 all A B (in(A,B)->subset(A,union(B))).
% 2.14/2.29 all A (union(powerset(A))=A).
% 2.14/2.29 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))))).
% 2.14/2.29 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 2.14/2.29 end_of_list.
% 2.14/2.29
% 2.14/2.29 -------> usable clausifies to:
% 2.14/2.29
% 2.14/2.29 list(usable).
% 2.14/2.29 0 [] A=A.
% 2.14/2.29 0 [] -in(A,B)| -in(B,A).
% 2.14/2.29 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.14/2.29 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.14/2.29 0 [] set_union2(A,B)=set_union2(B,A).
% 2.14/2.29 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.14/2.29 0 [] A!=B|subset(A,B).
% 2.14/2.29 0 [] A!=B|subset(B,A).
% 2.14/2.29 0 [] A=B| -subset(A,B)| -subset(B,A).
% 2.14/2.29 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 2.14/2.29 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 2.14/2.29 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 2.14/2.29 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 2.14/2.29 0 [] A!=empty_set| -in(B,A).
% 2.14/2.29 0 [] A=empty_set|in($f2(A),A).
% 2.14/2.29 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 2.14/2.29 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 2.14/2.29 0 [] B=powerset(A)|in($f3(A,B),B)|subset($f3(A,B),A).
% 2.14/2.29 0 [] B=powerset(A)| -in($f3(A,B),B)| -subset($f3(A,B),A).
% 2.14/2.29 0 [] empty(A)| -element(B,A)|in(B,A).
% 2.14/2.29 0 [] empty(A)|element(B,A)| -in(B,A).
% 2.14/2.29 0 [] -empty(A)| -element(B,A)|empty(B).
% 2.14/2.29 0 [] -empty(A)|element(B,A)| -empty(B).
% 2.14/2.29 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 2.14/2.29 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 2.14/2.29 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 2.14/2.29 0 [] C=unordered_pair(A,B)|in($f4(A,B,C),C)|$f4(A,B,C)=A|$f4(A,B,C)=B.
% 2.14/2.29 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=A.
% 2.14/2.29 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=B.
% 2.14/2.29 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 2.14/2.29 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 2.14/2.29 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 2.14/2.29 0 [] C=set_union2(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 2.14/2.29 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A).
% 2.14/2.29 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 2.14/2.29 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f7(A,B,C,D),A).
% 2.14/2.29 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f6(A,B,C,D),B).
% 2.14/2.29 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f7(A,B,C,D),$f6(A,B,C,D)).
% 2.14/2.29 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 2.14/2.29 0 [] C=cartesian_product2(A,B)|in($f10(A,B,C),C)|in($f9(A,B,C),A).
% 2.14/2.29 0 [] C=cartesian_product2(A,B)|in($f10(A,B,C),C)|in($f8(A,B,C),B).
% 2.14/2.29 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)).
% 2.14/2.29 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).
% 2.14/2.29 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.14/2.29 0 [] subset(A,B)|in($f11(A,B),A).
% 2.14/2.29 0 [] subset(A,B)| -in($f11(A,B),B).
% 2.14/2.29 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 2.14/2.29 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 2.14/2.29 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 2.14/2.29 0 [] C=set_intersection2(A,B)|in($f12(A,B,C),C)|in($f12(A,B,C),A).
% 2.14/2.29 0 [] C=set_intersection2(A,B)|in($f12(A,B,C),C)|in($f12(A,B,C),B).
% 2.14/2.29 0 [] C=set_intersection2(A,B)| -in($f12(A,B,C),C)| -in($f12(A,B,C),A)| -in($f12(A,B,C),B).
% 2.14/2.29 0 [] B!=union(A)| -in(C,B)|in(C,$f13(A,B,C)).
% 2.14/2.29 0 [] B!=union(A)| -in(C,B)|in($f13(A,B,C),A).
% 2.14/2.29 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 2.14/2.29 0 [] B=union(A)|in($f15(A,B),B)|in($f15(A,B),$f14(A,B)).
% 2.14/2.29 0 [] B=union(A)|in($f15(A,B),B)|in($f14(A,B),A).
% 2.14/2.29 0 [] B=union(A)| -in($f15(A,B),B)| -in($f15(A,B),X3)| -in(X3,A).
% 2.14/2.29 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 2.14/2.29 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 2.14/2.29 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 2.14/2.29 0 [] C=set_difference(A,B)|in($f16(A,B,C),C)|in($f16(A,B,C),A).
% 2.14/2.29 0 [] C=set_difference(A,B)|in($f16(A,B,C),C)| -in($f16(A,B,C),B).
% 2.14/2.29 0 [] C=set_difference(A,B)| -in($f16(A,B,C),C)| -in($f16(A,B,C),A)|in($f16(A,B,C),B).
% 2.14/2.29 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 2.14/2.29 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.14/2.29 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.14/2.29 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.14/2.29 0 [] -proper_subset(A,B)|subset(A,B).
% 2.14/2.29 0 [] -proper_subset(A,B)|A!=B.
% 2.14/2.29 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] $T.
% 2.14/2.29 0 [] element($f17(A),A).
% 2.14/2.29 0 [] -empty(powerset(A)).
% 2.14/2.29 0 [] empty(empty_set).
% 2.14/2.29 0 [] -empty(ordered_pair(A,B)).
% 2.14/2.29 0 [] empty(A)| -empty(set_union2(A,B)).
% 2.14/2.29 0 [] empty(A)| -empty(set_union2(B,A)).
% 2.14/2.29 0 [] set_union2(A,A)=A.
% 2.14/2.29 0 [] set_intersection2(A,A)=A.
% 2.14/2.29 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 2.14/2.29 0 [] -proper_subset(A,A).
% 2.14/2.29 0 [] singleton(A)!=empty_set.
% 2.14/2.29 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.14/2.29 0 [] -disjoint(singleton(A),B)| -in(A,B).
% 2.14/2.29 0 [] in(A,B)|disjoint(singleton(A),B).
% 2.14/2.29 0 [] -subset(singleton(A),B)|in(A,B).
% 2.14/2.29 0 [] subset(singleton(A),B)| -in(A,B).
% 2.14/2.29 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.14/2.29 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.14/2.29 0 [] -element(B,powerset(A))| -in(C,B)|in(C,A).
% 2.14/2.29 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 2.14/2.29 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.14/2.29 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.14/2.29 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.14/2.29 0 [] -in(A,B)|subset(A,union(B)).
% 2.14/2.29 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.14/2.29 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.14/2.29 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.14/2.29 0 [] empty(A)|element($f18(A),powerset(A)).
% 2.14/2.29 0 [] empty(A)| -empty($f18(A)).
% 2.14/2.29 0 [] empty($c1).
% 2.14/2.29 0 [] element($f19(A),powerset(A)).
% 2.14/2.29 0 [] empty($f19(A)).
% 2.14/2.29 0 [] -empty($c2).
% 2.14/2.29 0 [] subset(A,A).
% 2.14/2.29 0 [] -disjoint(A,B)|disjoint(B,A).
% 2.14/2.29 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.14/2.29 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.14/2.29 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.14/2.29 0 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 2.14/2.29 0 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 2.14/2.29 0 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 2.14/2.29 0 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 2.14/2.29 0 [] -subset(A,B)|set_union2(A,B)=B.
% 2.14/2.29 0 [] in(A,$f20(A)).
% 2.14/2.29 0 [] -in(C,$f20(A))| -subset(D,C)|in(D,$f20(A)).
% 2.14/2.29 0 [] -in(X4,$f20(A))|in(powerset(X4),$f20(A)).
% 2.14/2.29 0 [] -subset(X5,$f20(A))|are_e_quipotent(X5,$f20(A))|in(X5,$f20(A)).
% 2.14/2.29 0 [] subset(set_intersection2(A,B),A).
% 2.14/2.29 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.14/2.29 0 [] set_union2(A,empty_set)=A.
% 2.14/2.29 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.14/2.29 0 [] powerset(empty_set)=singleton(empty_set).
% 2.14/2.29 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.14/2.29 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.14/2.29 0 [] set_intersection2(A,empty_set)=empty_set.
% 2.14/2.29 0 [] in($f21(A,B),A)|in($f21(A,B),B)|A=B.
% 2.14/2.29 0 [] -in($f21(A,B),A)| -in($f21(A,B),B)|A=B.
% 2.14/2.29 0 [] subset(empty_set,A).
% 2.14/2.29 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.14/2.29 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 2.14/2.29 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 2.14/2.29 0 [] subset(set_difference(A,B),A).
% 2.14/2.29 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.14/2.29 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.14/2.29 0 [] -subset(singleton(A),B)|in(A,B).
% 2.14/2.29 0 [] subset(singleton(A),B)| -in(A,B).
% 2.14/2.29 0 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 2.14/2.29 0 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 2.14/2.29 0 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 2.14/2.29 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.14/2.29 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.14/2.29 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.14/2.29 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.14/2.29 0 [] set_difference(A,empty_set)=A.
% 2.14/2.29 0 [] disjoint(A,B)|in($f22(A,B),A).
% 2.14/2.29 0 [] disjoint(A,B)|in($f22(A,B),B).
% 2.14/2.29 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 2.14/2.29 0 [] -subset(A,empty_set)|A=empty_set.
% 2.14/2.29 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.14/2.29 0 [] -element(B,powerset(A))| -element(C,powerset(A))| -disjoint(B,C)|subset(B,subset_complement(A,C)).
% 2.14/2.29 0 [] -element(B,powerset(A))| -element(C,powerset(A))|disjoint(B,C)| -subset(B,subset_complement(A,C)).
% 2.14/2.29 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 2.14/2.29 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.14/2.29 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 2.14/2.29 0 [] set_difference(empty_set,A)=empty_set.
% 2.14/2.29 0 [] disjoint(A,B)|in($f23(A,B),set_intersection2(A,B)).
% 2.14/2.29 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 2.14/2.29 0 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 2.14/2.29 0 [] element($c3,powerset($c5)).
% 2.14/2.29 0 [] in($c4,subset_complement($c5,$c3)).
% 2.14/2.29 0 [] in($c4,$c3).
% 2.14/2.29 0 [] -subset(A,B)| -proper_subset(B,A).
% 2.14/2.29 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 2.14/2.29 0 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 2.14/2.29 0 [] set_difference(A,singleton(B))=A|in(B,A).
% 2.14/2.29 0 [] unordered_pair(A,A)=singleton(A).
% 2.14/2.29 0 [] -empty(A)|A=empty_set.
% 2.14/2.29 0 [] -subset(singleton(A),singleton(B))|A=B.
% 2.14/2.29 0 [] -in(A,B)| -empty(B).
% 2.14/2.29 0 [] subset(A,set_union2(A,B)).
% 2.14/2.29 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 2.14/2.29 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 2.14/2.29 0 [] -empty(A)|A=B| -empty(B).
% 2.14/2.29 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.14/2.29 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 2.14/2.29 0 [] -in(A,B)|subset(A,union(B)).
% 2.14/2.29 0 [] union(powerset(A))=A.
% 2.14/2.29 0 [] in(A,$f25(A)).
% 2.14/2.29 0 [] -in(C,$f25(A))| -subset(D,C)|in(D,$f25(A)).
% 2.14/2.29 0 [] -in(X6,$f25(A))|in($f24(A,X6),$f25(A)).
% 2.14/2.29 0 [] -in(X6,$f25(A))| -subset(E,X6)|in(E,$f24(A,X6)).
% 2.14/2.29 0 [] -subset(X7,$f25(A))|are_e_quipotent(X7,$f25(A))|in(X7,$f25(A)).
% 2.14/2.29 0 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 2.14/2.29 end_of_list.
% 2.14/2.29
% 2.14/2.29 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.14/2.29
% 2.14/2.29 This ia a non-Horn set with equality. The strategy will be
% 2.14/2.29 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.14/2.29 deletion, with positive clauses in sos and nonpositive
% 2.14/2.29 clauses in usable.
% 2.14/2.29
% 2.14/2.29 dependent: set(knuth_bendix).
% 2.14/2.29 dependent: set(anl_eq).
% 2.14/2.29 dependent: set(para_from).
% 2.14/2.29 dependent: set(para_into).
% 2.14/2.29 dependent: clear(para_from_right).
% 2.14/2.29 dependent: clear(para_into_right).
% 2.14/2.29 dependent: set(para_from_vars).
% 2.14/2.29 dependent: set(eq_units_both_ways).
% 2.14/2.29 dependent: set(dynamic_demod_all).
% 2.14/2.29 dependent: set(dynamic_demod).
% 2.14/2.29 dependent: set(order_eq).
% 2.14/2.29 dependent: set(back_demod).
% 2.14/2.29 dependent: set(lrpo).
% 2.14/2.29 dependent: set(hyper_res).
% 2.14/2.29 dependent: set(unit_deletion).
% 2.14/2.29 dependent: set(factor).
% 2.14/2.29
% 2.14/2.29 ------------> process usable:
% 2.14/2.29 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.14/2.29 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.14/2.29 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 2.14/2.29 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 2.14/2.29 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 2.14/2.29 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)| -in(C,A)|C=B.
% 2.14/2.29 ** KEPT (pick-wt=10): 7 [] A!=singleton(B)|in(C,A)|C!=B.
% 2.14/2.29 ** KEPT (pick-wt=14): 8 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 2.14/2.29 ** KEPT (pick-wt=6): 9 [] A!=empty_set| -in(B,A).
% 2.14/2.29 ** KEPT (pick-wt=10): 10 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 2.14/2.29 ** KEPT (pick-wt=10): 11 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 2.14/2.29 ** KEPT (pick-wt=14): 12 [] A=powerset(B)| -in($f3(B,A),A)| -subset($f3(B,A),B).
% 2.14/2.29 ** KEPT (pick-wt=8): 13 [] empty(A)| -element(B,A)|in(B,A).
% 2.14/2.29 ** KEPT (pick-wt=8): 14 [] empty(A)|element(B,A)| -in(B,A).
% 2.14/2.29 ** KEPT (pick-wt=7): 15 [] -empty(A)| -element(B,A)|empty(B).
% 2.14/2.29 ** KEPT (pick-wt=7): 16 [] -empty(A)|element(B,A)| -empty(B).
% 2.14/2.29 ** KEPT (pick-wt=14): 17 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 2.14/2.29 ** KEPT (pick-wt=11): 18 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 2.14/2.29 ** KEPT (pick-wt=11): 19 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 2.14/2.29 ** KEPT (pick-wt=17): 20 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=B.
% 2.14/2.29 ** KEPT (pick-wt=17): 21 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=C.
% 2.14/2.29 ** KEPT (pick-wt=14): 22 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 2.14/2.29 ** KEPT (pick-wt=11): 23 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 2.14/2.29 ** KEPT (pick-wt=11): 24 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 2.14/2.29 ** KEPT (pick-wt=17): 25 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B).
% 2.14/2.29 ** KEPT (pick-wt=17): 26 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 2.14/2.29 ** KEPT (pick-wt=15): 27 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f7(B,C,A,D),B).
% 2.14/2.29 ** KEPT (pick-wt=15): 28 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f6(B,C,A,D),C).
% 2.14/2.29 ** KEPT (pick-wt=21): 30 [copy,29,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f7(B,C,A,D),$f6(B,C,A,D))=D.
% 2.14/2.29 ** KEPT (pick-wt=19): 31 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 2.14/2.29 ** KEPT (pick-wt=25): 32 [] A=cartesian_product2(B,C)| -in($f10(B,C,A),A)| -in(D,B)| -in(E,C)|$f10(B,C,A)!=ordered_pair(D,E).
% 2.14/2.29 ** KEPT (pick-wt=9): 33 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.14/2.29 ** KEPT (pick-wt=8): 34 [] subset(A,B)| -in($f11(A,B),B).
% 2.14/2.29 ** KEPT (pick-wt=11): 35 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 2.14/2.29 ** KEPT (pick-wt=11): 36 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 2.14/2.29 ** KEPT (pick-wt=14): 37 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 2.14/2.29 ** KEPT (pick-wt=23): 38 [] A=set_intersection2(B,C)| -in($f12(B,C,A),A)| -in($f12(B,C,A),B)| -in($f12(B,C,A),C).
% 2.14/2.29 ** KEPT (pick-wt=13): 39 [] A!=union(B)| -in(C,A)|in(C,$f13(B,A,C)).
% 2.14/2.29 ** KEPT (pick-wt=13): 40 [] A!=union(B)| -in(C,A)|in($f13(B,A,C),B).
% 2.14/2.29 ** KEPT (pick-wt=13): 41 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 2.14/2.29 ** KEPT (pick-wt=17): 42 [] A=union(B)| -in($f15(B,A),A)| -in($f15(B,A),C)| -in(C,B).
% 2.14/2.29 ** KEPT (pick-wt=11): 43 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 2.14/2.29 ** KEPT (pick-wt=11): 44 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 2.14/2.29 ** KEPT (pick-wt=14): 45 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 2.14/2.29 ** KEPT (pick-wt=17): 46 [] A=set_difference(B,C)|in($f16(B,C,A),A)| -in($f16(B,C,A),C).
% 2.14/2.29 ** KEPT (pick-wt=23): 47 [] A=set_difference(B,C)| -in($f16(B,C,A),A)| -in($f16(B,C,A),B)|in($f16(B,C,A),C).
% 2.14/2.29 ** KEPT (pick-wt=11): 48 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 2.14/2.29 ** KEPT (pick-wt=8): 49 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.14/2.29 ** KEPT (pick-wt=8): 50 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.14/2.29 ** KEPT (pick-wt=6): 51 [] -proper_subset(A,B)|subset(A,B).
% 2.14/2.29 ** KEPT (pick-wt=6): 52 [] -proper_subset(A,B)|A!=B.
% 2.14/2.29 ** KEPT (pick-wt=9): 53 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.14/2.29 ** KEPT (pick-wt=10): 54 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 2.14/2.30 ** KEPT (pick-wt=3): 55 [] -empty(powerset(A)).
% 2.14/2.30 ** KEPT (pick-wt=4): 56 [] -empty(ordered_pair(A,B)).
% 2.14/2.30 ** KEPT (pick-wt=6): 57 [] empty(A)| -empty(set_union2(A,B)).
% 2.14/2.30 ** KEPT (pick-wt=6): 58 [] empty(A)| -empty(set_union2(B,A)).
% 2.14/2.30 ** KEPT (pick-wt=11): 59 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 2.14/2.30 ** KEPT (pick-wt=3): 60 [] -proper_subset(A,A).
% 2.14/2.30 ** KEPT (pick-wt=4): 61 [] singleton(A)!=empty_set.
% 2.14/2.30 ** KEPT (pick-wt=9): 62 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.14/2.30 ** KEPT (pick-wt=7): 63 [] -disjoint(singleton(A),B)| -in(A,B).
% 2.14/2.30 ** KEPT (pick-wt=7): 64 [] -subset(singleton(A),B)|in(A,B).
% 2.14/2.30 ** KEPT (pick-wt=7): 65 [] subset(singleton(A),B)| -in(A,B).
% 2.14/2.30 ** KEPT (pick-wt=8): 66 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.14/2.30 ** KEPT (pick-wt=8): 67 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.14/2.30 ** KEPT (pick-wt=10): 68 [] -element(A,powerset(B))| -in(C,A)|in(C,B).
% 2.14/2.30 ** KEPT (pick-wt=12): 69 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 2.14/2.30 ** KEPT (pick-wt=11): 70 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.14/2.30 ** KEPT (pick-wt=7): 71 [] subset(A,singleton(B))|A!=empty_set.
% 2.14/2.30 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.14/2.30 ** KEPT (pick-wt=7): 72 [] -in(A,B)|subset(A,union(B)).
% 2.14/2.30 ** KEPT (pick-wt=10): 73 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.14/2.30 ** KEPT (pick-wt=10): 74 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.14/2.30 ** KEPT (pick-wt=13): 75 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.14/2.30 ** KEPT (pick-wt=5): 76 [] empty(A)| -empty($f18(A)).
% 2.14/2.30 ** KEPT (pick-wt=2): 77 [] -empty($c2).
% 2.14/2.30 ** KEPT (pick-wt=6): 78 [] -disjoint(A,B)|disjoint(B,A).
% 2.14/2.30 Following clause subsumed by 73 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 2.14/2.30 Following clause subsumed by 74 during input processing: 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 2.14/2.30 Following clause subsumed by 75 during input processing: 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 2.14/2.30 ** KEPT (pick-wt=13): 79 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 2.14/2.30 ** KEPT (pick-wt=10): 80 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 2.14/2.30 ** KEPT (pick-wt=10): 81 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 2.14/2.30 ** KEPT (pick-wt=13): 82 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 2.14/2.30 ** KEPT (pick-wt=8): 83 [] -subset(A,B)|set_union2(A,B)=B.
% 2.14/2.30 ** KEPT (pick-wt=11): 84 [] -in(A,$f20(B))| -subset(C,A)|in(C,$f20(B)).
% 2.14/2.30 ** KEPT (pick-wt=9): 85 [] -in(A,$f20(B))|in(powerset(A),$f20(B)).
% 2.14/2.30 ** KEPT (pick-wt=12): 86 [] -subset(A,$f20(B))|are_e_quipotent(A,$f20(B))|in(A,$f20(B)).
% 2.14/2.30 ** KEPT (pick-wt=11): 87 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.14/2.30 ** KEPT (pick-wt=9): 88 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.14/2.30 ** KEPT (pick-wt=10): 89 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.14/2.30 ** KEPT (pick-wt=8): 90 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.14/2.30 ** KEPT (pick-wt=13): 91 [] -in($f21(A,B),A)| -in($f21(A,B),B)|A=B.
% 2.14/2.30 ** KEPT (pick-wt=10): 92 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.14/2.30 ** KEPT (pick-wt=10): 93 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 2.14/2.30 ** KEPT (pick-wt=10): 94 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 2.14/2.30 Following clause subsumed by 66 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.14/2.30 Following clause subsumed by 67 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.14/2.30 Following clause subsumed by 64 during input processing: 0 [] -subset(singleton(A),B)|in(A,B).
% 2.14/2.30 Following clause subsumed by 65 during input processing: 0 [] subset(singleton(A),B)| -in(A,B).
% 2.14/2.30 ** KEPT (pick-wt=8): 95 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 2.14/2.30 ** KEPT (pick-wt=8): 96 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 2.14/2.30 ** KEPT (pick-wt=11): 97 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 2.14/2.30 Following clause subsumed by 70 during input processing: 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 2.14/2.30 Following clause subsumed by 71 during input processing: 0 [] subset(A,singleton(B))|A!=empty_set.
% 2.14/2.30 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 2.14/2.30 ** KEPT (pick-wt=9): 98 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 2.14/2.30 ** KEPT (pick-wt=6): 99 [] -subset(A,empty_set)|A=empty_set.
% 2.14/2.30 ** KEPT (pick-wt=16): 100 [] -element(A,powerset(B))| -element(C,powerset(B))| -disjoint(A,C)|subset(A,subset_complement(B,C)).
% 2.14/2.30 ** KEPT (pick-wt=16): 101 [] -element(A,powerset(B))| -element(C,powerset(B))|disjoint(A,C)| -subset(A,subset_complement(B,C)).
% 2.14/2.30 ** KEPT (pick-wt=10): 103 [copy,102,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 2.14/2.30 Following clause subsumed by 62 during input processing: 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 2.14/2.30 ** KEPT (pick-wt=8): 104 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 2.14/2.30 ** KEPT (pick-wt=18): 105 [] A=empty_set| -element(B,powerset(A))| -element(C,A)|in(C,B)|in(C,subset_complement(A,B)).
% 2.14/2.30 ** KEPT (pick-wt=6): 106 [] -subset(A,B)| -proper_subset(B,A).
% 2.14/2.30 ** KEPT (pick-wt=9): 107 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 2.14/2.30 ** KEPT (pick-wt=9): 108 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 2.14/2.30 ** KEPT (pick-wt=5): 109 [] -empty(A)|A=empty_set.
% 2.14/2.30 ** KEPT (pick-wt=8): 110 [] -subset(singleton(A),singleton(B))|A=B.
% 2.14/2.30 ** KEPT (pick-wt=5): 111 [] -in(A,B)| -empty(B).
% 2.14/2.30 ** KEPT (pick-wt=8): 112 [] -disjoint(A,B)|set_difference(A,B)=A.
% 2.14/2.30 ** KEPT (pick-wt=8): 113 [] disjoint(A,B)|set_difference(A,B)!=A.
% 2.14/2.30 ** KEPT (pick-wt=7): 114 [] -empty(A)|A=B| -empty(B).
% 2.14/2.30 ** KEPT (pick-wt=11): 115 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.14/2.30 ** KEPT (pick-wt=9): 116 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 2.14/2.30 Following clause subsumed by 72 during input processing: 0 [] -in(A,B)|subset(A,union(B)).
% 2.14/2.30 ** KEPT (pick-wt=11): 117 [] -in(A,$f25(B))| -subset(C,A)|in(C,$f25(B)).
% 2.14/2.30 ** KEPT (pick-wt=10): 118 [] -in(A,$f25(B))|in($f24(B,A),$f25(B)).
% 2.14/2.30 ** KEPT (pick-wt=12): 119 [] -in(A,$f25(B))| -subset(C,A)|in(C,$f24(B,A)).
% 2.14/2.30 ** KEPT (pick-wt=12): 120 [] -subset(A,$f25(B))|are_e_quipotent(A,$f25(B))|in(A,$f25(B)).
% 2.14/2.30 ** KEPT (pick-wt=9): 121 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 2.14/2.30
% 2.14/2.30 ------------> process sos:
% 2.14/2.30 ** KEPT (pick-wt=3): 154 [] A=A.
% 2.14/2.30 ** KEPT (pick-wt=7): 155 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.14/2.30 ** KEPT (pick-wt=7): 156 [] set_union2(A,B)=set_union2(B,A).
% 2.14/2.30 ** KEPT (pick-wt=7): 157 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.14/2.30 ** KEPT (pick-wt=14): 158 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 2.14/2.30 ** KEPT (pick-wt=7): 159 [] A=empty_set|in($f2(A),A).
% 2.14/2.30 ** KEPT (pick-wt=14): 160 [] A=powerset(B)|in($f3(B,A),A)|subset($f3(B,A),B).
% 2.14/2.30 ** KEPT (pick-wt=23): 161 [] A=unordered_pair(B,C)|in($f4(B,C,A),A)|$f4(B,C,A)=B|$f4(B,C,A)=C.
% 2.14/2.30 ** KEPT (pick-wt=23): 162 [] A=set_union2(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 2.14/2.30 ** KEPT (pick-wt=17): 163 [] A=cartesian_product2(B,C)|in($f10(B,C,A),A)|in($f9(B,C,A),B).
% 2.14/2.30 ** KEPT (pick-wt=17): 164 [] A=cartesian_product2(B,C)|in($f10(B,C,A),A)|in($f8(B,C,A),C).
% 2.14/2.30 ** KEPT (pick-wt=25): 166 [copy,165,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).
% 2.14/2.30 ** KEPT (pick-wt=8): 167 [] subset(A,B)|in($f11(A,B),A).
% 2.14/2.30 ** KEPT (pick-wt=17): 168 [] A=set_intersection2(B,C)|in($f12(B,C,A),A)|in($f12(B,C,A),B).
% 2.14/2.30 ** KEPT (pick-wt=17): 169 [] A=set_intersection2(B,C)|in($f12(B,C,A),A)|in($f12(B,C,A),C).
% 2.14/2.30 ** KEPT (pick-wt=16): 170 [] A=union(B)|in($f15(B,A),A)|in($f15(B,A),$f14(B,A)).
% 2.14/2.30 ** KEPT (pick-wt=14): 171 [] A=union(B)|in($f15(B,A),A)|in($f14(B,A),B).
% 2.14/2.30 ** KEPT (pick-wt=17): 172 [] A=set_difference(B,C)|in($f16(B,C,A),A)|in($f16(B,C,A),B).
% 2.14/2.30 ** KEPT (pick-wt=10): 174 [copy,173,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.14/2.30 ---> New Demodulator: 175 [new_demod,174] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.14/2.30 ** KEPT (pick-wt=4): 176 [] element($f17(A),A).
% 2.14/2.30 ** KEPT (pick-wt=2): 177 [] empty(empty_set).
% 2.14/2.30 ** KEPT (pick-wt=5): 178 [] set_union2(A,A)=A.
% 2.14/2.30 ---> New Demodulator: 179 [new_demod,178] set_union2(A,A)=A.
% 2.14/2.30 ** KEPT (pick-wt=5): 180 [] set_intersection2(A,A)=A.
% 2.14/2.30 ---> New Demodulator: 181 [new_demod,180] set_intersection2(A,A)=A.
% 2.14/2.30 ** KEPT (pick-wt=7): 182 [] in(A,B)|disjoint(singleton(A),B).
% 2.14/2.30 ** KEPT (pick-wt=7): 183 [] empty(A)|element($f18(A),powerset(A)).
% 2.14/2.30 ** KEPT (pick-wt=2): 184 [] empty($c1).
% 2.14/2.30 ** KEPT (pick-wt=5): 185 [] element($f19(A),powerset(A)).
% 2.14/2.30 ** KEPT (pick-wt=3): 186 [] empty($f19(A)).
% 2.14/2.30 ** KEPT (pick-wt=3): 187 [] subset(A,A).
% 2.14/2.30 ** KEPT (pick-wt=4): 188 [] in(A,$f20(A)).
% 2.14/2.30 ** KEPT (pick-wt=5): 189 [] subset(set_intersection2(A,B),A).
% 2.14/2.30 ** KEPT (pick-wt=5): 190 [] set_union2(A,empty_set)=A.
% 2.14/2.30 ---> New Demodulator: 191 [new_demod,190] set_union2(A,empty_set)=A.
% 2.14/2.30 ** KEPT (pick-wt=5): 193 [copy,192,flip.1] singleton(empty_set)=powerset(empty_set).
% 2.14/2.30 ---> New Demodulator: 194 [new_demod,193] singleton(empty_set)=powerset(empty_set).
% 2.14/2.30 ** KEPT (pick-wt=5): 195 [] set_intersection2(A,empty_set)=empty_set.
% 2.14/2.30 ---> New Demodulator: 196 [new_demod,195] set_intersection2(A,empty_set)=empty_set.
% 2.14/2.30 ** KEPT (pick-wt=13): 197 [] in($f21(A,B),A)|in($f21(A,B),B)|A=B.
% 2.14/2.30 ** KEPT (pick-wt=3): 198 [] subset(empty_set,A).
% 2.14/2.30 ** KEPT (pick-wt=5): 199 [] subset(set_difference(A,B),A).
% 2.14/2.30 ** KEPT (pick-wt=9): 200 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.14/2.30 ---> New Demodulator: 201 [new_demod,200] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.14/2.30 ** KEPT (pick-wt=5): 202 [] set_difference(A,empty_set)=A.
% 2.14/2.30 ---> New Demodulator: 203 [new_demod,202] set_difference(A,empty_set)=A.
% 2.14/2.30 ** KEPT (pick-wt=8): 204 [] disjoint(A,B)|in($f22(A,B),A).
% 2.14/2.30 ** KEPT (pick-wt=8): 205 [] disjoint(A,B)|in($f22(A,B),B).
% 2.14/2.30 ** KEPT (pick-wt=9): 206 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.14/2.30 ---> New Demodulator: 207 [new_demod,206] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.14/2.30 ** KEPT (pick-wt=9): 209 [copy,208,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 2.14/2.30 ---> New Demodulator: 210 [new_demod,209] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 2.14/2.30 ** KEPT (pick-wt=5): 211 [] set_difference(empty_set,A)=empty_set.
% 2.14/2.30 ---> New Demodulator: 212 [new_demod,211] set_difference(empty_set,A)=empty_set.
% 2.14/2.30 ** KEPT (pick-wt=12): 214 [copy,213,demod,210] disjoint(A,B)|in($f23(A,B),set_difference(A,set_difference(A,B))).
% 2.14/2.30 ** KEPT (pick-wt=4): 215 [] element($c3,powerset($c5)).
% 2.14/2.30 ** KEPT (pick-wt=5): 216 [] in($c4,subset_complement($c5,$c3)).
% 2.14/2.30 ** KEPT (pick-wt=3): 217 [] in($c4,$c3).
% 2.14/2.30 ** KEPT (pick-wt=9): 218 [] set_difference(A,singleton(B))=A|in(B,A).
% 2.14/2.30 ** KEPT (pick-wt=6): 220 [copy,219,flip.1] singleton(A)=unordered_pair(A,A).
% 2.14/2.30 ---> New Demodulator: 221 [new_demod,220] singleton(A)=unordered_pair(A,A).
% 2.14/2.30 ** KEPT (pick-wt=5): 222 [] subset(A,set_union2(A,B)).
% 2.14/2.30 ** KEPT (pick-wt=5): 223 [] union(powerset(A))=A.
% 2.14/2.30 ---> New Demodulator: 224 [new_demod,223] union(powerset(A))=A.
% 2.14/2.30 ** KEPT (pick-wt=4): 225 [] in(A,$f25(A)).
% 2.14/2.30 Following clause subsumed by 154 during input processing: 0 [copy,154,flip.1] A=A.
% 2.14/2.30 154 back subsumes 150.
% 2.14/2.30 154 back subsumes 145.
% 2.14/2.30 154 back subsumes 123.
% 2.14/2.30 Following clause subsumed by 155 during input processing: 0 [copy,155,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.14/2.30 Following clause subsumed by 156 during input processing: 0 [copy,156,flip.1] set_union2(A,B)=set_union2(B,A).
% 2.14/2.30 ** KEPT (pick-wt=11): 226 [copy,157,flip.1,demod,210,210] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 2.14/2.30 >>>> Starting back demodulation with 175.
% 2.14/2.30 >>>> Starting back demodulation with 179.
% 2.14/2.30 >> back demodulating 151 with 179.
% 2.14/2.30 >> back demodulating 126 with 179.
% 2.14/2.30 >>>> Starting back demodulation with 181.
% 2.14/2.30 >> back demodulating 153 with 181.
% 2.14/2.30 >> back demodulating 144 with 181.
% 2.14/2.30 >> back demodulating 136 with 181.
% 2.14/2.30 >> back demodulating 133 with 181.
% 2.14/2.30 >>>> Starting back demodulation with 191.
% 2.14/2.30 >>>> Starting back demodulation with 194.
% 2.14/2.30 >>>> Starting back demodulation with 196.
% 2.14/2.30 >>>> Starting back demodulation with 201.
% 2.14/2.30 >> back demodulating 103 with 201.
% 2.14/2.30 >>>> Starting back demodulation with 203.
% 2.14/2.30 >>>> Starting back demodulation with 207.
% 2.14/2.30 >>>> Starting back demodulation with 210.
% 2.14/2.30 >> back demodulating 195 with 210.
% 2.14/2.30 >> back demodulating 189 with 210.
% 3.24/3.46 >> back demodulating 180 with 210.
% 3.24/3.46 >> back demodulating 169 with 210.
% 3.24/3.46 >> back demodulating 168 with 210.
% 3.24/3.46 >> back demodulating 157 with 210.
% 3.24/3.46 >> back demodulating 135 with 210.
% 3.24/3.46 >> back demodulating 134 with 210.
% 3.24/3.46 >> back demodulating 104 with 210.
% 3.24/3.46 >> back demodulating 90 with 210.
% 3.24/3.46 >> back demodulating 89 with 210.
% 3.24/3.46 >> back demodulating 87 with 210.
% 3.24/3.46 >> back demodulating 50 with 210.
% 3.24/3.46 >> back demodulating 49 with 210.
% 3.24/3.46 >> back demodulating 38 with 210.
% 3.24/3.46 >> back demodulating 37 with 210.
% 3.24/3.46 >> back demodulating 36 with 210.
% 3.24/3.46 >> back demodulating 35 with 210.
% 3.24/3.46 >>>> Starting back demodulation with 212.
% 3.24/3.46 >>>> Starting back demodulation with 221.
% 3.24/3.46 >> back demodulating 218 with 221.
% 3.24/3.46 >> back demodulating 193 with 221.
% 3.24/3.46 >> back demodulating 182 with 221.
% 3.24/3.46 >> back demodulating 174 with 221.
% 3.24/3.46 >> back demodulating 158 with 221.
% 3.24/3.46 >> back demodulating 121 with 221.
% 3.24/3.46 >> back demodulating 116 with 221.
% 3.24/3.46 >> back demodulating 110 with 221.
% 3.24/3.46 >> back demodulating 108 with 221.
% 3.24/3.46 >> back demodulating 71 with 221.
% 3.24/3.46 >> back demodulating 70 with 221.
% 3.24/3.46 >> back demodulating 69 with 221.
% 3.24/3.46 >> back demodulating 65 with 221.
% 3.24/3.46 >> back demodulating 64 with 221.
% 3.24/3.46 >> back demodulating 63 with 221.
% 3.24/3.46 >> back demodulating 62 with 221.
% 3.24/3.46 >> back demodulating 61 with 221.
% 3.24/3.46 >> back demodulating 8 with 221.
% 3.24/3.46 >> back demodulating 7 with 221.
% 3.24/3.46 >> back demodulating 6 with 221.
% 3.24/3.46 >>>> Starting back demodulation with 224.
% 3.24/3.46 Following clause subsumed by 226 during input processing: 0 [copy,226,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 3.24/3.46 >>>> Starting back demodulation with 238.
% 3.24/3.46 >>>> Starting back demodulation with 254.
% 3.24/3.46 >>>> Starting back demodulation with 257.
% 3.24/3.46
% 3.24/3.46 ======= end of input processing =======
% 3.24/3.46
% 3.24/3.46 =========== start of search ===========
% 3.24/3.46
% 3.24/3.46
% 3.24/3.46 Resetting weight limit to 5.
% 3.24/3.46
% 3.24/3.46
% 3.24/3.46 Resetting weight limit to 5.
% 3.24/3.46
% 3.24/3.46 sos_size=515
% 3.24/3.46
% 3.24/3.46 -------- PROOF --------
% 3.24/3.46
% 3.24/3.46 -----> EMPTY CLAUSE at 1.18 sec ----> 882 [hyper,702,44,154,217] $F.
% 3.24/3.46
% 3.24/3.46 Length of proof is 2. Level of proof is 2.
% 3.24/3.46
% 3.24/3.46 ---------------- PROOF ----------------
% 3.24/3.46 % SZS status Theorem
% 3.24/3.46 % SZS output start Refutation
% See solution above
% 3.24/3.46 ------------ end of proof -------------
% 3.24/3.46
% 3.24/3.46
% 3.24/3.46 Search stopped by max_proofs option.
% 3.24/3.46
% 3.24/3.46
% 3.24/3.46 Search stopped by max_proofs option.
% 3.24/3.46
% 3.24/3.46 ============ end of search ============
% 3.24/3.46
% 3.24/3.46 -------------- statistics -------------
% 3.24/3.46 clauses given 92
% 3.24/3.46 clauses generated 71144
% 3.24/3.46 clauses kept 839
% 3.24/3.46 clauses forward subsumed 1159
% 3.24/3.46 clauses back subsumed 23
% 3.24/3.46 Kbytes malloced 5859
% 3.24/3.46
% 3.24/3.46 ----------- times (seconds) -----------
% 3.24/3.46 user CPU time 1.18 (0 hr, 0 min, 1 sec)
% 3.24/3.46 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.24/3.46 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.24/3.46
% 3.24/3.46 That finishes the proof of the theorem.
% 3.24/3.46
% 3.24/3.46 Process 8508 finished Wed Jul 27 07:42:04 2022
% 3.24/3.46 Otter interrupted
% 3.24/3.46 PROOF FOUND
%------------------------------------------------------------------------------