TSTP Solution File: SEU158+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU158+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:14:58 EDT 2022
% Result : Theorem 12.39s 12.57s
% Output : Refutation 12.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 36 ( 19 unt; 7 nHn; 23 RR)
% Number of literals : 61 ( 27 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 42 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SEU158+2.p',unknown),
[] ).
cnf(13,axiom,
( A != unordered_pair(B,C)
| ~ in(D,A)
| D = B
| D = C ),
file('SEU158+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU158+2.p',unknown),
[] ).
cnf(53,axiom,
singleton(A) != empty_set,
file('SEU158+2.p',unknown),
[] ).
cnf(57,axiom,
( subset(singleton(A),B)
| ~ in(A,B) ),
file('SEU158+2.p',unknown),
[] ).
cnf(70,axiom,
( ~ subset(A,B)
| set_union2(A,B) = B ),
file('SEU158+2.p',unknown),
[] ).
cnf(79,axiom,
( ~ subset(singleton(dollar_c4),dollar_c3)
| ~ in(dollar_c4,dollar_c3) ),
file('SEU158+2.p',unknown),
[] ).
cnf(92,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU158+2.p',unknown),
[] ).
cnf(98,plain,
( A != unordered_pair(B,B)
| ~ in(C,A)
| C = B ),
inference(factor,[status(thm)],[13]),
[iquote('factor,13.3.4')] ).
cnf(124,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SEU158+2.p',unknown),
[] ).
cnf(128,axiom,
( A = empty_set
| in(dollar_f2(A),A) ),
file('SEU158+2.p',unknown),
[] ).
cnf(130,axiom,
( A = unordered_pair(B,C)
| in(dollar_f4(B,C,A),A)
| dollar_f4(B,C,A) = B
| dollar_f4(B,C,A) = C ),
file('SEU158+2.p',unknown),
[] ).
cnf(145,axiom,
empty(empty_set),
file('SEU158+2.p',unknown),
[] ).
cnf(147,axiom,
set_union2(A,A) = A,
file('SEU158+2.p',unknown),
[] ).
cnf(151,axiom,
empty(dollar_c1),
file('SEU158+2.p',unknown),
[] ).
cnf(162,axiom,
subset(empty_set,A),
file('SEU158+2.p',unknown),
[] ).
cnf(164,axiom,
( subset(singleton(dollar_c4),dollar_c3)
| in(dollar_c4,dollar_c3) ),
file('SEU158+2.p',unknown),
[] ).
cnf(180,axiom,
unordered_pair(A,A) = singleton(A),
file('SEU158+2.p',unknown),
[] ).
cnf(182,plain,
singleton(A) = unordered_pair(A,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[180])]),
[iquote('copy,180,flip.1')] ).
cnf(185,plain,
( A = unordered_pair(B,B)
| in(dollar_f4(B,B,A),A)
| dollar_f4(B,B,A) = B ),
inference(factor,[status(thm)],[130]),
[iquote('factor,130.3.4')] ).
cnf(210,plain,
( subset(unordered_pair(dollar_c4,dollar_c4),dollar_c3)
| in(dollar_c4,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[164]),182]),
[iquote('back_demod,164,demod,182')] ).
cnf(220,plain,
( ~ subset(unordered_pair(dollar_c4,dollar_c4),dollar_c3)
| ~ in(dollar_c4,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),182]),
[iquote('back_demod,79,demod,182')] ).
cnf(224,plain,
( subset(unordered_pair(A,A),B)
| ~ in(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),182]),
[iquote('back_demod,57,demod,182')] ).
cnf(228,plain,
unordered_pair(A,A) != empty_set,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[53]),182]),
[iquote('back_demod,53,demod,182')] ).
cnf(260,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[151,92,145]),
[iquote('hyper,151,92,145')] ).
cnf(288,plain,
unordered_pair(A,A) != dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[228]),260]),
[iquote('back_demod,228,demod,260')] ).
cnf(301,plain,
subset(dollar_c1,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[162]),260]),
[iquote('back_demod,162,demod,260')] ).
cnf(304,plain,
( A = dollar_c1
| in(dollar_f2(A),A) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[128]),260]),
[iquote('back_demod,128,demod,260')] ).
cnf(309,plain,
( A != dollar_c1
| ~ in(B,A) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),260]),
[iquote('back_demod,9,demod,260')] ).
cnf(368,plain,
set_union2(dollar_c1,A) = A,
inference(hyper,[status(thm)],[301,70]),
[iquote('hyper,301,70')] ).
cnf(987,plain,
dollar_f4(A,A,dollar_c1) = A,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[185,309,368]),147,147]),288]),
[iquote('hyper,185,309,368,demod,147,147,unit_del,288')] ).
cnf(996,plain,
dollar_f2(unordered_pair(A,A)) = A,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[304,98,987]),987,987]),288]),
[iquote('hyper,304,98,986,demod,987,987,unit_del,288')] ).
cnf(1013,plain,
in(dollar_c4,dollar_c3),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[210,29,304]),996]),288])]),
[iquote('hyper,210,29,304,demod,996,unit_del,288,factor_simp')] ).
cnf(1081,plain,
~ subset(unordered_pair(dollar_c4,dollar_c4),dollar_c3),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[220,124]),1013]),
[iquote('para_into,220.1.1,124.1.1,unit_del,1013')] ).
cnf(1086,plain,
subset(unordered_pair(dollar_c4,dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[224,1013]),
[iquote('hyper,224,1013')] ).
cnf(1087,plain,
$false,
inference(binary,[status(thm)],[1086,1081]),
[iquote('binary,1086.1,1081.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU158+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 08:07:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.17 ----- Otter 3.3f, August 2004 -----
% 1.95/2.17 The process was started by sandbox on n019.cluster.edu,
% 1.95/2.17 Wed Jul 27 08:07:52 2022
% 1.95/2.17 The command was "./otter". The process ID is 15824.
% 1.95/2.17
% 1.95/2.17 set(prolog_style_variables).
% 1.95/2.17 set(auto).
% 1.95/2.17 dependent: set(auto1).
% 1.95/2.17 dependent: set(process_input).
% 1.95/2.17 dependent: clear(print_kept).
% 1.95/2.17 dependent: clear(print_new_demod).
% 1.95/2.17 dependent: clear(print_back_demod).
% 1.95/2.17 dependent: clear(print_back_sub).
% 1.95/2.17 dependent: set(control_memory).
% 1.95/2.17 dependent: assign(max_mem, 12000).
% 1.95/2.17 dependent: assign(pick_given_ratio, 4).
% 1.95/2.17 dependent: assign(stats_level, 1).
% 1.95/2.17 dependent: assign(max_seconds, 10800).
% 1.95/2.17 clear(print_given).
% 1.95/2.17
% 1.95/2.17 formula_list(usable).
% 1.95/2.17 all A (A=A).
% 1.95/2.17 all A B (in(A,B)-> -in(B,A)).
% 1.95/2.17 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 1.95/2.17 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.95/2.17 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.95/2.17 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.95/2.17 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.95/2.17 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.95/2.17 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.95/2.17 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 1.95/2.17 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.95/2.17 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.95/2.17 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)))))).
% 1.95/2.17 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.95/2.17 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.95/2.17 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 1.95/2.17 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.95/2.17 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.95/2.17 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.95/2.17 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 $T.
% 1.95/2.17 empty(empty_set).
% 1.95/2.17 all A B (-empty(ordered_pair(A,B))).
% 1.95/2.17 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.95/2.17 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.95/2.17 all A B (set_union2(A,A)=A).
% 1.95/2.17 all A B (set_intersection2(A,A)=A).
% 1.95/2.17 all A B (-proper_subset(A,A)).
% 1.95/2.17 all A (singleton(A)!=empty_set).
% 1.95/2.17 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 1.95/2.17 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 1.95/2.17 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 1.95/2.17 all A B (subset(singleton(A),B)<->in(A,B)).
% 1.95/2.17 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.95/2.17 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 1.95/2.17 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 1.95/2.17 all A B (in(A,B)->subset(A,union(B))).
% 1.95/2.17 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 1.95/2.17 exists A empty(A).
% 1.95/2.17 exists A (-empty(A)).
% 1.95/2.17 all A B subset(A,A).
% 1.95/2.17 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.95/2.17 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 1.95/2.17 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.95/2.17 all A B subset(set_intersection2(A,B),A).
% 1.95/2.17 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 1.95/2.17 all A (set_union2(A,empty_set)=A).
% 1.95/2.17 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.95/2.17 powerset(empty_set)=singleton(empty_set).
% 1.95/2.17 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 1.95/2.17 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.95/2.17 all A (set_intersection2(A,empty_set)=empty_set).
% 1.95/2.17 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.95/2.17 all A subset(empty_set,A).
% 1.95/2.17 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 1.95/2.17 all A B C D (ordered_pair(A,B)=ordered_pair(C,D)->A=C&B=D).
% 1.95/2.17 all A B subset(set_difference(A,B),A).
% 1.95/2.17 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.95/2.17 -(all A B (subset(singleton(A),B)<->in(A,B))).
% 1.95/2.17 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 1.95/2.17 all A (set_difference(A,empty_set)=A).
% 1.95/2.17 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))).
% 1.95/2.17 all A (subset(A,empty_set)->A=empty_set).
% 1.95/2.17 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 1.95/2.17 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 1.95/2.17 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 1.95/2.17 all A (set_difference(empty_set,A)=empty_set).
% 1.95/2.17 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))).
% 1.95/2.17 all A B (-(subset(A,B)&proper_subset(B,A))).
% 1.95/2.17 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 1.95/2.17 all A (unordered_pair(A,A)=singleton(A)).
% 1.95/2.17 all A (empty(A)->A=empty_set).
% 1.95/2.17 all A B (subset(singleton(A),singleton(B))->A=B).
% 1.95/2.17 all A B (-(in(A,B)&empty(B))).
% 1.95/2.17 all A B subset(A,set_union2(A,B)).
% 1.95/2.17 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 1.95/2.17 all A B (-(empty(A)&A!=B&empty(B))).
% 1.95/2.17 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.95/2.17 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 1.95/2.17 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 1.95/2.17 end_of_list.
% 1.95/2.17
% 1.95/2.17 -------> usable clausifies to:
% 1.95/2.17
% 1.95/2.17 list(usable).
% 1.95/2.17 0 [] A=A.
% 1.95/2.17 0 [] -in(A,B)| -in(B,A).
% 1.95/2.17 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.95/2.17 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.95/2.17 0 [] set_union2(A,B)=set_union2(B,A).
% 1.95/2.17 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.95/2.17 0 [] A!=B|subset(A,B).
% 1.95/2.17 0 [] A!=B|subset(B,A).
% 1.95/2.17 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.95/2.17 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.95/2.17 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.95/2.17 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.95/2.17 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.95/2.17 0 [] A!=empty_set| -in(B,A).
% 1.95/2.17 0 [] A=empty_set|in($f2(A),A).
% 1.95/2.17 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 1.95/2.17 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 1.95/2.17 0 [] B=powerset(A)|in($f3(A,B),B)|subset($f3(A,B),A).
% 1.95/2.17 0 [] B=powerset(A)| -in($f3(A,B),B)| -subset($f3(A,B),A).
% 1.95/2.17 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.95/2.17 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.95/2.17 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.95/2.17 0 [] C=unordered_pair(A,B)|in($f4(A,B,C),C)|$f4(A,B,C)=A|$f4(A,B,C)=B.
% 1.95/2.17 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=A.
% 1.95/2.17 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=B.
% 1.95/2.17 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.95/2.17 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.95/2.17 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.95/2.17 0 [] C=set_union2(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 1.95/2.17 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A).
% 1.95/2.17 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 1.95/2.17 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f7(A,B,C,D),A).
% 1.95/2.17 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f6(A,B,C,D),B).
% 1.95/2.17 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f7(A,B,C,D),$f6(A,B,C,D)).
% 1.95/2.17 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 1.95/2.17 0 [] C=cartesian_product2(A,B)|in($f10(A,B,C),C)|in($f9(A,B,C),A).
% 1.95/2.17 0 [] C=cartesian_product2(A,B)|in($f10(A,B,C),C)|in($f8(A,B,C),B).
% 1.95/2.17 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)).
% 1.95/2.17 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).
% 1.95/2.17 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.95/2.17 0 [] subset(A,B)|in($f11(A,B),A).
% 1.95/2.17 0 [] subset(A,B)| -in($f11(A,B),B).
% 1.95/2.17 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.95/2.17 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.95/2.17 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.95/2.17 0 [] C=set_intersection2(A,B)|in($f12(A,B,C),C)|in($f12(A,B,C),A).
% 1.95/2.17 0 [] C=set_intersection2(A,B)|in($f12(A,B,C),C)|in($f12(A,B,C),B).
% 1.95/2.17 0 [] C=set_intersection2(A,B)| -in($f12(A,B,C),C)| -in($f12(A,B,C),A)| -in($f12(A,B,C),B).
% 1.95/2.17 0 [] B!=union(A)| -in(C,B)|in(C,$f13(A,B,C)).
% 1.95/2.17 0 [] B!=union(A)| -in(C,B)|in($f13(A,B,C),A).
% 1.95/2.17 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 1.95/2.17 0 [] B=union(A)|in($f15(A,B),B)|in($f15(A,B),$f14(A,B)).
% 1.95/2.17 0 [] B=union(A)|in($f15(A,B),B)|in($f14(A,B),A).
% 1.95/2.17 0 [] B=union(A)| -in($f15(A,B),B)| -in($f15(A,B),X3)| -in(X3,A).
% 1.95/2.17 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.95/2.17 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.95/2.17 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.95/2.17 0 [] C=set_difference(A,B)|in($f16(A,B,C),C)|in($f16(A,B,C),A).
% 1.95/2.17 0 [] C=set_difference(A,B)|in($f16(A,B,C),C)| -in($f16(A,B,C),B).
% 1.95/2.17 0 [] C=set_difference(A,B)| -in($f16(A,B,C),C)| -in($f16(A,B,C),A)|in($f16(A,B,C),B).
% 1.95/2.17 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.95/2.17 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.95/2.17 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.95/2.17 0 [] -proper_subset(A,B)|subset(A,B).
% 1.95/2.17 0 [] -proper_subset(A,B)|A!=B.
% 1.95/2.17 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] empty(empty_set).
% 1.95/2.17 0 [] -empty(ordered_pair(A,B)).
% 1.95/2.17 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.95/2.17 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.95/2.17 0 [] set_union2(A,A)=A.
% 1.95/2.17 0 [] set_intersection2(A,A)=A.
% 1.95/2.17 0 [] -proper_subset(A,A).
% 1.95/2.17 0 [] singleton(A)!=empty_set.
% 1.95/2.17 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 1.95/2.17 0 [] -disjoint(singleton(A),B)| -in(A,B).
% 1.95/2.17 0 [] in(A,B)|disjoint(singleton(A),B).
% 1.95/2.17 0 [] -subset(singleton(A),B)|in(A,B).
% 1.95/2.17 0 [] subset(singleton(A),B)| -in(A,B).
% 1.95/2.17 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.95/2.17 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.95/2.17 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.95/2.17 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.95/2.17 0 [] subset(A,singleton(B))|A!=empty_set.
% 1.95/2.17 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.95/2.17 0 [] -in(A,B)|subset(A,union(B)).
% 1.95/2.17 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.95/2.17 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.95/2.17 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.95/2.17 0 [] empty($c1).
% 1.95/2.17 0 [] -empty($c2).
% 1.95/2.17 0 [] subset(A,A).
% 1.95/2.17 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.95/2.17 0 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 1.95/2.17 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.95/2.17 0 [] subset(set_intersection2(A,B),A).
% 1.95/2.17 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.95/2.17 0 [] set_union2(A,empty_set)=A.
% 1.95/2.17 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.95/2.17 0 [] powerset(empty_set)=singleton(empty_set).
% 1.95/2.17 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.95/2.17 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.95/2.17 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.95/2.17 0 [] in($f17(A,B),A)|in($f17(A,B),B)|A=B.
% 1.95/2.17 0 [] -in($f17(A,B),A)| -in($f17(A,B),B)|A=B.
% 1.95/2.17 0 [] subset(empty_set,A).
% 1.95/2.17 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.95/2.17 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 1.95/2.17 0 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 1.95/2.17 0 [] subset(set_difference(A,B),A).
% 1.95/2.17 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.95/2.17 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.95/2.17 0 [] subset(singleton($c4),$c3)|in($c4,$c3).
% 1.95/2.17 0 [] -subset(singleton($c4),$c3)| -in($c4,$c3).
% 1.95/2.17 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.95/2.17 0 [] set_difference(A,empty_set)=A.
% 1.95/2.17 0 [] disjoint(A,B)|in($f18(A,B),A).
% 1.95/2.17 0 [] disjoint(A,B)|in($f18(A,B),B).
% 1.95/2.17 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.95/2.17 0 [] -subset(A,empty_set)|A=empty_set.
% 1.95/2.17 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.95/2.17 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 1.95/2.17 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 1.95/2.17 0 [] set_difference(empty_set,A)=empty_set.
% 1.95/2.17 0 [] disjoint(A,B)|in($f19(A,B),set_intersection2(A,B)).
% 1.95/2.17 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.95/2.17 0 [] -subset(A,B)| -proper_subset(B,A).
% 1.95/2.17 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.95/2.17 0 [] unordered_pair(A,A)=singleton(A).
% 1.95/2.17 0 [] -empty(A)|A=empty_set.
% 1.95/2.17 0 [] -subset(singleton(A),singleton(B))|A=B.
% 1.95/2.17 0 [] -in(A,B)| -empty(B).
% 1.95/2.17 0 [] subset(A,set_union2(A,B)).
% 1.95/2.17 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.95/2.17 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.95/2.17 0 [] -empty(A)|A=B| -empty(B).
% 1.95/2.17 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.95/2.17 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 1.95/2.17 0 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 1.95/2.17 end_of_list.
% 1.95/2.17
% 1.95/2.17 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.95/2.17
% 1.95/2.17 This ia a non-Horn set with equality. The strategy will be
% 1.95/2.17 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.95/2.17 deletion, with positive clauses in sos and nonpositive
% 1.95/2.17 clauses in usable.
% 1.95/2.17
% 1.95/2.17 dependent: set(knuth_bendix).
% 1.95/2.17 dependent: set(anl_eq).
% 1.95/2.17 dependent: set(para_from).
% 1.95/2.17 dependent: set(para_into).
% 1.95/2.17 dependent: clear(para_from_right).
% 1.95/2.17 dependent: clear(para_into_right).
% 1.95/2.17 dependent: set(para_from_vars).
% 1.95/2.17 dependent: set(eq_units_both_ways).
% 1.95/2.17 dependent: set(dynamic_demod_all).
% 1.95/2.17 dependent: set(dynamic_demod).
% 1.95/2.17 dependent: set(order_eq).
% 1.95/2.17 dependent: set(back_demod).
% 1.95/2.17 dependent: set(lrpo).
% 1.95/2.17 dependent: set(hyper_res).
% 1.95/2.17 dependent: set(unit_deletion).
% 1.95/2.17 dependent: set(factor).
% 1.95/2.17
% 1.95/2.17 ------------> process usable:
% 1.95/2.17 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.95/2.17 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.95/2.17 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 1.95/2.17 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 1.95/2.17 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 1.95/2.17 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.95/2.17 ** KEPT (pick-wt=10): 7 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.95/2.17 ** KEPT (pick-wt=14): 8 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.95/2.17 ** KEPT (pick-wt=6): 9 [] A!=empty_set| -in(B,A).
% 1.95/2.17 ** KEPT (pick-wt=10): 10 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 1.95/2.17 ** KEPT (pick-wt=10): 11 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 1.95/2.17 ** KEPT (pick-wt=14): 12 [] A=powerset(B)| -in($f3(B,A),A)| -subset($f3(B,A),B).
% 1.95/2.17 ** KEPT (pick-wt=14): 13 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.95/2.17 ** KEPT (pick-wt=11): 14 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.95/2.17 ** KEPT (pick-wt=11): 15 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.95/2.17 ** KEPT (pick-wt=17): 16 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=B.
% 1.95/2.17 ** KEPT (pick-wt=17): 17 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=C.
% 1.95/2.17 ** KEPT (pick-wt=14): 18 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.95/2.17 ** KEPT (pick-wt=11): 19 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.95/2.17 ** KEPT (pick-wt=11): 20 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.95/2.17 ** KEPT (pick-wt=17): 21 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B).
% 1.95/2.17 ** KEPT (pick-wt=17): 22 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 1.95/2.17 ** KEPT (pick-wt=15): 23 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f7(B,C,A,D),B).
% 1.95/2.17 ** KEPT (pick-wt=15): 24 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f6(B,C,A,D),C).
% 1.95/2.17 ** KEPT (pick-wt=21): 26 [copy,25,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f7(B,C,A,D),$f6(B,C,A,D))=D.
% 1.95/2.17 ** KEPT (pick-wt=19): 27 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 1.95/2.17 ** KEPT (pick-wt=25): 28 [] 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).
% 1.95/2.17 ** KEPT (pick-wt=9): 29 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.95/2.17 ** KEPT (pick-wt=8): 30 [] subset(A,B)| -in($f11(A,B),B).
% 1.95/2.17 ** KEPT (pick-wt=11): 31 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.95/2.17 ** KEPT (pick-wt=11): 32 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.95/2.17 ** KEPT (pick-wt=14): 33 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.95/2.17 ** KEPT (pick-wt=23): 34 [] A=set_intersection2(B,C)| -in($f12(B,C,A),A)| -in($f12(B,C,A),B)| -in($f12(B,C,A),C).
% 1.95/2.17 ** KEPT (pick-wt=13): 35 [] A!=union(B)| -in(C,A)|in(C,$f13(B,A,C)).
% 1.95/2.17 ** KEPT (pick-wt=13): 36 [] A!=union(B)| -in(C,A)|in($f13(B,A,C),B).
% 1.95/2.17 ** KEPT (pick-wt=13): 37 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 1.95/2.17 ** KEPT (pick-wt=17): 38 [] A=union(B)| -in($f15(B,A),A)| -in($f15(B,A),C)| -in(C,B).
% 1.95/2.17 ** KEPT (pick-wt=11): 39 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.95/2.17 ** KEPT (pick-wt=11): 40 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.95/2.17 ** KEPT (pick-wt=14): 41 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.95/2.17 ** KEPT (pick-wt=17): 42 [] A=set_difference(B,C)|in($f16(B,C,A),A)| -in($f16(B,C,A),C).
% 1.95/2.17 ** KEPT (pick-wt=23): 43 [] A=set_difference(B,C)| -in($f16(B,C,A),A)| -in($f16(B,C,A),B)|in($f16(B,C,A),C).
% 1.95/2.17 ** KEPT (pick-wt=8): 44 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.95/2.17 ** KEPT (pick-wt=8): 45 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.95/2.17 ** KEPT (pick-wt=6): 46 [] -proper_subset(A,B)|subset(A,B).
% 1.95/2.17 ** KEPT (pick-wt=6): 47 [] -proper_subset(A,B)|A!=B.
% 1.95/2.17 ** KEPT (pick-wt=9): 48 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.95/2.17 ** KEPT (pick-wt=4): 49 [] -empty(ordered_pair(A,B)).
% 1.95/2.17 ** KEPT (pick-wt=6): 50 [] empty(A)| -empty(set_union2(A,B)).
% 1.95/2.17 ** KEPT (pick-wt=6): 51 [] empty(A)| -empty(set_union2(B,A)).
% 1.95/2.17 ** KEPT (pick-wt=3): 52 [] -proper_subset(A,A).
% 1.95/2.17 ** KEPT (pick-wt=4): 53 [] singleton(A)!=empty_set.
% 1.95/2.17 ** KEPT (pick-wt=9): 54 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 1.95/2.17 ** KEPT (pick-wt=7): 55 [] -disjoint(singleton(A),B)| -in(A,B).
% 1.95/2.17 ** KEPT (pick-wt=7): 56 [] -subset(singleton(A),B)|in(A,B).
% 1.95/2.17 ** KEPT (pick-wt=7): 57 [] subset(singleton(A),B)| -in(A,B).
% 1.95/2.18 ** KEPT (pick-wt=8): 58 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.95/2.18 ** KEPT (pick-wt=8): 59 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.95/2.18 ** KEPT (pick-wt=12): 60 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.95/2.18 ** KEPT (pick-wt=11): 61 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.95/2.18 ** KEPT (pick-wt=7): 62 [] subset(A,singleton(B))|A!=empty_set.
% 1.95/2.18 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.95/2.18 ** KEPT (pick-wt=7): 63 [] -in(A,B)|subset(A,union(B)).
% 1.95/2.18 ** KEPT (pick-wt=10): 64 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.95/2.18 ** KEPT (pick-wt=10): 65 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.95/2.18 ** KEPT (pick-wt=13): 66 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.95/2.18 ** KEPT (pick-wt=2): 67 [] -empty($c2).
% 1.95/2.18 ** KEPT (pick-wt=6): 68 [] -disjoint(A,B)|disjoint(B,A).
% 1.95/2.18 ** KEPT (pick-wt=13): 69 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 1.95/2.18 ** KEPT (pick-wt=8): 70 [] -subset(A,B)|set_union2(A,B)=B.
% 1.95/2.18 ** KEPT (pick-wt=11): 71 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.95/2.18 ** KEPT (pick-wt=9): 72 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.95/2.18 ** KEPT (pick-wt=10): 73 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.95/2.18 ** KEPT (pick-wt=8): 74 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.95/2.18 ** KEPT (pick-wt=13): 75 [] -in($f17(A,B),A)| -in($f17(A,B),B)|A=B.
% 1.95/2.18 ** KEPT (pick-wt=10): 76 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.95/2.18 ** KEPT (pick-wt=10): 77 [] ordered_pair(A,B)!=ordered_pair(C,D)|A=C.
% 1.95/2.18 ** KEPT (pick-wt=10): 78 [] ordered_pair(A,B)!=ordered_pair(C,D)|B=D.
% 1.95/2.18 Following clause subsumed by 58 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.95/2.18 Following clause subsumed by 59 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.95/2.18 ** KEPT (pick-wt=7): 79 [] -subset(singleton($c4),$c3)| -in($c4,$c3).
% 1.95/2.18 ** KEPT (pick-wt=9): 80 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.95/2.18 ** KEPT (pick-wt=6): 81 [] -subset(A,empty_set)|A=empty_set.
% 1.95/2.18 ** KEPT (pick-wt=10): 83 [copy,82,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 1.95/2.18 ** KEPT (pick-wt=8): 84 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.95/2.18 ** KEPT (pick-wt=6): 85 [] -subset(A,B)| -proper_subset(B,A).
% 1.95/2.18 ** KEPT (pick-wt=9): 86 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.95/2.18 ** KEPT (pick-wt=5): 87 [] -empty(A)|A=empty_set.
% 1.95/2.18 ** KEPT (pick-wt=8): 88 [] -subset(singleton(A),singleton(B))|A=B.
% 1.95/2.18 ** KEPT (pick-wt=5): 89 [] -in(A,B)| -empty(B).
% 1.95/2.18 ** KEPT (pick-wt=8): 90 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.95/2.18 ** KEPT (pick-wt=8): 91 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.95/2.18 ** KEPT (pick-wt=7): 92 [] -empty(A)|A=B| -empty(B).
% 1.95/2.18 ** KEPT (pick-wt=11): 93 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.95/2.18 ** KEPT (pick-wt=9): 94 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 1.95/2.18 ** KEPT (pick-wt=9): 95 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 1.95/2.18
% 1.95/2.18 ------------> process sos:
% 1.95/2.18 ** KEPT (pick-wt=3): 123 [] A=A.
% 1.95/2.18 ** KEPT (pick-wt=7): 124 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.95/2.18 ** KEPT (pick-wt=7): 125 [] set_union2(A,B)=set_union2(B,A).
% 1.95/2.18 ** KEPT (pick-wt=7): 126 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.95/2.18 ** KEPT (pick-wt=14): 127 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.95/2.18 ** KEPT (pick-wt=7): 128 [] A=empty_set|in($f2(A),A).
% 1.95/2.18 ** KEPT (pick-wt=14): 129 [] A=powerset(B)|in($f3(B,A),A)|subset($f3(B,A),B).
% 1.95/2.18 ** KEPT (pick-wt=23): 130 [] A=unordered_pair(B,C)|in($f4(B,C,A),A)|$f4(B,C,A)=B|$f4(B,C,A)=C.
% 1.95/2.18 ** KEPT (pick-wt=23): 131 [] A=set_union2(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 1.95/2.18 ** KEPT (pick-wt=17): 132 [] A=cartesian_product2(B,C)|in($f10(B,C,A),A)|in($f9(B,C,A),B).
% 1.95/2.18 ** KEPT (pick-wt=17): 133 [] A=cartesian_product2(B,C)|in($f10(B,C,A),A)|in($f8(B,C,A),C).
% 1.95/2.18 ** KEPT (pick-wt=25): 135 [copy,134,flip.3] A=cartesian_product2(B,C)|in($f10(B,C,A),A)|ordered_pair($f9(B,C,A),$f8(B,C,A))=$f10(B,C,A).
% 1.95/2.18 ** KEPT (pick-wt=8): 136 [] subset(A,B)|in($f11(A,B),A).
% 1.95/2.18 ** KEPT (pick-wt=17): 137 [] A=set_intersection2(B,C)|in($f12(B,C,A),A)|in($f12(B,C,A),B).
% 1.95/2.18 ** KEPT (pick-wt=17): 138 [] A=set_intersection2(B,C)|in($f12(B,C,A),A)|in($f12(B,C,A),C).
% 1.95/2.18 ** KEPT (pick-wt=16): 139 [] A=union(B)|in($f15(B,A),A)|in($f15(B,A),$f14(B,A)).
% 1.95/2.18 ** KEPT (pick-wt=14): 140 [] A=union(B)|in($f15(B,A),A)|in($f14(B,A),B).
% 1.95/2.18 ** KEPT (pick-wt=17): 141 [] A=set_difference(B,C)|in($f16(B,C,A),A)|in($f16(B,C,A),B).
% 1.95/2.18 ** KEPT (pick-wt=10): 143 [copy,142,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.95/2.18 ---> New Demodulator: 144 [new_demod,143] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.95/2.18 ** KEPT (pick-wt=2): 145 [] empty(empty_set).
% 1.95/2.18 ** KEPT (pick-wt=5): 146 [] set_union2(A,A)=A.
% 1.95/2.18 ---> New Demodulator: 147 [new_demod,146] set_union2(A,A)=A.
% 1.95/2.18 ** KEPT (pick-wt=5): 148 [] set_intersection2(A,A)=A.
% 1.95/2.18 ---> New Demodulator: 149 [new_demod,148] set_intersection2(A,A)=A.
% 1.95/2.18 ** KEPT (pick-wt=7): 150 [] in(A,B)|disjoint(singleton(A),B).
% 1.95/2.18 ** KEPT (pick-wt=2): 151 [] empty($c1).
% 1.95/2.18 ** KEPT (pick-wt=3): 152 [] subset(A,A).
% 1.95/2.18 ** KEPT (pick-wt=5): 153 [] subset(set_intersection2(A,B),A).
% 1.95/2.18 ** KEPT (pick-wt=5): 154 [] set_union2(A,empty_set)=A.
% 1.95/2.18 ---> New Demodulator: 155 [new_demod,154] set_union2(A,empty_set)=A.
% 1.95/2.18 ** KEPT (pick-wt=5): 157 [copy,156,flip.1] singleton(empty_set)=powerset(empty_set).
% 1.95/2.18 ---> New Demodulator: 158 [new_demod,157] singleton(empty_set)=powerset(empty_set).
% 1.95/2.18 ** KEPT (pick-wt=5): 159 [] set_intersection2(A,empty_set)=empty_set.
% 1.95/2.18 ---> New Demodulator: 160 [new_demod,159] set_intersection2(A,empty_set)=empty_set.
% 1.95/2.18 ** KEPT (pick-wt=13): 161 [] in($f17(A,B),A)|in($f17(A,B),B)|A=B.
% 1.95/2.18 ** KEPT (pick-wt=3): 162 [] subset(empty_set,A).
% 1.95/2.18 ** KEPT (pick-wt=5): 163 [] subset(set_difference(A,B),A).
% 1.95/2.18 ** KEPT (pick-wt=7): 164 [] subset(singleton($c4),$c3)|in($c4,$c3).
% 1.95/2.18 ** KEPT (pick-wt=9): 165 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.95/2.18 ---> New Demodulator: 166 [new_demod,165] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.95/2.18 ** KEPT (pick-wt=5): 167 [] set_difference(A,empty_set)=A.
% 1.95/2.18 ---> New Demodulator: 168 [new_demod,167] set_difference(A,empty_set)=A.
% 1.95/2.18 ** KEPT (pick-wt=8): 169 [] disjoint(A,B)|in($f18(A,B),A).
% 1.95/2.18 ** KEPT (pick-wt=8): 170 [] disjoint(A,B)|in($f18(A,B),B).
% 1.95/2.18 ** KEPT (pick-wt=9): 171 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.95/2.18 ---> New Demodulator: 172 [new_demod,171] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.95/2.18 ** KEPT (pick-wt=9): 174 [copy,173,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.95/2.18 ---> New Demodulator: 175 [new_demod,174] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.95/2.18 ** KEPT (pick-wt=5): 176 [] set_difference(empty_set,A)=empty_set.
% 1.95/2.18 ---> New Demodulator: 177 [new_demod,176] set_difference(empty_set,A)=empty_set.
% 1.95/2.18 ** KEPT (pick-wt=12): 179 [copy,178,demod,175] disjoint(A,B)|in($f19(A,B),set_difference(A,set_difference(A,B))).
% 1.95/2.18 ** KEPT (pick-wt=6): 181 [copy,180,flip.1] singleton(A)=unordered_pair(A,A).
% 1.95/2.18 ---> New Demodulator: 182 [new_demod,181] singleton(A)=unordered_pair(A,A).
% 1.95/2.18 ** KEPT (pick-wt=5): 183 [] subset(A,set_union2(A,B)).
% 1.95/2.18 Following clause subsumed by 123 during input processing: 0 [copy,123,flip.1] A=A.
% 1.95/2.18 123 back subsumes 119.
% 1.95/2.18 123 back subsumes 117.
% 1.95/2.18 123 back subsumes 97.
% 1.95/2.18 Following clause subsumed by 124 during input processing: 0 [copy,124,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.95/2.18 Following clause subsumed by 125 during input processing: 0 [copy,125,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.95/2.18 ** KEPT (pick-wt=11): 184 [copy,126,flip.1,demod,175,175] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 1.95/2.18 >>>> Starting back demodulation with 144.
% 1.95/2.18 >>>> Starting back demodulation with 147.
% 1.95/2.18 >> back demodulating 120 with 147.
% 1.95/2.18 >> back demodulating 99 with 147.
% 1.95/2.18 >>>> Starting back demodulation with 149.
% 1.95/2.18 >> back demodulating 122 with 149.
% 1.95/2.18 >> back demodulating 116 with 149.
% 1.95/2.18 >> back demodulating 109 with 149.
% 1.95/2.18 >> back demodulating 106 with 149.
% 1.95/2.18 >>>> Starting back demodulation with 155.
% 1.95/2.18 >>>> Starting back demodulation with 158.
% 1.95/2.18 >>>> Starting back demodulation with 160.
% 1.95/2.18 >>>> Starting back demodulation with 166.
% 1.95/2.18 >> back demodulating 83 with 166.
% 1.95/2.18 >>>> Starting back demodulation with 168.
% 1.95/2.18 >>>> Starting back demodulation with 172.
% 12.39/12.57 >>>> Starting back demodulation with 175.
% 12.39/12.57 >> back demodulating 159 with 175.
% 12.39/12.57 >> back demodulating 153 with 175.
% 12.39/12.57 >> back demodulating 148 with 175.
% 12.39/12.57 >> back demodulating 138 with 175.
% 12.39/12.57 >> back demodulating 137 with 175.
% 12.39/12.57 >> back demodulating 126 with 175.
% 12.39/12.57 >> back demodulating 108 with 175.
% 12.39/12.57 >> back demodulating 107 with 175.
% 12.39/12.57 >> back demodulating 84 with 175.
% 12.39/12.57 >> back demodulating 74 with 175.
% 12.39/12.57 >> back demodulating 73 with 175.
% 12.39/12.57 >> back demodulating 71 with 175.
% 12.39/12.57 >> back demodulating 45 with 175.
% 12.39/12.57 >> back demodulating 44 with 175.
% 12.39/12.57 >> back demodulating 34 with 175.
% 12.39/12.57 >> back demodulating 33 with 175.
% 12.39/12.57 >> back demodulating 32 with 175.
% 12.39/12.57 >> back demodulating 31 with 175.
% 12.39/12.57 >>>> Starting back demodulation with 177.
% 12.39/12.57 >>>> Starting back demodulation with 182.
% 12.39/12.57 >> back demodulating 164 with 182.
% 12.39/12.57 >> back demodulating 157 with 182.
% 12.39/12.57 >> back demodulating 150 with 182.
% 12.39/12.57 >> back demodulating 143 with 182.
% 12.39/12.57 >> back demodulating 127 with 182.
% 12.39/12.57 >> back demodulating 95 with 182.
% 12.39/12.57 >> back demodulating 94 with 182.
% 12.39/12.57 >> back demodulating 88 with 182.
% 12.39/12.57 >> back demodulating 79 with 182.
% 12.39/12.57 >> back demodulating 62 with 182.
% 12.39/12.57 >> back demodulating 61 with 182.
% 12.39/12.57 >> back demodulating 60 with 182.
% 12.39/12.57 >> back demodulating 57 with 182.
% 12.39/12.57 >> back demodulating 56 with 182.
% 12.39/12.57 >> back demodulating 55 with 182.
% 12.39/12.57 >> back demodulating 54 with 182.
% 12.39/12.57 >> back demodulating 53 with 182.
% 12.39/12.57 >> back demodulating 8 with 182.
% 12.39/12.57 >> back demodulating 7 with 182.
% 12.39/12.57 >> back demodulating 6 with 182.
% 12.39/12.57 Following clause subsumed by 184 during input processing: 0 [copy,184,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 12.39/12.57 >>>> Starting back demodulation with 196.
% 12.39/12.57 >>>> Starting back demodulation with 212.
% 12.39/12.57 >>>> Starting back demodulation with 215.
% 12.39/12.57
% 12.39/12.57 ======= end of input processing =======
% 12.39/12.57
% 12.39/12.57 =========== start of search ===========
% 12.39/12.57
% 12.39/12.57
% 12.39/12.57 Resetting weight limit to 7.
% 12.39/12.57
% 12.39/12.57
% 12.39/12.57 Resetting weight limit to 7.
% 12.39/12.57
% 12.39/12.57 sos_size=641
% 12.39/12.57
% 12.39/12.57
% 12.39/12.57 Resetting weight limit to 6.
% 12.39/12.57
% 12.39/12.57
% 12.39/12.57 Resetting weight limit to 6.
% 12.39/12.57
% 12.39/12.57 sos_size=654
% 12.39/12.57
% 12.39/12.57 -- HEY sandbox, WE HAVE A PROOF!! --
% 12.39/12.57
% 12.39/12.57 ----> UNIT CONFLICT at 10.40 sec ----> 1087 [binary,1086.1,1081.1] $F.
% 12.39/12.57
% 12.39/12.57 Length of proof is 18. Level of proof is 7.
% 12.39/12.57
% 12.39/12.57 ---------------- PROOF ----------------
% 12.39/12.57 % SZS status Theorem
% 12.39/12.57 % SZS output start Refutation
% See solution above
% 12.39/12.57 ------------ end of proof -------------
% 12.39/12.57
% 12.39/12.57
% 12.39/12.57 Search stopped by max_proofs option.
% 12.39/12.57
% 12.39/12.57
% 12.39/12.57 Search stopped by max_proofs option.
% 12.39/12.57
% 12.39/12.57 ============ end of search ============
% 12.39/12.57
% 12.39/12.57 -------------- statistics -------------
% 12.39/12.57 clauses given 256
% 12.39/12.57 clauses generated 679810
% 12.39/12.57 clauses kept 1051
% 12.39/12.57 clauses forward subsumed 4726
% 12.39/12.57 clauses back subsumed 108
% 12.39/12.57 Kbytes malloced 5859
% 12.39/12.57
% 12.39/12.57 ----------- times (seconds) -----------
% 12.39/12.57 user CPU time 10.40 (0 hr, 0 min, 10 sec)
% 12.39/12.57 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 12.39/12.57 wall-clock time 12 (0 hr, 0 min, 12 sec)
% 12.39/12.57
% 12.39/12.57 That finishes the proof of the theorem.
% 12.39/12.57
% 12.39/12.57 Process 15824 finished Wed Jul 27 08:08:04 2022
% 12.39/12.57 Otter interrupted
% 12.39/12.57 PROOF FOUND
%------------------------------------------------------------------------------