TSTP Solution File: SEU146+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU146+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:14:54 EDT 2022
% Result : Theorem 14.93s 15.13s
% Output : Refutation 14.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 29
% Syntax : Number of clauses : 76 ( 35 unt; 14 nHn; 48 RR)
% Number of literals : 136 ( 62 equ; 54 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 : 87 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A != B
| subset(B,A) ),
file('SEU146+2.p',unknown),
[] ).
cnf(5,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SEU146+2.p',unknown),
[] ).
cnf(10,axiom,
( A != unordered_pair(B,C)
| ~ in(D,A)
| D = B
| D = C ),
file('SEU146+2.p',unknown),
[] ).
cnf(11,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SEU146+2.p',unknown),
[] ).
cnf(12,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != C ),
file('SEU146+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU146+2.p',unknown),
[] ).
cnf(39,axiom,
singleton(A) != empty_set,
file('SEU146+2.p',unknown),
[] ).
cnf(41,axiom,
( subset(singleton(A),B)
| ~ in(A,B) ),
file('SEU146+2.p',unknown),
[] ).
cnf(45,axiom,
( ~ subset(dollar_c2,singleton(dollar_c1))
| dollar_c2 != empty_set ),
file('SEU146+2.p',unknown),
[] ).
cnf(46,plain,
( ~ subset(dollar_c2,singleton(dollar_c1))
| empty_set != dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[45])]),
[iquote('copy,45,flip.2')] ).
cnf(47,axiom,
( ~ subset(dollar_c2,singleton(dollar_c1))
| dollar_c2 != singleton(dollar_c1) ),
file('SEU146+2.p',unknown),
[] ).
cnf(48,plain,
( ~ subset(dollar_c2,singleton(dollar_c1))
| singleton(dollar_c1) != dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[47])]),
[iquote('copy,47,flip.2')] ).
cnf(51,axiom,
( ~ subset(A,B)
| set_union2(A,B) = B ),
file('SEU146+2.p',unknown),
[] ).
cnf(53,axiom,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('SEU146+2.p',unknown),
[] ).
cnf(59,axiom,
( ~ subset(A,empty_set)
| A = empty_set ),
file('SEU146+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ empty(A)
| A = empty_set ),
file('SEU146+2.p',unknown),
[] ).
cnf(66,axiom,
( ~ in(A,B)
| ~ empty(B) ),
file('SEU146+2.p',unknown),
[] ).
cnf(69,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU146+2.p',unknown),
[] ).
cnf(90,axiom,
A = A,
file('SEU146+2.p',unknown),
[] ).
cnf(91,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SEU146+2.p',unknown),
[] ).
cnf(95,axiom,
( A = empty_set
| in(dollar_f2(A),A) ),
file('SEU146+2.p',unknown),
[] ).
cnf(96,axiom,
( A = unordered_pair(B,C)
| in(dollar_f3(B,C,A),A)
| dollar_f3(B,C,A) = B
| dollar_f3(B,C,A) = C ),
file('SEU146+2.p',unknown),
[] ).
cnf(102,axiom,
empty(empty_set),
file('SEU146+2.p',unknown),
[] ).
cnf(104,axiom,
set_union2(A,A) = A,
file('SEU146+2.p',unknown),
[] ).
cnf(107,axiom,
( subset(dollar_c2,singleton(dollar_c1))
| dollar_c2 = empty_set
| dollar_c2 = singleton(dollar_c1) ),
file('SEU146+2.p',unknown),
[] ).
cnf(108,plain,
( subset(dollar_c2,singleton(dollar_c1))
| empty_set = dollar_c2
| singleton(dollar_c1) = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[107])])]),
[iquote('copy,107,flip.2,flip.3')] ).
cnf(109,axiom,
empty(dollar_c3),
file('SEU146+2.p',unknown),
[] ).
cnf(110,axiom,
subset(A,A),
file('SEU146+2.p',unknown),
[] ).
cnf(112,axiom,
set_union2(A,empty_set) = A,
file('SEU146+2.p',unknown),
[] ).
cnf(117,axiom,
subset(empty_set,A),
file('SEU146+2.p',unknown),
[] ).
cnf(134,axiom,
unordered_pair(A,A) = singleton(A),
file('SEU146+2.p',unknown),
[] ).
cnf(136,plain,
singleton(A) = unordered_pair(A,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[134])]),
[iquote('copy,134,flip.1')] ).
cnf(137,axiom,
subset(A,set_union2(A,B)),
file('SEU146+2.p',unknown),
[] ).
cnf(164,plain,
( subset(dollar_c2,unordered_pair(dollar_c1,dollar_c1))
| empty_set = dollar_c2
| unordered_pair(dollar_c1,dollar_c1) = dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[108]),136,136]),
[iquote('back_demod,108,demod,136,136')] ).
cnf(166,plain,
( ~ subset(dollar_c2,unordered_pair(dollar_c1,dollar_c1))
| unordered_pair(dollar_c1,dollar_c1) != dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),136,136]),
[iquote('back_demod,48,demod,136,136')] ).
cnf(167,plain,
( ~ subset(dollar_c2,unordered_pair(dollar_c1,dollar_c1))
| empty_set != dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[46]),136]),
[iquote('back_demod,46,demod,136')] ).
cnf(169,plain,
( subset(unordered_pair(A,A),B)
| ~ in(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),136]),
[iquote('back_demod,41,demod,136')] ).
cnf(171,plain,
unordered_pair(A,A) != empty_set,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[39]),136]),
[iquote('back_demod,39,demod,136')] ).
cnf(173,plain,
in(A,unordered_pair(B,A)),
inference(hyper,[status(thm)],[90,12,90]),
[iquote('hyper,90,12,90')] ).
cnf(174,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[90,11,90]),
[iquote('hyper,90,11,90')] ).
cnf(190,plain,
empty_set = dollar_c3,
inference(hyper,[status(thm)],[109,69,102]),
[iquote('hyper,109,69,102')] ).
cnf(205,plain,
unordered_pair(A,A) != dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[171]),190]),
[iquote('back_demod,171,demod,190')] ).
cnf(206,plain,
( ~ subset(dollar_c2,unordered_pair(dollar_c1,dollar_c1))
| dollar_c3 != dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[167]),190]),
[iquote('back_demod,167,demod,190')] ).
cnf(207,plain,
( subset(dollar_c2,unordered_pair(dollar_c1,dollar_c1))
| dollar_c3 = dollar_c2
| unordered_pair(dollar_c1,dollar_c1) = dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[164]),190]),
[iquote('back_demod,164,demod,190')] ).
cnf(216,plain,
subset(dollar_c3,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[117]),190]),
[iquote('back_demod,117,demod,190')] ).
cnf(218,plain,
set_union2(A,dollar_c3) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[112]),190]),
[iquote('back_demod,112,demod,190')] ).
cnf(219,plain,
( A = dollar_c3
| in(dollar_f2(A),A) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[95]),190]),
[iquote('back_demod,95,demod,190')] ).
cnf(220,plain,
( ~ empty(A)
| A = dollar_c3 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[65]),190]),
[iquote('back_demod,65,demod,190')] ).
cnf(221,plain,
( ~ subset(A,dollar_c3)
| A = dollar_c3 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),190,190]),
[iquote('back_demod,59,demod,190,190')] ).
cnf(239,plain,
subset(unordered_pair(A,B),unordered_pair(B,A)),
inference(hyper,[status(thm)],[91,4]),
[iquote('hyper,91,4')] ).
cnf(252,plain,
( A = unordered_pair(B,C)
| ~ subset(unordered_pair(C,B),A)
| ~ subset(A,unordered_pair(C,B)) ),
inference(para_into,[status(thm),theory(equality)],[91,5]),
[iquote('para_into,91.1.1,5.1.1')] ).
cnf(286,plain,
( A = B
| C != unordered_pair(A,D)
| ~ in(B,C)
| B = D ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[104,10]),104,104]),
[iquote('para_into,103.1.1,10.3.1,demod,104,104')] ).
cnf(429,plain,
( unordered_pair(A,B) = dollar_c3
| dollar_f3(A,B,dollar_c3) = A
| dollar_f3(A,B,dollar_c3) = B ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[96,66,109])]),
[iquote('hyper,96,66,109,flip.1')] ).
cnf(441,plain,
dollar_f3(A,A,dollar_c3) = A,
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[429]),205]),
[iquote('factor,429.2.3,unit_del,205')] ).
cnf(1360,plain,
( dollar_c3 = A
| ~ empty(A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[220,218]),218]),
[iquote('para_from,220.2.1,217.1.1,demod,218')] ).
cnf(1792,plain,
( dollar_c3 = A
| in(dollar_f2(A),A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[219,441]),441,441]),
[iquote('para_from,219.1.1,440.1.1,demod,441,441')] ).
cnf(1897,plain,
( empty(A)
| in(dollar_f2(A),A) ),
inference(para_from,[status(thm),theory(equality)],[1792,109]),
[iquote('para_from,1792.1.1,109.1.1')] ).
cnf(1927,plain,
subset(unordered_pair(A,A),unordered_pair(A,B)),
inference(hyper,[status(thm)],[169,174]),
[iquote('hyper,169,174')] ).
cnf(1928,plain,
subset(unordered_pair(A,A),unordered_pair(B,A)),
inference(hyper,[status(thm)],[169,173]),
[iquote('hyper,169,173')] ).
cnf(1948,plain,
( dollar_c3 != dollar_c2
| ~ empty(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[206,220]),216]),
[iquote('para_into,206.1.1,220.2.1,unit_del,216')] ).
cnf(1950,plain,
( A != dollar_c2
| ~ empty(dollar_c2)
| ~ empty(A) ),
inference(para_into,[status(thm),theory(equality)],[1948,1360]),
[iquote('para_into,1948.1.1,1360.1.1')] ).
cnf(1954,plain,
~ empty(dollar_c2),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[1950]),90]),
[iquote('factor,1950.2.3,unit_del,90')] ).
cnf(1955,plain,
in(dollar_f2(dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[1954,1897]),
[iquote('hyper,1954,1897')] ).
cnf(1961,plain,
~ subset(dollar_c2,dollar_c3),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1954,221]),109]),
[iquote('para_into,1954.1.1,221.2.1,unit_del,109')] ).
cnf(1970,plain,
( subset(dollar_c2,unordered_pair(dollar_c1,dollar_c1))
| dollar_c3 = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[207,239])]),
[iquote('para_from,207.3.1,239.1.1,factor_simp')] ).
cnf(1977,plain,
subset(unordered_pair(dollar_f2(dollar_c2),dollar_f2(dollar_c2)),dollar_c2),
inference(hyper,[status(thm)],[1955,169]),
[iquote('hyper,1955,169')] ).
cnf(1983,plain,
in(dollar_f2(dollar_c2),set_union2(dollar_c2,A)),
inference(hyper,[status(thm)],[1955,20,137]),
[iquote('hyper,1955,20,137')] ).
cnf(2046,plain,
( in(dollar_f2(dollar_c2),A)
| ~ subset(dollar_c2,A) ),
inference(para_into,[status(thm),theory(equality)],[1983,51]),
[iquote('para_into,1983.1.2,51.2.1')] ).
cnf(2304,plain,
( dollar_c3 = dollar_c2
| subset(dollar_c2,unordered_pair(A,dollar_c1)) ),
inference(hyper,[status(thm)],[1970,53,1928]),
[iquote('hyper,1970,53,1928')] ).
cnf(2447,plain,
subset(dollar_c2,unordered_pair(A,dollar_c1)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2304,1961]),110]),
[iquote('para_from,2304.1.1,1961.1.2,unit_del,110')] ).
cnf(2452,plain,
in(dollar_f2(dollar_c2),unordered_pair(A,dollar_c1)),
inference(hyper,[status(thm)],[2447,2046]),
[iquote('hyper,2447,2046')] ).
cnf(2460,plain,
subset(dollar_c2,unordered_pair(dollar_c1,A)),
inference(hyper,[status(thm)],[2447,53,1927]),
[iquote('hyper,2447,53,1927')] ).
cnf(2484,plain,
dollar_f2(dollar_c2) = dollar_c1,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2452,286,91])]),
[iquote('hyper,2452,286,91,factor_simp')] ).
cnf(2507,plain,
subset(unordered_pair(dollar_c1,dollar_c1),dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1977]),2484,2484]),
[iquote('back_demod,1977,demod,2484,2484')] ).
cnf(2567,plain,
unordered_pair(dollar_c1,dollar_c1) = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2507,252,2460])]),
[iquote('hyper,2507,252,2460,flip.1')] ).
cnf(2569,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[166]),2567,2567]),110,90]),
[iquote('back_demod,166,demod,2567,2567,unit_del,110,90')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU146+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 07:42:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.88/2.09 ----- Otter 3.3f, August 2004 -----
% 1.88/2.09 The process was started by sandbox on n028.cluster.edu,
% 1.88/2.09 Wed Jul 27 07:42:04 2022
% 1.88/2.09 The command was "./otter". The process ID is 4860.
% 1.88/2.09
% 1.88/2.09 set(prolog_style_variables).
% 1.88/2.09 set(auto).
% 1.88/2.09 dependent: set(auto1).
% 1.88/2.09 dependent: set(process_input).
% 1.88/2.09 dependent: clear(print_kept).
% 1.88/2.09 dependent: clear(print_new_demod).
% 1.88/2.09 dependent: clear(print_back_demod).
% 1.88/2.09 dependent: clear(print_back_sub).
% 1.88/2.09 dependent: set(control_memory).
% 1.88/2.09 dependent: assign(max_mem, 12000).
% 1.88/2.09 dependent: assign(pick_given_ratio, 4).
% 1.88/2.09 dependent: assign(stats_level, 1).
% 1.88/2.09 dependent: assign(max_seconds, 10800).
% 1.88/2.09 clear(print_given).
% 1.88/2.09
% 1.88/2.09 formula_list(usable).
% 1.88/2.09 all A (A=A).
% 1.88/2.09 all A B (in(A,B)-> -in(B,A)).
% 1.88/2.09 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 1.88/2.09 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.88/2.09 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.88/2.09 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.88/2.09 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.88/2.09 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.88/2.09 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.88/2.09 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.88/2.09 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.88/2.09 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.88/2.09 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.88/2.09 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.88/2.09 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.88/2.09 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 1.88/2.09 $T.
% 1.88/2.09 $T.
% 1.88/2.09 $T.
% 1.88/2.09 $T.
% 1.88/2.09 $T.
% 1.88/2.09 $T.
% 1.88/2.09 empty(empty_set).
% 1.88/2.09 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.88/2.09 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.88/2.09 all A B (set_union2(A,A)=A).
% 1.88/2.09 all A B (set_intersection2(A,A)=A).
% 1.88/2.09 all A B (-proper_subset(A,A)).
% 1.88/2.09 all A (singleton(A)!=empty_set).
% 1.88/2.09 all A B (subset(singleton(A),B)<->in(A,B)).
% 1.88/2.09 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.88/2.09 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 1.88/2.09 -(all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B))).
% 1.88/2.09 exists A empty(A).
% 1.88/2.09 exists A (-empty(A)).
% 1.88/2.09 all A B subset(A,A).
% 1.88/2.09 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.88/2.09 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.88/2.09 all A B subset(set_intersection2(A,B),A).
% 1.88/2.09 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 1.88/2.09 all A (set_union2(A,empty_set)=A).
% 1.88/2.09 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.88/2.09 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 1.88/2.09 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.88/2.09 all A (set_intersection2(A,empty_set)=empty_set).
% 1.88/2.09 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.88/2.09 all A subset(empty_set,A).
% 1.88/2.09 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 1.88/2.09 all A B subset(set_difference(A,B),A).
% 1.88/2.09 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.88/2.09 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 1.88/2.09 all A (set_difference(A,empty_set)=A).
% 1.88/2.09 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))).
% 1.88/2.09 all A (subset(A,empty_set)->A=empty_set).
% 1.88/2.09 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 1.88/2.09 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 1.88/2.09 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 1.88/2.09 all A (set_difference(empty_set,A)=empty_set).
% 1.88/2.09 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))).
% 1.88/2.09 all A B (-(subset(A,B)&proper_subset(B,A))).
% 1.88/2.09 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 1.88/2.09 all A (unordered_pair(A,A)=singleton(A)).
% 1.88/2.09 all A (empty(A)->A=empty_set).
% 1.88/2.09 all A B (-(in(A,B)&empty(B))).
% 1.88/2.09 all A B subset(A,set_union2(A,B)).
% 1.88/2.09 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 1.88/2.09 all A B (-(empty(A)&A!=B&empty(B))).
% 1.88/2.09 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.88/2.09 end_of_list.
% 1.88/2.09
% 1.88/2.09 -------> usable clausifies to:
% 1.88/2.09
% 1.88/2.09 list(usable).
% 1.88/2.09 0 [] A=A.
% 1.88/2.09 0 [] -in(A,B)| -in(B,A).
% 1.88/2.09 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.88/2.09 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.88/2.09 0 [] set_union2(A,B)=set_union2(B,A).
% 1.88/2.09 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.88/2.09 0 [] A!=B|subset(A,B).
% 1.88/2.09 0 [] A!=B|subset(B,A).
% 1.88/2.09 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.88/2.09 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.88/2.09 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.88/2.09 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.88/2.09 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.88/2.09 0 [] A!=empty_set| -in(B,A).
% 1.88/2.09 0 [] A=empty_set|in($f2(A),A).
% 1.88/2.09 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.88/2.09 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.88/2.09 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.88/2.09 0 [] C=unordered_pair(A,B)|in($f3(A,B,C),C)|$f3(A,B,C)=A|$f3(A,B,C)=B.
% 1.88/2.09 0 [] C=unordered_pair(A,B)| -in($f3(A,B,C),C)|$f3(A,B,C)!=A.
% 1.88/2.09 0 [] C=unordered_pair(A,B)| -in($f3(A,B,C),C)|$f3(A,B,C)!=B.
% 1.88/2.09 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.88/2.09 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.88/2.09 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.88/2.09 0 [] C=set_union2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A)|in($f4(A,B,C),B).
% 1.88/2.09 0 [] C=set_union2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A).
% 1.88/2.09 0 [] C=set_union2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),B).
% 1.88/2.09 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.88/2.09 0 [] subset(A,B)|in($f5(A,B),A).
% 1.88/2.09 0 [] subset(A,B)| -in($f5(A,B),B).
% 1.88/2.09 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.88/2.09 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.88/2.09 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.88/2.09 0 [] C=set_intersection2(A,B)|in($f6(A,B,C),C)|in($f6(A,B,C),A).
% 1.88/2.09 0 [] C=set_intersection2(A,B)|in($f6(A,B,C),C)|in($f6(A,B,C),B).
% 1.88/2.09 0 [] C=set_intersection2(A,B)| -in($f6(A,B,C),C)| -in($f6(A,B,C),A)| -in($f6(A,B,C),B).
% 1.88/2.09 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.88/2.09 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.88/2.09 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.88/2.09 0 [] C=set_difference(A,B)|in($f7(A,B,C),C)|in($f7(A,B,C),A).
% 1.88/2.09 0 [] C=set_difference(A,B)|in($f7(A,B,C),C)| -in($f7(A,B,C),B).
% 1.88/2.09 0 [] C=set_difference(A,B)| -in($f7(A,B,C),C)| -in($f7(A,B,C),A)|in($f7(A,B,C),B).
% 1.88/2.09 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.88/2.09 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.88/2.09 0 [] -proper_subset(A,B)|subset(A,B).
% 1.88/2.09 0 [] -proper_subset(A,B)|A!=B.
% 1.88/2.09 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.88/2.09 0 [] $T.
% 1.88/2.09 0 [] $T.
% 1.88/2.09 0 [] $T.
% 1.88/2.09 0 [] $T.
% 1.88/2.09 0 [] $T.
% 1.88/2.09 0 [] $T.
% 1.88/2.09 0 [] empty(empty_set).
% 1.88/2.09 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.88/2.09 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.88/2.09 0 [] set_union2(A,A)=A.
% 1.88/2.09 0 [] set_intersection2(A,A)=A.
% 1.88/2.09 0 [] -proper_subset(A,A).
% 1.88/2.09 0 [] singleton(A)!=empty_set.
% 1.88/2.09 0 [] -subset(singleton(A),B)|in(A,B).
% 1.88/2.09 0 [] subset(singleton(A),B)| -in(A,B).
% 1.88/2.09 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.88/2.09 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.88/2.09 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.88/2.09 0 [] subset($c2,singleton($c1))|$c2=empty_set|$c2=singleton($c1).
% 1.88/2.09 0 [] -subset($c2,singleton($c1))|$c2!=empty_set.
% 1.88/2.09 0 [] -subset($c2,singleton($c1))|$c2!=singleton($c1).
% 1.88/2.09 0 [] empty($c3).
% 1.88/2.09 0 [] -empty($c4).
% 1.88/2.09 0 [] subset(A,A).
% 1.88/2.09 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.88/2.09 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.88/2.09 0 [] subset(set_intersection2(A,B),A).
% 1.88/2.09 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.88/2.09 0 [] set_union2(A,empty_set)=A.
% 1.88/2.09 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.88/2.09 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.88/2.09 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.88/2.09 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.88/2.09 0 [] in($f8(A,B),A)|in($f8(A,B),B)|A=B.
% 1.88/2.09 0 [] -in($f8(A,B),A)| -in($f8(A,B),B)|A=B.
% 1.88/2.09 0 [] subset(empty_set,A).
% 1.88/2.09 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.88/2.09 0 [] subset(set_difference(A,B),A).
% 1.88/2.09 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.88/2.09 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.88/2.09 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.88/2.09 0 [] set_difference(A,empty_set)=A.
% 1.88/2.09 0 [] disjoint(A,B)|in($f9(A,B),A).
% 1.88/2.09 0 [] disjoint(A,B)|in($f9(A,B),B).
% 1.88/2.09 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.88/2.09 0 [] -subset(A,empty_set)|A=empty_set.
% 1.88/2.09 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.88/2.09 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 1.88/2.09 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 1.88/2.09 0 [] set_difference(empty_set,A)=empty_set.
% 1.88/2.09 0 [] disjoint(A,B)|in($f10(A,B),set_intersection2(A,B)).
% 1.88/2.09 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.88/2.09 0 [] -subset(A,B)| -proper_subset(B,A).
% 1.88/2.09 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.88/2.09 0 [] unordered_pair(A,A)=singleton(A).
% 1.88/2.09 0 [] -empty(A)|A=empty_set.
% 1.88/2.09 0 [] -in(A,B)| -empty(B).
% 1.88/2.09 0 [] subset(A,set_union2(A,B)).
% 1.88/2.09 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.88/2.09 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.88/2.09 0 [] -empty(A)|A=B| -empty(B).
% 1.88/2.09 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.88/2.09 end_of_list.
% 1.88/2.09
% 1.88/2.09 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.88/2.09
% 1.88/2.09 This ia a non-Horn set with equality. The strategy will be
% 1.88/2.09 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.88/2.09 deletion, with positive clauses in sos and nonpositive
% 1.88/2.09 clauses in usable.
% 1.88/2.09
% 1.88/2.09 dependent: set(knuth_bendix).
% 1.88/2.09 dependent: set(anl_eq).
% 1.88/2.09 dependent: set(para_from).
% 1.88/2.09 dependent: set(para_into).
% 1.88/2.09 dependent: clear(para_from_right).
% 1.88/2.09 dependent: clear(para_into_right).
% 1.88/2.09 dependent: set(para_from_vars).
% 1.88/2.09 dependent: set(eq_units_both_ways).
% 1.88/2.09 dependent: set(dynamic_demod_all).
% 1.88/2.09 dependent: set(dynamic_demod).
% 1.88/2.09 dependent: set(order_eq).
% 1.88/2.09 dependent: set(back_demod).
% 1.88/2.09 dependent: set(lrpo).
% 1.88/2.09 dependent: set(hyper_res).
% 1.88/2.09 dependent: set(unit_deletion).
% 1.88/2.09 dependent: set(factor).
% 1.88/2.09
% 1.88/2.09 ------------> process usable:
% 1.88/2.09 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.88/2.09 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.88/2.09 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 1.88/2.09 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 1.88/2.09 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 1.88/2.09 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.88/2.09 ** KEPT (pick-wt=10): 7 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.88/2.09 ** KEPT (pick-wt=14): 8 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.88/2.09 ** KEPT (pick-wt=6): 9 [] A!=empty_set| -in(B,A).
% 1.88/2.09 ** KEPT (pick-wt=14): 10 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.88/2.09 ** KEPT (pick-wt=11): 11 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.88/2.09 ** KEPT (pick-wt=11): 12 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.88/2.09 ** KEPT (pick-wt=17): 13 [] A=unordered_pair(B,C)| -in($f3(B,C,A),A)|$f3(B,C,A)!=B.
% 1.88/2.09 ** KEPT (pick-wt=17): 14 [] A=unordered_pair(B,C)| -in($f3(B,C,A),A)|$f3(B,C,A)!=C.
% 1.88/2.09 ** KEPT (pick-wt=14): 15 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.88/2.09 ** KEPT (pick-wt=11): 16 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.88/2.09 ** KEPT (pick-wt=11): 17 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.88/2.09 ** KEPT (pick-wt=17): 18 [] A=set_union2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B).
% 1.88/2.09 ** KEPT (pick-wt=17): 19 [] A=set_union2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),C).
% 1.88/2.09 ** KEPT (pick-wt=9): 20 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.88/2.09 ** KEPT (pick-wt=8): 21 [] subset(A,B)| -in($f5(A,B),B).
% 1.88/2.09 ** KEPT (pick-wt=11): 22 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.88/2.09 ** KEPT (pick-wt=11): 23 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.88/2.09 ** KEPT (pick-wt=14): 24 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.88/2.09 ** KEPT (pick-wt=23): 25 [] A=set_intersection2(B,C)| -in($f6(B,C,A),A)| -in($f6(B,C,A),B)| -in($f6(B,C,A),C).
% 1.88/2.09 ** KEPT (pick-wt=11): 26 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.88/2.09 ** KEPT (pick-wt=11): 27 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.88/2.09 ** KEPT (pick-wt=14): 28 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.88/2.09 ** KEPT (pick-wt=17): 29 [] A=set_difference(B,C)|in($f7(B,C,A),A)| -in($f7(B,C,A),C).
% 1.88/2.09 ** KEPT (pick-wt=23): 30 [] A=set_difference(B,C)| -in($f7(B,C,A),A)| -in($f7(B,C,A),B)|in($f7(B,C,A),C).
% 1.88/2.09 ** KEPT (pick-wt=8): 31 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.88/2.09 ** KEPT (pick-wt=8): 32 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.88/2.09 ** KEPT (pick-wt=6): 33 [] -proper_subset(A,B)|subset(A,B).
% 1.88/2.09 ** KEPT (pick-wt=6): 34 [] -proper_subset(A,B)|A!=B.
% 1.88/2.09 ** KEPT (pick-wt=9): 35 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.88/2.09 ** KEPT (pick-wt=6): 36 [] empty(A)| -empty(set_union2(A,B)).
% 1.88/2.09 ** KEPT (pick-wt=6): 37 [] empty(A)| -empty(set_union2(B,A)).
% 1.88/2.09 ** KEPT (pick-wt=3): 38 [] -proper_subset(A,A).
% 1.88/2.09 ** KEPT (pick-wt=4): 39 [] singleton(A)!=empty_set.
% 1.88/2.09 ** KEPT (pick-wt=7): 40 [] -subset(singleton(A),B)|in(A,B).
% 1.88/2.09 ** KEPT (pick-wt=7): 41 [] subset(singleton(A),B)| -in(A,B).
% 1.88/2.09 ** KEPT (pick-wt=8): 42 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.88/2.09 ** KEPT (pick-wt=8): 43 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.88/2.09 ** KEPT (pick-wt=12): 44 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.88/2.09 ** KEPT (pick-wt=7): 46 [copy,45,flip.2] -subset($c2,singleton($c1))|empty_set!=$c2.
% 1.88/2.09 ** KEPT (pick-wt=8): 48 [copy,47,flip.2] -subset($c2,singleton($c1))|singleton($c1)!=$c2.
% 1.88/2.09 ** KEPT (pick-wt=2): 49 [] -empty($c4).
% 1.88/2.09 ** KEPT (pick-wt=6): 50 [] -disjoint(A,B)|disjoint(B,A).
% 1.88/2.09 ** KEPT (pick-wt=8): 51 [] -subset(A,B)|set_union2(A,B)=B.
% 1.88/2.09 ** KEPT (pick-wt=11): 52 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.88/2.09 ** KEPT (pick-wt=9): 53 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.88/2.09 ** KEPT (pick-wt=10): 54 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.88/2.09 ** KEPT (pick-wt=8): 55 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.88/2.09 ** KEPT (pick-wt=13): 56 [] -in($f8(A,B),A)| -in($f8(A,B),B)|A=B.
% 1.88/2.09 ** KEPT (pick-wt=10): 57 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.88/2.09 Following clause subsumed by 42 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.88/2.09 Following clause subsumed by 43 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.88/2.09 ** KEPT (pick-wt=9): 58 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.88/2.09 ** KEPT (pick-wt=6): 59 [] -subset(A,empty_set)|A=empty_set.
% 1.88/2.09 ** KEPT (pick-wt=10): 61 [copy,60,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 1.88/2.09 ** KEPT (pick-wt=8): 62 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.88/2.09 ** KEPT (pick-wt=6): 63 [] -subset(A,B)| -proper_subset(B,A).
% 1.88/2.09 ** KEPT (pick-wt=9): 64 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.88/2.09 ** KEPT (pick-wt=5): 65 [] -empty(A)|A=empty_set.
% 1.88/2.09 ** KEPT (pick-wt=5): 66 [] -in(A,B)| -empty(B).
% 1.88/2.09 ** KEPT (pick-wt=8): 67 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.88/2.09 ** KEPT (pick-wt=8): 68 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.88/2.09 ** KEPT (pick-wt=7): 69 [] -empty(A)|A=B| -empty(B).
% 1.88/2.09 ** KEPT (pick-wt=11): 70 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.88/2.09
% 1.88/2.09 ------------> process sos:
% 1.88/2.09 ** KEPT (pick-wt=3): 90 [] A=A.
% 1.88/2.09 ** KEPT (pick-wt=7): 91 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.88/2.09 ** KEPT (pick-wt=7): 92 [] set_union2(A,B)=set_union2(B,A).
% 1.88/2.09 ** KEPT (pick-wt=7): 93 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.88/2.09 ** KEPT (pick-wt=14): 94 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.88/2.09 ** KEPT (pick-wt=7): 95 [] A=empty_set|in($f2(A),A).
% 1.88/2.09 ** KEPT (pick-wt=23): 96 [] A=unordered_pair(B,C)|in($f3(B,C,A),A)|$f3(B,C,A)=B|$f3(B,C,A)=C.
% 1.88/2.09 ** KEPT (pick-wt=23): 97 [] A=set_union2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B)|in($f4(B,C,A),C).
% 1.88/2.09 ** KEPT (pick-wt=8): 98 [] subset(A,B)|in($f5(A,B),A).
% 1.88/2.09 ** KEPT (pick-wt=17): 99 [] A=set_intersection2(B,C)|in($f6(B,C,A),A)|in($f6(B,C,A),B).
% 1.88/2.09 ** KEPT (pick-wt=17): 100 [] A=set_intersection2(B,C)|in($f6(B,C,A),A)|in($f6(B,C,A),C).
% 1.88/2.09 ** KEPT (pick-wt=17): 101 [] A=set_difference(B,C)|in($f7(B,C,A),A)|in($f7(B,C,A),B).
% 1.88/2.09 ** KEPT (pick-wt=2): 102 [] empty(empty_set).
% 1.88/2.09 ** KEPT (pick-wt=5): 103 [] set_union2(A,A)=A.
% 1.88/2.09 ---> New Demodulator: 104 [new_demod,103] set_union2(A,A)=A.
% 1.88/2.09 ** KEPT (pick-wt=5): 105 [] set_intersection2(A,A)=A.
% 1.88/2.09 ---> New Demodulator: 106 [new_demod,105] set_intersection2(A,A)=A.
% 1.88/2.09 ** KEPT (pick-wt=11): 108 [copy,107,flip.2,flip.3] subset($c2,singleton($c1))|empty_set=$c2|singleton($c1)=$c2.
% 1.88/2.09 ** KEPT (pick-wt=2): 109 [] empty($c3).
% 1.88/2.09 ** KEPT (pick-wt=3): 110 [] subset(A,A).
% 1.88/2.09 ** KEPT (pick-wt=5): 111 [] subset(set_intersection2(A,B),A).
% 1.88/2.09 ** KEPT (pick-wt=5): 112 [] set_union2(A,empty_set)=A.
% 1.88/2.09 ---> New Demodulator: 113 [new_demod,112] set_union2(A,empty_set)=A.
% 1.88/2.09 ** KEPT (pick-wt=5): 114 [] set_intersection2(A,empty_set)=empty_set.
% 1.88/2.09 ---> New Demodulator: 115 [new_demod,114] set_intersection2(A,empty_set)=empty_set.
% 1.88/2.09 ** KEPT (pick-wt=13): 116 [] in($f8(A,B),A)|in($f8(A,B),B)|A=B.
% 1.88/2.09 ** KEPT (pick-wt=3): 117 [] subset(empty_set,A).
% 1.88/2.09 ** KEPT (pick-wt=5): 118 [] subset(set_difference(A,B),A).
% 1.88/2.09 ** KEPT (pick-wt=9): 119 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.88/2.09 ---> New Demodulator: 120 [new_demod,119] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.88/2.09 ** KEPT (pick-wt=5): 121 [] set_difference(A,empty_set)=A.
% 1.88/2.09 ---> New Demodulator: 122 [new_demod,121] set_difference(A,empty_set)=A.
% 1.88/2.09 ** KEPT (pick-wt=8): 123 [] disjoint(A,B)|in($f9(A,B),A).
% 14.93/15.13 ** KEPT (pick-wt=8): 124 [] disjoint(A,B)|in($f9(A,B),B).
% 14.93/15.13 ** KEPT (pick-wt=9): 125 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 14.93/15.13 ---> New Demodulator: 126 [new_demod,125] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 14.93/15.13 ** KEPT (pick-wt=9): 128 [copy,127,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 14.93/15.13 ---> New Demodulator: 129 [new_demod,128] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 14.93/15.13 ** KEPT (pick-wt=5): 130 [] set_difference(empty_set,A)=empty_set.
% 14.93/15.13 ---> New Demodulator: 131 [new_demod,130] set_difference(empty_set,A)=empty_set.
% 14.93/15.13 ** KEPT (pick-wt=12): 133 [copy,132,demod,129] disjoint(A,B)|in($f10(A,B),set_difference(A,set_difference(A,B))).
% 14.93/15.13 ** KEPT (pick-wt=6): 135 [copy,134,flip.1] singleton(A)=unordered_pair(A,A).
% 14.93/15.13 ---> New Demodulator: 136 [new_demod,135] singleton(A)=unordered_pair(A,A).
% 14.93/15.13 ** KEPT (pick-wt=5): 137 [] subset(A,set_union2(A,B)).
% 14.93/15.13 Following clause subsumed by 90 during input processing: 0 [copy,90,flip.1] A=A.
% 14.93/15.13 90 back subsumes 87.
% 14.93/15.13 90 back subsumes 85.
% 14.93/15.13 90 back subsumes 72.
% 14.93/15.13 Following clause subsumed by 91 during input processing: 0 [copy,91,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 14.93/15.13 Following clause subsumed by 92 during input processing: 0 [copy,92,flip.1] set_union2(A,B)=set_union2(B,A).
% 14.93/15.13 ** KEPT (pick-wt=11): 138 [copy,93,flip.1,demod,129,129] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 14.93/15.13 >>>> Starting back demodulation with 104.
% 14.93/15.13 >> back demodulating 88 with 104.
% 14.93/15.13 >> back demodulating 74 with 104.
% 14.93/15.13 >>>> Starting back demodulation with 106.
% 14.93/15.13 >> back demodulating 89 with 106.
% 14.93/15.13 >> back demodulating 84 with 106.
% 14.93/15.13 >> back demodulating 80 with 106.
% 14.93/15.13 >> back demodulating 77 with 106.
% 14.93/15.13 >>>> Starting back demodulation with 113.
% 14.93/15.13 >>>> Starting back demodulation with 115.
% 14.93/15.13 >>>> Starting back demodulation with 120.
% 14.93/15.13 >> back demodulating 61 with 120.
% 14.93/15.13 >>>> Starting back demodulation with 122.
% 14.93/15.13 >>>> Starting back demodulation with 126.
% 14.93/15.13 >>>> Starting back demodulation with 129.
% 14.93/15.13 >> back demodulating 114 with 129.
% 14.93/15.13 >> back demodulating 111 with 129.
% 14.93/15.13 >> back demodulating 105 with 129.
% 14.93/15.13 >> back demodulating 100 with 129.
% 14.93/15.13 >> back demodulating 99 with 129.
% 14.93/15.13 >> back demodulating 93 with 129.
% 14.93/15.13 >> back demodulating 79 with 129.
% 14.93/15.13 >> back demodulating 78 with 129.
% 14.93/15.13 >> back demodulating 62 with 129.
% 14.93/15.13 >> back demodulating 55 with 129.
% 14.93/15.13 >> back demodulating 54 with 129.
% 14.93/15.13 >> back demodulating 52 with 129.
% 14.93/15.13 >> back demodulating 32 with 129.
% 14.93/15.13 >> back demodulating 31 with 129.
% 14.93/15.13 >> back demodulating 25 with 129.
% 14.93/15.13 >> back demodulating 24 with 129.
% 14.93/15.13 >> back demodulating 23 with 129.
% 14.93/15.13 >> back demodulating 22 with 129.
% 14.93/15.13 >>>> Starting back demodulation with 131.
% 14.93/15.13 >>>> Starting back demodulation with 136.
% 14.93/15.13 >> back demodulating 108 with 136.
% 14.93/15.13 >> back demodulating 94 with 136.
% 14.93/15.13 >> back demodulating 48 with 136.
% 14.93/15.13 >> back demodulating 46 with 136.
% 14.93/15.13 >> back demodulating 44 with 136.
% 14.93/15.13 >> back demodulating 41 with 136.
% 14.93/15.13 >> back demodulating 40 with 136.
% 14.93/15.13 >> back demodulating 39 with 136.
% 14.93/15.13 >> back demodulating 8 with 136.
% 14.93/15.13 >> back demodulating 7 with 136.
% 14.93/15.13 >> back demodulating 6 with 136.
% 14.93/15.13 Following clause subsumed by 138 during input processing: 0 [copy,138,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 14.93/15.13 >>>> Starting back demodulation with 150.
% 14.93/15.13
% 14.93/15.13 ======= end of input processing =======
% 14.93/15.13
% 14.93/15.13 =========== start of search ===========
% 14.93/15.13
% 14.93/15.13
% 14.93/15.13 Resetting weight limit to 8.
% 14.93/15.13
% 14.93/15.13
% 14.93/15.13 Resetting weight limit to 8.
% 14.93/15.13
% 14.93/15.13 sos_size=1413
% 14.93/15.13
% 14.93/15.13 -- HEY sandbox, WE HAVE A PROOF!! --
% 14.93/15.13
% 14.93/15.13 -----> EMPTY CLAUSE at 13.04 sec ----> 2569 [back_demod,166,demod,2567,2567,unit_del,110,90] $F.
% 14.93/15.13
% 14.93/15.13 Length of proof is 46. Level of proof is 13.
% 14.93/15.13
% 14.93/15.13 ---------------- PROOF ----------------
% 14.93/15.13 % SZS status Theorem
% 14.93/15.13 % SZS output start Refutation
% See solution above
% 14.93/15.13 ------------ end of proof -------------
% 14.93/15.13
% 14.93/15.13
% 14.93/15.13 Search stopped by max_proofs option.
% 14.93/15.13
% 14.93/15.13
% 14.93/15.13 Search stopped by max_proofs option.
% 14.93/15.13
% 14.93/15.13 ============ end of search ============
% 14.93/15.13
% 14.93/15.13 -------------- statistics -------------
% 14.93/15.13 clauses given 923
% 14.93/15.13 clauses generated 636492
% 14.93/15.13 clauses kept 2526
% 14.93/15.13 clauses forward subsumed 76794
% 14.93/15.13 clauses back subsumed 308
% 14.93/15.13 Kbytes malloced 6835
% 14.93/15.13
% 14.93/15.13 ----------- times (seconds) -----------
% 14.93/15.13 user CPU time 13.04 (0 hr, 0 min, 13 sec)
% 14.93/15.13 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 14.93/15.13 wall-clock time 14 (0 hr, 0 min, 14 sec)
% 14.93/15.13
% 14.93/15.13 That finishes the proof of the theorem.
% 14.93/15.13
% 14.93/15.13 Process 4860 finished Wed Jul 27 07:42:18 2022
% 14.93/15.13 Otter interrupted
% 14.93/15.13 PROOF FOUND
%------------------------------------------------------------------------------