TSTP Solution File: SEU141+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:14:53 EDT 2022
% Result : Theorem 2.95s 3.13s
% Output : Refutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 30 ( 19 unt; 5 nHn; 14 RR)
% Number of literals : 43 ( 18 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(19,axiom,
( A != set_difference(B,C)
| ~ in(D,A)
| ~ in(D,C) ),
file('SEU141+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ subset(A,B)
| set_union2(A,B) = B ),
file('SEU141+2.p',unknown),
[] ).
cnf(46,axiom,
( ~ in(A,set_intersection2(B,C))
| ~ disjoint(B,C) ),
file('SEU141+2.p',unknown),
[] ).
cnf(51,axiom,
( ~ disjoint(dollar_c4,dollar_c3)
| set_difference(dollar_c4,dollar_c3) != dollar_c4 ),
file('SEU141+2.p',unknown),
[] ).
cnf(52,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU141+2.p',unknown),
[] ).
cnf(72,axiom,
A = A,
file('SEU141+2.p',unknown),
[] ).
cnf(75,axiom,
( A = empty_set
| in(dollar_f1(A),A) ),
file('SEU141+2.p',unknown),
[] ).
cnf(81,axiom,
empty(empty_set),
file('SEU141+2.p',unknown),
[] ).
cnf(86,axiom,
empty(dollar_c1),
file('SEU141+2.p',unknown),
[] ).
cnf(89,axiom,
set_union2(A,empty_set) = A,
file('SEU141+2.p',unknown),
[] ).
cnf(94,axiom,
subset(empty_set,A),
file('SEU141+2.p',unknown),
[] ).
cnf(95,axiom,
subset(set_difference(A,B),A),
file('SEU141+2.p',unknown),
[] ).
cnf(96,axiom,
set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('SEU141+2.p',unknown),
[] ).
cnf(100,axiom,
( disjoint(A,B)
| in(dollar_f7(A,B),A) ),
file('SEU141+2.p',unknown),
[] ).
cnf(101,axiom,
( disjoint(A,B)
| in(dollar_f7(A,B),B) ),
file('SEU141+2.p',unknown),
[] ).
cnf(104,axiom,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('SEU141+2.p',unknown),
[] ).
cnf(106,plain,
set_intersection2(A,B) = set_difference(A,set_difference(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[104])]),
[iquote('copy,104,flip.1')] ).
cnf(112,axiom,
( disjoint(dollar_c4,dollar_c3)
| set_difference(dollar_c4,dollar_c3) = dollar_c4 ),
file('SEU141+2.p',unknown),
[] ).
cnf(129,plain,
( ~ in(A,set_difference(B,set_difference(B,C)))
| ~ disjoint(B,C) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[46]),106]),
[iquote('back_demod,46,demod,106')] ).
cnf(148,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[86,52,81]),
[iquote('hyper,86,52,81')] ).
cnf(166,plain,
subset(dollar_c1,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[94]),148]),
[iquote('back_demod,94,demod,148')] ).
cnf(168,plain,
set_union2(A,dollar_c1) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[89]),148]),
[iquote('back_demod,89,demod,148')] ).
cnf(169,plain,
( A = dollar_c1
| in(dollar_f1(A),A) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[75]),148]),
[iquote('back_demod,75,demod,148')] ).
cnf(199,plain,
set_union2(dollar_c1,A) = A,
inference(hyper,[status(thm)],[166,35]),
[iquote('hyper,166,35')] ).
cnf(224,plain,
set_union2(set_difference(A,B),A) = A,
inference(hyper,[status(thm)],[95,35]),
[iquote('hyper,95,35')] ).
cnf(1695,plain,
disjoint(set_difference(A,B),B),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[101,19,199,100]),199,199])]),
[iquote('hyper,101,19,198,100,demod,199,199,factor_simp')] ).
cnf(1936,plain,
disjoint(dollar_c4,dollar_c3),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[112,1695])]),
[iquote('para_from,112.2.1,1695.1.1,factor_simp')] ).
cnf(2109,plain,
set_difference(dollar_c4,set_difference(dollar_c4,dollar_c3)) = dollar_c1,
inference(hyper,[status(thm)],[129,169,1936]),
[iquote('hyper,129,169,1936')] ).
cnf(2288,plain,
set_difference(dollar_c4,dollar_c3) = dollar_c4,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2109,96]),168,224]),
[iquote('para_from,2109.1.1,96.1.1.2,demod,168,224')] ).
cnf(2293,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[51]),2288]),1936,72]),
[iquote('back_demod,51,demod,2288,unit_del,1936,72')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 07:55:48 EDT 2022
% 0.11/0.33 % CPUTime :
% 2.07/2.27 ----- Otter 3.3f, August 2004 -----
% 2.07/2.27 The process was started by sandbox2 on n023.cluster.edu,
% 2.07/2.27 Wed Jul 27 07:55:48 2022
% 2.07/2.27 The command was "./otter". The process ID is 18496.
% 2.07/2.27
% 2.07/2.27 set(prolog_style_variables).
% 2.07/2.27 set(auto).
% 2.07/2.27 dependent: set(auto1).
% 2.07/2.27 dependent: set(process_input).
% 2.07/2.27 dependent: clear(print_kept).
% 2.07/2.27 dependent: clear(print_new_demod).
% 2.07/2.27 dependent: clear(print_back_demod).
% 2.07/2.27 dependent: clear(print_back_sub).
% 2.07/2.27 dependent: set(control_memory).
% 2.07/2.27 dependent: assign(max_mem, 12000).
% 2.07/2.27 dependent: assign(pick_given_ratio, 4).
% 2.07/2.27 dependent: assign(stats_level, 1).
% 2.07/2.27 dependent: assign(max_seconds, 10800).
% 2.07/2.27 clear(print_given).
% 2.07/2.27
% 2.07/2.27 formula_list(usable).
% 2.07/2.27 all A (A=A).
% 2.07/2.27 all A B (in(A,B)-> -in(B,A)).
% 2.07/2.27 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 2.07/2.27 all A B (set_union2(A,B)=set_union2(B,A)).
% 2.07/2.27 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.07/2.27 all A B (A=B<->subset(A,B)&subset(B,A)).
% 2.07/2.27 all A (A=empty_set<-> (all B (-in(B,A)))).
% 2.07/2.27 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 2.07/2.27 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.07/2.27 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 2.07/2.27 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 2.07/2.27 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 2.07/2.27 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 2.07/2.27 $T.
% 2.07/2.27 $T.
% 2.07/2.27 $T.
% 2.07/2.27 $T.
% 2.07/2.27 empty(empty_set).
% 2.07/2.27 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 2.07/2.27 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 2.07/2.27 all A B (set_union2(A,A)=A).
% 2.07/2.27 all A B (set_intersection2(A,A)=A).
% 2.07/2.27 all A B (-proper_subset(A,A)).
% 2.07/2.27 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.07/2.27 exists A empty(A).
% 2.07/2.27 exists A (-empty(A)).
% 2.07/2.27 all A B subset(A,A).
% 2.07/2.27 all A B (disjoint(A,B)->disjoint(B,A)).
% 2.07/2.27 all A B (subset(A,B)->set_union2(A,B)=B).
% 2.07/2.27 all A B subset(set_intersection2(A,B),A).
% 2.07/2.27 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 2.07/2.27 all A (set_union2(A,empty_set)=A).
% 2.07/2.27 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 2.07/2.27 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 2.07/2.27 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 2.07/2.27 all A (set_intersection2(A,empty_set)=empty_set).
% 2.07/2.27 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.07/2.27 all A subset(empty_set,A).
% 2.07/2.27 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 2.07/2.27 all A B subset(set_difference(A,B),A).
% 2.07/2.27 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.07/2.27 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 2.07/2.27 all A (set_difference(A,empty_set)=A).
% 2.07/2.27 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))).
% 2.07/2.27 all A (subset(A,empty_set)->A=empty_set).
% 2.07/2.27 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 2.07/2.27 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 2.07/2.27 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 2.07/2.27 all A (set_difference(empty_set,A)=empty_set).
% 2.07/2.27 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))).
% 2.07/2.27 all A B (-(subset(A,B)&proper_subset(B,A))).
% 2.07/2.27 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 2.07/2.27 all A (empty(A)->A=empty_set).
% 2.07/2.27 all A B (-(in(A,B)&empty(B))).
% 2.07/2.27 all A B subset(A,set_union2(A,B)).
% 2.07/2.27 -(all A B (disjoint(A,B)<->set_difference(A,B)=A)).
% 2.07/2.27 all A B (-(empty(A)&A!=B&empty(B))).
% 2.07/2.27 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 2.07/2.27 end_of_list.
% 2.07/2.27
% 2.07/2.27 -------> usable clausifies to:
% 2.07/2.27
% 2.07/2.27 list(usable).
% 2.07/2.27 0 [] A=A.
% 2.07/2.27 0 [] -in(A,B)| -in(B,A).
% 2.07/2.27 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.07/2.27 0 [] set_union2(A,B)=set_union2(B,A).
% 2.07/2.27 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.07/2.27 0 [] A!=B|subset(A,B).
% 2.07/2.27 0 [] A!=B|subset(B,A).
% 2.07/2.27 0 [] A=B| -subset(A,B)| -subset(B,A).
% 2.07/2.27 0 [] A!=empty_set| -in(B,A).
% 2.07/2.27 0 [] A=empty_set|in($f1(A),A).
% 2.07/2.27 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 2.07/2.27 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 2.07/2.27 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 2.07/2.27 0 [] C=set_union2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 2.07/2.27 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A).
% 2.07/2.27 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 2.07/2.27 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.07/2.27 0 [] subset(A,B)|in($f3(A,B),A).
% 2.07/2.27 0 [] subset(A,B)| -in($f3(A,B),B).
% 2.07/2.27 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 2.07/2.27 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 2.07/2.27 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 2.07/2.27 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A).
% 2.07/2.27 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),B).
% 2.07/2.27 0 [] C=set_intersection2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A)| -in($f4(A,B,C),B).
% 2.07/2.27 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 2.07/2.27 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 2.07/2.27 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 2.07/2.27 0 [] C=set_difference(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A).
% 2.07/2.27 0 [] C=set_difference(A,B)|in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 2.07/2.27 0 [] C=set_difference(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 2.07/2.27 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.07/2.27 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.07/2.27 0 [] -proper_subset(A,B)|subset(A,B).
% 2.07/2.27 0 [] -proper_subset(A,B)|A!=B.
% 2.07/2.27 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.07/2.27 0 [] $T.
% 2.07/2.27 0 [] $T.
% 2.07/2.27 0 [] $T.
% 2.07/2.27 0 [] $T.
% 2.07/2.27 0 [] empty(empty_set).
% 2.07/2.27 0 [] empty(A)| -empty(set_union2(A,B)).
% 2.07/2.27 0 [] empty(A)| -empty(set_union2(B,A)).
% 2.07/2.27 0 [] set_union2(A,A)=A.
% 2.07/2.27 0 [] set_intersection2(A,A)=A.
% 2.07/2.27 0 [] -proper_subset(A,A).
% 2.07/2.27 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.07/2.27 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.07/2.27 0 [] empty($c1).
% 2.07/2.27 0 [] -empty($c2).
% 2.07/2.27 0 [] subset(A,A).
% 2.07/2.27 0 [] -disjoint(A,B)|disjoint(B,A).
% 2.07/2.27 0 [] -subset(A,B)|set_union2(A,B)=B.
% 2.07/2.27 0 [] subset(set_intersection2(A,B),A).
% 2.07/2.27 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.07/2.27 0 [] set_union2(A,empty_set)=A.
% 2.07/2.27 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.07/2.27 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.07/2.27 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.07/2.27 0 [] set_intersection2(A,empty_set)=empty_set.
% 2.07/2.27 0 [] in($f6(A,B),A)|in($f6(A,B),B)|A=B.
% 2.07/2.27 0 [] -in($f6(A,B),A)| -in($f6(A,B),B)|A=B.
% 2.07/2.27 0 [] subset(empty_set,A).
% 2.07/2.27 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.07/2.27 0 [] subset(set_difference(A,B),A).
% 2.07/2.27 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.07/2.27 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.07/2.27 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.07/2.27 0 [] set_difference(A,empty_set)=A.
% 2.07/2.27 0 [] disjoint(A,B)|in($f7(A,B),A).
% 2.07/2.27 0 [] disjoint(A,B)|in($f7(A,B),B).
% 2.07/2.27 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 2.07/2.27 0 [] -subset(A,empty_set)|A=empty_set.
% 2.07/2.27 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.07/2.27 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 2.07/2.27 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 2.07/2.27 0 [] set_difference(empty_set,A)=empty_set.
% 2.07/2.27 0 [] disjoint(A,B)|in($f8(A,B),set_intersection2(A,B)).
% 2.07/2.27 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 2.07/2.27 0 [] -subset(A,B)| -proper_subset(B,A).
% 2.07/2.27 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 2.07/2.27 0 [] -empty(A)|A=empty_set.
% 2.07/2.27 0 [] -in(A,B)| -empty(B).
% 2.07/2.27 0 [] subset(A,set_union2(A,B)).
% 2.07/2.27 0 [] disjoint($c4,$c3)|set_difference($c4,$c3)=$c4.
% 2.07/2.27 0 [] -disjoint($c4,$c3)|set_difference($c4,$c3)!=$c4.
% 2.07/2.27 0 [] -empty(A)|A=B| -empty(B).
% 2.07/2.27 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.07/2.27 end_of_list.
% 2.07/2.27
% 2.07/2.27 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.07/2.27
% 2.07/2.27 This ia a non-Horn set with equality. The strategy will be
% 2.07/2.27 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.07/2.27 deletion, with positive clauses in sos and nonpositive
% 2.07/2.27 clauses in usable.
% 2.07/2.27
% 2.07/2.27 dependent: set(knuth_bendix).
% 2.07/2.27 dependent: set(anl_eq).
% 2.07/2.27 dependent: set(para_from).
% 2.07/2.27 dependent: set(para_into).
% 2.07/2.27 dependent: clear(para_from_right).
% 2.07/2.27 dependent: clear(para_into_right).
% 2.07/2.27 dependent: set(para_from_vars).
% 2.07/2.27 dependent: set(eq_units_both_ways).
% 2.07/2.27 dependent: set(dynamic_demod_all).
% 2.07/2.27 dependent: set(dynamic_demod).
% 2.07/2.27 dependent: set(order_eq).
% 2.07/2.27 dependent: set(back_demod).
% 2.07/2.27 dependent: set(lrpo).
% 2.07/2.27 dependent: set(hyper_res).
% 2.07/2.27 dependent: set(unit_deletion).
% 2.07/2.27 dependent: set(factor).
% 2.07/2.27
% 2.07/2.27 ------------> process usable:
% 2.07/2.27 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.07/2.27 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.07/2.27 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 2.07/2.27 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 2.07/2.27 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 2.07/2.27 ** KEPT (pick-wt=6): 6 [] A!=empty_set| -in(B,A).
% 2.07/2.27 ** KEPT (pick-wt=14): 7 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 2.07/2.27 ** KEPT (pick-wt=11): 8 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 2.07/2.27 ** KEPT (pick-wt=11): 9 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 2.07/2.27 ** KEPT (pick-wt=17): 10 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B).
% 2.07/2.27 ** KEPT (pick-wt=17): 11 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 2.07/2.27 ** KEPT (pick-wt=9): 12 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.07/2.27 ** KEPT (pick-wt=8): 13 [] subset(A,B)| -in($f3(A,B),B).
% 2.07/2.27 ** KEPT (pick-wt=11): 14 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 2.07/2.27 ** KEPT (pick-wt=11): 15 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 2.07/2.27 ** KEPT (pick-wt=14): 16 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 2.07/2.27 ** KEPT (pick-wt=23): 17 [] A=set_intersection2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B)| -in($f4(B,C,A),C).
% 2.07/2.27 ** KEPT (pick-wt=11): 18 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 2.07/2.27 ** KEPT (pick-wt=11): 19 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 2.07/2.27 ** KEPT (pick-wt=14): 20 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 2.07/2.27 ** KEPT (pick-wt=17): 21 [] A=set_difference(B,C)|in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 2.07/2.27 ** KEPT (pick-wt=23): 22 [] A=set_difference(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 2.07/2.27 ** KEPT (pick-wt=8): 23 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.07/2.27 ** KEPT (pick-wt=8): 24 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.07/2.27 ** KEPT (pick-wt=6): 25 [] -proper_subset(A,B)|subset(A,B).
% 2.07/2.27 ** KEPT (pick-wt=6): 26 [] -proper_subset(A,B)|A!=B.
% 2.07/2.27 ** KEPT (pick-wt=9): 27 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.07/2.27 ** KEPT (pick-wt=6): 28 [] empty(A)| -empty(set_union2(A,B)).
% 2.07/2.27 ** KEPT (pick-wt=6): 29 [] empty(A)| -empty(set_union2(B,A)).
% 2.07/2.27 ** KEPT (pick-wt=3): 30 [] -proper_subset(A,A).
% 2.07/2.27 ** KEPT (pick-wt=8): 31 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.07/2.27 ** KEPT (pick-wt=8): 32 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.07/2.27 ** KEPT (pick-wt=2): 33 [] -empty($c2).
% 2.07/2.27 ** KEPT (pick-wt=6): 34 [] -disjoint(A,B)|disjoint(B,A).
% 2.07/2.27 ** KEPT (pick-wt=8): 35 [] -subset(A,B)|set_union2(A,B)=B.
% 2.07/2.27 ** KEPT (pick-wt=11): 36 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.07/2.27 ** KEPT (pick-wt=9): 37 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.07/2.27 ** KEPT (pick-wt=10): 38 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.07/2.27 ** KEPT (pick-wt=8): 39 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.07/2.27 ** KEPT (pick-wt=13): 40 [] -in($f6(A,B),A)| -in($f6(A,B),B)|A=B.
% 2.07/2.27 ** KEPT (pick-wt=10): 41 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.07/2.27 Following clause subsumed by 31 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.07/2.27 Following clause subsumed by 32 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.07/2.27 ** KEPT (pick-wt=9): 42 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 2.07/2.27 ** KEPT (pick-wt=6): 43 [] -subset(A,empty_set)|A=empty_set.
% 2.07/2.27 ** KEPT (pick-wt=10): 45 [copy,44,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 2.07/2.27 ** KEPT (pick-wt=8): 46 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 2.07/2.27 ** KEPT (pick-wt=6): 47 [] -subset(A,B)| -proper_subset(B,A).
% 2.07/2.27 ** KEPT (pick-wt=9): 48 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 2.07/2.27 ** KEPT (pick-wt=5): 49 [] -empty(A)|A=empty_set.
% 2.07/2.27 ** KEPT (pick-wt=5): 50 [] -in(A,B)| -empty(B).
% 2.07/2.27 ** KEPT (pick-wt=8): 51 [] -disjoint($c4,$c3)|set_difference($c4,$c3)!=$c4.
% 2.07/2.27 ** KEPT (pick-wt=7): 52 [] -empty(A)|A=B| -empty(B).
% 2.07/2.27 ** KEPT (pick-wt=11): 53 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.07/2.27
% 2.07/2.27 ------------> process sos:
% 2.07/2.27 ** KEPT (pick-wt=3): 72 [] A=A.
% 2.07/2.27 ** KEPT (pick-wt=7): 73 [] set_union2(A,B)=set_union2(B,A).
% 2.07/2.27 ** KEPT (pick-wt=7): 74 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.07/2.27 ** KEPT (pick-wt=7): 75 [] A=empty_set|in($f1(A),A).
% 2.07/2.27 ** KEPT (pick-wt=23): 76 [] A=set_union2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 2.07/2.27 ** KEPT (pick-wt=8): 77 [] subset(A,B)|in($f3(A,B),A).
% 2.07/2.27 ** KEPT (pick-wt=17): 78 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B).
% 2.07/2.27 ** KEPT (pick-wt=17): 79 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),C).
% 2.07/2.27 ** KEPT (pick-wt=17): 80 [] A=set_difference(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B).
% 2.07/2.27 ** KEPT (pick-wt=2): 81 [] empty(empty_set).
% 2.07/2.27 ** KEPT (pick-wt=5): 82 [] set_union2(A,A)=A.
% 2.07/2.27 ---> New Demodulator: 83 [new_demod,82] set_union2(A,A)=A.
% 2.07/2.27 ** KEPT (pick-wt=5): 84 [] set_intersection2(A,A)=A.
% 2.07/2.27 ---> New Demodulator: 85 [new_demod,84] set_intersection2(A,A)=A.
% 2.07/2.27 ** KEPT (pick-wt=2): 86 [] empty($c1).
% 2.07/2.27 ** KEPT (pick-wt=3): 87 [] subset(A,A).
% 2.07/2.27 ** KEPT (pick-wt=5): 88 [] subset(set_intersection2(A,B),A).
% 2.07/2.27 ** KEPT (pick-wt=5): 89 [] set_union2(A,empty_set)=A.
% 2.07/2.27 ---> New Demodulator: 90 [new_demod,89] set_union2(A,empty_set)=A.
% 2.07/2.27 ** KEPT (pick-wt=5): 91 [] set_intersection2(A,empty_set)=empty_set.
% 2.07/2.27 ---> New Demodulator: 92 [new_demod,91] set_intersection2(A,empty_set)=empty_set.
% 2.07/2.27 ** KEPT (pick-wt=13): 93 [] in($f6(A,B),A)|in($f6(A,B),B)|A=B.
% 2.07/2.27 ** KEPT (pick-wt=3): 94 [] subset(empty_set,A).
% 2.07/2.27 ** KEPT (pick-wt=5): 95 [] subset(set_difference(A,B),A).
% 2.07/2.27 ** KEPT (pick-wt=9): 96 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.07/2.27 ---> New Demodulator: 97 [new_demod,96] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.07/2.27 ** KEPT (pick-wt=5): 98 [] set_difference(A,empty_set)=A.
% 2.07/2.27 ---> New Demodulator: 99 [new_demod,98] set_difference(A,empty_set)=A.
% 2.07/2.27 ** KEPT (pick-wt=8): 100 [] disjoint(A,B)|in($f7(A,B),A).
% 2.07/2.27 ** KEPT (pick-wt=8): 101 [] disjoint(A,B)|in($f7(A,B),B).
% 2.07/2.27 ** KEPT (pick-wt=9): 102 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.07/2.27 ---> New Demodulator: 103 [new_demod,102] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.07/2.27 ** KEPT (pick-wt=9): 105 [copy,104,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 2.07/2.27 ---> New Demodulator: 106 [new_demod,105] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 2.07/2.27 ** KEPT (pick-wt=5): 107 [] set_difference(empty_set,A)=empty_set.
% 2.07/2.27 ---> New Demodulator: 108 [new_demod,107] set_difference(empty_set,A)=empty_set.
% 2.07/2.27 ** KEPT (pick-wt=12): 110 [copy,109,demod,106] disjoint(A,B)|in($f8(A,B),set_difference(A,set_difference(A,B))).
% 2.07/2.27 ** KEPT (pick-wt=5): 111 [] subset(A,set_union2(A,B)).
% 2.07/2.27 ** KEPT (pick-wt=8): 112 [] disjoint($c4,$c3)|set_difference($c4,$c3)=$c4.
% 2.07/2.27 Following clause subsumed by 72 during input processing: 0 [copy,72,flip.1] A=A.
% 2.07/2.27 72 back subsumes 69.
% 2.07/2.27 72 back subsumes 67.
% 2.07/2.27 72 back subsumes 55.
% 2.07/2.27 Following clause subsumed by 73 during input processing: 0 [copy,73,flip.1] set_union2(A,B)=set_union2(B,A).
% 2.07/2.27 ** KEPT (pick-wt=11): 113 [copy,74,flip.1,demod,106,106] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 2.07/2.27 >>>> Starting back demodulation with 83.
% 2.07/2.27 >> back demodulating 70 with 83.
% 2.07/2.27 >> back demodulating 56 with 83.
% 2.07/2.27 >>>> Starting back demodulation with 85.
% 2.07/2.27 >> back demodulating 71 with 85.
% 2.07/2.27 >> back demodulating 66 with 85.
% 2.07/2.27 >> back demodulating 62 with 85.
% 2.07/2.27 >> back demodulating 59 with 85.
% 2.07/2.27 >>>> Starting back demodulation with 90.
% 2.07/2.27 >>>> Starting back demodulation with 92.
% 2.07/2.27 >>>> Starting back demodulation with 97.
% 2.07/2.27 >> back demodulating 45 with 97.
% 2.07/2.27 >>>> Starting back demodulation with 99.
% 2.07/2.27 >>>> Starting back demodulation with 103.
% 2.07/2.27 >>>> Starting back demodulation with 106.
% 2.07/2.27 >> back demodulating 91 with 106.
% 2.07/2.27 >> back demodulating 88 with 106.
% 2.07/2.27 >> back demodulating 84 with 106.
% 2.07/2.27 >> back demodulating 79 with 106.
% 2.07/2.27 >> back demodulating 78 with 106.
% 2.07/2.27 >> back demodulating 74 with 106.
% 2.07/2.27 >> back demodulating 61 with 106.
% 2.07/2.27 >> back demodulating 60 with 106.
% 2.07/2.27 >> back demodulating 46 with 106.
% 2.07/2.27 >> back demodulating 39 with 106.
% 2.07/2.27 >> back demodulating 38 with 106.
% 2.07/2.27 >> back demodulating 36 with 106.
% 2.07/2.27 >> back demodulating 24 with 106.
% 2.07/2.27 >> back demodulating 23 with 106.
% 2.07/2.27 >> back demodulating 17 with 106.
% 2.07/2.27 >> back demodulating 16 with 106.
% 2.07/2.27 >> back demodulating 15 with 106.
% 2.07/2.27 >> back demodulating 14 with 106.
% 2.07/2.27 >>>> Starting back demodulation with 108.
% 2.07/2.27 Following clause subsumed by 113 during input processing: 0 [copy,113,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 2.07/2.27 >>>> Starting back demodulation with 124.
% 2.07/2.27
% 2.07/2.27 ======= end of input processing =======
% 2.95/3.13
% 2.95/3.13 =========== start of search ===========
% 2.95/3.13
% 2.95/3.13
% 2.95/3.13 Resetting weight limit to 8.
% 2.95/3.13
% 2.95/3.13
% 2.95/3.13 Resetting weight limit to 8.
% 2.95/3.13
% 2.95/3.13 sos_size=1582
% 2.95/3.13
% 2.95/3.13
% 2.95/3.13 Resetting weight limit to 7.
% 2.95/3.13
% 2.95/3.13
% 2.95/3.13 Resetting weight limit to 7.
% 2.95/3.13
% 2.95/3.13 sos_size=1545
% 2.95/3.13
% 2.95/3.13 -------- PROOF --------
% 2.95/3.13
% 2.95/3.13 -----> EMPTY CLAUSE at 0.86 sec ----> 2293 [back_demod,51,demod,2288,unit_del,1936,72] $F.
% 2.95/3.13
% 2.95/3.13 Length of proof is 12. Level of proof is 7.
% 2.95/3.13
% 2.95/3.13 ---------------- PROOF ----------------
% 2.95/3.13 % SZS status Theorem
% 2.95/3.13 % SZS output start Refutation
% See solution above
% 2.95/3.13 ------------ end of proof -------------
% 2.95/3.13
% 2.95/3.13
% 2.95/3.13 Search stopped by max_proofs option.
% 2.95/3.13
% 2.95/3.13
% 2.95/3.13 Search stopped by max_proofs option.
% 2.95/3.13
% 2.95/3.13 ============ end of search ============
% 2.95/3.13
% 2.95/3.13 -------------- statistics -------------
% 2.95/3.13 clauses given 265
% 2.95/3.13 clauses generated 35214
% 2.95/3.13 clauses kept 2259
% 2.95/3.13 clauses forward subsumed 7048
% 2.95/3.13 clauses back subsumed 368
% 2.95/3.13 Kbytes malloced 4882
% 2.95/3.13
% 2.95/3.13 ----------- times (seconds) -----------
% 2.95/3.13 user CPU time 0.86 (0 hr, 0 min, 0 sec)
% 2.95/3.13 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.95/3.13 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.95/3.13
% 2.95/3.13 That finishes the proof of the theorem.
% 2.95/3.13
% 2.95/3.13 Process 18496 finished Wed Jul 27 07:55:51 2022
% 2.95/3.13 Otter interrupted
% 2.95/3.13 PROOF FOUND
%------------------------------------------------------------------------------