%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU153+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:14:57 EDT 2022
% Result : Theorem 1.94s 2.19s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 6 RR)
% Number of literals : 14 ( 5 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != C ),
file('SEU153+2.p',unknown),
[] ).
cnf(61,axiom,
( ~ in(A,B)
| ~ in(A,C)
| ~ disjoint(B,C) ),
file('SEU153+2.p',unknown),
[] ).
cnf(97,axiom,
A = A,
file('SEU153+2.p',unknown),
[] ).
cnf(115,axiom,
disjoint(singleton(dollar_c2),dollar_c1),
file('SEU153+2.p',unknown),
[] ).
cnf(116,axiom,
in(dollar_c2,dollar_c1),
file('SEU153+2.p',unknown),
[] ).
cnf(145,axiom,
unordered_pair(A,A) = singleton(A),
file('SEU153+2.p',unknown),
[] ).
cnf(147,plain,
singleton(A) = unordered_pair(A,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[145])]),
[iquote('copy,145,flip.1')] ).
cnf(177,plain,
disjoint(unordered_pair(dollar_c2,dollar_c2),dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[115]),147]),
[iquote('back_demod,115,demod,147')] ).
cnf(190,plain,
in(A,unordered_pair(B,A)),
inference(hyper,[status(thm)],[97,15,97]),
[iquote('hyper,97,15,97')] ).
cnf(843,plain,
$false,
inference(hyper,[status(thm)],[190,61,116,177]),
[iquote('hyper,190,61,116,177')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU153+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n029.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 07:55:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.94/2.14 ----- Otter 3.3f, August 2004 -----
% 1.94/2.14 The process was started by sandbox2 on n029.cluster.edu,
% 1.94/2.14 Wed Jul 27 07:55:44 2022
% 1.94/2.14 The command was "./otter". The process ID is 19696.
% 1.94/2.14
% 1.94/2.14 set(prolog_style_variables).
% 1.94/2.14 set(auto).
% 1.94/2.14 dependent: set(auto1).
% 1.94/2.14 dependent: set(process_input).
% 1.94/2.14 dependent: clear(print_kept).
% 1.94/2.14 dependent: clear(print_new_demod).
% 1.94/2.14 dependent: clear(print_back_demod).
% 1.94/2.14 dependent: clear(print_back_sub).
% 1.94/2.14 dependent: set(control_memory).
% 1.94/2.14 dependent: assign(max_mem, 12000).
% 1.94/2.14 dependent: assign(pick_given_ratio, 4).
% 1.94/2.14 dependent: assign(stats_level, 1).
% 1.94/2.14 dependent: assign(max_seconds, 10800).
% 1.94/2.14 clear(print_given).
% 1.94/2.14
% 1.94/2.14 formula_list(usable).
% 1.94/2.14 all A (A=A).
% 1.94/2.14 all A B (in(A,B)-> -in(B,A)).
% 1.94/2.14 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 1.94/2.14 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.94/2.14 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.94/2.14 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.94/2.14 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.94/2.14 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.94/2.14 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.94/2.14 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 1.94/2.14 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.94/2.14 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.94/2.14 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.94/2.14 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.94/2.14 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.94/2.14 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.94/2.14 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 1.94/2.14 $T.
% 1.94/2.14 $T.
% 1.94/2.14 $T.
% 1.94/2.14 $T.
% 1.94/2.14 $T.
% 1.94/2.14 $T.
% 1.94/2.14 $T.
% 1.94/2.14 empty(empty_set).
% 1.94/2.14 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.94/2.14 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.94/2.14 all A B (set_union2(A,A)=A).
% 1.94/2.14 all A B (set_intersection2(A,A)=A).
% 1.94/2.14 all A B (-proper_subset(A,A)).
% 1.94/2.14 all A (singleton(A)!=empty_set).
% 1.94/2.14 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 1.94/2.14 -(all A B (-(disjoint(singleton(A),B)&in(A,B)))).
% 1.94/2.14 all A B (subset(singleton(A),B)<->in(A,B)).
% 1.94/2.14 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.94/2.14 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 1.94/2.14 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 1.94/2.14 exists A empty(A).
% 1.94/2.14 exists A (-empty(A)).
% 1.94/2.14 all A B subset(A,A).
% 1.94/2.14 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.94/2.14 all A B C D (-(unordered_pair(A,B)=unordered_pair(C,D)&A!=C&A!=D)).
% 1.94/2.14 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.94/2.14 all A B subset(set_intersection2(A,B),A).
% 1.94/2.14 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 1.94/2.14 all A (set_union2(A,empty_set)=A).
% 1.94/2.14 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.94/2.14 powerset(empty_set)=singleton(empty_set).
% 1.94/2.14 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 1.94/2.14 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.94/2.14 all A (set_intersection2(A,empty_set)=empty_set).
% 1.94/2.14 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.94/2.14 all A subset(empty_set,A).
% 1.94/2.14 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 1.94/2.14 all A B subset(set_difference(A,B),A).
% 1.94/2.14 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.94/2.14 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 1.94/2.14 all A (set_difference(A,empty_set)=A).
% 1.94/2.14 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))).
% 1.94/2.14 all A (subset(A,empty_set)->A=empty_set).
% 1.94/2.14 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 1.94/2.14 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 1.94/2.14 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 1.94/2.14 all A (set_difference(empty_set,A)=empty_set).
% 1.94/2.14 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))).
% 1.94/2.14 all A B (-(subset(A,B)&proper_subset(B,A))).
% 1.94/2.14 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 1.94/2.14 all A (unordered_pair(A,A)=singleton(A)).
% 1.94/2.14 all A (empty(A)->A=empty_set).
% 1.94/2.14 all A B (subset(singleton(A),singleton(B))->A=B).
% 1.94/2.14 all A B (-(in(A,B)&empty(B))).
% 1.94/2.14 all A B subset(A,set_union2(A,B)).
% 1.94/2.14 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 1.94/2.14 all A B (-(empty(A)&A!=B&empty(B))).
% 1.94/2.14 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.94/2.14 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 1.94/2.15 all A B C (singleton(A)=unordered_pair(B,C)->B=C).
% 1.94/2.15 end_of_list.
% 1.94/2.15
% 1.94/2.15 -------> usable clausifies to:
% 1.94/2.15
% 1.94/2.15 list(usable).
% 1.94/2.15 0 [] A=A.
% 1.94/2.15 0 [] -in(A,B)| -in(B,A).
% 1.94/2.15 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.94/2.15 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.94/2.15 0 [] set_union2(A,B)=set_union2(B,A).
% 1.94/2.15 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.94/2.15 0 [] A!=B|subset(A,B).
% 1.94/2.15 0 [] A!=B|subset(B,A).
% 1.94/2.15 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.94/2.15 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.94/2.15 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.94/2.15 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.94/2.15 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.94/2.15 0 [] A!=empty_set| -in(B,A).
% 1.94/2.15 0 [] A=empty_set|in($f2(A),A).
% 1.94/2.15 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 1.94/2.15 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 1.94/2.15 0 [] B=powerset(A)|in($f3(A,B),B)|subset($f3(A,B),A).
% 1.94/2.15 0 [] B=powerset(A)| -in($f3(A,B),B)| -subset($f3(A,B),A).
% 1.94/2.15 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.94/2.15 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.94/2.15 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.94/2.15 0 [] C=unordered_pair(A,B)|in($f4(A,B,C),C)|$f4(A,B,C)=A|$f4(A,B,C)=B.
% 1.94/2.15 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=A.
% 1.94/2.15 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=B.
% 1.94/2.15 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.94/2.15 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.94/2.15 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.94/2.15 0 [] C=set_union2(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 1.94/2.15 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A).
% 1.94/2.15 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 1.94/2.15 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.94/2.15 0 [] subset(A,B)|in($f6(A,B),A).
% 1.94/2.15 0 [] subset(A,B)| -in($f6(A,B),B).
% 1.94/2.15 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.94/2.15 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.94/2.15 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.94/2.15 0 [] C=set_intersection2(A,B)|in($f7(A,B,C),C)|in($f7(A,B,C),A).
% 1.94/2.15 0 [] C=set_intersection2(A,B)|in($f7(A,B,C),C)|in($f7(A,B,C),B).
% 1.94/2.15 0 [] C=set_intersection2(A,B)| -in($f7(A,B,C),C)| -in($f7(A,B,C),A)| -in($f7(A,B,C),B).
% 1.94/2.15 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.94/2.15 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.94/2.15 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.94/2.15 0 [] C=set_difference(A,B)|in($f8(A,B,C),C)|in($f8(A,B,C),A).
% 1.94/2.15 0 [] C=set_difference(A,B)|in($f8(A,B,C),C)| -in($f8(A,B,C),B).
% 1.94/2.15 0 [] C=set_difference(A,B)| -in($f8(A,B,C),C)| -in($f8(A,B,C),A)|in($f8(A,B,C),B).
% 1.94/2.15 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.94/2.15 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.94/2.15 0 [] -proper_subset(A,B)|subset(A,B).
% 1.94/2.15 0 [] -proper_subset(A,B)|A!=B.
% 1.94/2.15 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.94/2.15 0 [] $T.
% 1.94/2.15 0 [] $T.
% 1.94/2.15 0 [] $T.
% 1.94/2.15 0 [] $T.
% 1.94/2.15 0 [] $T.
% 1.94/2.15 0 [] $T.
% 1.94/2.15 0 [] $T.
% 1.94/2.15 0 [] empty(empty_set).
% 1.94/2.15 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.94/2.15 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.94/2.15 0 [] set_union2(A,A)=A.
% 1.94/2.15 0 [] set_intersection2(A,A)=A.
% 1.94/2.15 0 [] -proper_subset(A,A).
% 1.94/2.15 0 [] singleton(A)!=empty_set.
% 1.94/2.15 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 1.94/2.15 0 [] disjoint(singleton($c2),$c1).
% 1.94/2.15 0 [] in($c2,$c1).
% 1.94/2.15 0 [] -subset(singleton(A),B)|in(A,B).
% 1.94/2.15 0 [] subset(singleton(A),B)| -in(A,B).
% 1.94/2.15 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.94/2.15 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.94/2.15 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.94/2.15 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.94/2.15 0 [] subset(A,singleton(B))|A!=empty_set.
% 1.94/2.15 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.94/2.15 0 [] empty($c3).
% 1.94/2.15 0 [] -empty($c4).
% 1.94/2.15 0 [] subset(A,A).
% 1.94/2.15 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.94/2.15 0 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 1.94/2.15 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.94/2.15 0 [] subset(set_intersection2(A,B),A).
% 1.94/2.15 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.94/2.15 0 [] set_union2(A,empty_set)=A.
% 1.94/2.15 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.94/2.15 0 [] powerset(empty_set)=singleton(empty_set).
% 1.94/2.15 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.94/2.15 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.94/2.15 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.94/2.15 0 [] in($f9(A,B),A)|in($f9(A,B),B)|A=B.
% 1.94/2.15 0 [] -in($f9(A,B),A)| -in($f9(A,B),B)|A=B.
% 1.94/2.15 0 [] subset(empty_set,A).
% 1.94/2.15 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.94/2.15 0 [] subset(set_difference(A,B),A).
% 1.94/2.15 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.94/2.15 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.94/2.15 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.94/2.15 0 [] set_difference(A,empty_set)=A.
% 1.94/2.15 0 [] disjoint(A,B)|in($f10(A,B),A).
% 1.94/2.15 0 [] disjoint(A,B)|in($f10(A,B),B).
% 1.94/2.15 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.94/2.15 0 [] -subset(A,empty_set)|A=empty_set.
% 1.94/2.15 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.94/2.15 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 1.94/2.15 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 1.94/2.15 0 [] set_difference(empty_set,A)=empty_set.
% 1.94/2.15 0 [] disjoint(A,B)|in($f11(A,B),set_intersection2(A,B)).
% 1.94/2.15 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.94/2.15 0 [] -subset(A,B)| -proper_subset(B,A).
% 1.94/2.15 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.94/2.15 0 [] unordered_pair(A,A)=singleton(A).
% 1.94/2.15 0 [] -empty(A)|A=empty_set.
% 1.94/2.15 0 [] -subset(singleton(A),singleton(B))|A=B.
% 1.94/2.15 0 [] -in(A,B)| -empty(B).
% 1.94/2.15 0 [] subset(A,set_union2(A,B)).
% 1.94/2.15 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.94/2.15 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.94/2.15 0 [] -empty(A)|A=B| -empty(B).
% 1.94/2.15 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.94/2.15 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 1.94/2.15 0 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 1.94/2.15 end_of_list.
% 1.94/2.15
% 1.94/2.15 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.94/2.15
% 1.94/2.15 This ia a non-Horn set with equality. The strategy will be
% 1.94/2.15 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.94/2.15 deletion, with positive clauses in sos and nonpositive
% 1.94/2.15 clauses in usable.
% 1.94/2.15
% 1.94/2.15 dependent: set(knuth_bendix).
% 1.94/2.15 dependent: set(anl_eq).
% 1.94/2.15 dependent: set(para_from).
% 1.94/2.15 dependent: set(para_into).
% 1.94/2.15 dependent: clear(para_from_right).
% 1.94/2.15 dependent: clear(para_into_right).
% 1.94/2.15 dependent: set(para_from_vars).
% 1.94/2.15 dependent: set(eq_units_both_ways).
% 1.94/2.15 dependent: set(dynamic_demod_all).
% 1.94/2.15 dependent: set(dynamic_demod).
% 1.94/2.15 dependent: set(order_eq).
% 1.94/2.15 dependent: set(back_demod).
% 1.94/2.15 dependent: set(lrpo).
% 1.94/2.15 dependent: set(hyper_res).
% 1.94/2.15 dependent: set(unit_deletion).
% 1.94/2.15 dependent: set(factor).
% 1.94/2.15
% 1.94/2.15 ------------> process usable:
% 1.94/2.15 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.94/2.15 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.94/2.15 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 1.94/2.15 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 1.94/2.15 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 1.94/2.15 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.94/2.15 ** KEPT (pick-wt=10): 7 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.94/2.15 ** KEPT (pick-wt=14): 8 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.94/2.15 ** KEPT (pick-wt=6): 9 [] A!=empty_set| -in(B,A).
% 1.94/2.15 ** KEPT (pick-wt=10): 10 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 1.94/2.15 ** KEPT (pick-wt=10): 11 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 1.94/2.15 ** KEPT (pick-wt=14): 12 [] A=powerset(B)| -in($f3(B,A),A)| -subset($f3(B,A),B).
% 1.94/2.15 ** KEPT (pick-wt=14): 13 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.94/2.15 ** KEPT (pick-wt=11): 14 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.94/2.15 ** KEPT (pick-wt=11): 15 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.94/2.15 ** KEPT (pick-wt=17): 16 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=B.
% 1.94/2.15 ** KEPT (pick-wt=17): 17 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=C.
% 1.94/2.15 ** KEPT (pick-wt=14): 18 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.94/2.15 ** KEPT (pick-wt=11): 19 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.94/2.15 ** KEPT (pick-wt=11): 20 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.94/2.15 ** KEPT (pick-wt=17): 21 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B).
% 1.94/2.15 ** KEPT (pick-wt=17): 22 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 1.94/2.15 ** KEPT (pick-wt=9): 23 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.94/2.15 ** KEPT (pick-wt=8): 24 [] subset(A,B)| -in($f6(A,B),B).
% 1.94/2.15 ** KEPT (pick-wt=11): 25 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.94/2.15 ** KEPT (pick-wt=11): 26 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.94/2.15 ** KEPT (pick-wt=14): 27 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.94/2.15 ** KEPT (pick-wt=23): 28 [] A=set_intersection2(B,C)| -in($f7(B,C,A),A)| -in($f7(B,C,A),B)| -in($f7(B,C,A),C).
% 1.94/2.15 ** KEPT (pick-wt=11): 29 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.94/2.15 ** KEPT (pick-wt=11): 30 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.94/2.15 ** KEPT (pick-wt=14): 31 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.94/2.15 ** KEPT (pick-wt=17): 32 [] A=set_difference(B,C)|in($f8(B,C,A),A)| -in($f8(B,C,A),C).
% 1.94/2.15 ** KEPT (pick-wt=23): 33 [] A=set_difference(B,C)| -in($f8(B,C,A),A)| -in($f8(B,C,A),B)|in($f8(B,C,A),C).
% 1.94/2.15 ** KEPT (pick-wt=8): 34 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.94/2.15 ** KEPT (pick-wt=8): 35 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.94/2.15 ** KEPT (pick-wt=6): 36 [] -proper_subset(A,B)|subset(A,B).
% 1.94/2.15 ** KEPT (pick-wt=6): 37 [] -proper_subset(A,B)|A!=B.
% 1.94/2.15 ** KEPT (pick-wt=9): 38 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.94/2.15 ** KEPT (pick-wt=6): 39 [] empty(A)| -empty(set_union2(A,B)).
% 1.94/2.15 ** KEPT (pick-wt=6): 40 [] empty(A)| -empty(set_union2(B,A)).
% 1.94/2.15 ** KEPT (pick-wt=3): 41 [] -proper_subset(A,A).
% 1.94/2.15 ** KEPT (pick-wt=4): 42 [] singleton(A)!=empty_set.
% 1.94/2.15 ** KEPT (pick-wt=9): 43 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 1.94/2.15 ** KEPT (pick-wt=7): 44 [] -subset(singleton(A),B)|in(A,B).
% 1.94/2.15 ** KEPT (pick-wt=7): 45 [] subset(singleton(A),B)| -in(A,B).
% 1.94/2.15 ** KEPT (pick-wt=8): 46 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.94/2.15 ** KEPT (pick-wt=8): 47 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.94/2.15 ** KEPT (pick-wt=12): 48 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.94/2.15 ** KEPT (pick-wt=11): 49 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.94/2.15 ** KEPT (pick-wt=7): 50 [] subset(A,singleton(B))|A!=empty_set.
% 1.94/2.15 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.94/2.15 ** KEPT (pick-wt=2): 51 [] -empty($c4).
% 1.94/2.15 ** KEPT (pick-wt=6): 52 [] -disjoint(A,B)|disjoint(B,A).
% 1.94/2.15 ** KEPT (pick-wt=13): 53 [] unordered_pair(A,B)!=unordered_pair(C,D)|A=C|A=D.
% 1.94/2.15 ** KEPT (pick-wt=8): 54 [] -subset(A,B)|set_union2(A,B)=B.
% 1.94/2.15 ** KEPT (pick-wt=11): 55 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.94/2.15 ** KEPT (pick-wt=9): 56 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.94/2.15 ** KEPT (pick-wt=10): 57 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.94/2.15 ** KEPT (pick-wt=8): 58 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.94/2.15 ** KEPT (pick-wt=13): 59 [] -in($f9(A,B),A)| -in($f9(A,B),B)|A=B.
% 1.94/2.15 ** KEPT (pick-wt=10): 60 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.94/2.15 Following clause subsumed by 46 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.94/2.15 Following clause subsumed by 47 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.94/2.15 ** KEPT (pick-wt=9): 61 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.94/2.15 ** KEPT (pick-wt=6): 62 [] -subset(A,empty_set)|A=empty_set.
% 1.94/2.15 ** KEPT (pick-wt=10): 64 [copy,63,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 1.94/2.15 ** KEPT (pick-wt=8): 65 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.94/2.15 ** KEPT (pick-wt=6): 66 [] -subset(A,B)| -proper_subset(B,A).
% 1.94/2.15 ** KEPT (pick-wt=9): 67 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.94/2.15 ** KEPT (pick-wt=5): 68 [] -empty(A)|A=empty_set.
% 1.94/2.15 ** KEPT (pick-wt=8): 69 [] -subset(singleton(A),singleton(B))|A=B.
% 1.94/2.15 ** KEPT (pick-wt=5): 70 [] -in(A,B)| -empty(B).
% 1.94/2.15 ** KEPT (pick-wt=8): 71 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.94/2.15 ** KEPT (pick-wt=8): 72 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.94/2.15 ** KEPT (pick-wt=7): 73 [] -empty(A)|A=B| -empty(B).
% 1.94/2.15 ** KEPT (pick-wt=11): 74 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.94/2.15 ** KEPT (pick-wt=9): 75 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 1.94/2.15 ** KEPT (pick-wt=9): 76 [] singleton(A)!=unordered_pair(B,C)|B=C.
% 1.94/2.15
% 1.94/2.15 ------------> process sos:
% 1.94/2.15 ** KEPT (pick-wt=3): 97 [] A=A.
% 1.94/2.15 ** KEPT (pick-wt=7): 98 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.94/2.15 ** KEPT (pick-wt=7): 99 [] set_union2(A,B)=set_union2(B,A).
% 1.94/2.15 ** KEPT (pick-wt=7): 100 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.94/2.15 ** KEPT (pick-wt=14): 101 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.94/2.15 ** KEPT (pick-wt=7): 102 [] A=empty_set|in($f2(A),A).
% 1.94/2.15 ** KEPT (pick-wt=14): 103 [] A=powerset(B)|in($f3(B,A),A)|subset($f3(B,A),B).
% 1.94/2.15 ** KEPT (pick-wt=23): 104 [] A=unordered_pair(B,C)|in($f4(B,C,A),A)|$f4(B,C,A)=B|$f4(B,C,A)=C.
% 1.94/2.15 ** KEPT (pick-wt=23): 105 [] A=set_union2(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 1.94/2.15 ** KEPT (pick-wt=8): 106 [] subset(A,B)|in($f6(A,B),A).
% 1.94/2.15 ** KEPT (pick-wt=17): 107 [] A=set_intersection2(B,C)|in($f7(B,C,A),A)|in($f7(B,C,A),B).
% 1.94/2.15 ** KEPT (pick-wt=17): 108 [] A=set_intersection2(B,C)|in($f7(B,C,A),A)|in($f7(B,C,A),C).
% 1.94/2.15 ** KEPT (pick-wt=17): 109 [] A=set_difference(B,C)|in($f8(B,C,A),A)|in($f8(B,C,A),B).
% 1.94/2.15 ** KEPT (pick-wt=2): 110 [] empty(empty_set).
% 1.94/2.15 ** KEPT (pick-wt=5): 111 [] set_union2(A,A)=A.
% 1.94/2.15 ---> New Demodulator: 112 [new_demod,111] set_union2(A,A)=A.
% 1.94/2.15 ** KEPT (pick-wt=5): 113 [] set_intersection2(A,A)=A.
% 1.94/2.15 ---> New Demodulator: 114 [new_demod,113] set_intersection2(A,A)=A.
% 1.94/2.15 ** KEPT (pick-wt=4): 115 [] disjoint(singleton($c2),$c1).
% 1.94/2.15 ** KEPT (pick-wt=3): 116 [] in($c2,$c1).
% 1.94/2.15 ** KEPT (pick-wt=2): 117 [] empty($c3).
% 1.94/2.15 ** KEPT (pick-wt=3): 118 [] subset(A,A).
% 1.94/2.15 ** KEPT (pick-wt=5): 119 [] subset(set_intersection2(A,B),A).
% 1.94/2.15 ** KEPT (pick-wt=5): 120 [] set_union2(A,empty_set)=A.
% 1.94/2.15 ---> New Demodulator: 121 [new_demod,120] set_union2(A,empty_set)=A.
% 1.94/2.15 ** KEPT (pick-wt=5): 123 [copy,122,flip.1] singleton(empty_set)=powerset(empty_set).
% 1.94/2.15 ---> New Demodulator: 124 [new_demod,123] singleton(empty_set)=powerset(empty_set).
% 1.94/2.15 ** KEPT (pick-wt=5): 125 [] set_intersection2(A,empty_set)=empty_set.
% 1.94/2.15 ---> New Demodulator: 126 [new_demod,125] set_intersection2(A,empty_set)=empty_set.
% 1.94/2.15 ** KEPT (pick-wt=13): 127 [] in($f9(A,B),A)|in($f9(A,B),B)|A=B.
% 1.94/2.15 ** KEPT (pick-wt=3): 128 [] subset(empty_set,A).
% 1.94/2.15 ** KEPT (pick-wt=5): 129 [] subset(set_difference(A,B),A).
% 1.94/2.15 ** KEPT (pick-wt=9): 130 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.94/2.15 ---> New Demodulator: 131 [new_demod,130] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.94/2.15 ** KEPT (pick-wt=5): 132 [] set_difference(A,empty_set)=A.
% 1.94/2.15 ---> New Demodulator: 133 [new_demod,132] set_difference(A,empty_set)=A.
% 1.94/2.15 ** KEPT (pick-wt=8): 134 [] disjoint(A,B)|in($f10(A,B),A).
% 1.94/2.15 ** KEPT (pick-wt=8): 135 [] disjoint(A,B)|in($f10(A,B),B).
% 1.94/2.15 ** KEPT (pick-wt=9): 136 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.94/2.15 ---> New Demodulator: 137 [new_demod,136] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.94/2.15 ** KEPT (pick-wt=9): 139 [copy,138,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.94/2.15 ---> New Demodulator: 140 [new_demod,139] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.94/2.15 ** KEPT (pick-wt=5): 141 [] set_difference(empty_set,A)=empty_set.
% 1.94/2.15 ---> New Demodulator: 142 [new_demod,141] set_difference(empty_set,A)=empty_set.
% 1.94/2.15 ** KEPT (pick-wt=12): 144 [copy,143,demod,140] disjoint(A,B)|in($f11(A,B),set_difference(A,set_difference(A,B))).
% 1.94/2.15 ** KEPT (pick-wt=6): 146 [copy,145,flip.1] singleton(A)=unordered_pair(A,A).
% 1.94/2.15 ---> New Demodulator: 147 [new_demod,146] singleton(A)=unordered_pair(A,A).
% 1.94/2.15 ** KEPT (pick-wt=5): 148 [] subset(A,set_union2(A,B)).
% 1.94/2.15 Following clause subsumed by 97 during input processing: 0 [copy,97,flip.1] A=A.
% 1.94/2.15 97 back subsumes 94.
% 1.94/2.15 97 back subsumes 92.
% 1.94/2.15 97 back subsumes 78.
% 1.94/2.15 Following clause subsumed by 98 during input processing: 0 [copy,98,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.94/2.15 Following clause subsumed by 99 during input processing: 0 [copy,99,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.94/2.15 ** KEPT (pick-wt=11): 149 [copy,100,flip.1,demod,140,140] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 1.94/2.15 >>>> Starting back demodulation with 112.
% 1.94/2.15 >> back demodulating 95 with 112.
% 1.94/2.15 >> back demodulating 80 with 112.
% 1.94/2.15 >>>> Starting back demodulation with 114.
% 1.94/2.15 >> back demodulating 96 with 114.
% 1.94/2.15 >> back demodulating 91 with 114.
% 1.94/2.15 >> back demodulating 86 with 114.
% 1.94/2.15 >> back demodulating 83 with 114.
% 1.94/2.15 >>>> Starting back demodulation with 121.
% 1.94/2.15 >>>> Starting back demodulation with 124.
% 1.94/2.15 >>>> Starting back demodulation with 126.
% 1.94/2.15 >>>> Starting back demodulation with 131.
% 1.94/2.15 >> back demodulating 64 with 131.
% 1.94/2.15 >>>> Starting back demodulation with 133.
% 1.94/2.15 >>>> Starting back demodulation with 137.
% 1.94/2.15 >>>> Starting back demodulation with 140.
% 1.94/2.15 >> back demodulating 125 with 140.
% 1.94/2.15 >> back demodulating 119 with 140.
% 1.94/2.15 >> back demodulating 113 with 140.
% 1.94/2.15 >> back demodulating 108 with 140.
% 1.94/2.15 >> back demodulating 107 with 140.
% 1.94/2.15 >> back demodulating 100 with 140.
% 1.94/2.19 >> back demodulating 85 with 140.
% 1.94/2.19 >> back demodulating 84 with 140.
% 1.94/2.19 >> back demodulating 65 with 140.
% 1.94/2.19 >> back demodulating 58 with 140.
% 1.94/2.19 >> back demodulating 57 with 140.
% 1.94/2.19 >> back demodulating 55 with 140.
% 1.94/2.19 >> back demodulating 35 with 140.
% 1.94/2.19 >> back demodulating 34 with 140.
% 1.94/2.19 >> back demodulating 28 with 140.
% 1.94/2.19 >> back demodulating 27 with 140.
% 1.94/2.19 >> back demodulating 26 with 140.
% 1.94/2.19 >> back demodulating 25 with 140.
% 1.94/2.19 >>>> Starting back demodulation with 142.
% 1.94/2.19 >>>> Starting back demodulation with 147.
% 1.94/2.19 >> back demodulating 123 with 147.
% 1.94/2.19 >> back demodulating 115 with 147.
% 1.94/2.19 >> back demodulating 101 with 147.
% 1.94/2.19 >> back demodulating 76 with 147.
% 1.94/2.19 >> back demodulating 75 with 147.
% 1.94/2.19 >> back demodulating 69 with 147.
% 1.94/2.19 >> back demodulating 50 with 147.
% 1.94/2.19 >> back demodulating 49 with 147.
% 1.94/2.19 >> back demodulating 48 with 147.
% 1.94/2.19 >> back demodulating 45 with 147.
% 1.94/2.19 >> back demodulating 44 with 147.
% 1.94/2.19 >> back demodulating 43 with 147.
% 1.94/2.19 >> back demodulating 42 with 147.
% 1.94/2.19 >> back demodulating 8 with 147.
% 1.94/2.19 >> back demodulating 7 with 147.
% 1.94/2.19 >> back demodulating 6 with 147.
% 1.94/2.19 Following clause subsumed by 149 during input processing: 0 [copy,149,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 1.94/2.19 >>>> Starting back demodulation with 161.
% 1.94/2.19 >>>> Starting back demodulation with 176.
% 1.94/2.19
% 1.94/2.19 ======= end of input processing =======
% 1.94/2.19
% 1.94/2.19 =========== start of search ===========
% 1.94/2.19
% 1.94/2.19 -------- PROOF --------
% 1.94/2.19
% 1.94/2.19 -----> EMPTY CLAUSE at 0.05 sec ----> 843 [hyper,190,61,116,177] $F.
% 1.94/2.19
% 1.94/2.19 Length of proof is 3. Level of proof is 2.
% 1.94/2.19
% 1.94/2.19 ---------------- PROOF ----------------
% 1.94/2.19 % SZS status Theorem
% 1.94/2.19 % SZS output start Refutation
% See solution above
% 1.94/2.19 ------------ end of proof -------------
% 1.94/2.19
% 1.94/2.19
% 1.94/2.19 Search stopped by max_proofs option.
% 1.94/2.19
% 1.94/2.19
% 1.94/2.19 Search stopped by max_proofs option.
% 1.94/2.19
% 1.94/2.19 ============ end of search ============
% 1.94/2.19
% 1.94/2.19 -------------- statistics -------------
% 1.94/2.19 clauses given 20
% 1.94/2.19 clauses generated 957
% 1.94/2.19 clauses kept 814
% 1.94/2.19 clauses forward subsumed 333
% 1.94/2.19 clauses back subsumed 21
% 1.94/2.19 Kbytes malloced 3906
% 1.94/2.19
% 1.94/2.19 ----------- times (seconds) -----------
% 1.94/2.19 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.94/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.94/2.19
% 1.94/2.19 That finishes the proof of the theorem.
% 1.94/2.19
% 1.94/2.19 Process 19696 finished Wed Jul 27 07:55:46 2022
% 1.94/2.19 Otter interrupted
% 1.94/2.19 PROOF FOUND
%------------------------------------------------------------------------------