%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU143+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 1.98s 2.15s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 15 unt; 3 nHn; 14 RR)
% Number of literals : 30 ( 11 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(11,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SEU143+2.p',unknown),
[] ).
cnf(35,axiom,
( proper_subset(A,B)
| ~ subset(A,B)
| A = B ),
file('SEU143+2.p',unknown),
[] ).
cnf(38,axiom,
~ proper_subset(A,A),
file('SEU143+2.p',unknown),
[] ).
cnf(58,axiom,
( ~ in(A,B)
| ~ empty(B) ),
file('SEU143+2.p',unknown),
[] ).
cnf(61,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU143+2.p',unknown),
[] ).
cnf(82,axiom,
A = A,
file('SEU143+2.p',unknown),
[] ).
cnf(94,axiom,
empty(empty_set),
file('SEU143+2.p',unknown),
[] ).
cnf(99,axiom,
singleton(dollar_c1) = empty_set,
file('SEU143+2.p',unknown),
[] ).
cnf(101,axiom,
empty(dollar_c2),
file('SEU143+2.p',unknown),
[] ).
cnf(109,axiom,
subset(empty_set,A),
file('SEU143+2.p',unknown),
[] ).
cnf(126,axiom,
unordered_pair(A,A) = singleton(A),
file('SEU143+2.p',unknown),
[] ).
cnf(128,plain,
singleton(A) = unordered_pair(A,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[126])]),
[iquote('copy,126,flip.1')] ).
cnf(156,plain,
unordered_pair(dollar_c1,dollar_c1) = empty_set,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[99]),128]),
[iquote('back_demod,99,demod,128')] ).
cnf(161,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[82,11,82]),
[iquote('hyper,82,11,82')] ).
cnf(164,plain,
( empty(A)
| proper_subset(empty_set,A) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[94,35]),109]),
[iquote('para_into,94.1.1,35.3.1,unit_del,109')] ).
cnf(177,plain,
empty_set = dollar_c2,
inference(hyper,[status(thm)],[101,61,94]),
[iquote('hyper,101,61,94')] ).
cnf(189,plain,
( empty(A)
| proper_subset(dollar_c2,A) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[164]),177]),
[iquote('back_demod,164,demod,177')] ).
cnf(192,plain,
unordered_pair(dollar_c1,dollar_c1) = dollar_c2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[156]),177]),
[iquote('back_demod,156,demod,177')] ).
cnf(681,plain,
in(dollar_c1,dollar_c2),
inference(para_from,[status(thm),theory(equality)],[192,161]),
[iquote('para_from,192.1.1,161.1.2')] ).
cnf(682,plain,
proper_subset(dollar_c2,dollar_c2),
inference(hyper,[status(thm)],[681,58,189]),
[iquote('hyper,681,58,189')] ).
cnf(683,plain,
$false,
inference(binary,[status(thm)],[682,38]),
[iquote('binary,682.1,38.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU143+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:49:16 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.91/2.09 ----- Otter 3.3f, August 2004 -----
% 1.91/2.09 The process was started by sandbox2 on n007.cluster.edu,
% 1.91/2.09 Wed Jul 27 07:49:16 2022
% 1.91/2.09 The command was "./otter". The process ID is 13669.
% 1.91/2.09
% 1.91/2.09 set(prolog_style_variables).
% 1.91/2.09 set(auto).
% 1.91/2.09 dependent: set(auto1).
% 1.91/2.09 dependent: set(process_input).
% 1.91/2.09 dependent: clear(print_kept).
% 1.91/2.09 dependent: clear(print_new_demod).
% 1.91/2.09 dependent: clear(print_back_demod).
% 1.91/2.09 dependent: clear(print_back_sub).
% 1.91/2.09 dependent: set(control_memory).
% 1.91/2.09 dependent: assign(max_mem, 12000).
% 1.91/2.09 dependent: assign(pick_given_ratio, 4).
% 1.91/2.09 dependent: assign(stats_level, 1).
% 1.91/2.09 dependent: assign(max_seconds, 10800).
% 1.91/2.09 clear(print_given).
% 1.91/2.09
% 1.91/2.09 formula_list(usable).
% 1.91/2.09 all A (A=A).
% 1.91/2.09 all A B (in(A,B)-> -in(B,A)).
% 1.91/2.09 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 1.91/2.09 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.91/2.09 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.91/2.09 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.91/2.09 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.91/2.09 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.91/2.09 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.91/2.10 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.91/2.10 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.91/2.10 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.91/2.10 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.91/2.10 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.91/2.10 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.91/2.10 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 empty(empty_set).
% 1.91/2.10 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.91/2.10 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.91/2.10 all A B (set_union2(A,A)=A).
% 1.91/2.10 all A B (set_intersection2(A,A)=A).
% 1.91/2.10 all A B (-proper_subset(A,A)).
% 1.91/2.10 -(all A (singleton(A)!=empty_set)).
% 1.91/2.10 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.91/2.10 exists A empty(A).
% 1.91/2.10 exists A (-empty(A)).
% 1.91/2.10 all A B subset(A,A).
% 1.91/2.10 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.91/2.10 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.91/2.10 all A B subset(set_intersection2(A,B),A).
% 1.91/2.10 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 1.91/2.10 all A (set_union2(A,empty_set)=A).
% 1.91/2.10 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.91/2.10 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 1.91/2.10 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.91/2.10 all A (set_intersection2(A,empty_set)=empty_set).
% 1.91/2.10 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.91/2.10 all A subset(empty_set,A).
% 1.91/2.10 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 1.91/2.10 all A B subset(set_difference(A,B),A).
% 1.91/2.10 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.91/2.10 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 1.91/2.10 all A (set_difference(A,empty_set)=A).
% 1.91/2.10 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))).
% 1.91/2.10 all A (subset(A,empty_set)->A=empty_set).
% 1.91/2.10 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 1.91/2.10 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 1.91/2.10 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 1.91/2.10 all A (set_difference(empty_set,A)=empty_set).
% 1.91/2.10 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))).
% 1.91/2.10 all A B (-(subset(A,B)&proper_subset(B,A))).
% 1.91/2.10 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 1.91/2.10 all A (unordered_pair(A,A)=singleton(A)).
% 1.91/2.10 all A (empty(A)->A=empty_set).
% 1.91/2.10 all A B (-(in(A,B)&empty(B))).
% 1.91/2.10 all A B subset(A,set_union2(A,B)).
% 1.91/2.10 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 1.91/2.10 all A B (-(empty(A)&A!=B&empty(B))).
% 1.91/2.10 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 -------> usable clausifies to:
% 1.91/2.10
% 1.91/2.10 list(usable).
% 1.91/2.10 0 [] A=A.
% 1.91/2.10 0 [] -in(A,B)| -in(B,A).
% 1.91/2.10 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.91/2.10 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.91/2.10 0 [] set_union2(A,B)=set_union2(B,A).
% 1.91/2.10 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.91/2.10 0 [] A!=B|subset(A,B).
% 1.91/2.10 0 [] A!=B|subset(B,A).
% 1.91/2.10 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.91/2.10 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.91/2.10 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.91/2.10 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.91/2.10 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.91/2.10 0 [] A!=empty_set| -in(B,A).
% 1.91/2.10 0 [] A=empty_set|in($f2(A),A).
% 1.91/2.10 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.91/2.10 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.91/2.10 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.91/2.10 0 [] C=unordered_pair(A,B)|in($f3(A,B,C),C)|$f3(A,B,C)=A|$f3(A,B,C)=B.
% 1.91/2.10 0 [] C=unordered_pair(A,B)| -in($f3(A,B,C),C)|$f3(A,B,C)!=A.
% 1.91/2.10 0 [] C=unordered_pair(A,B)| -in($f3(A,B,C),C)|$f3(A,B,C)!=B.
% 1.91/2.10 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.91/2.10 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.91/2.10 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.91/2.10 0 [] C=set_union2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A)|in($f4(A,B,C),B).
% 1.91/2.10 0 [] C=set_union2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A).
% 1.91/2.10 0 [] C=set_union2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),B).
% 1.91/2.10 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.91/2.10 0 [] subset(A,B)|in($f5(A,B),A).
% 1.91/2.10 0 [] subset(A,B)| -in($f5(A,B),B).
% 1.91/2.10 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.91/2.10 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.91/2.10 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.91/2.10 0 [] C=set_intersection2(A,B)|in($f6(A,B,C),C)|in($f6(A,B,C),A).
% 1.91/2.10 0 [] C=set_intersection2(A,B)|in($f6(A,B,C),C)|in($f6(A,B,C),B).
% 1.91/2.10 0 [] C=set_intersection2(A,B)| -in($f6(A,B,C),C)| -in($f6(A,B,C),A)| -in($f6(A,B,C),B).
% 1.91/2.10 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.91/2.10 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.91/2.10 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.91/2.10 0 [] C=set_difference(A,B)|in($f7(A,B,C),C)|in($f7(A,B,C),A).
% 1.91/2.10 0 [] C=set_difference(A,B)|in($f7(A,B,C),C)| -in($f7(A,B,C),B).
% 1.91/2.10 0 [] C=set_difference(A,B)| -in($f7(A,B,C),C)| -in($f7(A,B,C),A)|in($f7(A,B,C),B).
% 1.91/2.10 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.91/2.10 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.91/2.10 0 [] -proper_subset(A,B)|subset(A,B).
% 1.91/2.10 0 [] -proper_subset(A,B)|A!=B.
% 1.91/2.10 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] empty(empty_set).
% 1.91/2.10 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.91/2.10 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.91/2.10 0 [] set_union2(A,A)=A.
% 1.91/2.10 0 [] set_intersection2(A,A)=A.
% 1.91/2.10 0 [] -proper_subset(A,A).
% 1.91/2.10 0 [] singleton($c1)=empty_set.
% 1.91/2.10 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.91/2.10 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.91/2.10 0 [] empty($c2).
% 1.91/2.10 0 [] -empty($c3).
% 1.91/2.10 0 [] subset(A,A).
% 1.91/2.10 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.91/2.10 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.91/2.10 0 [] subset(set_intersection2(A,B),A).
% 1.91/2.10 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.91/2.10 0 [] set_union2(A,empty_set)=A.
% 1.91/2.10 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.91/2.10 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.91/2.10 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.91/2.10 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.91/2.10 0 [] in($f8(A,B),A)|in($f8(A,B),B)|A=B.
% 1.91/2.10 0 [] -in($f8(A,B),A)| -in($f8(A,B),B)|A=B.
% 1.91/2.10 0 [] subset(empty_set,A).
% 1.91/2.10 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.91/2.10 0 [] subset(set_difference(A,B),A).
% 1.91/2.10 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.91/2.10 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.91/2.10 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.91/2.10 0 [] set_difference(A,empty_set)=A.
% 1.91/2.10 0 [] disjoint(A,B)|in($f9(A,B),A).
% 1.91/2.10 0 [] disjoint(A,B)|in($f9(A,B),B).
% 1.91/2.10 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.91/2.10 0 [] -subset(A,empty_set)|A=empty_set.
% 1.91/2.10 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.91/2.10 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 1.91/2.10 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 1.91/2.10 0 [] set_difference(empty_set,A)=empty_set.
% 1.91/2.10 0 [] disjoint(A,B)|in($f10(A,B),set_intersection2(A,B)).
% 1.91/2.10 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.91/2.10 0 [] -subset(A,B)| -proper_subset(B,A).
% 1.91/2.10 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.91/2.10 0 [] unordered_pair(A,A)=singleton(A).
% 1.91/2.10 0 [] -empty(A)|A=empty_set.
% 1.91/2.10 0 [] -in(A,B)| -empty(B).
% 1.91/2.10 0 [] subset(A,set_union2(A,B)).
% 1.91/2.10 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.91/2.10 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.91/2.10 0 [] -empty(A)|A=B| -empty(B).
% 1.91/2.10 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.91/2.10
% 1.91/2.10 This ia a non-Horn set with equality. The strategy will be
% 1.91/2.10 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.91/2.10 deletion, with positive clauses in sos and nonpositive
% 1.91/2.10 clauses in usable.
% 1.91/2.10
% 1.91/2.10 dependent: set(knuth_bendix).
% 1.91/2.10 dependent: set(anl_eq).
% 1.91/2.10 dependent: set(para_from).
% 1.91/2.10 dependent: set(para_into).
% 1.91/2.10 dependent: clear(para_from_right).
% 1.91/2.10 dependent: clear(para_into_right).
% 1.91/2.10 dependent: set(para_from_vars).
% 1.91/2.10 dependent: set(eq_units_both_ways).
% 1.91/2.10 dependent: set(dynamic_demod_all).
% 1.91/2.10 dependent: set(dynamic_demod).
% 1.91/2.10 dependent: set(order_eq).
% 1.91/2.10 dependent: set(back_demod).
% 1.91/2.10 dependent: set(lrpo).
% 1.91/2.10 dependent: set(hyper_res).
% 1.91/2.10 dependent: set(unit_deletion).
% 1.91/2.10 dependent: set(factor).
% 1.91/2.10
% 1.91/2.10 ------------> process usable:
% 1.91/2.10 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.91/2.10 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.91/2.10 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 1.91/2.10 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 1.91/2.10 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 1.91/2.10 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.91/2.10 ** KEPT (pick-wt=10): 7 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.91/2.10 ** KEPT (pick-wt=14): 8 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.91/2.10 ** KEPT (pick-wt=6): 9 [] A!=empty_set| -in(B,A).
% 1.91/2.10 ** KEPT (pick-wt=14): 10 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.91/2.10 ** KEPT (pick-wt=11): 11 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.91/2.10 ** KEPT (pick-wt=11): 12 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.91/2.10 ** KEPT (pick-wt=17): 13 [] A=unordered_pair(B,C)| -in($f3(B,C,A),A)|$f3(B,C,A)!=B.
% 1.91/2.10 ** KEPT (pick-wt=17): 14 [] A=unordered_pair(B,C)| -in($f3(B,C,A),A)|$f3(B,C,A)!=C.
% 1.91/2.10 ** KEPT (pick-wt=14): 15 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.91/2.10 ** KEPT (pick-wt=11): 16 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.91/2.10 ** KEPT (pick-wt=11): 17 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.91/2.10 ** KEPT (pick-wt=17): 18 [] A=set_union2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B).
% 1.91/2.10 ** KEPT (pick-wt=17): 19 [] A=set_union2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),C).
% 1.91/2.10 ** KEPT (pick-wt=9): 20 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.91/2.10 ** KEPT (pick-wt=8): 21 [] subset(A,B)| -in($f5(A,B),B).
% 1.91/2.10 ** KEPT (pick-wt=11): 22 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.91/2.10 ** KEPT (pick-wt=11): 23 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.91/2.10 ** KEPT (pick-wt=14): 24 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.91/2.10 ** KEPT (pick-wt=23): 25 [] A=set_intersection2(B,C)| -in($f6(B,C,A),A)| -in($f6(B,C,A),B)| -in($f6(B,C,A),C).
% 1.91/2.10 ** KEPT (pick-wt=11): 26 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.91/2.10 ** KEPT (pick-wt=11): 27 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.91/2.10 ** KEPT (pick-wt=14): 28 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.91/2.10 ** KEPT (pick-wt=17): 29 [] A=set_difference(B,C)|in($f7(B,C,A),A)| -in($f7(B,C,A),C).
% 1.91/2.10 ** KEPT (pick-wt=23): 30 [] A=set_difference(B,C)| -in($f7(B,C,A),A)| -in($f7(B,C,A),B)|in($f7(B,C,A),C).
% 1.91/2.10 ** KEPT (pick-wt=8): 31 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=8): 32 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=6): 33 [] -proper_subset(A,B)|subset(A,B).
% 1.91/2.10 ** KEPT (pick-wt=6): 34 [] -proper_subset(A,B)|A!=B.
% 1.91/2.10 ** KEPT (pick-wt=9): 35 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.91/2.10 ** KEPT (pick-wt=6): 36 [] empty(A)| -empty(set_union2(A,B)).
% 1.91/2.10 ** KEPT (pick-wt=6): 37 [] empty(A)| -empty(set_union2(B,A)).
% 1.91/2.10 ** KEPT (pick-wt=3): 38 [] -proper_subset(A,A).
% 1.91/2.10 ** KEPT (pick-wt=8): 39 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.91/2.10 ** KEPT (pick-wt=8): 40 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.91/2.10 ** KEPT (pick-wt=2): 41 [] -empty($c3).
% 1.91/2.10 ** KEPT (pick-wt=6): 42 [] -disjoint(A,B)|disjoint(B,A).
% 1.91/2.10 ** KEPT (pick-wt=8): 43 [] -subset(A,B)|set_union2(A,B)=B.
% 1.91/2.10 ** KEPT (pick-wt=11): 44 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.91/2.10 ** KEPT (pick-wt=9): 45 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.91/2.10 ** KEPT (pick-wt=10): 46 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.91/2.10 ** KEPT (pick-wt=8): 47 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.91/2.10 ** KEPT (pick-wt=13): 48 [] -in($f8(A,B),A)| -in($f8(A,B),B)|A=B.
% 1.91/2.10 ** KEPT (pick-wt=10): 49 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.91/2.10 Following clause subsumed by 39 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.91/2.10 Following clause subsumed by 40 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.91/2.10 ** KEPT (pick-wt=9): 50 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.91/2.10 ** KEPT (pick-wt=6): 51 [] -subset(A,empty_set)|A=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=10): 53 [copy,52,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 1.91/2.10 ** KEPT (pick-wt=8): 54 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.91/2.10 ** KEPT (pick-wt=6): 55 [] -subset(A,B)| -proper_subset(B,A).
% 1.91/2.10 ** KEPT (pick-wt=9): 56 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.91/2.10 ** KEPT (pick-wt=5): 57 [] -empty(A)|A=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=5): 58 [] -in(A,B)| -empty(B).
% 1.91/2.10 ** KEPT (pick-wt=8): 59 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.91/2.10 ** KEPT (pick-wt=8): 60 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.91/2.10 ** KEPT (pick-wt=7): 61 [] -empty(A)|A=B| -empty(B).
% 1.91/2.10 ** KEPT (pick-wt=11): 62 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.91/2.10
% 1.91/2.10 ------------> process sos:
% 1.91/2.10 ** KEPT (pick-wt=3): 82 [] A=A.
% 1.91/2.10 ** KEPT (pick-wt=7): 83 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.91/2.10 ** KEPT (pick-wt=7): 84 [] set_union2(A,B)=set_union2(B,A).
% 1.91/2.10 ** KEPT (pick-wt=7): 85 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.91/2.10 ** KEPT (pick-wt=14): 86 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.91/2.10 ** KEPT (pick-wt=7): 87 [] A=empty_set|in($f2(A),A).
% 1.91/2.10 ** KEPT (pick-wt=23): 88 [] A=unordered_pair(B,C)|in($f3(B,C,A),A)|$f3(B,C,A)=B|$f3(B,C,A)=C.
% 1.91/2.10 ** KEPT (pick-wt=23): 89 [] A=set_union2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B)|in($f4(B,C,A),C).
% 1.91/2.10 ** KEPT (pick-wt=8): 90 [] subset(A,B)|in($f5(A,B),A).
% 1.91/2.10 ** KEPT (pick-wt=17): 91 [] A=set_intersection2(B,C)|in($f6(B,C,A),A)|in($f6(B,C,A),B).
% 1.91/2.10 ** KEPT (pick-wt=17): 92 [] A=set_intersection2(B,C)|in($f6(B,C,A),A)|in($f6(B,C,A),C).
% 1.91/2.10 ** KEPT (pick-wt=17): 93 [] A=set_difference(B,C)|in($f7(B,C,A),A)|in($f7(B,C,A),B).
% 1.91/2.10 ** KEPT (pick-wt=2): 94 [] empty(empty_set).
% 1.91/2.10 ** KEPT (pick-wt=5): 95 [] set_union2(A,A)=A.
% 1.91/2.10 ---> New Demodulator: 96 [new_demod,95] set_union2(A,A)=A.
% 1.91/2.10 ** KEPT (pick-wt=5): 97 [] set_intersection2(A,A)=A.
% 1.91/2.10 ---> New Demodulator: 98 [new_demod,97] set_intersection2(A,A)=A.
% 1.91/2.10 ** KEPT (pick-wt=4): 99 [] singleton($c1)=empty_set.
% 1.91/2.10 ---> New Demodulator: 100 [new_demod,99] singleton($c1)=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=2): 101 [] empty($c2).
% 1.91/2.10 ** KEPT (pick-wt=3): 102 [] subset(A,A).
% 1.91/2.10 ** KEPT (pick-wt=5): 103 [] subset(set_intersection2(A,B),A).
% 1.91/2.10 ** KEPT (pick-wt=5): 104 [] set_union2(A,empty_set)=A.
% 1.91/2.10 ---> New Demodulator: 105 [new_demod,104] set_union2(A,empty_set)=A.
% 1.91/2.10 ** KEPT (pick-wt=5): 106 [] set_intersection2(A,empty_set)=empty_set.
% 1.91/2.10 ---> New Demodulator: 107 [new_demod,106] set_intersection2(A,empty_set)=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=13): 108 [] in($f8(A,B),A)|in($f8(A,B),B)|A=B.
% 1.91/2.10 ** KEPT (pick-wt=3): 109 [] subset(empty_set,A).
% 1.91/2.10 ** KEPT (pick-wt=5): 110 [] subset(set_difference(A,B),A).
% 1.91/2.10 ** KEPT (pick-wt=9): 111 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.91/2.10 ---> New Demodulator: 112 [new_demod,111] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.91/2.10 ** KEPT (pick-wt=5): 113 [] set_difference(A,empty_set)=A.
% 1.91/2.10 ---> New Demodulator: 114 [new_demod,113] set_difference(A,empty_set)=A.
% 1.91/2.10 ** KEPT (pick-wt=8): 115 [] disjoint(A,B)|in($f9(A,B),A).
% 1.91/2.10 ** KEPT (pick-wt=8): 116 [] disjoint(A,B)|in($f9(A,B),B).
% 1.91/2.10 ** KEPT (pick-wt=9): 117 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.91/2.10 ---> New Demodulator: 118 [new_demod,117] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.91/2.10 ** KEPT (pick-wt=9): 120 [copy,119,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.91/2.10 ---> New Demodulator: 121 [new_demod,120] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.91/2.10 ** KEPT (pick-wt=5): 122 [] set_difference(empty_set,A)=empty_set.
% 1.91/2.10 ---> New Demodulator: 123 [new_demod,122] set_difference(empty_set,A)=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=12): 125 [copy,124,demod,121] disjoint(A,B)|in($f10(A,B),set_difference(A,set_difference(A,B))).
% 1.91/2.10 ** KEPT (pick-wt=6): 127 [copy,126,flip.1] singleton(A)=unordered_pair(A,A).
% 1.91/2.10 ---> New Demodulator: 128 [new_demod,127] singleton(A)=unordered_pair(A,A).
% 1.91/2.10 ** KEPT (pick-wt=5): 129 [] subset(A,set_union2(A,B)).
% 1.91/2.10 Following clause subsumed by 82 during input processing: 0 [copy,82,flip.1] A=A.
% 1.98/2.15 82 back subsumes 79.
% 1.98/2.15 82 back subsumes 77.
% 1.98/2.15 82 back subsumes 64.
% 1.98/2.15 Following clause subsumed by 83 during input processing: 0 [copy,83,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.98/2.15 Following clause subsumed by 84 during input processing: 0 [copy,84,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.98/2.15 ** KEPT (pick-wt=11): 130 [copy,85,flip.1,demod,121,121] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 1.98/2.15 >>>> Starting back demodulation with 96.
% 1.98/2.15 >> back demodulating 80 with 96.
% 1.98/2.15 >> back demodulating 66 with 96.
% 1.98/2.15 >>>> Starting back demodulation with 98.
% 1.98/2.15 >> back demodulating 81 with 98.
% 1.98/2.15 >> back demodulating 76 with 98.
% 1.98/2.15 >> back demodulating 72 with 98.
% 1.98/2.15 >> back demodulating 69 with 98.
% 1.98/2.15 >>>> Starting back demodulation with 100.
% 1.98/2.15 >>>> Starting back demodulation with 105.
% 1.98/2.15 >>>> Starting back demodulation with 107.
% 1.98/2.15 >>>> Starting back demodulation with 112.
% 1.98/2.15 >> back demodulating 53 with 112.
% 1.98/2.15 >>>> Starting back demodulation with 114.
% 1.98/2.15 >>>> Starting back demodulation with 118.
% 1.98/2.15 >>>> Starting back demodulation with 121.
% 1.98/2.15 >> back demodulating 106 with 121.
% 1.98/2.15 >> back demodulating 103 with 121.
% 1.98/2.15 >> back demodulating 97 with 121.
% 1.98/2.15 >> back demodulating 92 with 121.
% 1.98/2.15 >> back demodulating 91 with 121.
% 1.98/2.15 >> back demodulating 85 with 121.
% 1.98/2.15 >> back demodulating 71 with 121.
% 1.98/2.15 >> back demodulating 70 with 121.
% 1.98/2.15 >> back demodulating 54 with 121.
% 1.98/2.15 >> back demodulating 47 with 121.
% 1.98/2.15 >> back demodulating 46 with 121.
% 1.98/2.15 >> back demodulating 44 with 121.
% 1.98/2.15 >> back demodulating 32 with 121.
% 1.98/2.15 >> back demodulating 31 with 121.
% 1.98/2.15 >> back demodulating 25 with 121.
% 1.98/2.15 >> back demodulating 24 with 121.
% 1.98/2.15 >> back demodulating 23 with 121.
% 1.98/2.15 >> back demodulating 22 with 121.
% 1.98/2.15 >>>> Starting back demodulation with 123.
% 1.98/2.15 >>>> Starting back demodulation with 128.
% 1.98/2.15 >> back demodulating 99 with 128.
% 1.98/2.15 >> back demodulating 86 with 128.
% 1.98/2.15 >> back demodulating 8 with 128.
% 1.98/2.15 >> back demodulating 7 with 128.
% 1.98/2.15 >> back demodulating 6 with 128.
% 1.98/2.15 Following clause subsumed by 130 during input processing: 0 [copy,130,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 1.98/2.15 >>>> Starting back demodulation with 142.
% 1.98/2.15 >>>> Starting back demodulation with 157.
% 1.98/2.15
% 1.98/2.15 ======= end of input processing =======
% 1.98/2.15
% 1.98/2.15 =========== start of search ===========
% 1.98/2.15
% 1.98/2.15 -------- PROOF --------
% 1.98/2.15
% 1.98/2.15 ----> UNIT CONFLICT at 0.06 sec ----> 683 [binary,682.1,38.1] $F.
% 1.98/2.15
% 1.98/2.15 Length of proof is 9. Level of proof is 5.
% 1.98/2.15
% 1.98/2.15 ---------------- PROOF ----------------
% 1.98/2.15 % SZS status Theorem
% 1.98/2.15 % SZS output start Refutation
% See solution above
% 1.98/2.15 ------------ end of proof -------------
% 1.98/2.15
% 1.98/2.15
% 1.98/2.15 Search stopped by max_proofs option.
% 1.98/2.15
% 1.98/2.15
% 1.98/2.15 Search stopped by max_proofs option.
% 1.98/2.15
% 1.98/2.15 ============ end of search ============
% 1.98/2.15
% 1.98/2.15 -------------- statistics -------------
% 1.98/2.15 clauses given 19
% 1.98/2.15 clauses generated 894
% 1.98/2.15 clauses kept 656
% 1.98/2.15 clauses forward subsumed 387
% 1.98/2.15 clauses back subsumed 13
% 1.98/2.15 Kbytes malloced 2929
% 1.98/2.15
% 1.98/2.15 ----------- times (seconds) -----------
% 1.98/2.15 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.98/2.15 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.15 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.15
% 1.98/2.15 That finishes the proof of the theorem.
% 1.98/2.15
% 1.98/2.15 Process 13669 finished Wed Jul 27 07:49:18 2022
% 1.98/2.15 Otter interrupted
% 1.98/2.15 PROOF FOUND
%------------------------------------------------------------------------------