TSTP Solution File: SEU149+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU149+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 13:14:55 EDT 2022
% Result : Theorem 2.88s 3.13s
% Output : Refutation 2.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 12 unt; 1 nHn; 11 RR)
% Number of literals : 22 ( 17 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(13,axiom,
( A != unordered_pair(B,C)
| ~ in(D,A)
| D = B
| D = C ),
file('SEU149+2.p',unknown),
[] ).
cnf(14,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SEU149+2.p',unknown),
[] ).
cnf(73,axiom,
dollar_c5 != dollar_c4,
file('SEU149+2.p',unknown),
[] ).
cnf(76,plain,
( A != unordered_pair(B,B)
| ~ in(C,A)
| C = B ),
inference(factor,[status(thm)],[13]),
[iquote('factor,13.3.4')] ).
cnf(93,axiom,
A = A,
file('SEU149+2.p',unknown),
[] ).
cnf(139,axiom,
unordered_pair(A,A) = singleton(A),
file('SEU149+2.p',unknown),
[] ).
cnf(141,plain,
singleton(A) = unordered_pair(A,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[139])]),
[iquote('copy,139,flip.1')] ).
cnf(143,axiom,
singleton(dollar_c5) = unordered_pair(dollar_c4,dollar_c3),
file('SEU149+2.p',unknown),
[] ).
cnf(144,plain,
unordered_pair(dollar_c5,dollar_c5) = unordered_pair(dollar_c4,dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[143]),141]),
[iquote('copy,143,demod,141')] ).
cnf(184,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[93,14,93]),
[iquote('hyper,93,14,93')] ).
cnf(1632,plain,
dollar_c5 = dollar_c3,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[144,13,184]),73]),
[iquote('hyper,144,13,184,unit_del,73')] ).
cnf(1655,plain,
unordered_pair(dollar_c4,dollar_c3) = unordered_pair(dollar_c3,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[144]),1632,1632])]),
[iquote('back_demod,144,demod,1632,1632,flip.1')] ).
cnf(1657,plain,
dollar_c4 != dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[73]),1632])]),
[iquote('back_demod,73,demod,1632,flip.1')] ).
cnf(1811,plain,
dollar_c4 = dollar_c3,
inference(hyper,[status(thm)],[1655,76,184]),
[iquote('hyper,1655,76,184')] ).
cnf(1813,plain,
$false,
inference(binary,[status(thm)],[1811,1657]),
[iquote('binary,1811.1,1657.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU149+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n029.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 07:48:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.54/2.09 ----- Otter 3.3f, August 2004 -----
% 1.54/2.09 The process was started by sandbox2 on n029.cluster.edu,
% 1.54/2.09 Wed Jul 27 07:48:44 2022
% 1.54/2.09 The command was "./otter". The process ID is 6080.
% 1.54/2.09
% 1.54/2.09 set(prolog_style_variables).
% 1.54/2.09 set(auto).
% 1.54/2.09 dependent: set(auto1).
% 1.54/2.09 dependent: set(process_input).
% 1.54/2.09 dependent: clear(print_kept).
% 1.54/2.09 dependent: clear(print_new_demod).
% 1.54/2.09 dependent: clear(print_back_demod).
% 1.54/2.09 dependent: clear(print_back_sub).
% 1.54/2.09 dependent: set(control_memory).
% 1.54/2.09 dependent: assign(max_mem, 12000).
% 1.54/2.09 dependent: assign(pick_given_ratio, 4).
% 1.54/2.09 dependent: assign(stats_level, 1).
% 1.54/2.09 dependent: assign(max_seconds, 10800).
% 1.54/2.09 clear(print_given).
% 1.54/2.09
% 1.54/2.09 formula_list(usable).
% 1.54/2.09 all A (A=A).
% 1.54/2.09 all A B (in(A,B)-> -in(B,A)).
% 1.54/2.09 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 1.54/2.09 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.54/2.09 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.54/2.09 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.54/2.09 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.54/2.09 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.54/2.09 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.54/2.10 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 1.54/2.10 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.54/2.10 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.54/2.10 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.54/2.10 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.54/2.10 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.54/2.10 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.54/2.10 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 1.54/2.10 $T.
% 1.54/2.10 $T.
% 1.54/2.10 $T.
% 1.54/2.10 $T.
% 1.54/2.10 $T.
% 1.54/2.10 $T.
% 1.54/2.10 $T.
% 1.54/2.10 empty(empty_set).
% 1.54/2.10 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.54/2.10 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.54/2.10 all A B (set_union2(A,A)=A).
% 1.54/2.10 all A B (set_intersection2(A,A)=A).
% 1.54/2.10 all A B (-proper_subset(A,A)).
% 1.54/2.10 all A (singleton(A)!=empty_set).
% 1.54/2.10 all A B (subset(singleton(A),B)<->in(A,B)).
% 1.54/2.10 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.54/2.10 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 1.54/2.10 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 1.54/2.10 exists A empty(A).
% 1.54/2.10 exists A (-empty(A)).
% 1.54/2.10 all A B subset(A,A).
% 1.54/2.10 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.54/2.10 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.54/2.10 all A B subset(set_intersection2(A,B),A).
% 1.54/2.10 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 1.54/2.10 all A (set_union2(A,empty_set)=A).
% 1.54/2.10 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.54/2.10 powerset(empty_set)=singleton(empty_set).
% 1.54/2.10 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 1.54/2.10 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.54/2.10 all A (set_intersection2(A,empty_set)=empty_set).
% 1.54/2.10 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.54/2.10 all A subset(empty_set,A).
% 1.54/2.10 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 1.54/2.10 all A B subset(set_difference(A,B),A).
% 1.54/2.10 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.54/2.10 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 1.54/2.10 all A (set_difference(A,empty_set)=A).
% 1.54/2.10 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))).
% 1.54/2.10 all A (subset(A,empty_set)->A=empty_set).
% 1.54/2.10 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 1.54/2.10 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 1.54/2.10 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 1.54/2.10 all A (set_difference(empty_set,A)=empty_set).
% 1.54/2.10 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))).
% 1.54/2.10 all A B (-(subset(A,B)&proper_subset(B,A))).
% 1.54/2.10 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 1.54/2.10 all A (unordered_pair(A,A)=singleton(A)).
% 1.54/2.10 all A (empty(A)->A=empty_set).
% 1.54/2.10 all A B (subset(singleton(A),singleton(B))->A=B).
% 1.54/2.10 all A B (-(in(A,B)&empty(B))).
% 1.54/2.10 all A B subset(A,set_union2(A,B)).
% 1.54/2.10 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 1.54/2.10 all A B (-(empty(A)&A!=B&empty(B))).
% 1.54/2.10 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.54/2.10 -(all A B C (singleton(A)=unordered_pair(B,C)->A=B)).
% 1.54/2.10 end_of_list.
% 1.54/2.10
% 1.54/2.10 -------> usable clausifies to:
% 1.54/2.10
% 1.54/2.10 list(usable).
% 1.54/2.10 0 [] A=A.
% 1.54/2.10 0 [] -in(A,B)| -in(B,A).
% 1.54/2.10 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.54/2.10 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.54/2.10 0 [] set_union2(A,B)=set_union2(B,A).
% 1.54/2.10 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.54/2.10 0 [] A!=B|subset(A,B).
% 1.54/2.10 0 [] A!=B|subset(B,A).
% 1.54/2.10 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.54/2.10 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.54/2.10 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.54/2.10 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.54/2.10 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.54/2.10 0 [] A!=empty_set| -in(B,A).
% 1.54/2.10 0 [] A=empty_set|in($f2(A),A).
% 1.54/2.10 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 1.54/2.10 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 1.54/2.10 0 [] B=powerset(A)|in($f3(A,B),B)|subset($f3(A,B),A).
% 1.54/2.10 0 [] B=powerset(A)| -in($f3(A,B),B)| -subset($f3(A,B),A).
% 1.54/2.10 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.54/2.10 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.54/2.10 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.54/2.10 0 [] C=unordered_pair(A,B)|in($f4(A,B,C),C)|$f4(A,B,C)=A|$f4(A,B,C)=B.
% 1.54/2.10 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=A.
% 1.54/2.10 0 [] C=unordered_pair(A,B)| -in($f4(A,B,C),C)|$f4(A,B,C)!=B.
% 1.54/2.10 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.54/2.10 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.54/2.10 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.54/2.10 0 [] C=set_union2(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 1.54/2.10 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A).
% 1.54/2.10 0 [] C=set_union2(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 1.54/2.10 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.54/2.10 0 [] subset(A,B)|in($f6(A,B),A).
% 1.54/2.10 0 [] subset(A,B)| -in($f6(A,B),B).
% 1.54/2.10 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.54/2.10 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.54/2.10 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.54/2.10 0 [] C=set_intersection2(A,B)|in($f7(A,B,C),C)|in($f7(A,B,C),A).
% 1.54/2.10 0 [] C=set_intersection2(A,B)|in($f7(A,B,C),C)|in($f7(A,B,C),B).
% 1.54/2.10 0 [] C=set_intersection2(A,B)| -in($f7(A,B,C),C)| -in($f7(A,B,C),A)| -in($f7(A,B,C),B).
% 1.54/2.10 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.54/2.10 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.54/2.10 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.54/2.10 0 [] C=set_difference(A,B)|in($f8(A,B,C),C)|in($f8(A,B,C),A).
% 1.54/2.10 0 [] C=set_difference(A,B)|in($f8(A,B,C),C)| -in($f8(A,B,C),B).
% 1.54/2.10 0 [] C=set_difference(A,B)| -in($f8(A,B,C),C)| -in($f8(A,B,C),A)|in($f8(A,B,C),B).
% 1.54/2.10 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.54/2.10 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.54/2.10 0 [] -proper_subset(A,B)|subset(A,B).
% 1.54/2.10 0 [] -proper_subset(A,B)|A!=B.
% 1.54/2.10 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.54/2.10 0 [] $T.
% 1.54/2.10 0 [] $T.
% 1.54/2.10 0 [] $T.
% 1.54/2.10 0 [] $T.
% 1.54/2.10 0 [] $T.
% 1.54/2.10 0 [] $T.
% 1.54/2.10 0 [] $T.
% 1.54/2.10 0 [] empty(empty_set).
% 1.54/2.10 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.54/2.10 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.54/2.10 0 [] set_union2(A,A)=A.
% 1.54/2.10 0 [] set_intersection2(A,A)=A.
% 1.54/2.10 0 [] -proper_subset(A,A).
% 1.54/2.10 0 [] singleton(A)!=empty_set.
% 1.54/2.10 0 [] -subset(singleton(A),B)|in(A,B).
% 1.54/2.10 0 [] subset(singleton(A),B)| -in(A,B).
% 1.54/2.10 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.54/2.10 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.54/2.10 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.54/2.10 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.54/2.10 0 [] subset(A,singleton(B))|A!=empty_set.
% 1.54/2.10 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.54/2.10 0 [] empty($c1).
% 1.54/2.10 0 [] -empty($c2).
% 1.54/2.10 0 [] subset(A,A).
% 1.54/2.10 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.54/2.10 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.54/2.10 0 [] subset(set_intersection2(A,B),A).
% 1.54/2.10 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.54/2.10 0 [] set_union2(A,empty_set)=A.
% 1.54/2.10 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.54/2.10 0 [] powerset(empty_set)=singleton(empty_set).
% 1.54/2.10 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.54/2.10 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.54/2.10 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.54/2.10 0 [] in($f9(A,B),A)|in($f9(A,B),B)|A=B.
% 1.54/2.10 0 [] -in($f9(A,B),A)| -in($f9(A,B),B)|A=B.
% 1.54/2.10 0 [] subset(empty_set,A).
% 1.54/2.10 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.54/2.10 0 [] subset(set_difference(A,B),A).
% 1.54/2.10 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.54/2.10 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.54/2.10 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.54/2.10 0 [] set_difference(A,empty_set)=A.
% 1.54/2.10 0 [] disjoint(A,B)|in($f10(A,B),A).
% 1.54/2.10 0 [] disjoint(A,B)|in($f10(A,B),B).
% 1.54/2.10 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.54/2.10 0 [] -subset(A,empty_set)|A=empty_set.
% 1.54/2.10 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.54/2.10 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 1.54/2.10 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 1.54/2.10 0 [] set_difference(empty_set,A)=empty_set.
% 1.54/2.10 0 [] disjoint(A,B)|in($f11(A,B),set_intersection2(A,B)).
% 1.54/2.10 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.54/2.10 0 [] -subset(A,B)| -proper_subset(B,A).
% 1.54/2.10 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.54/2.10 0 [] unordered_pair(A,A)=singleton(A).
% 1.54/2.10 0 [] -empty(A)|A=empty_set.
% 1.54/2.10 0 [] -subset(singleton(A),singleton(B))|A=B.
% 1.54/2.10 0 [] -in(A,B)| -empty(B).
% 1.54/2.10 0 [] subset(A,set_union2(A,B)).
% 1.54/2.10 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.54/2.10 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.54/2.10 0 [] -empty(A)|A=B| -empty(B).
% 1.54/2.10 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.54/2.10 0 [] singleton($c5)=unordered_pair($c4,$c3).
% 1.54/2.10 0 [] $c5!=$c4.
% 1.54/2.10 end_of_list.
% 1.54/2.10
% 1.54/2.10 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.54/2.10
% 1.54/2.10 This ia a non-Horn set with equality. The strategy will be
% 1.54/2.10 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.54/2.10 deletion, with positive clauses in sos and nonpositive
% 1.54/2.10 clauses in usable.
% 1.54/2.10
% 1.54/2.10 dependent: set(knuth_bendix).
% 1.54/2.10 dependent: set(anl_eq).
% 1.54/2.10 dependent: set(para_from).
% 1.54/2.10 dependent: set(para_into).
% 1.54/2.10 dependent: clear(para_from_right).
% 1.54/2.10 dependent: clear(para_into_right).
% 1.54/2.10 dependent: set(para_from_vars).
% 1.54/2.10 dependent: set(eq_units_both_ways).
% 1.54/2.10 dependent: set(dynamic_demod_all).
% 1.54/2.10 dependent: set(dynamic_demod).
% 1.54/2.10 dependent: set(order_eq).
% 1.54/2.10 dependent: set(back_demod).
% 1.54/2.10 dependent: set(lrpo).
% 1.54/2.10 dependent: set(hyper_res).
% 1.54/2.10 dependent: set(unit_deletion).
% 1.54/2.10 dependent: set(factor).
% 1.54/2.10
% 1.54/2.10 ------------> process usable:
% 1.54/2.10 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.54/2.10 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.54/2.10 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 1.54/2.10 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 1.54/2.10 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 1.54/2.10 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.54/2.10 ** KEPT (pick-wt=10): 7 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.54/2.10 ** KEPT (pick-wt=14): 8 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.54/2.10 ** KEPT (pick-wt=6): 9 [] A!=empty_set| -in(B,A).
% 1.54/2.10 ** KEPT (pick-wt=10): 10 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 1.54/2.10 ** KEPT (pick-wt=10): 11 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 1.54/2.10 ** KEPT (pick-wt=14): 12 [] A=powerset(B)| -in($f3(B,A),A)| -subset($f3(B,A),B).
% 1.54/2.10 ** KEPT (pick-wt=14): 13 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.54/2.10 ** KEPT (pick-wt=11): 14 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.54/2.10 ** KEPT (pick-wt=11): 15 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.54/2.10 ** KEPT (pick-wt=17): 16 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=B.
% 1.54/2.10 ** KEPT (pick-wt=17): 17 [] A=unordered_pair(B,C)| -in($f4(B,C,A),A)|$f4(B,C,A)!=C.
% 1.54/2.10 ** KEPT (pick-wt=14): 18 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.54/2.10 ** KEPT (pick-wt=11): 19 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.54/2.10 ** KEPT (pick-wt=11): 20 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.54/2.10 ** KEPT (pick-wt=17): 21 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B).
% 1.54/2.10 ** KEPT (pick-wt=17): 22 [] A=set_union2(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 1.54/2.10 ** KEPT (pick-wt=9): 23 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.54/2.10 ** KEPT (pick-wt=8): 24 [] subset(A,B)| -in($f6(A,B),B).
% 1.54/2.10 ** KEPT (pick-wt=11): 25 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.54/2.10 ** KEPT (pick-wt=11): 26 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.54/2.10 ** KEPT (pick-wt=14): 27 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.54/2.10 ** KEPT (pick-wt=23): 28 [] A=set_intersection2(B,C)| -in($f7(B,C,A),A)| -in($f7(B,C,A),B)| -in($f7(B,C,A),C).
% 1.54/2.10 ** KEPT (pick-wt=11): 29 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.54/2.10 ** KEPT (pick-wt=11): 30 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.54/2.10 ** KEPT (pick-wt=14): 31 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.54/2.10 ** KEPT (pick-wt=17): 32 [] A=set_difference(B,C)|in($f8(B,C,A),A)| -in($f8(B,C,A),C).
% 1.54/2.10 ** KEPT (pick-wt=23): 33 [] A=set_difference(B,C)| -in($f8(B,C,A),A)| -in($f8(B,C,A),B)|in($f8(B,C,A),C).
% 1.54/2.10 ** KEPT (pick-wt=8): 34 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.54/2.10 ** KEPT (pick-wt=8): 35 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.54/2.10 ** KEPT (pick-wt=6): 36 [] -proper_subset(A,B)|subset(A,B).
% 1.54/2.10 ** KEPT (pick-wt=6): 37 [] -proper_subset(A,B)|A!=B.
% 1.54/2.10 ** KEPT (pick-wt=9): 38 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.54/2.10 ** KEPT (pick-wt=6): 39 [] empty(A)| -empty(set_union2(A,B)).
% 1.54/2.10 ** KEPT (pick-wt=6): 40 [] empty(A)| -empty(set_union2(B,A)).
% 1.54/2.10 ** KEPT (pick-wt=3): 41 [] -proper_subset(A,A).
% 1.54/2.10 ** KEPT (pick-wt=4): 42 [] singleton(A)!=empty_set.
% 1.54/2.10 ** KEPT (pick-wt=7): 43 [] -subset(singleton(A),B)|in(A,B).
% 1.54/2.10 ** KEPT (pick-wt=7): 44 [] subset(singleton(A),B)| -in(A,B).
% 1.54/2.10 ** KEPT (pick-wt=8): 45 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.54/2.10 ** KEPT (pick-wt=8): 46 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.54/2.10 ** KEPT (pick-wt=12): 47 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.54/2.10 ** KEPT (pick-wt=11): 48 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.54/2.10 ** KEPT (pick-wt=7): 49 [] subset(A,singleton(B))|A!=empty_set.
% 1.54/2.10 Following clause subsumed by 3 during input processing: 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.54/2.10 ** KEPT (pick-wt=2): 50 [] -empty($c2).
% 1.54/2.10 ** KEPT (pick-wt=6): 51 [] -disjoint(A,B)|disjoint(B,A).
% 1.54/2.10 ** KEPT (pick-wt=8): 52 [] -subset(A,B)|set_union2(A,B)=B.
% 1.54/2.10 ** KEPT (pick-wt=11): 53 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.54/2.10 ** KEPT (pick-wt=9): 54 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.54/2.10 ** KEPT (pick-wt=10): 55 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.54/2.10 ** KEPT (pick-wt=8): 56 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.54/2.10 ** KEPT (pick-wt=13): 57 [] -in($f9(A,B),A)| -in($f9(A,B),B)|A=B.
% 1.54/2.10 ** KEPT (pick-wt=10): 58 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.54/2.10 Following clause subsumed by 45 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.54/2.10 Following clause subsumed by 46 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.54/2.10 ** KEPT (pick-wt=9): 59 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.54/2.10 ** KEPT (pick-wt=6): 60 [] -subset(A,empty_set)|A=empty_set.
% 1.54/2.10 ** KEPT (pick-wt=10): 62 [copy,61,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 1.54/2.10 ** KEPT (pick-wt=8): 63 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.54/2.10 ** KEPT (pick-wt=6): 64 [] -subset(A,B)| -proper_subset(B,A).
% 1.54/2.10 ** KEPT (pick-wt=9): 65 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.54/2.10 ** KEPT (pick-wt=5): 66 [] -empty(A)|A=empty_set.
% 1.54/2.10 ** KEPT (pick-wt=8): 67 [] -subset(singleton(A),singleton(B))|A=B.
% 1.54/2.10 ** KEPT (pick-wt=5): 68 [] -in(A,B)| -empty(B).
% 1.54/2.10 ** KEPT (pick-wt=8): 69 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.54/2.10 ** KEPT (pick-wt=8): 70 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.54/2.10 ** KEPT (pick-wt=7): 71 [] -empty(A)|A=B| -empty(B).
% 1.54/2.10 ** KEPT (pick-wt=11): 72 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.54/2.10 ** KEPT (pick-wt=3): 73 [] $c5!=$c4.
% 1.54/2.10
% 1.54/2.10 ------------> process sos:
% 1.54/2.10 ** KEPT (pick-wt=3): 93 [] A=A.
% 1.54/2.10 ** KEPT (pick-wt=7): 94 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.54/2.10 ** KEPT (pick-wt=7): 95 [] set_union2(A,B)=set_union2(B,A).
% 1.54/2.10 ** KEPT (pick-wt=7): 96 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.54/2.10 ** KEPT (pick-wt=14): 97 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.54/2.10 ** KEPT (pick-wt=7): 98 [] A=empty_set|in($f2(A),A).
% 1.54/2.10 ** KEPT (pick-wt=14): 99 [] A=powerset(B)|in($f3(B,A),A)|subset($f3(B,A),B).
% 1.54/2.10 ** KEPT (pick-wt=23): 100 [] A=unordered_pair(B,C)|in($f4(B,C,A),A)|$f4(B,C,A)=B|$f4(B,C,A)=C.
% 1.54/2.10 ** KEPT (pick-wt=23): 101 [] A=set_union2(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 1.54/2.10 ** KEPT (pick-wt=8): 102 [] subset(A,B)|in($f6(A,B),A).
% 1.54/2.10 ** KEPT (pick-wt=17): 103 [] A=set_intersection2(B,C)|in($f7(B,C,A),A)|in($f7(B,C,A),B).
% 1.54/2.10 ** KEPT (pick-wt=17): 104 [] A=set_intersection2(B,C)|in($f7(B,C,A),A)|in($f7(B,C,A),C).
% 1.54/2.10 ** KEPT (pick-wt=17): 105 [] A=set_difference(B,C)|in($f8(B,C,A),A)|in($f8(B,C,A),B).
% 1.54/2.10 ** KEPT (pick-wt=2): 106 [] empty(empty_set).
% 1.54/2.10 ** KEPT (pick-wt=5): 107 [] set_union2(A,A)=A.
% 1.54/2.10 ---> New Demodulator: 108 [new_demod,107] set_union2(A,A)=A.
% 1.54/2.10 ** KEPT (pick-wt=5): 109 [] set_intersection2(A,A)=A.
% 1.54/2.10 ---> New Demodulator: 110 [new_demod,109] set_intersection2(A,A)=A.
% 1.54/2.10 ** KEPT (pick-wt=2): 111 [] empty($c1).
% 1.54/2.10 ** KEPT (pick-wt=3): 112 [] subset(A,A).
% 1.54/2.10 ** KEPT (pick-wt=5): 113 [] subset(set_intersection2(A,B),A).
% 1.54/2.10 ** KEPT (pick-wt=5): 114 [] set_union2(A,empty_set)=A.
% 1.54/2.10 ---> New Demodulator: 115 [new_demod,114] set_union2(A,empty_set)=A.
% 1.54/2.10 ** KEPT (pick-wt=5): 117 [copy,116,flip.1] singleton(empty_set)=powerset(empty_set).
% 1.54/2.10 ---> New Demodulator: 118 [new_demod,117] singleton(empty_set)=powerset(empty_set).
% 1.54/2.10 ** KEPT (pick-wt=5): 119 [] set_intersection2(A,empty_set)=empty_set.
% 1.54/2.10 ---> New Demodulator: 120 [new_demod,119] set_intersection2(A,empty_set)=empty_set.
% 1.54/2.10 ** KEPT (pick-wt=13): 121 [] in($f9(A,B),A)|in($f9(A,B),B)|A=B.
% 1.54/2.10 ** KEPT (pick-wt=3): 122 [] subset(empty_set,A).
% 1.54/2.10 ** KEPT (pick-wt=5): 123 [] subset(set_difference(A,B),A).
% 1.54/2.10 ** KEPT (pick-wt=9): 124 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.54/2.10 ---> New Demodulator: 125 [new_demod,124] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.54/2.10 ** KEPT (pick-wt=5): 126 [] set_difference(A,empty_set)=A.
% 1.54/2.10 ---> New Demodulator: 127 [new_demod,126] set_difference(A,empty_set)=A.
% 1.54/2.10 ** KEPT (pick-wt=8): 128 [] disjoint(A,B)|in($f10(A,B),A).
% 1.54/2.10 ** KEPT (pick-wt=8): 129 [] disjoint(A,B)|in($f10(A,B),B).
% 1.54/2.10 ** KEPT (pick-wt=9): 130 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.54/2.10 ---> New Demodulator: 131 [new_demod,130] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.54/2.10 ** KEPT (pick-wt=9): 133 [copy,132,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.54/2.10 ---> New Demodulator: 134 [new_demod,133] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.54/2.10 ** KEPT (pick-wt=5): 135 [] set_difference(empty_set,A)=empty_set.
% 1.54/2.10 ---> New Demodulator: 136 [new_demod,135] set_difference(empty_set,A)=empty_set.
% 1.54/2.10 ** KEPT (pick-wt=12): 138 [copy,137,demod,134] disjoint(A,B)|in($f11(A,B),set_difference(A,set_difference(A,B))).
% 1.54/2.10 ** KEPT (pick-wt=6): 140 [copy,139,flip.1] singleton(A)=unordered_pair(A,A).
% 1.54/2.10 ---> New Demodulator: 141 [new_demod,140] singleton(A)=unordered_pair(A,A).
% 1.54/2.10 ** KEPT (pick-wt=5): 142 [] subset(A,set_union2(A,B)).
% 1.54/2.10 ** KEPT (pick-wt=7): 144 [copy,143,demod,141] unordered_pair($c5,$c5)=unordered_pair($c4,$c3).
% 1.54/2.10 ---> New Demodulator: 145 [new_demod,144] unordered_pair($c5,$c5)=unordered_pair($c4,$c3).
% 1.54/2.10 Following clause subsumed by 93 during input processing: 0 [copy,93,flip.1] A=A.
% 1.54/2.10 93 back subsumes 90.
% 1.54/2.10 93 back subsumes 88.
% 1.54/2.10 93 back subsumes 75.
% 1.54/2.10 Following clause subsumed by 94 during input processing: 0 [copy,94,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.54/2.10 Following clause subsumed by 95 during input processing: 0 [copy,95,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.54/2.10 ** KEPT (pick-wt=11): 146 [copy,96,flip.1,demod,134,134] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 1.54/2.10 >>>> Starting back demodulation with 108.
% 1.54/2.10 >> back demodulating 91 with 108.
% 1.54/2.10 >> back demodulating 77 with 108.
% 1.54/2.10 >>>> Starting back demodulation with 110.
% 1.54/2.10 >> back demodulating 92 with 110.
% 1.54/2.10 >> back demodulating 87 with 110.
% 1.54/2.10 >> back demodulating 83 with 110.
% 1.54/2.10 >> back demodulating 80 with 110.
% 1.54/2.10 >>>> Starting back demodulation with 115.
% 1.54/2.10 >>>> Starting back demodulation with 118.
% 1.54/2.10 >>>> Starting back demodulation with 120.
% 1.54/2.10 >>>> Starting back demodulation with 125.
% 1.54/2.10 >> back demodulating 62 with 125.
% 1.54/2.10 >>>> Starting back demodulation with 127.
% 1.54/2.10 >>>> Starting back demodulation with 131.
% 1.54/2.10 >>>> Starting back demodulation with 134.
% 1.54/2.10 >> back demodulating 119 with 134.
% 1.54/2.10 >> back demodulating 113 with 134.
% 1.54/2.10 >> back demodulating 109 with 134.
% 1.54/2.10 >> back demodulating 104 with 134.
% 1.54/2.10 >> back demodulating 103 with 134.
% 1.54/2.10 >> back demodulating 96 with 134.
% 1.54/2.10 >> back demodulating 82 with 134.
% 1.54/2.10 >> back demodulating 81 with 134.
% 1.54/2.10 >> back demodulating 63 with 134.
% 1.54/2.10 >> back demodulating 56 with 134.
% 1.54/2.10 >> back demodulating 55 with 134.
% 1.54/2.10 >> back demodulating 53 with 134.
% 1.54/2.10 >> back demodulating 35 with 134.
% 1.54/2.10 >> back demodulating 34 with 134.
% 1.54/2.10 >> back demodulating 28 with 134.
% 1.54/2.10 >> back demodulating 27 with 134.
% 1.54/2.10 >> back demodulating 26 with 134.
% 1.54/2.10 >> back demodulating 25 with 134.
% 1.54/2.10 >>>> Starting back demodulation with 136.
% 1.54/2.10 >>>> Starting back demodulation with 141.
% 2.88/3.13 >> back demodulating 117 with 141.
% 2.88/3.13 >> back demodulating 97 with 141.
% 2.88/3.13 >> back demodulating 67 with 141.
% 2.88/3.13 >> back demodulating 49 with 141.
% 2.88/3.13 >> back demodulating 48 with 141.
% 2.88/3.13 >> back demodulating 47 with 141.
% 2.88/3.13 >> back demodulating 44 with 141.
% 2.88/3.13 >> back demodulating 43 with 141.
% 2.88/3.13 >> back demodulating 42 with 141.
% 2.88/3.13 >> back demodulating 8 with 141.
% 2.88/3.13 >> back demodulating 7 with 141.
% 2.88/3.13 >> back demodulating 6 with 141.
% 2.88/3.13 >>>> Starting back demodulation with 145.
% 2.88/3.13 Following clause subsumed by 146 during input processing: 0 [copy,146,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 2.88/3.13 >>>> Starting back demodulation with 158.
% 2.88/3.13 >>>> Starting back demodulation with 173.
% 2.88/3.13
% 2.88/3.13 ======= end of input processing =======
% 2.88/3.13
% 2.88/3.13 =========== start of search ===========
% 2.88/3.13
% 2.88/3.13
% 2.88/3.13 Resetting weight limit to 8.
% 2.88/3.13
% 2.88/3.13
% 2.88/3.13 Resetting weight limit to 8.
% 2.88/3.13
% 2.88/3.13 sos_size=1305
% 2.88/3.13
% 2.88/3.13
% 2.88/3.13 Resetting weight limit to 7.
% 2.88/3.13
% 2.88/3.13
% 2.88/3.13 Resetting weight limit to 7.
% 2.88/3.13
% 2.88/3.13 sos_size=1295
% 2.88/3.13
% 2.88/3.13 -------- PROOF --------
% 2.88/3.13
% 2.88/3.13 ----> UNIT CONFLICT at 1.03 sec ----> 1813 [binary,1811.1,1657.1] $F.
% 2.88/3.13
% 2.88/3.13 Length of proof is 8. Level of proof is 5.
% 2.88/3.13
% 2.88/3.13 ---------------- PROOF ----------------
% 2.88/3.13 % SZS status Theorem
% 2.88/3.13 % SZS output start Refutation
% See solution above
% 2.88/3.13 ------------ end of proof -------------
% 2.88/3.13
% 2.88/3.13
% 2.88/3.13 Search stopped by max_proofs option.
% 2.88/3.13
% 2.88/3.13
% 2.88/3.13 Search stopped by max_proofs option.
% 2.88/3.13
% 2.88/3.13 ============ end of search ============
% 2.88/3.13
% 2.88/3.13 -------------- statistics -------------
% 2.88/3.13 clauses given 272
% 2.88/3.13 clauses generated 53777
% 2.88/3.13 clauses kept 1769
% 2.88/3.13 clauses forward subsumed 6492
% 2.88/3.13 clauses back subsumed 190
% 2.88/3.13 Kbytes malloced 5859
% 2.88/3.13
% 2.88/3.13 ----------- times (seconds) -----------
% 2.88/3.13 user CPU time 1.03 (0 hr, 0 min, 1 sec)
% 2.88/3.13 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.88/3.13 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.88/3.13
% 2.88/3.13 That finishes the proof of the theorem.
% 2.88/3.13
% 2.88/3.13 Process 6080 finished Wed Jul 27 07:48:47 2022
% 2.88/3.13 Otter interrupted
% 2.88/3.13 PROOF FOUND
%------------------------------------------------------------------------------