TSTP Solution File: SET681+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% 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 13:14:04 EDT 2022
% Result : Theorem 4.69s 4.88s
% Output : Refutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 23 ( 12 unt; 2 nHn; 22 RR)
% Number of literals : 55 ( 2 equ; 32 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 25 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,binary_relation_type)
| ~ member(A,range_of(B))
| member(ordered_pair(dollar_f1(A,B),A),B) ),
file('SET681+3.p',unknown),
[] ).
cnf(3,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,binary_relation_type)
| member(A,range_of(B))
| ~ ilf_type(C,set_type)
| ~ member(ordered_pair(C,A),B) ),
file('SET681+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(A,B))
| ~ member(ordered_pair(C,D),E)
| member(C,A) ),
file('SET681+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| ilf_type(C,subset_type(cross_product(A,B))) ),
file('SET681+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ ilf_type(A,set_type)
| empty(B)
| ~ ilf_type(B,set_type)
| ilf_type(A,member_type(B))
| ~ member(A,B) ),
file('SET681+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ ilf_type(A,set_type)
| ilf_type(A,binary_relation_type)
| ~ relation_like(A) ),
file('SET681+3.p',unknown),
[] ).
cnf(51,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| relation_like(C) ),
file('SET681+3.p',unknown),
[] ).
cnf(54,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| range(A,B,C) = range_of(C) ),
file('SET681+3.p',unknown),
[] ).
cnf(57,axiom,
~ empty(dollar_c5),
file('SET681+3.p',unknown),
[] ).
cnf(58,axiom,
( ~ member(dollar_c3,range(dollar_c5,dollar_c6,dollar_c4))
| ~ ilf_type(A,member_type(dollar_c5))
| ~ member(ordered_pair(A,dollar_c3),dollar_c4) ),
file('SET681+3.p',unknown),
[] ).
cnf(134,axiom,
ilf_type(A,set_type),
file('SET681+3.p',unknown),
[] ).
cnf(135,axiom,
ilf_type(dollar_c4,relation_type(dollar_c5,dollar_c6)),
file('SET681+3.p',unknown),
[] ).
cnf(138,axiom,
( member(dollar_c3,range(dollar_c5,dollar_c6,dollar_c4))
| member(ordered_pair(dollar_c2,dollar_c3),dollar_c4) ),
file('SET681+3.p',unknown),
[] ).
cnf(176,plain,
range_of(dollar_c4) = range(dollar_c5,dollar_c6,dollar_c4),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[135,54,134,134])]),
[iquote('hyper,135,54,134,134,flip.1')] ).
cnf(180,plain,
ilf_type(dollar_c4,subset_type(cross_product(dollar_c5,dollar_c6))),
inference(hyper,[status(thm)],[135,13,134,134]),
[iquote('hyper,135,13,134,134')] ).
cnf(250,plain,
relation_like(dollar_c4),
inference(hyper,[status(thm)],[180,51,134,134]),
[iquote('hyper,180,51,134,134')] ).
cnf(258,plain,
ilf_type(dollar_c4,binary_relation_type),
inference(hyper,[status(thm)],[250,28,134]),
[iquote('hyper,250,28,134')] ).
cnf(261,plain,
member(dollar_c3,range(dollar_c5,dollar_c6,dollar_c4)),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[258,3,134,134,138]),176])]),
[iquote('hyper,258,3,134,134,138,demod,176,factor_simp')] ).
cnf(403,plain,
( ~ member(A,range(dollar_c5,dollar_c6,dollar_c4))
| member(ordered_pair(dollar_f1(A,dollar_c4),A),dollar_c4) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[176,2]),134,258]),
[iquote('para_from,175.1.1,2.3.2,unit_del,134,258')] ).
cnf(1776,plain,
member(ordered_pair(dollar_f1(dollar_c3,dollar_c4),dollar_c3),dollar_c4),
inference(hyper,[status(thm)],[403,261]),
[iquote('hyper,403,261')] ).
cnf(1784,plain,
member(dollar_f1(dollar_c3,dollar_c4),dollar_c5),
inference(hyper,[status(thm)],[1776,5,134,134,134,134,135]),
[iquote('hyper,1776,5,134,134,134,134,135')] ).
cnf(1793,plain,
ilf_type(dollar_f1(dollar_c3,dollar_c4),member_type(dollar_c5)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[1784,16,134,134]),57]),
[iquote('hyper,1784,16,134,134,unit_del,57')] ).
cnf(1811,plain,
$false,
inference(hyper,[status(thm)],[1793,58,261,1776]),
[iquote('hyper,1793,58,261,1776')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n023.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 11:04:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.12/2.31 ----- Otter 3.3f, August 2004 -----
% 2.12/2.31 The process was started by sandbox on n023.cluster.edu,
% 2.12/2.31 Wed Jul 27 11:04:33 2022
% 2.12/2.31 The command was "./otter". The process ID is 27327.
% 2.12/2.31
% 2.12/2.31 set(prolog_style_variables).
% 2.12/2.31 set(auto).
% 2.12/2.31 dependent: set(auto1).
% 2.12/2.31 dependent: set(process_input).
% 2.12/2.31 dependent: clear(print_kept).
% 2.12/2.31 dependent: clear(print_new_demod).
% 2.12/2.31 dependent: clear(print_back_demod).
% 2.12/2.31 dependent: clear(print_back_sub).
% 2.12/2.31 dependent: set(control_memory).
% 2.12/2.31 dependent: assign(max_mem, 12000).
% 2.12/2.31 dependent: assign(pick_given_ratio, 4).
% 2.12/2.31 dependent: assign(stats_level, 1).
% 2.12/2.31 dependent: assign(max_seconds, 10800).
% 2.12/2.31 clear(print_given).
% 2.12/2.31
% 2.12/2.31 formula_list(usable).
% 2.12/2.31 all A (A=A).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,binary_relation_type)-> (member(B,range_of(C))<-> (exists D (ilf_type(D,set_type)&member(ordered_pair(D,B),C))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,binary_relation_type)-> (member(ordered_pair(B,C),D)->member(B,domain_of(D))&member(C,range_of(D)))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,set_type)-> (all E (ilf_type(E,set_type)-> (all F (ilf_type(F,relation_type(B,C))-> (member(ordered_pair(D,E),F)->member(D,B)&member(E,C))))))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,set_type)-> (all E (ilf_type(E,set_type)-> (all F (ilf_type(F,set_type)-> (F=ordered_pair(D,E)<->F=unordered_pair(unordered_pair(D,E),singleton(D)))))))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,subset_type(cross_product(B,C)))->ilf_type(D,relation_type(B,C))))& (all E (ilf_type(E,relation_type(B,C))->ilf_type(E,subset_type(cross_product(B,C)))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (exists D ilf_type(D,relation_type(C,B)))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (-empty(C)&ilf_type(C,set_type)-> (ilf_type(B,member_type(C))<->member(B,C))))).
% 2.12/2.31 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 2.12/2.31 all B (ilf_type(B,binary_relation_type)->ilf_type(domain_of(B),set_type)).
% 2.12/2.31 all B (ilf_type(B,set_type)->ilf_type(singleton(B),set_type)).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 2.12/2.31 all B (ilf_type(B,binary_relation_type)->ilf_type(range_of(B),set_type)).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(unordered_pair(B,C),set_type)))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->unordered_pair(B,C)=unordered_pair(C,B)))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (ilf_type(B,binary_relation_type)<->relation_like(B)&ilf_type(B,set_type))).
% 2.12/2.31 exists B ilf_type(B,binary_relation_type).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (ilf_type(C,subset_type(B))<->ilf_type(C,member_type(power_set(B))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (B=C<-> (all D (ilf_type(D,set_type)-> (member(D,B)<->member(D,C)))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (member(B,power_set(C))<-> (all D (ilf_type(D,set_type)-> (member(D,B)->member(D,C)))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (relation_like(B)<-> (all C (ilf_type(C,set_type)-> (member(C,B)-> (exists D (ilf_type(D,set_type)& (exists E (ilf_type(E,set_type)&C=ordered_pair(D,E)))))))))).
% 2.12/2.31 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,subset_type(cross_product(B,C)))->relation_like(D)))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->domain(B,C,D)=domain_of(D)))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->ilf_type(domain(B,C,D),subset_type(B))))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->range(B,C,D)=range_of(D)))))).
% 2.12/2.31 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->ilf_type(range(B,C,D),subset_type(C))))))).
% 2.12/2.31 all B ilf_type(B,set_type).
% 2.12/2.31 -(all B (-empty(B)&ilf_type(B,set_type)-> (all C (-empty(C)&ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(C,B))-> (all E (ilf_type(E,member_type(B))-> (member(E,range(C,B,D))<-> (exists F (ilf_type(F,member_type(C))&member(ordered_pair(F,E),D)))))))))))).
% 2.12/2.31 end_of_list.
% 2.12/2.31
% 2.12/2.31 -------> usable clausifies to:
% 2.12/2.31
% 2.12/2.31 list(usable).
% 2.12/2.31 0 [] A=A.
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,binary_relation_type)| -member(B,range_of(C))|ilf_type($f1(B,C),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,binary_relation_type)| -member(B,range_of(C))|member(ordered_pair($f1(B,C),B),C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,binary_relation_type)|member(B,range_of(C))| -ilf_type(D,set_type)| -member(ordered_pair(D,B),C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,binary_relation_type)| -member(ordered_pair(B,C),D)|member(B,domain_of(D)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,binary_relation_type)| -member(ordered_pair(B,C),D)|member(C,range_of(D)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -ilf_type(F,relation_type(B,C))| -member(ordered_pair(D,E),F)|member(D,B).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -ilf_type(F,relation_type(B,C))| -member(ordered_pair(D,E),F)|member(E,C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -ilf_type(F,set_type)|F!=ordered_pair(D,E)|F=unordered_pair(unordered_pair(D,E),singleton(D)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -ilf_type(F,set_type)|F=ordered_pair(D,E)|F!=unordered_pair(unordered_pair(D,E),singleton(D)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|ilf_type(D,relation_type(B,C)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(E,relation_type(B,C))|ilf_type(E,subset_type(cross_product(B,C))).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type($f2(B,C),relation_type(C,B)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 2.12/2.31 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f3(B),member_type(B)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f4(B),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|empty(B)|member($f4(B),B).
% 2.12/2.31 0 [] -ilf_type(B,binary_relation_type)|ilf_type(domain_of(B),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|ilf_type(singleton(B),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 2.12/2.31 0 [] -ilf_type(B,binary_relation_type)|ilf_type(range_of(B),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(unordered_pair(B,C),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|unordered_pair(B,C)=unordered_pair(C,B).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(B,binary_relation_type)|relation_like(B).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|ilf_type(B,binary_relation_type)| -relation_like(B).
% 2.12/2.31 0 [] ilf_type($c1,binary_relation_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(C,subset_type(B))|ilf_type(C,member_type(power_set(B))).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(C,subset_type(B))| -ilf_type(C,member_type(power_set(B))).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|ilf_type($f5(B),subset_type(B)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C| -ilf_type(D,set_type)|member(D,B)| -member(D,C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C|ilf_type($f6(B,C),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C|member($f6(B,C),B)|member($f6(B,C),C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C| -member($f6(B,C),B)| -member($f6(B,C),C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(B,power_set(C))| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f7(B,C),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f7(B,C),B).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f7(B,C),C).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f9(B,C),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f8(B,C),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|C=ordered_pair($f9(B,C),$f8(B,C)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f10(B),set_type).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f10(B),B).
% 2.12/2.31 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f10(B)!=ordered_pair(D,E).
% 2.12/2.31 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|domain(B,C,D)=domain_of(D).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|ilf_type(domain(B,C,D),subset_type(B)).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|range(B,C,D)=range_of(D).
% 2.12/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|ilf_type(range(B,C,D),subset_type(C)).
% 2.12/2.31 0 [] ilf_type(B,set_type).
% 2.12/2.31 0 [] -empty($c6).
% 2.12/2.31 0 [] ilf_type($c6,set_type).
% 2.12/2.31 0 [] -empty($c5).
% 2.12/2.31 0 [] ilf_type($c5,set_type).
% 2.12/2.31 0 [] ilf_type($c4,relation_type($c5,$c6)).
% 2.12/2.31 0 [] ilf_type($c3,member_type($c6)).
% 2.12/2.31 0 [] member($c3,range($c5,$c6,$c4))|ilf_type($c2,member_type($c5)).
% 2.12/2.31 0 [] member($c3,range($c5,$c6,$c4))|member(ordered_pair($c2,$c3),$c4).
% 2.12/2.31 0 [] -member($c3,range($c5,$c6,$c4))| -ilf_type(F,member_type($c5))| -member(ordered_pair(F,$c3),$c4).
% 2.12/2.31 end_of_list.
% 2.12/2.31
% 2.12/2.31 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 2.12/2.31
% 2.12/2.31 This ia a non-Horn set with equality. The strategy will be
% 2.12/2.31 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.12/2.31 deletion, with positive clauses in sos and nonpositive
% 2.12/2.31 clauses in usable.
% 2.12/2.31
% 2.12/2.31 dependent: set(knuth_bendix).
% 2.12/2.31 dependent: set(anl_eq).
% 2.12/2.31 dependent: set(para_from).
% 2.12/2.31 dependent: set(para_into).
% 2.12/2.31 dependent: clear(para_from_right).
% 2.12/2.31 dependent: clear(para_into_right).
% 2.12/2.31 dependent: set(para_from_vars).
% 2.12/2.31 dependent: set(eq_units_both_ways).
% 2.12/2.31 dependent: set(dynamic_demod_all).
% 2.12/2.31 dependent: set(dynamic_demod).
% 2.12/2.31 dependent: set(order_eq).
% 2.12/2.31 dependent: set(back_demod).
% 2.12/2.31 dependent: set(lrpo).
% 2.12/2.31 dependent: set(hyper_res).
% 2.12/2.31 dependent: set(unit_deletion).
% 2.12/2.31 dependent: set(factor).
% 2.12/2.31
% 2.12/2.31 ------------> process usable:
% 2.12/2.31 ** KEPT (pick-wt=15): 1 [] -ilf_type(A,set_type)| -ilf_type(B,binary_relation_type)| -member(A,range_of(B))|ilf_type($f1(A,B),set_type).
% 2.12/2.31 ** KEPT (pick-wt=17): 2 [] -ilf_type(A,set_type)| -ilf_type(B,binary_relation_type)| -member(A,range_of(B))|member(ordered_pair($f1(A,B),A),B).
% 2.12/2.31 ** KEPT (pick-wt=18): 3 [] -ilf_type(A,set_type)| -ilf_type(B,binary_relation_type)|member(A,range_of(B))| -ilf_type(C,set_type)| -member(ordered_pair(C,A),B).
% 2.12/2.31 ** KEPT (pick-wt=18): 4 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,binary_relation_type)| -member(ordered_pair(A,B),C)|member(A,domain_of(C)).
% 2.12/2.31 Following clause subsumed by 3 during input processing: 0 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,binary_relation_type)| -member(ordered_pair(A,B),C)|member(B,range_of(C)).
% 2.19/2.34 ** KEPT (pick-wt=25): 5 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,relation_type(A,B))| -member(ordered_pair(C,D),E)|member(C,A).
% 2.19/2.34 ** KEPT (pick-wt=25): 6 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,relation_type(A,B))| -member(ordered_pair(C,D),E)|member(D,B).
% 2.19/2.34 ** KEPT (pick-wt=22): 8 [copy,7,factor_simp,factor_simp] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|C!=ordered_pair(A,B)|C=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.19/2.34 ** KEPT (pick-wt=22): 10 [copy,9,factor_simp,factor_simp] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|C=ordered_pair(A,B)|C!=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.19/2.34 ** KEPT (pick-wt=11): 11 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 2.19/2.34 ** KEPT (pick-wt=17): 12 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B)).
% 2.19/2.34 ** KEPT (pick-wt=17): 13 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(C,subset_type(cross_product(A,B))).
% 2.19/2.34 ** KEPT (pick-wt=13): 14 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type($f2(A,B),relation_type(B,A)).
% 2.19/2.34 ** KEPT (pick-wt=15): 15 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 2.19/2.34 ** KEPT (pick-wt=15): 16 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)|ilf_type(A,member_type(B))| -member(A,B).
% 2.19/2.34 ** KEPT (pick-wt=10): 17 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f3(A),member_type(A)).
% 2.19/2.34 ** KEPT (pick-wt=11): 18 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 2.19/2.34 ** KEPT (pick-wt=9): 19 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f4(A),set_type).
% 2.19/2.34 ** KEPT (pick-wt=9): 20 [] -ilf_type(A,set_type)|empty(A)|member($f4(A),A).
% 2.19/2.34 ** KEPT (pick-wt=7): 21 [] -ilf_type(A,binary_relation_type)|ilf_type(domain_of(A),set_type).
% 2.19/2.34 ** KEPT (pick-wt=7): 22 [] -ilf_type(A,set_type)|ilf_type(singleton(A),set_type).
% 2.19/2.34 ** KEPT (pick-wt=11): 23 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 2.19/2.34 ** KEPT (pick-wt=7): 24 [] -ilf_type(A,binary_relation_type)|ilf_type(range_of(A),set_type).
% 2.19/2.34 ** KEPT (pick-wt=11): 25 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(unordered_pair(A,B),set_type).
% 2.19/2.34 ** KEPT (pick-wt=13): 26 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|unordered_pair(A,B)=unordered_pair(B,A).
% 2.19/2.34 ** KEPT (pick-wt=8): 27 [] -ilf_type(A,set_type)| -ilf_type(A,binary_relation_type)|relation_like(A).
% 2.19/2.34 ** KEPT (pick-wt=8): 28 [] -ilf_type(A,set_type)|ilf_type(A,binary_relation_type)| -relation_like(A).
% 2.19/2.34 ** KEPT (pick-wt=15): 29 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A))).
% 2.19/2.34 ** KEPT (pick-wt=15): 30 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,subset_type(A))| -ilf_type(B,member_type(power_set(A))).
% 2.19/2.34 ** KEPT (pick-wt=8): 31 [] -ilf_type(A,set_type)|ilf_type($f5(A),subset_type(A)).
% 2.19/2.34 ** KEPT (pick-wt=18): 32 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 2.19/2.34 ** KEPT (pick-wt=18): 33 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B| -ilf_type(C,set_type)|member(C,A)| -member(C,B).
% 2.19/2.34 ** KEPT (pick-wt=14): 34 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B|ilf_type($f6(A,B),set_type).
% 2.19/2.34 ** KEPT (pick-wt=19): 35 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B|member($f6(A,B),A)|member($f6(A,B),B).
% 2.19/2.34 ** KEPT (pick-wt=19): 36 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B| -member($f6(A,B),A)| -member($f6(A,B),B).
% 2.19/2.34 ** KEPT (pick-wt=19): 37 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -member(A,power_set(B))| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 2.19/2.34 ** KEPT (pick-wt=15): 38 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f7(A,B),set_type).
% 2.19/2.34 ** KEPT (pick-wt=15): 39 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f7(A,B),A).
% 4.69/4.88 ** KEPT (pick-wt=15): 40 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f7(A,B),B).
% 4.69/4.88 ** KEPT (pick-wt=6): 41 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 4.69/4.88 ** KEPT (pick-wt=7): 42 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 4.69/4.88 ** KEPT (pick-wt=16): 43 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f9(A,B),set_type).
% 4.69/4.88 ** KEPT (pick-wt=16): 44 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f8(A,B),set_type).
% 4.69/4.88 ** KEPT (pick-wt=20): 46 [copy,45,flip.5] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ordered_pair($f9(A,B),$f8(A,B))=B.
% 4.69/4.88 ** KEPT (pick-wt=9): 47 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f10(A),set_type).
% 4.69/4.88 ** KEPT (pick-wt=9): 48 [] -ilf_type(A,set_type)|relation_like(A)|member($f10(A),A).
% 4.69/4.88 ** KEPT (pick-wt=17): 49 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f10(A)!=ordered_pair(B,C).
% 4.69/4.88 ** KEPT (pick-wt=7): 50 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 4.69/4.88 ** KEPT (pick-wt=14): 51 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 4.69/4.88 ** KEPT (pick-wt=18): 52 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|domain(A,B,C)=domain_of(C).
% 4.69/4.88 ** KEPT (pick-wt=18): 53 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(domain(A,B,C),subset_type(A)).
% 4.69/4.88 ** KEPT (pick-wt=18): 54 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|range(A,B,C)=range_of(C).
% 4.69/4.88 ** KEPT (pick-wt=18): 55 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(range(A,B,C),subset_type(B)).
% 4.69/4.88 ** KEPT (pick-wt=2): 56 [] -empty($c6).
% 4.69/4.88 ** KEPT (pick-wt=2): 57 [] -empty($c5).
% 4.69/4.88 ** KEPT (pick-wt=15): 58 [] -member($c3,range($c5,$c6,$c4))| -ilf_type(A,member_type($c5))| -member(ordered_pair(A,$c3),$c4).
% 4.69/4.88
% 4.69/4.88 ------------> process sos:
% 4.69/4.88 ** KEPT (pick-wt=3): 132 [] A=A.
% 4.69/4.88 ** KEPT (pick-wt=3): 133 [] ilf_type($c1,binary_relation_type).
% 4.69/4.88 ** KEPT (pick-wt=3): 134 [] ilf_type(A,set_type).
% 4.69/4.88 Following clause subsumed by 134 during input processing: 0 [] ilf_type($c6,set_type).
% 4.69/4.88 Following clause subsumed by 134 during input processing: 0 [] ilf_type($c5,set_type).
% 4.69/4.88 ** KEPT (pick-wt=5): 135 [] ilf_type($c4,relation_type($c5,$c6)).
% 4.69/4.88 ** KEPT (pick-wt=4): 136 [] ilf_type($c3,member_type($c6)).
% 4.69/4.88 ** KEPT (pick-wt=10): 137 [] member($c3,range($c5,$c6,$c4))|ilf_type($c2,member_type($c5)).
% 4.69/4.88 ** KEPT (pick-wt=11): 138 [] member($c3,range($c5,$c6,$c4))|member(ordered_pair($c2,$c3),$c4).
% 4.69/4.88 Following clause subsumed by 132 during input processing: 0 [copy,132,flip.1] A=A.
% 4.69/4.88 132 back subsumes 97.
% 4.69/4.88 132 back subsumes 96.
% 4.69/4.88 132 back subsumes 95.
% 4.69/4.88 132 back subsumes 88.
% 4.69/4.88 134 back subsumes 105.
% 4.69/4.88 134 back subsumes 104.
% 4.69/4.88 134 back subsumes 101.
% 4.69/4.88 134 back subsumes 87.
% 4.69/4.88 134 back subsumes 86.
% 4.69/4.88 134 back subsumes 79.
% 4.69/4.88 134 back subsumes 47.
% 4.69/4.88 134 back subsumes 44.
% 4.69/4.88 134 back subsumes 43.
% 4.69/4.88 134 back subsumes 42.
% 4.69/4.88 134 back subsumes 38.
% 4.69/4.88 134 back subsumes 34.
% 4.69/4.88 134 back subsumes 25.
% 4.69/4.88 134 back subsumes 24.
% 4.69/4.88 134 back subsumes 23.
% 4.69/4.88 134 back subsumes 22.
% 4.69/4.88 134 back subsumes 21.
% 4.69/4.88 134 back subsumes 19.
% 4.69/4.88 134 back subsumes 11.
% 4.69/4.88 134 back subsumes 1.
% 4.69/4.88
% 4.69/4.88 ======= end of input processing =======
% 4.69/4.88
% 4.69/4.88 =========== start of search ===========
% 4.69/4.88
% 4.69/4.88
% 4.69/4.88 Resetting weight limit to 11.
% 4.69/4.88
% 4.69/4.88
% 4.69/4.88 Resetting weight limit to 11.
% 4.69/4.88
% 4.69/4.88 sos_size=782
% 4.69/4.88
% 4.69/4.88
% 4.69/4.88 Resetting weight limit to 10.
% 4.69/4.88
% 4.69/4.88
% 4.69/4.88 Resetting weight limit to 10.
% 4.69/4.88
% 4.69/4.88 sos_size=798
% 4.69/4.88
% 4.69/4.88 -------- PROOF --------
% 4.69/4.88
% 4.69/4.88 -----> EMPTY CLAUSE at 2.55 sec ----> 1811 [hyper,1793,58,261,1776] $F.
% 4.69/4.88
% 4.69/4.88 Length of proof is 9. Level of proof is 7.
% 4.69/4.88
% 4.69/4.88 ---------------- PROOF ----------------
% 4.69/4.88 % SZS status Theorem
% 4.69/4.88 % SZS output start Refutation
% See solution above
% 4.69/4.88 ------------ end of proof -------------
% 4.69/4.88
% 4.69/4.88
% 4.69/4.88 Search stopped by max_proofs option.
% 4.69/4.88
% 4.69/4.88
% 4.69/4.88 Search stopped by max_proofs option.
% 4.69/4.88
% 4.69/4.88 ============ end of search ============
% 4.69/4.88
% 4.69/4.88 -------------- statistics -------------
% 4.69/4.88 clauses given 284
% 4.69/4.88 clauses generated 73964
% 4.69/4.88 clauses kept 1792
% 4.69/4.88 clauses forward subsumed 2181
% 4.69/4.88 clauses back subsumed 734
% 4.69/4.88 Kbytes malloced 7812
% 4.69/4.88
% 4.69/4.88 ----------- times (seconds) -----------
% 4.69/4.88 user CPU time 2.55 (0 hr, 0 min, 2 sec)
% 4.69/4.88 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 4.69/4.88 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 4.69/4.88
% 4.69/4.88 That finishes the proof of the theorem.
% 4.69/4.88
% 4.69/4.88 Process 27327 finished Wed Jul 27 11:04:37 2022
% 4.69/4.88 Otter interrupted
% 4.69/4.88 PROOF FOUND
%------------------------------------------------------------------------------