TSTP Solution File: SET682+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET682+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 1.99s 2.19s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 31 ( 16 unt; 3 nHn; 30 RR)
% Number of literals : 71 ( 4 equ; 40 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 31 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,binary_relation_type)
| ~ member(A,domain_of(B))
| member(dollar_f1(A,B),range_of(B)) ),
file('SET682+3.p',unknown),
[] ).
cnf(4,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('SET682+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ ilf_type(A,set_type)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,member_type(B))
| member(A,B) ),
file('SET682+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ ilf_type(A,set_type)
| empty(B)
| ~ ilf_type(B,set_type)
| ilf_type(A,member_type(B))
| ~ member(A,B) ),
file('SET682+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ ilf_type(A,set_type)
| ilf_type(A,binary_relation_type)
| ~ relation_like(A) ),
file('SET682+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(B,subset_type(A))
| ilf_type(B,member_type(power_set(A))) ),
file('SET682+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ 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) ),
file('SET682+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ ilf_type(A,set_type)
| ~ empty(power_set(A)) ),
file('SET682+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| relation_like(C) ),
file('SET682+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| domain(A,B,C) = domain_of(C) ),
file('SET682+3.p',unknown),
[] ).
cnf(38,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('SET682+3.p',unknown),
[] ).
cnf(39,axiom,
( ~ 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)) ),
file('SET682+3.p',unknown),
[] ).
cnf(41,axiom,
~ empty(dollar_c4),
file('SET682+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ ilf_type(A,member_type(dollar_c4))
| ~ member(A,range(dollar_c5,dollar_c4,dollar_c3)) ),
file('SET682+3.p',unknown),
[] ).
cnf(73,axiom,
ilf_type(A,set_type),
file('SET682+3.p',unknown),
[] ).
cnf(74,axiom,
ilf_type(dollar_c3,relation_type(dollar_c5,dollar_c4)),
file('SET682+3.p',unknown),
[] ).
cnf(76,axiom,
member(dollar_c2,domain(dollar_c5,dollar_c4,dollar_c3)),
file('SET682+3.p',unknown),
[] ).
cnf(87,plain,
ilf_type(range(dollar_c5,dollar_c4,dollar_c3),subset_type(dollar_c4)),
inference(hyper,[status(thm)],[74,39,73,73]),
[iquote('hyper,74,39,73,73')] ).
cnf(88,plain,
range_of(dollar_c3) = range(dollar_c5,dollar_c4,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[74,38,73,73])]),
[iquote('hyper,74,38,73,73,flip.1')] ).
cnf(92,plain,
domain_of(dollar_c3) = domain(dollar_c5,dollar_c4,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[74,36,73,73])]),
[iquote('hyper,74,36,73,73,flip.1')] ).
cnf(93,plain,
ilf_type(dollar_c3,subset_type(cross_product(dollar_c5,dollar_c4))),
inference(hyper,[status(thm)],[74,4,73,73]),
[iquote('hyper,74,4,73,73')] ).
cnf(145,plain,
relation_like(dollar_c3),
inference(hyper,[status(thm)],[93,34,73,73]),
[iquote('hyper,93,34,73,73')] ).
cnf(148,plain,
ilf_type(dollar_c3,binary_relation_type),
inference(hyper,[status(thm)],[145,16,73]),
[iquote('hyper,145,16,73')] ).
cnf(182,plain,
ilf_type(range(dollar_c5,dollar_c4,dollar_c3),member_type(power_set(dollar_c4))),
inference(hyper,[status(thm)],[87,17,73,73]),
[iquote('hyper,87,17,73,73')] ).
cnf(188,plain,
( ~ member(A,domain(dollar_c5,dollar_c4,dollar_c3))
| member(dollar_f1(A,dollar_c3),range(dollar_c5,dollar_c4,dollar_c3)) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[88,2]),92]),73,148]),
[iquote('para_from,88.1.1,2.4.2,demod,92,unit_del,73,148')] ).
cnf(382,plain,
( empty(power_set(dollar_c4))
| member(range(dollar_c5,dollar_c4,dollar_c3),power_set(dollar_c4)) ),
inference(hyper,[status(thm)],[182,6,73,73]),
[iquote('hyper,182,6,73,73')] ).
cnf(467,plain,
member(range(dollar_c5,dollar_c4,dollar_c3),power_set(dollar_c4)),
inference(hyper,[status(thm)],[382,24,73]),
[iquote('hyper,382,24,73')] ).
cnf(478,plain,
member(dollar_f1(dollar_c2,dollar_c3),range(dollar_c5,dollar_c4,dollar_c3)),
inference(hyper,[status(thm)],[188,76]),
[iquote('hyper,188,76')] ).
cnf(479,plain,
member(dollar_f1(dollar_c2,dollar_c3),dollar_c4),
inference(hyper,[status(thm)],[478,20,73,73,467,73]),
[iquote('hyper,478,20,73,73,467,73')] ).
cnf(480,plain,
ilf_type(dollar_f1(dollar_c2,dollar_c3),member_type(dollar_c4)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[479,7,73,73]),41]),
[iquote('hyper,479,7,73,73,unit_del,41')] ).
cnf(481,plain,
$false,
inference(hyper,[status(thm)],[480,42,478]),
[iquote('hyper,480,42,478')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET682+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 10:57:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.83/2.04 ----- Otter 3.3f, August 2004 -----
% 1.83/2.04 The process was started by sandbox2 on n018.cluster.edu,
% 1.83/2.04 Wed Jul 27 10:57:16 2022
% 1.83/2.04 The command was "./otter". The process ID is 21119.
% 1.83/2.04
% 1.83/2.04 set(prolog_style_variables).
% 1.83/2.04 set(auto).
% 1.83/2.04 dependent: set(auto1).
% 1.83/2.04 dependent: set(process_input).
% 1.83/2.04 dependent: clear(print_kept).
% 1.83/2.04 dependent: clear(print_new_demod).
% 1.83/2.04 dependent: clear(print_back_demod).
% 1.83/2.04 dependent: clear(print_back_sub).
% 1.83/2.04 dependent: set(control_memory).
% 1.83/2.04 dependent: assign(max_mem, 12000).
% 1.83/2.04 dependent: assign(pick_given_ratio, 4).
% 1.83/2.04 dependent: assign(stats_level, 1).
% 1.83/2.04 dependent: assign(max_seconds, 10800).
% 1.83/2.04 clear(print_given).
% 1.83/2.04
% 1.83/2.04 formula_list(usable).
% 1.83/2.04 all A (A=A).
% 1.83/2.04 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,binary_relation_type)-> (member(B,domain_of(C))-> (exists D (ilf_type(D,set_type)&member(D,range_of(C)))))))).
% 1.83/2.04 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)))))))).
% 1.83/2.04 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (exists D ilf_type(D,relation_type(C,B)))))).
% 1.83/2.04 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))))).
% 1.83/2.04 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 1.83/2.04 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 1.83/2.04 all B (ilf_type(B,binary_relation_type)->ilf_type(domain_of(B),set_type)).
% 1.83/2.04 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 1.83/2.04 all B (ilf_type(B,binary_relation_type)->ilf_type(range_of(B),set_type)).
% 1.83/2.04 all B (ilf_type(B,set_type)-> (ilf_type(B,binary_relation_type)<->relation_like(B)&ilf_type(B,set_type))).
% 1.83/2.04 exists B ilf_type(B,binary_relation_type).
% 1.83/2.04 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))))))).
% 1.83/2.04 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 1.83/2.04 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)))))))).
% 1.83/2.04 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 1.83/2.04 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)))))))))).
% 1.83/2.04 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 1.83/2.04 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)))))).
% 1.83/2.04 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 1.83/2.04 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)))))).
% 1.83/2.04 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))))))).
% 1.83/2.04 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)))))).
% 1.83/2.04 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))))))).
% 1.83/2.04 all B ilf_type(B,set_type).
% 1.83/2.04 -(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(B,C))-> (all E (ilf_type(E,member_type(B))-> (member(E,domain(B,C,D))-> (exists F (ilf_type(F,member_type(C))&member(F,range(B,C,D))))))))))))).
% 1.83/2.04 end_of_list.
% 1.83/2.04
% 1.83/2.04 -------> usable clausifies to:
% 1.83/2.04
% 1.83/2.04 list(usable).
% 1.83/2.04 0 [] A=A.
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,binary_relation_type)| -member(B,domain_of(C))|ilf_type($f1(B,C),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,binary_relation_type)| -member(B,domain_of(C))|member($f1(B,C),range_of(C)).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|ilf_type(D,relation_type(B,C)).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(E,relation_type(B,C))|ilf_type(E,subset_type(cross_product(B,C))).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type($f2(B,C),relation_type(C,B)).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 1.83/2.04 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f3(B),member_type(B)).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f4(B),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|empty(B)|member($f4(B),B).
% 1.83/2.04 0 [] -ilf_type(B,binary_relation_type)|ilf_type(domain_of(B),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 1.83/2.04 0 [] -ilf_type(B,binary_relation_type)|ilf_type(range_of(B),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(B,binary_relation_type)|relation_like(B).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|ilf_type(B,binary_relation_type)| -relation_like(B).
% 1.83/2.04 0 [] ilf_type($c1,binary_relation_type).
% 1.83/2.04 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))).
% 1.83/2.04 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))).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|ilf_type($f5(B),subset_type(B)).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(B,power_set(C))| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f6(B,C),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f6(B,C),B).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f6(B,C),C).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f8(B,C),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f7(B,C),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|C=ordered_pair($f8(B,C),$f7(B,C)).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f9(B),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f9(B),B).
% 1.83/2.04 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f9(B)!=ordered_pair(D,E).
% 1.83/2.04 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|domain(B,C,D)=domain_of(D).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|ilf_type(domain(B,C,D),subset_type(B)).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|range(B,C,D)=range_of(D).
% 1.83/2.04 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|ilf_type(range(B,C,D),subset_type(C)).
% 1.83/2.04 0 [] ilf_type(B,set_type).
% 1.83/2.04 0 [] -empty($c5).
% 1.83/2.04 0 [] ilf_type($c5,set_type).
% 1.83/2.04 0 [] -empty($c4).
% 1.83/2.04 0 [] ilf_type($c4,set_type).
% 1.83/2.04 0 [] ilf_type($c3,relation_type($c5,$c4)).
% 1.83/2.04 0 [] ilf_type($c2,member_type($c5)).
% 1.83/2.04 0 [] member($c2,domain($c5,$c4,$c3)).
% 1.83/2.04 0 [] -ilf_type(F,member_type($c4))| -member(F,range($c5,$c4,$c3)).
% 1.83/2.04 end_of_list.
% 1.83/2.04
% 1.83/2.04 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.83/2.04
% 1.83/2.04 This ia a non-Horn set with equality. The strategy will be
% 1.83/2.04 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.83/2.04 deletion, with positive clauses in sos and nonpositive
% 1.83/2.04 clauses in usable.
% 1.83/2.04
% 1.83/2.04 dependent: set(knuth_bendix).
% 1.83/2.04 dependent: set(anl_eq).
% 1.83/2.04 dependent: set(para_from).
% 1.83/2.04 dependent: set(para_into).
% 1.83/2.04 dependent: clear(para_from_right).
% 1.83/2.04 dependent: clear(para_into_right).
% 1.83/2.04 dependent: set(para_from_vars).
% 1.83/2.04 dependent: set(eq_units_both_ways).
% 1.83/2.04 dependent: set(dynamic_demod_all).
% 1.83/2.04 dependent: set(dynamic_demod).
% 1.83/2.04 dependent: set(order_eq).
% 1.83/2.04 dependent: set(back_demod).
% 1.83/2.04 dependent: set(lrpo).
% 1.83/2.04 dependent: set(hyper_res).
% 1.83/2.04 dependent: set(unit_deletion).
% 1.83/2.04 dependent: set(factor).
% 1.83/2.04
% 1.83/2.04 ------------> process usable:
% 1.83/2.04 ** KEPT (pick-wt=15): 1 [] -ilf_type(A,set_type)| -ilf_type(B,binary_relation_type)| -member(A,domain_of(B))|ilf_type($f1(A,B),set_type).
% 1.83/2.04 ** KEPT (pick-wt=16): 2 [] -ilf_type(A,set_type)| -ilf_type(B,binary_relation_type)| -member(A,domain_of(B))|member($f1(A,B),range_of(B)).
% 1.83/2.04 ** KEPT (pick-wt=17): 3 [] -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)).
% 1.83/2.04 ** KEPT (pick-wt=17): 4 [] -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))).
% 1.83/2.04 ** KEPT (pick-wt=13): 5 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type($f2(A,B),relation_type(B,A)).
% 1.83/2.04 ** KEPT (pick-wt=15): 6 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 1.83/2.04 ** KEPT (pick-wt=15): 7 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)|ilf_type(A,member_type(B))| -member(A,B).
% 1.83/2.04 ** KEPT (pick-wt=10): 8 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f3(A),member_type(A)).
% 1.83/2.04 ** KEPT (pick-wt=11): 9 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 1.83/2.04 ** KEPT (pick-wt=9): 10 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f4(A),set_type).
% 1.83/2.04 ** KEPT (pick-wt=9): 11 [] -ilf_type(A,set_type)|empty(A)|member($f4(A),A).
% 1.83/2.04 ** KEPT (pick-wt=7): 12 [] -ilf_type(A,binary_relation_type)|ilf_type(domain_of(A),set_type).
% 1.83/2.04 ** KEPT (pick-wt=11): 13 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 1.83/2.04 ** KEPT (pick-wt=7): 14 [] -ilf_type(A,binary_relation_type)|ilf_type(range_of(A),set_type).
% 1.83/2.04 ** KEPT (pick-wt=8): 15 [] -ilf_type(A,set_type)| -ilf_type(A,binary_relation_type)|relation_like(A).
% 1.83/2.04 ** KEPT (pick-wt=8): 16 [] -ilf_type(A,set_type)|ilf_type(A,binary_relation_type)| -relation_like(A).
% 1.83/2.04 ** KEPT (pick-wt=15): 17 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A))).
% 1.83/2.04 ** KEPT (pick-wt=15): 18 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,subset_type(A))| -ilf_type(B,member_type(power_set(A))).
% 1.83/2.04 ** KEPT (pick-wt=8): 19 [] -ilf_type(A,set_type)|ilf_type($f5(A),subset_type(A)).
% 1.83/2.04 ** KEPT (pick-wt=19): 20 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -member(A,power_set(B))| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 1.83/2.04 ** KEPT (pick-wt=15): 21 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f6(A,B),set_type).
% 1.83/2.04 ** KEPT (pick-wt=15): 22 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f6(A,B),A).
% 1.83/2.04 ** KEPT (pick-wt=15): 23 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f6(A,B),B).
% 1.83/2.04 ** KEPT (pick-wt=6): 24 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 1.83/2.04 ** KEPT (pick-wt=7): 25 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 1.83/2.04 ** KEPT (pick-wt=16): 26 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f8(A,B),set_type).
% 1.83/2.04 ** KEPT (pick-wt=16): 27 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f7(A,B),set_type).
% 1.83/2.04 ** KEPT (pick-wt=20): 29 [copy,28,flip.5] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ordered_pair($f8(A,B),$f7(A,B))=B.
% 1.83/2.04 ** KEPT (pick-wt=9): 30 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f9(A),set_type).
% 1.83/2.04 ** KEPT (pick-wt=9): 31 [] -ilf_type(A,set_type)|relation_like(A)|member($f9(A),A).
% 1.83/2.04 ** KEPT (pick-wt=17): 32 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f9(A)!=ordered_pair(B,C).
% 1.83/2.04 ** KEPT (pick-wt=7): 33 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 1.83/2.04 ** KEPT (pick-wt=14): 34 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 1.83/2.04 ** KEPT (pick-wt=11): 35 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 1.99/2.19 ** KEPT (pick-wt=18): 36 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|domain(A,B,C)=domain_of(C).
% 1.99/2.19 ** KEPT (pick-wt=18): 37 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(domain(A,B,C),subset_type(A)).
% 1.99/2.19 ** KEPT (pick-wt=18): 38 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|range(A,B,C)=range_of(C).
% 1.99/2.19 ** KEPT (pick-wt=18): 39 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(range(A,B,C),subset_type(B)).
% 1.99/2.19 ** KEPT (pick-wt=2): 40 [] -empty($c5).
% 1.99/2.19 ** KEPT (pick-wt=2): 41 [] -empty($c4).
% 1.99/2.19 ** KEPT (pick-wt=10): 42 [] -ilf_type(A,member_type($c4))| -member(A,range($c5,$c4,$c3)).
% 1.99/2.19
% 1.99/2.19 ------------> process sos:
% 1.99/2.19 ** KEPT (pick-wt=3): 71 [] A=A.
% 1.99/2.19 ** KEPT (pick-wt=3): 72 [] ilf_type($c1,binary_relation_type).
% 1.99/2.19 ** KEPT (pick-wt=3): 73 [] ilf_type(A,set_type).
% 1.99/2.19 Following clause subsumed by 73 during input processing: 0 [] ilf_type($c5,set_type).
% 1.99/2.19 Following clause subsumed by 73 during input processing: 0 [] ilf_type($c4,set_type).
% 1.99/2.19 ** KEPT (pick-wt=5): 74 [] ilf_type($c3,relation_type($c5,$c4)).
% 1.99/2.19 ** KEPT (pick-wt=4): 75 [] ilf_type($c2,member_type($c5)).
% 1.99/2.19 ** KEPT (pick-wt=6): 76 [] member($c2,domain($c5,$c4,$c3)).
% 1.99/2.19 Following clause subsumed by 71 during input processing: 0 [copy,71,flip.1] A=A.
% 1.99/2.19 73 back subsumes 65.
% 1.99/2.19 73 back subsumes 59.
% 1.99/2.19 73 back subsumes 58.
% 1.99/2.19 73 back subsumes 55.
% 1.99/2.19 73 back subsumes 49.
% 1.99/2.19 73 back subsumes 35.
% 1.99/2.19 73 back subsumes 30.
% 1.99/2.19 73 back subsumes 27.
% 1.99/2.19 73 back subsumes 26.
% 1.99/2.19 73 back subsumes 25.
% 1.99/2.19 73 back subsumes 21.
% 1.99/2.19 73 back subsumes 14.
% 1.99/2.19 73 back subsumes 13.
% 1.99/2.19 73 back subsumes 12.
% 1.99/2.19 73 back subsumes 10.
% 1.99/2.19 73 back subsumes 1.
% 1.99/2.19
% 1.99/2.19 ======= end of input processing =======
% 1.99/2.19
% 1.99/2.19 =========== start of search ===========
% 1.99/2.19
% 1.99/2.19
% 1.99/2.19 Resetting weight limit to 9.
% 1.99/2.19
% 1.99/2.19
% 1.99/2.19 Resetting weight limit to 9.
% 1.99/2.19
% 1.99/2.19 sos_size=180
% 1.99/2.19
% 1.99/2.19 -------- PROOF --------
% 1.99/2.19
% 1.99/2.19 -----> EMPTY CLAUSE at 0.15 sec ----> 481 [hyper,480,42,478] $F.
% 1.99/2.19
% 1.99/2.19 Length of proof is 13. Level of proof is 7.
% 1.99/2.19
% 1.99/2.19 ---------------- PROOF ----------------
% 1.99/2.19 % SZS status Theorem
% 1.99/2.19 % SZS output start Refutation
% See solution above
% 1.99/2.19 ------------ end of proof -------------
% 1.99/2.19
% 1.99/2.19
% 1.99/2.19 Search stopped by max_proofs option.
% 1.99/2.19
% 1.99/2.19
% 1.99/2.19 Search stopped by max_proofs option.
% 1.99/2.19
% 1.99/2.19 ============ end of search ============
% 1.99/2.19
% 1.99/2.19 -------------- statistics -------------
% 1.99/2.19 clauses given 174
% 1.99/2.19 clauses generated 12301
% 1.99/2.19 clauses kept 465
% 1.99/2.19 clauses forward subsumed 579
% 1.99/2.19 clauses back subsumed 146
% 1.99/2.19 Kbytes malloced 5859
% 1.99/2.19
% 1.99/2.19 ----------- times (seconds) -----------
% 1.99/2.19 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 1.99/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.99/2.19
% 1.99/2.19 That finishes the proof of the theorem.
% 1.99/2.19
% 1.99/2.19 Process 21119 finished Wed Jul 27 10:57:18 2022
% 1.99/2.19 Otter interrupted
% 1.99/2.19 PROOF FOUND
%------------------------------------------------------------------------------