TSTP Solution File: SET645+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:13:58 EDT 2022
% Result : Theorem 2.66s 2.82s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 35 ( 16 unt; 8 nHn; 24 RR)
% Number of literals : 81 ( 0 equ; 41 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(A,B),cross_product(C,D))
| member(A,C) ),
file('SET645+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(A,B),cross_product(C,D))
| member(B,D) ),
file('SET645+3.p',unknown),
[] ).
cnf(10,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('SET645+3.p',unknown),
[] ).
cnf(16,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('SET645+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ ilf_type(A,set_type)
| ilf_type(dollar_f2(A),subset_type(A)) ),
file('SET645+3.p',unknown),
[] ).
cnf(24,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('SET645+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| member(A,power_set(B))
| member(dollar_f4(A,B),A) ),
file('SET645+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| member(A,power_set(B))
| ~ member(dollar_f4(A,B),B) ),
file('SET645+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ ilf_type(A,set_type)
| ~ empty(power_set(A)) ),
file('SET645+3.p',unknown),
[] ).
cnf(30,axiom,
( ~ ilf_type(A,set_type)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,member_type(B))
| member(A,B) ),
file('SET645+3.p',unknown),
[] ).
cnf(32,axiom,
( empty(A)
| ~ ilf_type(A,set_type)
| ilf_type(dollar_f5(A),member_type(A)) ),
file('SET645+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ ilf_type(A,set_type)
| ~ empty(A)
| ~ ilf_type(B,set_type)
| ~ member(B,A) ),
file('SET645+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ member(dollar_c3,dollar_c5)
| ~ member(dollar_c2,dollar_c4) ),
file('SET645+3.p',unknown),
[] ).
cnf(92,plain,
( ~ ilf_type(A,set_type)
| member(A,power_set(A))
| ~ member(dollar_f4(A,A),A) ),
inference(factor,[status(thm)],[27]),
[iquote('factor,27.1.2')] ).
cnf(128,axiom,
ilf_type(A,set_type),
file('SET645+3.p',unknown),
[] ).
cnf(129,axiom,
ilf_type(dollar_c1,relation_type(dollar_c5,dollar_c4)),
file('SET645+3.p',unknown),
[] ).
cnf(130,axiom,
member(ordered_pair(dollar_c3,dollar_c2),dollar_c1),
file('SET645+3.p',unknown),
[] ).
cnf(137,plain,
( empty(A)
| ilf_type(dollar_f5(A),member_type(A)) ),
inference(hyper,[status(thm)],[128,32]),
[iquote('hyper,128,32')] ).
cnf(138,plain,
( member(A,power_set(B))
| member(dollar_f4(A,B),A) ),
inference(hyper,[status(thm)],[128,26,128]),
[iquote('hyper,128,26,128')] ).
cnf(140,plain,
ilf_type(dollar_f2(A),subset_type(A)),
inference(hyper,[status(thm)],[128,18]),
[iquote('hyper,128,18')] ).
cnf(146,plain,
ilf_type(dollar_c1,subset_type(cross_product(dollar_c5,dollar_c4))),
inference(hyper,[status(thm)],[129,10,128,128]),
[iquote('hyper,129,10,128,128')] ).
cnf(160,plain,
ilf_type(dollar_f2(A),member_type(power_set(A))),
inference(hyper,[status(thm)],[140,16,128,128]),
[iquote('hyper,140,16,128,128')] ).
cnf(181,plain,
ilf_type(dollar_c1,member_type(power_set(cross_product(dollar_c5,dollar_c4)))),
inference(hyper,[status(thm)],[146,16,128,128]),
[iquote('hyper,146,16,128,128')] ).
cnf(189,plain,
ilf_type(dollar_f5(power_set(A)),member_type(power_set(A))),
inference(hyper,[status(thm)],[137,28,128]),
[iquote('hyper,137,28,128')] ).
cnf(202,plain,
( empty(power_set(A))
| member(dollar_f2(A),power_set(A)) ),
inference(hyper,[status(thm)],[160,30,128,128]),
[iquote('hyper,160,30,128,128')] ).
cnf(267,plain,
member(A,power_set(A)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[138,92,128])]),
[iquote('hyper,138,92,128,factor_simp')] ).
cnf(1385,plain,
( empty(power_set(cross_product(dollar_c5,dollar_c4)))
| member(dollar_c1,power_set(cross_product(dollar_c5,dollar_c4))) ),
inference(hyper,[status(thm)],[181,30,128,128]),
[iquote('hyper,181,30,128,128')] ).
cnf(1402,plain,
( empty(power_set(A))
| member(dollar_f5(power_set(A)),power_set(A)) ),
inference(hyper,[status(thm)],[189,30,128,128]),
[iquote('hyper,189,30,128,128')] ).
cnf(1424,plain,
member(dollar_f2(A),power_set(A)),
inference(hyper,[status(thm)],[202,33,128,128,267]),
[iquote('hyper,202,33,128,128,267')] ).
cnf(1453,plain,
member(dollar_f5(power_set(A)),power_set(A)),
inference(hyper,[status(thm)],[1402,33,128,128,1424]),
[iquote('hyper,1402,33,128,128,1424')] ).
cnf(1487,plain,
member(dollar_c1,power_set(cross_product(dollar_c5,dollar_c4))),
inference(hyper,[status(thm)],[1385,33,128,128,1453]),
[iquote('hyper,1385,33,128,128,1453')] ).
cnf(1491,plain,
member(ordered_pair(dollar_c3,dollar_c2),cross_product(dollar_c5,dollar_c4)),
inference(hyper,[status(thm)],[1487,24,128,128,128,130]),
[iquote('hyper,1487,24,128,128,128,130')] ).
cnf(1494,plain,
member(dollar_c2,dollar_c4),
inference(hyper,[status(thm)],[1491,2,128,128,128,128]),
[iquote('hyper,1491,2,128,128,128,128')] ).
cnf(1495,plain,
member(dollar_c3,dollar_c5),
inference(hyper,[status(thm)],[1491,1,128,128,128,128]),
[iquote('hyper,1491,1,128,128,128,128')] ).
cnf(1542,plain,
$false,
inference(hyper,[status(thm)],[1495,45,1494]),
[iquote('hyper,1495,45,1494')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n011.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 10:24:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.05/2.23 ----- Otter 3.3f, August 2004 -----
% 2.05/2.23 The process was started by sandbox on n011.cluster.edu,
% 2.05/2.23 Wed Jul 27 10:24:40 2022
% 2.05/2.23 The command was "./otter". The process ID is 22177.
% 2.05/2.23
% 2.05/2.23 set(prolog_style_variables).
% 2.05/2.23 set(auto).
% 2.05/2.23 dependent: set(auto1).
% 2.05/2.23 dependent: set(process_input).
% 2.05/2.23 dependent: clear(print_kept).
% 2.05/2.23 dependent: clear(print_new_demod).
% 2.05/2.23 dependent: clear(print_back_demod).
% 2.05/2.23 dependent: clear(print_back_sub).
% 2.05/2.23 dependent: set(control_memory).
% 2.05/2.23 dependent: assign(max_mem, 12000).
% 2.05/2.23 dependent: assign(pick_given_ratio, 4).
% 2.05/2.23 dependent: assign(stats_level, 1).
% 2.05/2.23 dependent: assign(max_seconds, 10800).
% 2.05/2.23 clear(print_given).
% 2.05/2.23
% 2.05/2.23 formula_list(usable).
% 2.05/2.23 all A (A=A).
% 2.05/2.23 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)-> (member(ordered_pair(B,C),cross_product(D,E))<->member(B,D)&member(C,E))))))))).
% 2.05/2.23 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)))))))))))).
% 2.05/2.23 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 2.05/2.23 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)))))))).
% 2.05/2.23 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (exists D ilf_type(D,relation_type(C,B)))))).
% 2.05/2.23 all B (ilf_type(B,set_type)->ilf_type(singleton(B),set_type)).
% 2.05/2.23 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 2.05/2.23 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(unordered_pair(B,C),set_type)))).
% 2.05/2.23 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->unordered_pair(B,C)=unordered_pair(C,B)))).
% 2.05/2.23 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))))))).
% 2.05/2.23 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 2.05/2.23 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)))))))).
% 2.05/2.23 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)))))))).
% 2.05/2.23 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 2.05/2.23 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))))).
% 2.05/2.23 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 2.05/2.23 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 2.05/2.23 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)))))))))).
% 2.05/2.23 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 2.05/2.23 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)))))).
% 2.05/2.23 all B ilf_type(B,set_type).
% 2.05/2.23 -(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)))))))))))).
% 2.05/2.23 end_of_list.
% 2.05/2.23
% 2.05/2.23 -------> usable clausifies to:
% 2.05/2.23
% 2.05/2.23 list(usable).
% 2.05/2.23 0 [] A=A.
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -member(ordered_pair(B,C),cross_product(D,E))|member(B,D).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -member(ordered_pair(B,C),cross_product(D,E))|member(C,E).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|member(ordered_pair(B,C),cross_product(D,E))| -member(B,D)| -member(C,E).
% 2.05/2.23 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)).
% 2.05/2.23 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)).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 2.05/2.23 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)).
% 2.05/2.23 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))).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type($f1(B,C),relation_type(C,B)).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|ilf_type(singleton(B),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(unordered_pair(B,C),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|unordered_pair(B,C)=unordered_pair(C,B).
% 2.05/2.23 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))).
% 2.05/2.23 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))).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|ilf_type($f2(B),subset_type(B)).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C| -ilf_type(D,set_type)|member(D,B)| -member(D,C).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C|ilf_type($f3(B,C),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C|member($f3(B,C),B)|member($f3(B,C),C).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C| -member($f3(B,C),B)| -member($f3(B,C),C).
% 2.05/2.23 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).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f4(B,C),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f4(B,C),B).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f4(B,C),C).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 2.05/2.23 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f5(B),member_type(B)).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f6(B),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|empty(B)|member($f6(B),B).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f8(B,C),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f7(B,C),set_type).
% 2.05/2.23 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)).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f9(B),set_type).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f9(B),B).
% 2.05/2.23 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f9(B)!=ordered_pair(D,E).
% 2.05/2.23 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 2.05/2.23 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 2.05/2.23 0 [] ilf_type(B,set_type).
% 2.05/2.23 0 [] ilf_type($c5,set_type).
% 2.05/2.23 0 [] ilf_type($c4,set_type).
% 2.05/2.23 0 [] ilf_type($c3,set_type).
% 2.05/2.23 0 [] ilf_type($c2,set_type).
% 2.05/2.23 0 [] ilf_type($c1,relation_type($c5,$c4)).
% 2.05/2.23 0 [] member(ordered_pair($c3,$c2),$c1).
% 2.05/2.23 0 [] -member($c3,$c5)| -member($c2,$c4).
% 2.05/2.23 end_of_list.
% 2.05/2.23
% 2.05/2.23 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 2.05/2.23
% 2.05/2.23 This ia a non-Horn set with equality. The strategy will be
% 2.05/2.23 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.05/2.23 deletion, with positive clauses in sos and nonpositive
% 2.05/2.23 clauses in usable.
% 2.12/2.26
% 2.12/2.26 dependent: set(knuth_bendix).
% 2.12/2.26 dependent: set(anl_eq).
% 2.12/2.26 dependent: set(para_from).
% 2.12/2.26 dependent: set(para_into).
% 2.12/2.26 dependent: clear(para_from_right).
% 2.12/2.26 dependent: clear(para_into_right).
% 2.12/2.26 dependent: set(para_from_vars).
% 2.12/2.26 dependent: set(eq_units_both_ways).
% 2.12/2.26 dependent: set(dynamic_demod_all).
% 2.12/2.26 dependent: set(dynamic_demod).
% 2.12/2.26 dependent: set(order_eq).
% 2.12/2.26 dependent: set(back_demod).
% 2.12/2.26 dependent: set(lrpo).
% 2.12/2.26 dependent: set(hyper_res).
% 2.12/2.26 dependent: set(unit_deletion).
% 2.12/2.26 dependent: set(factor).
% 2.12/2.26
% 2.12/2.26 ------------> process usable:
% 2.12/2.26 ** KEPT (pick-wt=22): 1 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(ordered_pair(A,B),cross_product(C,D))|member(A,C).
% 2.12/2.26 ** KEPT (pick-wt=22): 2 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(ordered_pair(A,B),cross_product(C,D))|member(B,D).
% 2.12/2.26 ** KEPT (pick-wt=25): 3 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)|member(ordered_pair(A,B),cross_product(C,D))| -member(A,C)| -member(B,D).
% 2.12/2.26 ** KEPT (pick-wt=22): 5 [copy,4,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)).
% 2.12/2.26 ** KEPT (pick-wt=22): 7 [copy,6,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)).
% 2.12/2.26 ** KEPT (pick-wt=11): 8 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 2.12/2.26 ** KEPT (pick-wt=17): 9 [] -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)).
% 2.12/2.26 ** KEPT (pick-wt=17): 10 [] -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))).
% 2.12/2.26 ** KEPT (pick-wt=13): 11 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type($f1(A,B),relation_type(B,A)).
% 2.12/2.26 ** KEPT (pick-wt=7): 12 [] -ilf_type(A,set_type)|ilf_type(singleton(A),set_type).
% 2.12/2.26 ** KEPT (pick-wt=11): 13 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 2.12/2.26 ** KEPT (pick-wt=11): 14 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(unordered_pair(A,B),set_type).
% 2.12/2.26 ** KEPT (pick-wt=13): 15 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|unordered_pair(A,B)=unordered_pair(B,A).
% 2.12/2.26 ** KEPT (pick-wt=15): 16 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A))).
% 2.12/2.26 ** 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))).
% 2.12/2.26 ** KEPT (pick-wt=8): 18 [] -ilf_type(A,set_type)|ilf_type($f2(A),subset_type(A)).
% 2.12/2.26 ** KEPT (pick-wt=18): 19 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 2.12/2.26 ** KEPT (pick-wt=18): 20 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B| -ilf_type(C,set_type)|member(C,A)| -member(C,B).
% 2.12/2.26 ** KEPT (pick-wt=14): 21 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B|ilf_type($f3(A,B),set_type).
% 2.12/2.26 ** KEPT (pick-wt=19): 22 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B|member($f3(A,B),A)|member($f3(A,B),B).
% 2.12/2.26 ** KEPT (pick-wt=19): 23 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B| -member($f3(A,B),A)| -member($f3(A,B),B).
% 2.12/2.26 ** KEPT (pick-wt=19): 24 [] -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).
% 2.12/2.26 ** KEPT (pick-wt=15): 25 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f4(A,B),set_type).
% 2.12/2.26 ** KEPT (pick-wt=15): 26 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f4(A,B),A).
% 2.12/2.26 ** KEPT (pick-wt=15): 27 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f4(A,B),B).
% 2.12/2.26 ** KEPT (pick-wt=6): 28 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 2.12/2.26 ** KEPT (pick-wt=7): 29 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 2.12/2.26 ** KEPT (pick-wt=15): 30 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 2.66/2.82 ** KEPT (pick-wt=15): 31 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)|ilf_type(A,member_type(B))| -member(A,B).
% 2.66/2.82 ** KEPT (pick-wt=10): 32 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f5(A),member_type(A)).
% 2.66/2.82 ** KEPT (pick-wt=11): 33 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 2.66/2.82 ** KEPT (pick-wt=9): 34 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f6(A),set_type).
% 2.66/2.82 ** KEPT (pick-wt=9): 35 [] -ilf_type(A,set_type)|empty(A)|member($f6(A),A).
% 2.66/2.82 ** KEPT (pick-wt=16): 36 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f8(A,B),set_type).
% 2.66/2.82 ** KEPT (pick-wt=16): 37 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f7(A,B),set_type).
% 2.66/2.82 ** KEPT (pick-wt=20): 39 [copy,38,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.
% 2.66/2.82 ** KEPT (pick-wt=9): 40 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f9(A),set_type).
% 2.66/2.82 ** KEPT (pick-wt=9): 41 [] -ilf_type(A,set_type)|relation_like(A)|member($f9(A),A).
% 2.66/2.82 ** KEPT (pick-wt=17): 42 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f9(A)!=ordered_pair(B,C).
% 2.66/2.82 ** KEPT (pick-wt=7): 43 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 2.66/2.82 ** KEPT (pick-wt=14): 44 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 2.66/2.82 ** KEPT (pick-wt=6): 45 [] -member($c3,$c5)| -member($c2,$c4).
% 2.66/2.82
% 2.66/2.82 ------------> process sos:
% 2.66/2.82 ** KEPT (pick-wt=3): 127 [] A=A.
% 2.66/2.82 ** KEPT (pick-wt=3): 128 [] ilf_type(A,set_type).
% 2.66/2.82 Following clause subsumed by 128 during input processing: 0 [] ilf_type($c5,set_type).
% 2.66/2.82 Following clause subsumed by 128 during input processing: 0 [] ilf_type($c4,set_type).
% 2.66/2.82 Following clause subsumed by 128 during input processing: 0 [] ilf_type($c3,set_type).
% 2.66/2.82 Following clause subsumed by 128 during input processing: 0 [] ilf_type($c2,set_type).
% 2.66/2.82 ** KEPT (pick-wt=5): 129 [] ilf_type($c1,relation_type($c5,$c4)).
% 2.66/2.82 ** KEPT (pick-wt=5): 130 [] member(ordered_pair($c3,$c2),$c1).
% 2.66/2.82 Following clause subsumed by 127 during input processing: 0 [copy,127,flip.1] A=A.
% 2.66/2.82 127 back subsumes 86.
% 2.66/2.82 127 back subsumes 85.
% 2.66/2.82 127 back subsumes 84.
% 2.66/2.82 127 back subsumes 77.
% 2.66/2.82 128 back subsumes 97.
% 2.66/2.82 128 back subsumes 96.
% 2.66/2.82 128 back subsumes 90.
% 2.66/2.82 128 back subsumes 76.
% 2.66/2.82 128 back subsumes 75.
% 2.66/2.82 128 back subsumes 71.
% 2.66/2.82 128 back subsumes 40.
% 2.66/2.82 128 back subsumes 37.
% 2.66/2.82 128 back subsumes 36.
% 2.66/2.82 128 back subsumes 34.
% 2.66/2.82 128 back subsumes 29.
% 2.66/2.82 128 back subsumes 25.
% 2.66/2.82 128 back subsumes 21.
% 2.66/2.82 128 back subsumes 14.
% 2.66/2.82 128 back subsumes 13.
% 2.66/2.82 128 back subsumes 12.
% 2.66/2.82 128 back subsumes 8.
% 2.66/2.82
% 2.66/2.82 ======= end of input processing =======
% 2.66/2.82
% 2.66/2.82 =========== start of search ===========
% 2.66/2.82
% 2.66/2.82
% 2.66/2.82 Resetting weight limit to 10.
% 2.66/2.82
% 2.66/2.82
% 2.66/2.82 Resetting weight limit to 10.
% 2.66/2.82
% 2.66/2.82 sos_size=522
% 2.66/2.82
% 2.66/2.82 -------- PROOF --------
% 2.66/2.82
% 2.66/2.82 -----> EMPTY CLAUSE at 0.59 sec ----> 1542 [hyper,1495,45,1494] $F.
% 2.66/2.82
% 2.66/2.82 Length of proof is 18. Level of proof is 8.
% 2.66/2.82
% 2.66/2.82 ---------------- PROOF ----------------
% 2.66/2.82 % SZS status Theorem
% 2.66/2.82 % SZS output start Refutation
% See solution above
% 2.66/2.82 ------------ end of proof -------------
% 2.66/2.82
% 2.66/2.82
% 2.66/2.82 Search stopped by max_proofs option.
% 2.66/2.82
% 2.66/2.82
% 2.66/2.82 Search stopped by max_proofs option.
% 2.66/2.82
% 2.66/2.82 ============ end of search ============
% 2.66/2.82
% 2.66/2.82 -------------- statistics -------------
% 2.66/2.82 clauses given 135
% 2.66/2.82 clauses generated 23844
% 2.66/2.82 clauses kept 1529
% 2.66/2.82 clauses forward subsumed 1409
% 2.66/2.82 clauses back subsumed 813
% 2.66/2.82 Kbytes malloced 4882
% 2.66/2.82
% 2.66/2.82 ----------- times (seconds) -----------
% 2.66/2.82 user CPU time 0.59 (0 hr, 0 min, 0 sec)
% 2.66/2.82 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.66/2.82 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.66/2.82
% 2.66/2.82 That finishes the proof of the theorem.
% 2.66/2.82
% 2.66/2.82 Process 22177 finished Wed Jul 27 10:24:43 2022
% 2.66/2.82 Otter interrupted
% 2.66/2.82 PROOF FOUND
%------------------------------------------------------------------------------