%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET640+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 13:13:57 EDT 2022
% Result : Theorem 6.40s 6.59s
% Output : Refutation 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 39 ( 18 unt; 11 nHn; 26 RR)
% Number of literals : 87 ( 0 equ; 40 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('SET640+3.p',unknown),
[] ).
cnf(11,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('SET640+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| subset(A,B)
| member(dollar_f4(A,B),A) ),
file('SET640+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| subset(A,B)
| ~ member(dollar_f4(A,B),B) ),
file('SET640+3.p',unknown),
[] ).
cnf(18,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('SET640+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ ilf_type(A,set_type)
| ilf_type(dollar_f5(A),subset_type(A)) ),
file('SET640+3.p',unknown),
[] ).
cnf(22,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('SET640+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| member(A,power_set(B))
| member(dollar_f6(A,B),A) ),
file('SET640+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| member(A,power_set(B))
| ~ member(dollar_f6(A,B),B) ),
file('SET640+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ ilf_type(A,set_type)
| ~ empty(power_set(A)) ),
file('SET640+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ ilf_type(A,set_type)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,member_type(B))
| member(A,B) ),
file('SET640+3.p',unknown),
[] ).
cnf(30,axiom,
( empty(A)
| ~ ilf_type(A,set_type)
| ilf_type(dollar_f7(A),member_type(A)) ),
file('SET640+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ ilf_type(A,set_type)
| ~ empty(A)
| ~ ilf_type(B,set_type)
| ~ member(B,A) ),
file('SET640+3.p',unknown),
[] ).
cnf(43,axiom,
~ subset(dollar_c4,cross_product(dollar_c3,dollar_c2)),
file('SET640+3.p',unknown),
[] ).
cnf(84,plain,
( ~ ilf_type(A,set_type)
| member(A,power_set(A))
| ~ member(dollar_f6(A,A),A) ),
inference(factor,[status(thm)],[25]),
[iquote('factor,25.1.2')] ).
cnf(142,axiom,
ilf_type(A,set_type),
file('SET640+3.p',unknown),
[] ).
cnf(143,axiom,
ilf_type(dollar_c1,relation_type(dollar_c3,dollar_c2)),
file('SET640+3.p',unknown),
[] ).
cnf(144,axiom,
subset(dollar_c4,dollar_c1),
file('SET640+3.p',unknown),
[] ).
cnf(149,plain,
( empty(A)
| ilf_type(dollar_f7(A),member_type(A)) ),
inference(hyper,[status(thm)],[142,30]),
[iquote('hyper,142,30')] ).
cnf(150,plain,
( member(A,power_set(B))
| member(dollar_f6(A,B),A) ),
inference(hyper,[status(thm)],[142,24,142]),
[iquote('hyper,142,24,142')] ).
cnf(152,plain,
ilf_type(dollar_f5(A),subset_type(A)),
inference(hyper,[status(thm)],[142,20]),
[iquote('hyper,142,20')] ).
cnf(153,plain,
( subset(A,B)
| member(dollar_f4(A,B),A) ),
inference(hyper,[status(thm)],[142,15,142]),
[iquote('hyper,142,15,142')] ).
cnf(155,plain,
ilf_type(dollar_c1,subset_type(cross_product(dollar_c3,dollar_c2))),
inference(hyper,[status(thm)],[143,11,142,142]),
[iquote('hyper,143,11,142,142')] ).
cnf(159,plain,
ilf_type(dollar_f5(A),member_type(power_set(A))),
inference(hyper,[status(thm)],[152,18,142,142]),
[iquote('hyper,152,18,142,142')] ).
cnf(164,plain,
ilf_type(dollar_c1,member_type(power_set(cross_product(dollar_c3,dollar_c2)))),
inference(hyper,[status(thm)],[155,18,142,142]),
[iquote('hyper,155,18,142,142')] ).
cnf(166,plain,
ilf_type(dollar_f7(power_set(A)),member_type(power_set(A))),
inference(hyper,[status(thm)],[149,26,142]),
[iquote('hyper,149,26,142')] ).
cnf(167,plain,
( empty(power_set(A))
| member(dollar_f5(A),power_set(A)) ),
inference(hyper,[status(thm)],[159,28,142,142]),
[iquote('hyper,159,28,142,142')] ).
cnf(226,plain,
member(A,power_set(A)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[150,84,142])]),
[iquote('hyper,150,84,142,factor_simp')] ).
cnf(302,plain,
( empty(power_set(cross_product(dollar_c3,dollar_c2)))
| member(dollar_c1,power_set(cross_product(dollar_c3,dollar_c2))) ),
inference(hyper,[status(thm)],[164,28,142,142]),
[iquote('hyper,164,28,142,142')] ).
cnf(314,plain,
( member(dollar_f4(dollar_c1,A),dollar_c1)
| subset(dollar_c4,A) ),
inference(hyper,[status(thm)],[153,1,142,142,142,144]),
[iquote('hyper,153,1,142,142,142,144')] ).
cnf(316,plain,
( empty(power_set(A))
| member(dollar_f7(power_set(A)),power_set(A)) ),
inference(hyper,[status(thm)],[166,28,142,142]),
[iquote('hyper,166,28,142,142')] ).
cnf(465,plain,
member(dollar_f5(A),power_set(A)),
inference(hyper,[status(thm)],[167,31,142,142,226]),
[iquote('hyper,167,31,142,142,226')] ).
cnf(1057,plain,
member(dollar_f4(dollar_c1,cross_product(dollar_c3,dollar_c2)),dollar_c1),
inference(hyper,[status(thm)],[314,43]),
[iquote('hyper,314,43')] ).
cnf(1086,plain,
member(dollar_f7(power_set(A)),power_set(A)),
inference(hyper,[status(thm)],[316,31,142,142,465]),
[iquote('hyper,316,31,142,142,465')] ).
cnf(1116,plain,
member(dollar_c1,power_set(cross_product(dollar_c3,dollar_c2))),
inference(hyper,[status(thm)],[302,31,142,142,1086]),
[iquote('hyper,302,31,142,142,1086')] ).
cnf(1117,plain,
member(dollar_f4(dollar_c1,cross_product(dollar_c3,dollar_c2)),cross_product(dollar_c3,dollar_c2)),
inference(hyper,[status(thm)],[1116,22,142,142,142,1057]),
[iquote('hyper,1116,22,142,142,142,1057')] ).
cnf(1252,plain,
subset(dollar_c1,cross_product(dollar_c3,dollar_c2)),
inference(hyper,[status(thm)],[1117,16,142,142]),
[iquote('hyper,1117,16,142,142')] ).
cnf(1254,plain,
subset(dollar_c4,cross_product(dollar_c3,dollar_c2)),
inference(hyper,[status(thm)],[1252,1,142,142,142,144]),
[iquote('hyper,1252,1,142,142,142,144')] ).
cnf(1255,plain,
$false,
inference(binary,[status(thm)],[1254,43]),
[iquote('binary,1254.1,43.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET640+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 10:52:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.09/2.26 ----- Otter 3.3f, August 2004 -----
% 2.09/2.26 The process was started by sandbox2 on n023.cluster.edu,
% 2.09/2.26 Wed Jul 27 10:52:18 2022
% 2.09/2.26 The command was "./otter". The process ID is 30312.
% 2.09/2.26
% 2.09/2.26 set(prolog_style_variables).
% 2.09/2.26 set(auto).
% 2.09/2.26 dependent: set(auto1).
% 2.09/2.26 dependent: set(process_input).
% 2.09/2.26 dependent: clear(print_kept).
% 2.09/2.26 dependent: clear(print_new_demod).
% 2.09/2.26 dependent: clear(print_back_demod).
% 2.09/2.26 dependent: clear(print_back_sub).
% 2.09/2.26 dependent: set(control_memory).
% 2.09/2.26 dependent: assign(max_mem, 12000).
% 2.09/2.26 dependent: assign(pick_given_ratio, 4).
% 2.09/2.26 dependent: assign(stats_level, 1).
% 2.09/2.26 dependent: assign(max_seconds, 10800).
% 2.09/2.26 clear(print_given).
% 2.09/2.26
% 2.09/2.26 formula_list(usable).
% 2.09/2.26 all A (A=A).
% 2.09/2.26 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,set_type)-> (subset(B,C)&subset(C,D)->subset(B,D))))))).
% 2.09/2.26 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,set_type)-> (member(D,cross_product(B,C))<-> (exists E (ilf_type(E,set_type)& (exists F (ilf_type(F,set_type)&member(E,B)&member(F,C)&D=ordered_pair(E,F))))))))))).
% 2.09/2.26 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 2.09/2.26 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)))))))).
% 2.09/2.26 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (exists D ilf_type(D,relation_type(C,B)))))).
% 2.09/2.26 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (subset(B,C)<-> (all D (ilf_type(D,set_type)-> (member(D,B)->member(D,C)))))))).
% 2.09/2.26 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 2.09/2.26 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))))))).
% 2.09/2.26 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 2.09/2.26 all B (ilf_type(B,set_type)->subset(B,B)).
% 2.09/2.26 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)))))))).
% 2.09/2.26 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 2.09/2.26 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))))).
% 2.09/2.26 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 2.09/2.26 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 2.09/2.26 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)))))))))).
% 2.09/2.26 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 2.09/2.26 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)))))).
% 2.09/2.26 all B ilf_type(B,set_type).
% 2.09/2.26 -(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,relation_type(C,D))-> (subset(B,E)->subset(B,cross_product(C,D))))))))))).
% 2.09/2.26 end_of_list.
% 2.09/2.26
% 2.09/2.26 -------> usable clausifies to:
% 2.09/2.26
% 2.09/2.26 list(usable).
% 2.09/2.26 0 [] A=A.
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -subset(B,C)| -subset(C,D)|subset(B,D).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|ilf_type($f2(B,C,D),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|ilf_type($f1(B,C,D),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|member($f2(B,C,D),B).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|member($f1(B,C,D),C).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|D=ordered_pair($f2(B,C,D),$f1(B,C,D)).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)|member(D,cross_product(B,C))| -ilf_type(E,set_type)| -ilf_type(F,set_type)| -member(E,B)| -member(F,C)|D!=ordered_pair(E,F).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|ilf_type(D,relation_type(B,C)).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(E,relation_type(B,C))|ilf_type(E,subset_type(cross_product(B,C))).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type($f3(B,C),relation_type(C,B)).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -subset(B,C)| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|ilf_type($f4(B,C),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|member($f4(B,C),B).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)| -member($f4(B,C),C).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(C,subset_type(B))|ilf_type(C,member_type(power_set(B))).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(C,subset_type(B))| -ilf_type(C,member_type(power_set(B))).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|ilf_type($f5(B),subset_type(B)).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|subset(B,B).
% 2.09/2.26 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).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f6(B,C),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f6(B,C),B).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f6(B,C),C).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 2.09/2.26 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f7(B),member_type(B)).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f8(B),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|empty(B)|member($f8(B),B).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f10(B,C),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f9(B,C),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|C=ordered_pair($f10(B,C),$f9(B,C)).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f11(B),set_type).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f11(B),B).
% 2.09/2.26 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f11(B)!=ordered_pair(D,E).
% 2.09/2.26 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 2.09/2.26 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 2.09/2.26 0 [] ilf_type(B,set_type).
% 2.09/2.26 0 [] ilf_type($c4,set_type).
% 2.09/2.26 0 [] ilf_type($c3,set_type).
% 2.09/2.26 0 [] ilf_type($c2,set_type).
% 2.09/2.26 0 [] ilf_type($c1,relation_type($c3,$c2)).
% 2.09/2.26 0 [] subset($c4,$c1).
% 2.09/2.26 0 [] -subset($c4,cross_product($c3,$c2)).
% 2.09/2.26 end_of_list.
% 2.09/2.26
% 2.09/2.26 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=9.
% 2.09/2.26
% 2.09/2.26 This ia a non-Horn set with equality. The strategy will be
% 2.09/2.26 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.09/2.26 deletion, with positive clauses in sos and nonpositive
% 2.09/2.26 clauses in usable.
% 2.09/2.26
% 2.09/2.26 dependent: set(knuth_bendix).
% 2.09/2.26 dependent: set(anl_eq).
% 2.09/2.26 dependent: set(para_from).
% 2.09/2.26 dependent: set(para_into).
% 2.09/2.26 dependent: clear(para_from_right).
% 2.09/2.26 dependent: clear(para_into_right).
% 2.09/2.26 dependent: set(para_from_vars).
% 2.09/2.26 dependent: set(eq_units_both_ways).
% 2.09/2.26 dependent: set(dynamic_demod_all).
% 2.09/2.26 dependent: set(dynamic_demod).
% 2.09/2.26 dependent: set(order_eq).
% 2.09/2.26 dependent: set(back_demod).
% 2.09/2.26 dependent: set(lrpo).
% 2.09/2.26 dependent: set(hyper_res).
% 2.09/2.26 dependent: set(unit_deletion).
% 2.09/2.26 dependent: set(factor).
% 2.09/2.26
% 2.09/2.26 ------------> process usable:
% 2.09/2.26 ** KEPT (pick-wt=18): 1 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.15/2.31 ** KEPT (pick-wt=20): 2 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,cross_product(A,B))|ilf_type($f2(A,B,C),set_type).
% 2.15/2.31 ** KEPT (pick-wt=20): 3 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,cross_product(A,B))|ilf_type($f1(A,B,C),set_type).
% 2.15/2.31 ** KEPT (pick-wt=20): 4 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,cross_product(A,B))|member($f2(A,B,C),A).
% 2.15/2.31 ** KEPT (pick-wt=20): 5 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,cross_product(A,B))|member($f1(A,B,C),B).
% 2.15/2.31 ** KEPT (pick-wt=25): 7 [copy,6,flip.5] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,cross_product(A,B))|ordered_pair($f2(A,B,C),$f1(A,B,C))=C.
% 2.15/2.31 ** KEPT (pick-wt=31): 8 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(C,cross_product(A,B))| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -member(D,A)| -member(E,B)|C!=ordered_pair(D,E).
% 2.15/2.31 ** KEPT (pick-wt=11): 9 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 2.15/2.31 ** KEPT (pick-wt=17): 10 [] -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)).
% 2.15/2.31 ** KEPT (pick-wt=17): 11 [] -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))).
% 2.15/2.31 ** KEPT (pick-wt=13): 12 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type($f3(A,B),relation_type(B,A)).
% 2.15/2.31 ** KEPT (pick-wt=18): 13 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -subset(A,B)| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 2.15/2.31 ** KEPT (pick-wt=14): 14 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|ilf_type($f4(A,B),set_type).
% 2.15/2.31 ** KEPT (pick-wt=14): 15 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|member($f4(A,B),A).
% 2.15/2.31 ** KEPT (pick-wt=14): 16 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)| -member($f4(A,B),B).
% 2.15/2.31 ** KEPT (pick-wt=11): 17 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 2.15/2.31 ** 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))).
% 2.15/2.31 ** KEPT (pick-wt=15): 19 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,subset_type(A))| -ilf_type(B,member_type(power_set(A))).
% 2.15/2.31 ** KEPT (pick-wt=8): 20 [] -ilf_type(A,set_type)|ilf_type($f5(A),subset_type(A)).
% 2.15/2.31 ** KEPT (pick-wt=6): 21 [] -ilf_type(A,set_type)|subset(A,A).
% 2.15/2.31 ** KEPT (pick-wt=19): 22 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -member(A,power_set(B))| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 2.15/2.31 ** KEPT (pick-wt=15): 23 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f6(A,B),set_type).
% 2.15/2.31 ** KEPT (pick-wt=15): 24 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f6(A,B),A).
% 2.15/2.31 ** KEPT (pick-wt=15): 25 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f6(A,B),B).
% 2.15/2.31 ** KEPT (pick-wt=6): 26 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 2.15/2.31 ** KEPT (pick-wt=7): 27 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 2.15/2.31 ** KEPT (pick-wt=15): 28 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 2.15/2.31 ** KEPT (pick-wt=15): 29 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)|ilf_type(A,member_type(B))| -member(A,B).
% 2.15/2.31 ** KEPT (pick-wt=10): 30 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f7(A),member_type(A)).
% 2.15/2.31 ** KEPT (pick-wt=11): 31 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 2.15/2.31 ** KEPT (pick-wt=9): 32 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f8(A),set_type).
% 2.15/2.31 ** KEPT (pick-wt=9): 33 [] -ilf_type(A,set_type)|empty(A)|member($f8(A),A).
% 2.15/2.31 ** KEPT (pick-wt=16): 34 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f10(A,B),set_type).
% 2.15/2.31 ** KEPT (pick-wt=16): 35 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f9(A,B),set_type).
% 6.40/6.59 ** KEPT (pick-wt=20): 37 [copy,36,flip.5] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ordered_pair($f10(A,B),$f9(A,B))=B.
% 6.40/6.59 ** KEPT (pick-wt=9): 38 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f11(A),set_type).
% 6.40/6.59 ** KEPT (pick-wt=9): 39 [] -ilf_type(A,set_type)|relation_like(A)|member($f11(A),A).
% 6.40/6.59 ** KEPT (pick-wt=17): 40 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f11(A)!=ordered_pair(B,C).
% 6.40/6.59 ** KEPT (pick-wt=7): 41 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 6.40/6.59 ** KEPT (pick-wt=14): 42 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 6.40/6.59 ** KEPT (pick-wt=5): 43 [] -subset($c4,cross_product($c3,$c2)).
% 6.40/6.59
% 6.40/6.59 ------------> process sos:
% 6.40/6.59 ** KEPT (pick-wt=3): 141 [] A=A.
% 6.40/6.59 ** KEPT (pick-wt=3): 142 [] ilf_type(A,set_type).
% 6.40/6.59 Following clause subsumed by 142 during input processing: 0 [] ilf_type($c4,set_type).
% 6.40/6.59 Following clause subsumed by 142 during input processing: 0 [] ilf_type($c3,set_type).
% 6.40/6.59 Following clause subsumed by 142 during input processing: 0 [] ilf_type($c2,set_type).
% 6.40/6.59 ** KEPT (pick-wt=5): 143 [] ilf_type($c1,relation_type($c3,$c2)).
% 6.40/6.59 ** KEPT (pick-wt=3): 144 [] subset($c4,$c1).
% 6.40/6.59 Following clause subsumed by 141 during input processing: 0 [copy,141,flip.1] A=A.
% 6.40/6.59 142 back subsumes 96.
% 6.40/6.59 142 back subsumes 95.
% 6.40/6.59 142 back subsumes 89.
% 6.40/6.59 142 back subsumes 88.
% 6.40/6.59 142 back subsumes 82.
% 6.40/6.59 142 back subsumes 76.
% 6.40/6.59 142 back subsumes 70.
% 6.40/6.59 142 back subsumes 49.
% 6.40/6.59 142 back subsumes 48.
% 6.40/6.59 142 back subsumes 47.
% 6.40/6.59 142 back subsumes 46.
% 6.40/6.59 142 back subsumes 45.
% 6.40/6.59 142 back subsumes 44.
% 6.40/6.59 142 back subsumes 38.
% 6.40/6.59 142 back subsumes 35.
% 6.40/6.59 142 back subsumes 34.
% 6.40/6.59 142 back subsumes 32.
% 6.40/6.59 142 back subsumes 27.
% 6.40/6.59 142 back subsumes 23.
% 6.40/6.59 142 back subsumes 17.
% 6.40/6.59 142 back subsumes 14.
% 6.40/6.59 142 back subsumes 9.
% 6.40/6.59 142 back subsumes 3.
% 6.40/6.59 142 back subsumes 2.
% 6.40/6.59
% 6.40/6.59 ======= end of input processing =======
% 6.40/6.59
% 6.40/6.59 =========== start of search ===========
% 6.40/6.59
% 6.40/6.59
% 6.40/6.59 Resetting weight limit to 9.
% 6.40/6.59
% 6.40/6.59
% 6.40/6.59 Resetting weight limit to 9.
% 6.40/6.59
% 6.40/6.59 sos_size=411
% 6.40/6.59
% 6.40/6.59 -------- PROOF --------
% 6.40/6.59
% 6.40/6.59 ----> UNIT CONFLICT at 4.33 sec ----> 1255 [binary,1254.1,43.1] $F.
% 6.40/6.59
% 6.40/6.59 Length of proof is 21. Level of proof is 9.
% 6.40/6.59
% 6.40/6.59 ---------------- PROOF ----------------
% 6.40/6.59 % SZS status Theorem
% 6.40/6.59 % SZS output start Refutation
% See solution above
% 6.40/6.59 ------------ end of proof -------------
% 6.40/6.59
% 6.40/6.59
% 6.40/6.59 Search stopped by max_proofs option.
% 6.40/6.59
% 6.40/6.59
% 6.40/6.59 Search stopped by max_proofs option.
% 6.40/6.59
% 6.40/6.59 ============ end of search ============
% 6.40/6.59
% 6.40/6.59 -------------- statistics -------------
% 6.40/6.59 clauses given 270
% 6.40/6.59 clauses generated 240579
% 6.40/6.59 clauses kept 1245
% 6.40/6.59 clauses forward subsumed 1387
% 6.40/6.59 clauses back subsumed 508
% 6.40/6.59 Kbytes malloced 5859
% 6.40/6.59
% 6.40/6.59 ----------- times (seconds) -----------
% 6.40/6.59 user CPU time 4.33 (0 hr, 0 min, 4 sec)
% 6.40/6.59 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 6.40/6.59 wall-clock time 6 (0 hr, 0 min, 6 sec)
% 6.40/6.59
% 6.40/6.59 That finishes the proof of the theorem.
% 6.40/6.59
% 6.40/6.59 Process 30312 finished Wed Jul 27 10:52:24 2022
% 6.40/6.59 Otter interrupted
% 6.40/6.59 PROOF FOUND
%------------------------------------------------------------------------------