TSTP Solution File: SET656+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET656+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:14:00 EDT 2022
% Result : Theorem 4.18s 4.36s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of clauses : 31 ( 16 unt; 4 nHn; 26 RR)
% Number of literals : 66 ( 8 equ; 37 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ subset(A,B)
| intersection(A,B) = A ),
file('SET656+3.p',unknown),
[] ).
cnf(15,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('SET656+3.p',unknown),
[] ).
cnf(23,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| intersection(A,B) = intersection(B,A) ),
file('SET656+3.p',unknown),
[] ).
cnf(27,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('SET656+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| subset(A,B)
| member(dollar_f7(A,B),A) ),
file('SET656+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| subset(A,B)
| ~ member(dollar_f7(A,B),B) ),
file('SET656+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ ilf_type(A,set_type)
| subset(A,A) ),
file('SET656+3.p',unknown),
[] ).
cnf(37,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('SET656+3.p',unknown),
[] ).
cnf(41,axiom,
( ~ ilf_type(A,set_type)
| ~ empty(power_set(A)) ),
file('SET656+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ ilf_type(A,set_type)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,member_type(B))
| member(A,B) ),
file('SET656+3.p',unknown),
[] ).
cnf(65,axiom,
intersection(dollar_c2,cross_product(dollar_c4,dollar_c3)) != dollar_c2,
file('SET656+3.p',unknown),
[] ).
cnf(191,axiom,
A = A,
file('SET656+3.p',unknown),
[] ).
cnf(193,axiom,
ilf_type(A,set_type),
file('SET656+3.p',unknown),
[] ).
cnf(194,axiom,
ilf_type(dollar_c2,relation_type(dollar_c4,dollar_c3)),
file('SET656+3.p',unknown),
[] ).
cnf(209,plain,
subset(A,A),
inference(hyper,[status(thm)],[193,36]),
[iquote('hyper,193,36')] ).
cnf(210,plain,
( subset(A,B)
| member(dollar_f7(A,B),A) ),
inference(hyper,[status(thm)],[193,34,193]),
[iquote('hyper,193,34,193')] ).
cnf(213,plain,
intersection(A,B) = intersection(B,A),
inference(hyper,[status(thm)],[193,23,193]),
[iquote('hyper,193,23,193')] ).
cnf(230,plain,
ilf_type(dollar_c2,subset_type(cross_product(dollar_c4,dollar_c3))),
inference(hyper,[status(thm)],[194,15,193,193]),
[iquote('hyper,194,15,193,193')] ).
cnf(308,plain,
ilf_type(dollar_c2,member_type(power_set(cross_product(dollar_c4,dollar_c3)))),
inference(hyper,[status(thm)],[230,27,193,193]),
[iquote('hyper,230,27,193,193')] ).
cnf(490,plain,
( intersection(A,B) = B
| ~ subset(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[213,1]),193,193])]),
[iquote('para_into,213.1.1,1.4.1,unit_del,193,193,flip.1')] ).
cnf(491,plain,
intersection(cross_product(dollar_c4,dollar_c3),dollar_c2) != dollar_c2,
inference(para_from,[status(thm),theory(equality)],[213,65]),
[iquote('para_from,213.1.1,65.1.1')] ).
cnf(694,plain,
( empty(power_set(cross_product(dollar_c4,dollar_c3)))
| member(dollar_c2,power_set(cross_product(dollar_c4,dollar_c3))) ),
inference(hyper,[status(thm)],[308,43,193,193]),
[iquote('hyper,308,43,193,193')] ).
cnf(740,plain,
( A = B
| ~ subset(B,A)
| ~ subset(A,B) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[490,1]),193,193]),
[iquote('para_into,490.1.1,1.4.1,unit_del,193,193')] ).
cnf(741,plain,
~ subset(dollar_c2,cross_product(dollar_c4,dollar_c3)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[490,491]),191]),
[iquote('para_from,490.1.1,491.1.1,unit_del,191')] ).
cnf(742,plain,
member(dollar_f7(dollar_c2,cross_product(dollar_c4,dollar_c3)),dollar_c2),
inference(hyper,[status(thm)],[741,210]),
[iquote('hyper,741,210')] ).
cnf(852,plain,
( ~ empty(A)
| ~ subset(A,power_set(B))
| ~ subset(power_set(B),A) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[740,41]),193]),
[iquote('para_from,740.1.1,41.2.1,unit_del,193')] ).
cnf(856,plain,
~ empty(power_set(A)),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[852]),209]),
[iquote('factor,852.2.3,unit_del,209')] ).
cnf(893,plain,
member(dollar_c2,power_set(cross_product(dollar_c4,dollar_c3))),
inference(hyper,[status(thm)],[694,856]),
[iquote('hyper,694,856')] ).
cnf(898,plain,
member(dollar_f7(dollar_c2,cross_product(dollar_c4,dollar_c3)),cross_product(dollar_c4,dollar_c3)),
inference(hyper,[status(thm)],[893,37,193,193,193,742]),
[iquote('hyper,893,37,193,193,193,742')] ).
cnf(989,plain,
subset(dollar_c2,cross_product(dollar_c4,dollar_c3)),
inference(hyper,[status(thm)],[898,35,193,193]),
[iquote('hyper,898,35,193,193')] ).
cnf(990,plain,
$false,
inference(binary,[status(thm)],[989,741]),
[iquote('binary,989.1,741.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET656+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:42:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.91/2.09 ----- Otter 3.3f, August 2004 -----
% 1.91/2.09 The process was started by sandbox on n009.cluster.edu,
% 1.91/2.09 Wed Jul 27 10:42:36 2022
% 1.91/2.09 The command was "./otter". The process ID is 8273.
% 1.91/2.09
% 1.91/2.09 set(prolog_style_variables).
% 1.91/2.09 set(auto).
% 1.91/2.09 dependent: set(auto1).
% 1.91/2.09 dependent: set(process_input).
% 1.91/2.09 dependent: clear(print_kept).
% 1.91/2.09 dependent: clear(print_new_demod).
% 1.91/2.09 dependent: clear(print_back_demod).
% 1.91/2.09 dependent: clear(print_back_sub).
% 1.91/2.09 dependent: set(control_memory).
% 1.91/2.09 dependent: assign(max_mem, 12000).
% 1.91/2.09 dependent: assign(pick_given_ratio, 4).
% 1.91/2.09 dependent: assign(stats_level, 1).
% 1.91/2.09 dependent: assign(max_seconds, 10800).
% 1.91/2.09 clear(print_given).
% 1.91/2.09
% 1.91/2.09 formula_list(usable).
% 1.91/2.09 all A (A=A).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (subset(B,C)->intersection(B,C)=B)))).
% 1.91/2.09 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))))))))))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,set_type)-> (member(D,intersection(B,C))<->member(D,B)&member(D,C))))))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(intersection(B,C),set_type)))).
% 1.91/2.09 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)))))))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (exists D ilf_type(D,relation_type(C,B)))))).
% 1.91/2.09 all B (ilf_type(B,binary_relation_type)-> (all C (ilf_type(C,binary_relation_type)-> (B=C<-> (all D (ilf_type(D,set_type)-> (all E (ilf_type(E,set_type)-> (member(ordered_pair(D,E),B)<->member(ordered_pair(D,E),C)))))))))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->intersection(B,C)=intersection(C,B)))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (ilf_type(B,binary_relation_type)<->relation_like(B)&ilf_type(B,set_type))).
% 1.91/2.09 exists B ilf_type(B,binary_relation_type).
% 1.91/2.09 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))))))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 1.91/2.09 all B (ilf_type(B,binary_relation_type)-> (all C (ilf_type(C,binary_relation_type)-> (B=C->C=B)))).
% 1.91/2.09 all B (ilf_type(B,binary_relation_type)->B=B).
% 1.91/2.09 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)))))))).
% 1.91/2.09 all B (ilf_type(B,set_type)->subset(B,B)).
% 1.91/2.09 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)))))))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 1.91/2.09 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))))).
% 1.91/2.09 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 1.91/2.09 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)))))))).
% 1.91/2.09 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)))))))))).
% 1.91/2.09 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)))))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 1.91/2.09 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))-> (all E (ilf_type(E,relation_type(B,C))->intersection4(B,C,D,E)=intersection(D,E)))))))).
% 1.91/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))-> (all E (ilf_type(E,relation_type(B,C))->ilf_type(intersection4(B,C,D,E),relation_type(B,C))))))))).
% 1.91/2.09 all B ilf_type(B,set_type).
% 1.91/2.09 -(all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->intersection(D,cross_product(B,C))=D)))))).
% 1.91/2.09 end_of_list.
% 1.91/2.09
% 1.91/2.09 -------> usable clausifies to:
% 1.91/2.09
% 1.91/2.09 list(usable).
% 1.91/2.09 0 [] A=A.
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -subset(B,C)|intersection(B,C)=B.
% 1.91/2.09 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).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|ilf_type($f1(B,C,D),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|member($f2(B,C,D),B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|member($f1(B,C,D),C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,cross_product(B,C))|D=ordered_pair($f2(B,C,D),$f1(B,C,D)).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)|member(D,cross_product(B,C))| -ilf_type(E,set_type)| -ilf_type(F,set_type)| -member(E,B)| -member(F,C)|D!=ordered_pair(E,F).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,intersection(B,C))|member(D,B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(D,intersection(B,C))|member(D,C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)|member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(intersection(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|ilf_type(D,relation_type(B,C)).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(E,relation_type(B,C))|ilf_type(E,subset_type(cross_product(B,C))).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type($f3(B,C),relation_type(C,B)).
% 1.91/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B!=C| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -member(ordered_pair(D,E),B)|member(ordered_pair(D,E),C).
% 1.91/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B!=C| -ilf_type(D,set_type)| -ilf_type(E,set_type)|member(ordered_pair(D,E),B)| -member(ordered_pair(D,E),C).
% 1.91/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B=C|ilf_type($f5(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B=C|ilf_type($f4(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B=C|member(ordered_pair($f5(B,C),$f4(B,C)),B)|member(ordered_pair($f5(B,C),$f4(B,C)),C).
% 1.91/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B=C| -member(ordered_pair($f5(B,C),$f4(B,C)),B)| -member(ordered_pair($f5(B,C),$f4(B,C)),C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|intersection(B,C)=intersection(C,B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(B,binary_relation_type)|relation_like(B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|ilf_type(B,binary_relation_type)| -relation_like(B).
% 1.91/2.09 0 [] ilf_type($c1,binary_relation_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(C,subset_type(B))|ilf_type(C,member_type(power_set(B))).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(C,subset_type(B))| -ilf_type(C,member_type(power_set(B))).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|ilf_type($f6(B),subset_type(B)).
% 1.91/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B!=C|C=B.
% 1.91/2.09 0 [] -ilf_type(B,binary_relation_type)|B=B.
% 1.91/2.09 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).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|ilf_type($f7(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|member($f7(B,C),B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)| -member($f7(B,C),C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|subset(B,B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(B,power_set(C))| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f8(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f8(B,C),B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f8(B,C),C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 1.91/2.09 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f9(B),member_type(B)).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C| -ilf_type(D,set_type)|member(D,B)| -member(D,C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C|ilf_type($f10(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C|member($f10(B,C),B)|member($f10(B,C),C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C| -member($f10(B,C),B)| -member($f10(B,C),C).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f12(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f11(B,C),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|C=ordered_pair($f12(B,C),$f11(B,C)).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f13(B),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f13(B),B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f13(B)!=ordered_pair(D,E).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f14(B),set_type).
% 1.91/2.09 0 [] -ilf_type(B,set_type)|empty(B)|member($f14(B),B).
% 1.91/2.09 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))| -ilf_type(E,relation_type(B,C))|intersection4(B,C,D,E)=intersection(D,E).
% 1.91/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))| -ilf_type(E,relation_type(B,C))|ilf_type(intersection4(B,C,D,E),relation_type(B,C)).
% 1.91/2.09 0 [] ilf_type(B,set_type).
% 1.91/2.09 0 [] ilf_type($c4,set_type).
% 1.91/2.09 0 [] ilf_type($c3,set_type).
% 1.91/2.09 0 [] ilf_type($c2,relation_type($c4,$c3)).
% 1.91/2.09 0 [] intersection($c2,cross_product($c4,$c3))!=$c2.
% 1.91/2.09 end_of_list.
% 1.91/2.09
% 1.91/2.09 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=9.
% 1.91/2.09
% 1.91/2.09 This ia a non-Horn set with equality. The strategy will be
% 1.91/2.09 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.91/2.09 deletion, with positive clauses in sos and nonpositive
% 1.91/2.09 clauses in usable.
% 1.91/2.09
% 1.91/2.09 dependent: set(knuth_bendix).
% 1.91/2.09 dependent: set(anl_eq).
% 1.91/2.09 dependent: set(para_from).
% 1.91/2.09 dependent: set(para_into).
% 1.91/2.09 dependent: clear(para_from_right).
% 1.91/2.09 dependent: clear(para_into_right).
% 1.91/2.09 dependent: set(para_from_vars).
% 1.91/2.09 dependent: set(eq_units_both_ways).
% 1.91/2.09 dependent: set(dynamic_demod_all).
% 1.91/2.09 dependent: set(dynamic_demod).
% 1.91/2.09 dependent: set(order_eq).
% 1.91/2.09 dependent: set(back_demod).
% 1.91/2.09 dependent: set(lrpo).
% 1.91/2.09 dependent: set(hyper_res).
% 1.91/2.09 dependent: set(unit_deletion).
% 1.91/2.09 dependent: set(factor).
% 1.91/2.09
% 1.91/2.09 ------------> process usable:
% 1.91/2.09 ** KEPT (pick-wt=14): 1 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -subset(A,B)|intersection(A,B)=A.
% 1.91/2.09 ** 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($f2(A,B,C),set_type).
% 1.99/2.16 ** KEPT (pick-wt=20): 3 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,cross_product(A,B))|ilf_type($f1(A,B,C),set_type).
% 1.99/2.16 ** 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($f2(A,B,C),A).
% 1.99/2.16 ** KEPT (pick-wt=20): 5 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,cross_product(A,B))|member($f1(A,B,C),B).
% 1.99/2.16 ** 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.
% 1.99/2.16 ** 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).
% 1.99/2.16 ** KEPT (pick-wt=11): 9 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=17): 10 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,intersection(A,B))|member(C,A).
% 1.99/2.16 ** KEPT (pick-wt=17): 11 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,intersection(A,B))|member(C,B).
% 1.99/2.16 ** KEPT (pick-wt=20): 12 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(C,intersection(A,B))| -member(C,A)| -member(C,B).
% 1.99/2.16 ** KEPT (pick-wt=11): 13 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(intersection(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=17): 14 [] -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)).
% 1.99/2.16 ** KEPT (pick-wt=17): 15 [] -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))).
% 1.99/2.16 ** KEPT (pick-wt=13): 16 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type($f3(A,B),relation_type(B,A)).
% 1.99/2.16 ** KEPT (pick-wt=25): 17 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A!=B| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(ordered_pair(C,D),A)|member(ordered_pair(C,D),B).
% 1.99/2.16 ** KEPT (pick-wt=25): 18 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A!=B| -ilf_type(C,set_type)| -ilf_type(D,set_type)|member(ordered_pair(C,D),A)| -member(ordered_pair(C,D),B).
% 1.99/2.16 ** KEPT (pick-wt=14): 19 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A=B|ilf_type($f5(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=14): 20 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A=B|ilf_type($f4(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=27): 21 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A=B|member(ordered_pair($f5(A,B),$f4(A,B)),A)|member(ordered_pair($f5(A,B),$f4(A,B)),B).
% 1.99/2.16 ** KEPT (pick-wt=27): 22 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A=B| -member(ordered_pair($f5(A,B),$f4(A,B)),A)| -member(ordered_pair($f5(A,B),$f4(A,B)),B).
% 1.99/2.16 ** KEPT (pick-wt=13): 23 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|intersection(A,B)=intersection(B,A).
% 1.99/2.16 ** KEPT (pick-wt=11): 24 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=8): 25 [] -ilf_type(A,set_type)| -ilf_type(A,binary_relation_type)|relation_like(A).
% 1.99/2.16 ** KEPT (pick-wt=8): 26 [] -ilf_type(A,set_type)|ilf_type(A,binary_relation_type)| -relation_like(A).
% 1.99/2.16 ** KEPT (pick-wt=15): 27 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A))).
% 1.99/2.16 ** KEPT (pick-wt=15): 28 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,subset_type(A))| -ilf_type(B,member_type(power_set(A))).
% 1.99/2.16 ** KEPT (pick-wt=8): 29 [] -ilf_type(A,set_type)|ilf_type($f6(A),subset_type(A)).
% 1.99/2.16 ** KEPT (pick-wt=12): 30 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A!=B|B=A.
% 1.99/2.16 ** KEPT (pick-wt=6): 31 [] -ilf_type(A,binary_relation_type)|A=A.
% 1.99/2.16 ** KEPT (pick-wt=18): 32 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -subset(A,B)| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 1.99/2.16 ** KEPT (pick-wt=14): 33 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|ilf_type($f7(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=14): 34 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|member($f7(A,B),A).
% 1.99/2.16 ** KEPT (pick-wt=14): 35 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)| -member($f7(A,B),B).
% 1.99/2.16 ** KEPT (pick-wt=6): 36 [] -ilf_type(A,set_type)|subset(A,A).
% 1.99/2.16 ** KEPT (pick-wt=19): 37 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -member(A,power_set(B))| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 1.99/2.16 ** KEPT (pick-wt=15): 38 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f8(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=15): 39 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f8(A,B),A).
% 1.99/2.16 ** KEPT (pick-wt=15): 40 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f8(A,B),B).
% 1.99/2.16 ** KEPT (pick-wt=6): 41 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 1.99/2.16 ** KEPT (pick-wt=7): 42 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 1.99/2.16 ** KEPT (pick-wt=15): 43 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 1.99/2.16 ** KEPT (pick-wt=15): 44 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)|ilf_type(A,member_type(B))| -member(A,B).
% 1.99/2.16 ** KEPT (pick-wt=10): 45 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f9(A),member_type(A)).
% 1.99/2.16 ** KEPT (pick-wt=18): 46 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 1.99/2.16 ** KEPT (pick-wt=18): 47 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B| -ilf_type(C,set_type)|member(C,A)| -member(C,B).
% 1.99/2.16 ** KEPT (pick-wt=14): 48 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B|ilf_type($f10(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=19): 49 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B|member($f10(A,B),A)|member($f10(A,B),B).
% 1.99/2.16 ** KEPT (pick-wt=19): 50 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B| -member($f10(A,B),A)| -member($f10(A,B),B).
% 1.99/2.16 ** KEPT (pick-wt=16): 51 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f12(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=16): 52 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f11(A,B),set_type).
% 1.99/2.16 ** KEPT (pick-wt=20): 54 [copy,53,flip.5] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ordered_pair($f12(A,B),$f11(A,B))=B.
% 1.99/2.16 ** KEPT (pick-wt=9): 55 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f13(A),set_type).
% 1.99/2.16 ** KEPT (pick-wt=9): 56 [] -ilf_type(A,set_type)|relation_like(A)|member($f13(A),A).
% 1.99/2.16 ** KEPT (pick-wt=17): 57 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f13(A)!=ordered_pair(B,C).
% 1.99/2.16 ** KEPT (pick-wt=14): 58 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 1.99/2.16 ** KEPT (pick-wt=11): 59 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 1.99/2.16 ** KEPT (pick-wt=9): 60 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f14(A),set_type).
% 1.99/2.16 ** KEPT (pick-wt=9): 61 [] -ilf_type(A,set_type)|empty(A)|member($f14(A),A).
% 1.99/2.16 ** KEPT (pick-wt=7): 62 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 1.99/2.16 ** KEPT (pick-wt=25): 63 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))| -ilf_type(D,relation_type(A,B))|intersection4(A,B,C,D)=intersection(C,D).
% 1.99/2.16 ** KEPT (pick-wt=25): 64 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))| -ilf_type(D,relation_type(A,B))|ilf_type(intersection4(A,B,C,D),relation_type(A,B)).
% 1.99/2.16 ** KEPT (pick-wt=7): 65 [] intersection($c2,cross_product($c4,$c3))!=$c2.
% 1.99/2.16
% 1.99/2.16 ------------> process sos:
% 1.99/2.16 ** KEPT (pick-wt=3): 191 [] A=A.
% 1.99/2.16 ** KEPT (pick-wt=3): 192 [] ilf_type($c1,binary_relation_type).
% 1.99/2.16 ** KEPT (pick-wt=3): 193 [] ilf_type(A,set_type).
% 1.99/2.16 Following clause subsumed by 193 during input processing: 0 [] ilf_type($c4,set_type).
% 1.99/2.16 Following clause subsumed by 193 during input processing: 0 [] ilf_type($c3,set_type).
% 1.99/2.16 ** KEPT (pick-wt=5): 194 [] ilf_type($c2,relation_type($c4,$c3)).
% 1.99/2.16 Following clause subsumed by 191 during input processing: 0 [copy,191,flip.1] A=A.
% 4.18/4.36 191 back subsumes 128.
% 4.18/4.36 191 back subsumes 127.
% 4.18/4.36 191 back subsumes 126.
% 4.18/4.36 191 back subsumes 108.
% 4.18/4.36 191 back subsumes 31.
% 4.18/4.36 193 back subsumes 142.
% 4.18/4.36 193 back subsumes 141.
% 4.18/4.36 193 back subsumes 130.
% 4.18/4.36 193 back subsumes 129.
% 4.18/4.36 193 back subsumes 117.
% 4.18/4.36 193 back subsumes 109.
% 4.18/4.36 193 back subsumes 102.
% 4.18/4.36 193 back subsumes 93.
% 4.18/4.36 193 back subsumes 72.
% 4.18/4.36 193 back subsumes 71.
% 4.18/4.36 193 back subsumes 70.
% 4.18/4.36 193 back subsumes 69.
% 4.18/4.36 193 back subsumes 68.
% 4.18/4.36 193 back subsumes 67.
% 4.18/4.36 193 back subsumes 60.
% 4.18/4.36 193 back subsumes 55.
% 4.18/4.36 193 back subsumes 52.
% 4.18/4.36 193 back subsumes 51.
% 4.18/4.36 193 back subsumes 48.
% 4.18/4.36 193 back subsumes 42.
% 4.18/4.36 193 back subsumes 38.
% 4.18/4.36 193 back subsumes 33.
% 4.18/4.36 193 back subsumes 24.
% 4.18/4.36 193 back subsumes 20.
% 4.18/4.36 193 back subsumes 19.
% 4.18/4.36 193 back subsumes 13.
% 4.18/4.36 193 back subsumes 9.
% 4.18/4.36 193 back subsumes 3.
% 4.18/4.36 193 back subsumes 2.
% 4.18/4.36
% 4.18/4.36 ======= end of input processing =======
% 4.18/4.36
% 4.18/4.36 =========== start of search ===========
% 4.18/4.36
% 4.18/4.36
% 4.18/4.36 Resetting weight limit to 11.
% 4.18/4.36
% 4.18/4.36
% 4.18/4.36 Resetting weight limit to 11.
% 4.18/4.36
% 4.18/4.36 sos_size=413
% 4.18/4.36
% 4.18/4.36
% 4.18/4.36 Resetting weight limit to 10.
% 4.18/4.36
% 4.18/4.36
% 4.18/4.36 Resetting weight limit to 10.
% 4.18/4.36
% 4.18/4.36 sos_size=455
% 4.18/4.36
% 4.18/4.36
% 4.18/4.36 Resetting weight limit to 9.
% 4.18/4.36
% 4.18/4.36
% 4.18/4.36 Resetting weight limit to 9.
% 4.18/4.36
% 4.18/4.36 sos_size=455
% 4.18/4.36
% 4.18/4.36 -------- PROOF --------
% 4.18/4.36
% 4.18/4.36 ----> UNIT CONFLICT at 2.27 sec ----> 990 [binary,989.1,741.1] $F.
% 4.18/4.36
% 4.18/4.36 Length of proof is 16. Level of proof is 8.
% 4.18/4.36
% 4.18/4.36 ---------------- PROOF ----------------
% 4.18/4.36 % SZS status Theorem
% 4.18/4.36 % SZS output start Refutation
% See solution above
% 4.18/4.36 ------------ end of proof -------------
% 4.18/4.36
% 4.18/4.36
% 4.18/4.36 Search stopped by max_proofs option.
% 4.18/4.36
% 4.18/4.36
% 4.18/4.36 Search stopped by max_proofs option.
% 4.18/4.36
% 4.18/4.36 ============ end of search ============
% 4.18/4.36
% 4.18/4.36 -------------- statistics -------------
% 4.18/4.36 clauses given 243
% 4.18/4.36 clauses generated 101551
% 4.18/4.36 clauses kept 981
% 4.18/4.36 clauses forward subsumed 2735
% 4.18/4.36 clauses back subsumed 208
% 4.18/4.36 Kbytes malloced 5859
% 4.18/4.36
% 4.18/4.36 ----------- times (seconds) -----------
% 4.18/4.36 user CPU time 2.27 (0 hr, 0 min, 2 sec)
% 4.18/4.36 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 4.18/4.36 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 4.18/4.36
% 4.18/4.36 That finishes the proof of the theorem.
% 4.18/4.36
% 4.18/4.36 Process 8273 finished Wed Jul 27 10:42:40 2022
% 4.18/4.36 Otter interrupted
% 4.18/4.36 PROOF FOUND
%------------------------------------------------------------------------------