TSTP Solution File: SET675+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET675+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:14:02 EDT 2022
% Result : Theorem 1.88s 2.10s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of clauses : 34 ( 17 unt; 0 nHn; 30 RR)
% Number of literals : 74 ( 28 equ; 43 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 40 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ilf_type(A,binary_relation_type)
| image(A,domain_of(A)) = range_of(A) ),
file('SET675+3.p',unknown),
[] ).
cnf(2,plain,
( ~ ilf_type(A,binary_relation_type)
| range_of(A) = image(A,domain_of(A)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.2')] ).
cnf(3,axiom,
( ~ ilf_type(A,binary_relation_type)
| inverse2(A,range_of(A)) = domain_of(A) ),
file('SET675+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| image4(A,B,C,A) = range(A,B,C) ),
file('SET675+3.p',unknown),
[] ).
cnf(5,plain,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| range(A,B,C) = image4(A,B,C,A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.4')] ).
cnf(6,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| inverse4(A,B,C,B) = domain(A,B,C) ),
file('SET675+3.p',unknown),
[] ).
cnf(7,plain,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| domain(A,B,C) = inverse4(A,B,C,B) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.4')] ).
cnf(9,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('SET675+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ ilf_type(A,set_type)
| ilf_type(A,binary_relation_type)
| ~ relation_like(A) ),
file('SET675+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| relation_like(C) ),
file('SET675+3.p',unknown),
[] ).
cnf(51,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('SET675+3.p',unknown),
[] ).
cnf(53,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('SET675+3.p',unknown),
[] ).
cnf(55,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(D,set_type)
| image4(A,B,C,D) = image(C,D) ),
file('SET675+3.p',unknown),
[] ).
cnf(57,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(D,set_type)
| inverse4(A,B,C,D) = inverse2(C,D) ),
file('SET675+3.p',unknown),
[] ).
cnf(59,axiom,
( image4(dollar_c3,dollar_c4,dollar_c2,inverse4(dollar_c3,dollar_c4,dollar_c2,dollar_c4)) != range(dollar_c3,dollar_c4,dollar_c2)
| inverse4(dollar_c3,dollar_c4,dollar_c2,image4(dollar_c3,dollar_c4,dollar_c2,dollar_c3)) != domain(dollar_c3,dollar_c4,dollar_c2) ),
file('SET675+3.p',unknown),
[] ).
cnf(60,plain,
( range(dollar_c3,dollar_c4,dollar_c2) != image4(dollar_c3,dollar_c4,dollar_c2,inverse4(dollar_c3,dollar_c4,dollar_c2,dollar_c4))
| domain(dollar_c3,dollar_c4,dollar_c2) != inverse4(dollar_c3,dollar_c4,dollar_c2,image4(dollar_c3,dollar_c4,dollar_c2,dollar_c3)) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[59])])]),
[iquote('copy,59,flip.1,flip.2')] ).
cnf(110,axiom,
A = A,
file('SET675+3.p',unknown),
[] ).
cnf(112,axiom,
ilf_type(A,set_type),
file('SET675+3.p',unknown),
[] ).
cnf(113,axiom,
ilf_type(dollar_c2,relation_type(dollar_c3,dollar_c4)),
file('SET675+3.p',unknown),
[] ).
cnf(149,plain,
inverse2(dollar_c2,A) = inverse4(dollar_c3,dollar_c4,dollar_c2,A),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[113,57,112,112,112])]),
[iquote('hyper,113,57,112,112,112,flip.1')] ).
cnf(152,plain,
image(dollar_c2,A) = image4(dollar_c3,dollar_c4,dollar_c2,A),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[113,55,112,112,112])]),
[iquote('hyper,113,55,112,112,112,flip.1')] ).
cnf(154,plain,
range_of(dollar_c2) = range(dollar_c3,dollar_c4,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[113,53,112,112])]),
[iquote('hyper,113,53,112,112,flip.1')] ).
cnf(157,plain,
domain_of(dollar_c2) = domain(dollar_c3,dollar_c4,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[113,51,112,112])]),
[iquote('hyper,113,51,112,112,flip.1')] ).
cnf(159,plain,
ilf_type(dollar_c2,subset_type(cross_product(dollar_c3,dollar_c4))),
inference(hyper,[status(thm)],[113,9,112,112]),
[iquote('hyper,113,9,112,112')] ).
cnf(161,plain,
domain(dollar_c3,dollar_c4,dollar_c2) = inverse4(dollar_c3,dollar_c4,dollar_c2,dollar_c4),
inference(hyper,[status(thm)],[113,7,112,112]),
[iquote('hyper,113,7,112,112')] ).
cnf(163,plain,
range(dollar_c3,dollar_c4,dollar_c2) = image4(dollar_c3,dollar_c4,dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[113,5,112,112]),
[iquote('hyper,113,5,112,112')] ).
cnf(165,plain,
domain_of(dollar_c2) = inverse4(dollar_c3,dollar_c4,dollar_c2,dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[157]),161]),
[iquote('back_demod,157,demod,161')] ).
cnf(166,plain,
( image4(dollar_c3,dollar_c4,dollar_c2,inverse4(dollar_c3,dollar_c4,dollar_c2,dollar_c4)) != image4(dollar_c3,dollar_c4,dollar_c2,dollar_c3)
| inverse4(dollar_c3,dollar_c4,dollar_c2,image4(dollar_c3,dollar_c4,dollar_c2,dollar_c3)) != inverse4(dollar_c3,dollar_c4,dollar_c2,dollar_c4) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[60]),163,161])])]),
[iquote('back_demod,60,demod,163,161,flip.1,flip.2')] ).
cnf(168,plain,
range_of(dollar_c2) = image4(dollar_c3,dollar_c4,dollar_c2,dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[154]),163]),
[iquote('back_demod,154,demod,163')] ).
cnf(190,plain,
relation_like(dollar_c2),
inference(hyper,[status(thm)],[159,45,112,112]),
[iquote('hyper,159,45,112,112')] ).
cnf(197,plain,
ilf_type(dollar_c2,binary_relation_type),
inference(hyper,[status(thm)],[190,20,112]),
[iquote('hyper,190,20,112')] ).
cnf(200,plain,
inverse4(dollar_c3,dollar_c4,dollar_c2,image4(dollar_c3,dollar_c4,dollar_c2,dollar_c3)) = inverse4(dollar_c3,dollar_c4,dollar_c2,dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[197,3]),168,149,165]),
[iquote('hyper,197,3,demod,168,149,165')] ).
cnf(202,plain,
image4(dollar_c3,dollar_c4,dollar_c2,inverse4(dollar_c3,dollar_c4,dollar_c2,dollar_c4)) = image4(dollar_c3,dollar_c4,dollar_c2,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[197,2]),168,165,152])]),
[iquote('hyper,197,2,demod,168,165,152,flip.1')] ).
cnf(203,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[166]),202,200]),110,110]),
[iquote('back_demod,166,demod,202,200,unit_del,110,110')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET675+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 10:52:20 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.88/2.08 ----- Otter 3.3f, August 2004 -----
% 1.88/2.08 The process was started by sandbox on n012.cluster.edu,
% 1.88/2.08 Wed Jul 27 10:52:20 2022
% 1.88/2.08 The command was "./otter". The process ID is 9699.
% 1.88/2.08
% 1.88/2.08 set(prolog_style_variables).
% 1.88/2.08 set(auto).
% 1.88/2.08 dependent: set(auto1).
% 1.88/2.08 dependent: set(process_input).
% 1.88/2.08 dependent: clear(print_kept).
% 1.88/2.08 dependent: clear(print_new_demod).
% 1.88/2.08 dependent: clear(print_back_demod).
% 1.88/2.08 dependent: clear(print_back_sub).
% 1.88/2.08 dependent: set(control_memory).
% 1.88/2.08 dependent: assign(max_mem, 12000).
% 1.88/2.08 dependent: assign(pick_given_ratio, 4).
% 1.88/2.08 dependent: assign(stats_level, 1).
% 1.88/2.08 dependent: assign(max_seconds, 10800).
% 1.88/2.08 clear(print_given).
% 1.88/2.08
% 1.88/2.08 formula_list(usable).
% 1.88/2.08 all A (A=A).
% 1.88/2.08 all B (ilf_type(B,binary_relation_type)->image(B,domain_of(B))=range_of(B)).
% 1.88/2.08 all B (ilf_type(B,binary_relation_type)->inverse2(B,range_of(B))=domain_of(B)).
% 1.88/2.08 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->image4(B,C,D,B)=range(B,C,D)&inverse4(B,C,D,C)=domain(B,C,D)))))).
% 1.88/2.08 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)))))))).
% 1.88/2.08 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (exists D ilf_type(D,relation_type(C,B)))))).
% 1.88/2.08 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (B=C<->subset(B,C)&subset(C,B))))).
% 1.88/2.08 all B (ilf_type(B,binary_relation_type)-> (all C (ilf_type(C,set_type)->ilf_type(inverse2(B,C),set_type)))).
% 1.88/2.08 all B (ilf_type(B,binary_relation_type)->ilf_type(domain_of(B),set_type)).
% 1.88/2.08 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 1.88/2.08 all B (ilf_type(B,binary_relation_type)->ilf_type(range_of(B),set_type)).
% 1.88/2.08 all B (ilf_type(B,binary_relation_type)-> (all C (ilf_type(C,set_type)->ilf_type(image(B,C),set_type)))).
% 1.88/2.08 all B (ilf_type(B,set_type)-> (ilf_type(B,binary_relation_type)<->relation_like(B)&ilf_type(B,set_type))).
% 1.88/2.08 exists B ilf_type(B,binary_relation_type).
% 1.88/2.08 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))))))).
% 1.88/2.08 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 1.88/2.08 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)))))))).
% 1.88/2.08 all B (ilf_type(B,set_type)->subset(B,B)).
% 1.88/2.08 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)))))))).
% 1.88/2.08 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 1.88/2.08 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))))).
% 1.88/2.08 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 1.88/2.08 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)))))))))).
% 1.88/2.08 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)))))).
% 1.88/2.08 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 1.88/2.08 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 1.88/2.08 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 1.88/2.08 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)))))).
% 1.88/2.08 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))))))).
% 1.88/2.08 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)))))).
% 1.88/2.08 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))))))).
% 1.88/2.08 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,set_type)->image4(B,C,D,E)=image(D,E)))))))).
% 1.88/2.08 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,set_type)->ilf_type(image4(B,C,D,E),subset_type(C))))))))).
% 1.88/2.08 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,set_type)->inverse4(B,C,D,E)=inverse2(D,E)))))))).
% 1.88/2.08 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,set_type)->ilf_type(inverse4(B,C,D,E),subset_type(B))))))))).
% 1.88/2.08 all B ilf_type(B,set_type).
% 1.88/2.08 -(all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(C,B))->image4(C,B,D,inverse4(C,B,D,B))=range(C,B,D)&inverse4(C,B,D,image4(C,B,D,C))=domain(C,B,D))))))).
% 1.88/2.08 end_of_list.
% 1.88/2.08
% 1.88/2.08 -------> usable clausifies to:
% 1.88/2.08
% 1.88/2.08 list(usable).
% 1.88/2.08 0 [] A=A.
% 1.88/2.08 0 [] -ilf_type(B,binary_relation_type)|image(B,domain_of(B))=range_of(B).
% 1.88/2.08 0 [] -ilf_type(B,binary_relation_type)|inverse2(B,range_of(B))=domain_of(B).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|image4(B,C,D,B)=range(B,C,D).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|inverse4(B,C,D,C)=domain(B,C,D).
% 1.88/2.08 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)).
% 1.88/2.08 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))).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type($f1(B,C),relation_type(C,B)).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C|subset(B,C).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C|subset(C,B).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C| -subset(B,C)| -subset(C,B).
% 1.88/2.08 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,set_type)|ilf_type(inverse2(B,C),set_type).
% 1.88/2.08 0 [] -ilf_type(B,binary_relation_type)|ilf_type(domain_of(B),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 1.88/2.08 0 [] -ilf_type(B,binary_relation_type)|ilf_type(range_of(B),set_type).
% 1.88/2.08 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,set_type)|ilf_type(image(B,C),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(B,binary_relation_type)|relation_like(B).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|ilf_type(B,binary_relation_type)| -relation_like(B).
% 1.88/2.08 0 [] ilf_type($c1,binary_relation_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(C,subset_type(B))|ilf_type(C,member_type(power_set(B))).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(C,subset_type(B))| -ilf_type(C,member_type(power_set(B))).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|ilf_type($f2(B),subset_type(B)).
% 1.88/2.08 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).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|ilf_type($f3(B,C),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|member($f3(B,C),B).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)| -member($f3(B,C),C).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|subset(B,B).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(B,power_set(C))| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f4(B,C),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f4(B,C),B).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f4(B,C),C).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 1.88/2.08 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f5(B),member_type(B)).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f7(B,C),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f6(B,C),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|C=ordered_pair($f7(B,C),$f6(B,C)).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f8(B),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f8(B),B).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f8(B)!=ordered_pair(D,E).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f9(B),set_type).
% 1.88/2.08 0 [] -ilf_type(B,set_type)|empty(B)|member($f9(B),B).
% 1.88/2.08 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 1.88/2.08 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).
% 1.88/2.08 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)).
% 1.88/2.08 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).
% 1.88/2.08 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)).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))| -ilf_type(E,set_type)|image4(B,C,D,E)=image(D,E).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))| -ilf_type(E,set_type)|ilf_type(image4(B,C,D,E),subset_type(C)).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))| -ilf_type(E,set_type)|inverse4(B,C,D,E)=inverse2(D,E).
% 1.88/2.08 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))| -ilf_type(E,set_type)|ilf_type(inverse4(B,C,D,E),subset_type(B)).
% 1.88/2.08 0 [] ilf_type(B,set_type).
% 1.88/2.08 0 [] ilf_type($c4,set_type).
% 1.88/2.08 0 [] ilf_type($c3,set_type).
% 1.88/2.08 0 [] ilf_type($c2,relation_type($c3,$c4)).
% 1.88/2.08 0 [] image4($c3,$c4,$c2,inverse4($c3,$c4,$c2,$c4))!=range($c3,$c4,$c2)|inverse4($c3,$c4,$c2,image4($c3,$c4,$c2,$c3))!=domain($c3,$c4,$c2).
% 1.88/2.08 end_of_list.
% 1.88/2.08
% 1.88/2.08 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.88/2.08
% 1.88/2.08 This ia a non-Horn set with equality. The strategy will be
% 1.88/2.08 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.88/2.08 deletion, with positive clauses in sos and nonpositive
% 1.88/2.08 clauses in usable.
% 1.88/2.08
% 1.88/2.08 dependent: set(knuth_bendix).
% 1.88/2.08 dependent: set(anl_eq).
% 1.88/2.08 dependent: set(para_from).
% 1.88/2.08 dependent: set(para_into).
% 1.88/2.08 dependent: clear(para_from_right).
% 1.88/2.08 dependent: clear(para_into_right).
% 1.88/2.08 dependent: set(para_from_vars).
% 1.88/2.08 dependent: set(eq_units_both_ways).
% 1.88/2.08 dependent: set(dynamic_demod_all).
% 1.88/2.08 dependent: set(dynamic_demod).
% 1.88/2.08 dependent: set(order_eq).
% 1.88/2.08 dependent: set(back_demod).
% 1.88/2.08 dependent: set(lrpo).
% 1.88/2.08 dependent: set(hyper_res).
% 1.88/2.08 dependent: set(unit_deletion).
% 1.88/2.08 dependent: set(factor).
% 1.88/2.08
% 1.88/2.08 ------------> process usable:
% 1.88/2.08 ** KEPT (pick-wt=10): 2 [copy,1,flip.2] -ilf_type(A,binary_relation_type)|range_of(A)=image(A,domain_of(A)).
% 1.88/2.08 ** KEPT (pick-wt=10): 3 [] -ilf_type(A,binary_relation_type)|inverse2(A,range_of(A))=domain_of(A).
% 1.88/2.08 ** KEPT (pick-wt=21): 5 [copy,4,flip.4] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|range(A,B,C)=image4(A,B,C,A).
% 1.88/2.08 ** KEPT (pick-wt=21): 7 [copy,6,flip.4] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|domain(A,B,C)=inverse4(A,B,C,B).
% 1.88/2.08 ** KEPT (pick-wt=17): 8 [] -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)).
% 1.88/2.08 ** KEPT (pick-wt=17): 9 [] -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))).
% 1.88/2.08 ** KEPT (pick-wt=13): 10 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type($f1(A,B),relation_type(B,A)).
% 1.88/2.08 ** KEPT (pick-wt=12): 11 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B|subset(A,B).
% 1.88/2.08 ** KEPT (pick-wt=12): 12 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B|subset(B,A).
% 1.88/2.09 ** KEPT (pick-wt=15): 13 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B| -subset(A,B)| -subset(B,A).
% 1.88/2.09 ** KEPT (pick-wt=11): 14 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,set_type)|ilf_type(inverse2(A,B),set_type).
% 1.88/2.09 ** KEPT (pick-wt=7): 15 [] -ilf_type(A,binary_relation_type)|ilf_type(domain_of(A),set_type).
% 1.88/2.09 ** KEPT (pick-wt=11): 16 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 1.88/2.09 ** KEPT (pick-wt=7): 17 [] -ilf_type(A,binary_relation_type)|ilf_type(range_of(A),set_type).
% 1.88/2.09 ** KEPT (pick-wt=11): 18 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,set_type)|ilf_type(image(A,B),set_type).
% 1.88/2.09 ** KEPT (pick-wt=8): 19 [] -ilf_type(A,set_type)| -ilf_type(A,binary_relation_type)|relation_like(A).
% 1.88/2.09 ** KEPT (pick-wt=8): 20 [] -ilf_type(A,set_type)|ilf_type(A,binary_relation_type)| -relation_like(A).
% 1.88/2.09 ** KEPT (pick-wt=15): 21 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A))).
% 1.88/2.09 ** KEPT (pick-wt=15): 22 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,subset_type(A))| -ilf_type(B,member_type(power_set(A))).
% 1.88/2.09 ** KEPT (pick-wt=8): 23 [] -ilf_type(A,set_type)|ilf_type($f2(A),subset_type(A)).
% 1.88/2.09 ** KEPT (pick-wt=18): 24 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -subset(A,B)| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 1.88/2.09 ** KEPT (pick-wt=14): 25 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|ilf_type($f3(A,B),set_type).
% 1.88/2.09 ** KEPT (pick-wt=14): 26 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|member($f3(A,B),A).
% 1.88/2.09 ** KEPT (pick-wt=14): 27 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)| -member($f3(A,B),B).
% 1.88/2.09 ** KEPT (pick-wt=6): 28 [] -ilf_type(A,set_type)|subset(A,A).
% 1.88/2.09 ** KEPT (pick-wt=19): 29 [] -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).
% 1.88/2.09 ** KEPT (pick-wt=15): 30 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f4(A,B),set_type).
% 1.88/2.09 ** KEPT (pick-wt=15): 31 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f4(A,B),A).
% 1.88/2.09 ** KEPT (pick-wt=15): 32 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f4(A,B),B).
% 1.88/2.09 ** KEPT (pick-wt=6): 33 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 1.88/2.09 ** KEPT (pick-wt=7): 34 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 1.88/2.09 ** KEPT (pick-wt=15): 35 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 1.88/2.09 ** KEPT (pick-wt=15): 36 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)|ilf_type(A,member_type(B))| -member(A,B).
% 1.88/2.09 ** KEPT (pick-wt=10): 37 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f5(A),member_type(A)).
% 1.88/2.09 ** KEPT (pick-wt=16): 38 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f7(A,B),set_type).
% 1.88/2.09 ** KEPT (pick-wt=16): 39 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f6(A,B),set_type).
% 1.88/2.09 ** KEPT (pick-wt=20): 41 [copy,40,flip.5] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ordered_pair($f7(A,B),$f6(A,B))=B.
% 1.88/2.09 ** KEPT (pick-wt=9): 42 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f8(A),set_type).
% 1.88/2.09 ** KEPT (pick-wt=9): 43 [] -ilf_type(A,set_type)|relation_like(A)|member($f8(A),A).
% 1.88/2.09 ** KEPT (pick-wt=17): 44 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f8(A)!=ordered_pair(B,C).
% 1.88/2.09 ** KEPT (pick-wt=14): 45 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 1.88/2.09 ** KEPT (pick-wt=11): 46 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 1.88/2.09 ** KEPT (pick-wt=11): 47 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 1.88/2.09 ** KEPT (pick-wt=9): 48 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f9(A),set_type).
% 1.88/2.09 ** KEPT (pick-wt=9): 49 [] -ilf_type(A,set_type)|empty(A)|member($f9(A),A).
% 1.88/2.09 ** KEPT (pick-wt=7): 50 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 1.88/2.10 ** KEPT (pick-wt=18): 51 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|domain(A,B,C)=domain_of(C).
% 1.88/2.10 ** KEPT (pick-wt=18): 52 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(domain(A,B,C),subset_type(A)).
% 1.88/2.10 ** KEPT (pick-wt=18): 53 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|range(A,B,C)=range_of(C).
% 1.88/2.10 ** KEPT (pick-wt=18): 54 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(range(A,B,C),subset_type(B)).
% 1.88/2.10 ** KEPT (pick-wt=23): 55 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))| -ilf_type(D,set_type)|image4(A,B,C,D)=image(C,D).
% 1.88/2.10 ** KEPT (pick-wt=22): 56 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))| -ilf_type(D,set_type)|ilf_type(image4(A,B,C,D),subset_type(B)).
% 1.88/2.10 ** KEPT (pick-wt=23): 57 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))| -ilf_type(D,set_type)|inverse4(A,B,C,D)=inverse2(C,D).
% 1.88/2.10 ** KEPT (pick-wt=22): 58 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))| -ilf_type(D,set_type)|ilf_type(inverse4(A,B,C,D),subset_type(A)).
% 1.88/2.10 ** KEPT (pick-wt=28): 60 [copy,59,flip.1,flip.2] range($c3,$c4,$c2)!=image4($c3,$c4,$c2,inverse4($c3,$c4,$c2,$c4))|domain($c3,$c4,$c2)!=inverse4($c3,$c4,$c2,image4($c3,$c4,$c2,$c3)).
% 1.88/2.10
% 1.88/2.10 ------------> process sos:
% 1.88/2.10 ** KEPT (pick-wt=3): 110 [] A=A.
% 1.88/2.10 ** KEPT (pick-wt=3): 111 [] ilf_type($c1,binary_relation_type).
% 1.88/2.10 ** KEPT (pick-wt=3): 112 [] ilf_type(A,set_type).
% 1.88/2.10 Following clause subsumed by 112 during input processing: 0 [] ilf_type($c4,set_type).
% 1.88/2.10 Following clause subsumed by 112 during input processing: 0 [] ilf_type($c3,set_type).
% 1.88/2.10 ** KEPT (pick-wt=5): 113 [] ilf_type($c2,relation_type($c3,$c4)).
% 1.88/2.10 Following clause subsumed by 110 during input processing: 0 [copy,110,flip.1] A=A.
% 1.88/2.10 110 back subsumes 66.
% 1.88/2.10 112 back subsumes 87.
% 1.88/2.10 112 back subsumes 81.
% 1.88/2.10 112 back subsumes 80.
% 1.88/2.10 112 back subsumes 75.
% 1.88/2.10 112 back subsumes 67.
% 1.88/2.10 112 back subsumes 48.
% 1.88/2.10 112 back subsumes 46.
% 1.88/2.10 112 back subsumes 42.
% 1.88/2.10 112 back subsumes 39.
% 1.88/2.10 112 back subsumes 38.
% 1.88/2.10 112 back subsumes 34.
% 1.88/2.10 112 back subsumes 30.
% 1.88/2.10 112 back subsumes 25.
% 1.88/2.10 112 back subsumes 18.
% 1.88/2.10 112 back subsumes 17.
% 1.88/2.10 112 back subsumes 16.
% 1.88/2.10 112 back subsumes 15.
% 1.88/2.10 112 back subsumes 14.
% 1.88/2.10
% 1.88/2.10 ======= end of input processing =======
% 1.88/2.10
% 1.88/2.10 =========== start of search ===========
% 1.88/2.10
% 1.88/2.10 -------- PROOF --------
% 1.88/2.10
% 1.88/2.10 -----> EMPTY CLAUSE at 0.02 sec ----> 203 [back_demod,166,demod,202,200,unit_del,110,110] $F.
% 1.88/2.10
% 1.88/2.10 Length of proof is 18. Level of proof is 4.
% 1.88/2.10
% 1.88/2.10 ---------------- PROOF ----------------
% 1.88/2.10 % SZS status Theorem
% 1.88/2.10 % SZS output start Refutation
% See solution above
% 1.88/2.10 ------------ end of proof -------------
% 1.88/2.10
% 1.88/2.10
% 1.88/2.10 Search stopped by max_proofs option.
% 1.88/2.10
% 1.88/2.10
% 1.88/2.10 Search stopped by max_proofs option.
% 1.88/2.10
% 1.88/2.10 ============ end of search ============
% 1.88/2.10
% 1.88/2.10 -------------- statistics -------------
% 1.88/2.10 clauses given 14
% 1.88/2.10 clauses generated 181
% 1.88/2.10 clauses kept 180
% 1.88/2.10 clauses forward subsumed 67
% 1.88/2.10 clauses back subsumed 37
% 1.88/2.10 Kbytes malloced 1953
% 1.88/2.10
% 1.88/2.10 ----------- times (seconds) -----------
% 1.88/2.10 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.88/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.88/2.10
% 1.88/2.10 That finishes the proof of the theorem.
% 1.88/2.10
% 1.88/2.10 Process 9699 finished Wed Jul 27 10:52:22 2022
% 1.88/2.10 Otter interrupted
% 1.88/2.10 PROOF FOUND
%------------------------------------------------------------------------------