TSTP Solution File: SET664+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET664+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 13:14:01 EDT 2022
% Result : Theorem 1.99s 2.20s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 14 unt; 0 nHn; 20 RR)
% Number of literals : 39 ( 10 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ilf_type(A,set_type)
| ~ subset(A,empty_set)
| A = empty_set ),
file('SET664+3.p',unknown),
[] ).
cnf(3,axiom,
( ~ ilf_type(A,binary_relation_type)
| range_of(A) != empty_set
| A = empty_set ),
file('SET664+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| subset(range_of(C),B) ),
file('SET664+3.p',unknown),
[] ).
cnf(8,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('SET664+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ ilf_type(A,set_type)
| ilf_type(A,binary_relation_type)
| ~ relation_like(A) ),
file('SET664+3.p',unknown),
[] ).
cnf(52,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| relation_like(C) ),
file('SET664+3.p',unknown),
[] ).
cnf(55,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('SET664+3.p',unknown),
[] ).
cnf(57,axiom,
dollar_c2 != empty_set,
file('SET664+3.p',unknown),
[] ).
cnf(58,plain,
empty_set != dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[57])]),
[iquote('copy,57,flip.1')] ).
cnf(97,axiom,
ilf_type(A,set_type),
file('SET664+3.p',unknown),
[] ).
cnf(98,axiom,
ilf_type(dollar_c2,relation_type(dollar_c3,dollar_c4)),
file('SET664+3.p',unknown),
[] ).
cnf(99,axiom,
ilf_type(dollar_c2,relation_type(dollar_c3,empty_set)),
file('SET664+3.p',unknown),
[] ).
cnf(141,plain,
range_of(dollar_c2) = range(dollar_c3,dollar_c4,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[98,55,97,97])]),
[iquote('hyper,98,55,97,97,flip.1')] ).
cnf(145,plain,
ilf_type(dollar_c2,subset_type(cross_product(dollar_c3,dollar_c4))),
inference(hyper,[status(thm)],[98,8,97,97]),
[iquote('hyper,98,8,97,97')] ).
cnf(191,plain,
subset(range(dollar_c3,dollar_c4,dollar_c2),empty_set),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[99,5,97,97]),141]),
[iquote('hyper,99,5,97,97,demod,141')] ).
cnf(299,plain,
relation_like(dollar_c2),
inference(hyper,[status(thm)],[145,52,97,97]),
[iquote('hyper,145,52,97,97')] ).
cnf(405,plain,
ilf_type(dollar_c2,binary_relation_type),
inference(hyper,[status(thm)],[299,21,97]),
[iquote('hyper,299,21,97')] ).
cnf(596,plain,
range(dollar_c3,dollar_c4,dollar_c2) = empty_set,
inference(hyper,[status(thm)],[191,1,97]),
[iquote('hyper,191,1,97')] ).
cnf(606,plain,
range_of(dollar_c2) = empty_set,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[141]),596]),
[iquote('back_demod,140,demod,596')] ).
cnf(647,plain,
empty_set = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[606,3,405])]),
[iquote('hyper,606,3,405,flip.1')] ).
cnf(649,plain,
$false,
inference(binary,[status(thm)],[647,58]),
[iquote('binary,647.1,58.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.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 10:36:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.89/2.09 ----- Otter 3.3f, August 2004 -----
% 1.89/2.09 The process was started by sandbox on n009.cluster.edu,
% 1.89/2.09 Wed Jul 27 10:36:51 2022
% 1.89/2.09 The command was "./otter". The process ID is 969.
% 1.89/2.09
% 1.89/2.09 set(prolog_style_variables).
% 1.89/2.09 set(auto).
% 1.89/2.09 dependent: set(auto1).
% 1.89/2.09 dependent: set(process_input).
% 1.89/2.09 dependent: clear(print_kept).
% 1.89/2.09 dependent: clear(print_new_demod).
% 1.89/2.09 dependent: clear(print_back_demod).
% 1.89/2.09 dependent: clear(print_back_sub).
% 1.89/2.09 dependent: set(control_memory).
% 1.89/2.09 dependent: assign(max_mem, 12000).
% 1.89/2.09 dependent: assign(pick_given_ratio, 4).
% 1.89/2.09 dependent: assign(stats_level, 1).
% 1.89/2.09 dependent: assign(max_seconds, 10800).
% 1.89/2.09 clear(print_given).
% 1.89/2.09
% 1.89/2.09 formula_list(usable).
% 1.89/2.09 all A (A=A).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (subset(B,empty_set)->B=empty_set)).
% 1.89/2.09 all B (ilf_type(B,binary_relation_type)-> (domain_of(B)=empty_set|range_of(B)=empty_set->B=empty_set)).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->subset(domain_of(D),B)&subset(range_of(D),C)))))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> -member(B,empty_set)).
% 1.89/2.09 empty(empty_set).
% 1.89/2.09 type(empty_set,set_type).
% 1.89/2.09 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)))))))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (exists D ilf_type(D,relation_type(C,B)))))).
% 1.89/2.09 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)))))))))).
% 1.89/2.09 all B (ilf_type(B,binary_relation_type)->ilf_type(domain_of(B),set_type)).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 1.89/2.09 all B (ilf_type(B,binary_relation_type)->ilf_type(range_of(B),set_type)).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (ilf_type(B,binary_relation_type)<->relation_like(B)&ilf_type(B,set_type))).
% 1.89/2.09 exists B ilf_type(B,binary_relation_type).
% 1.89/2.09 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))))))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 1.89/2.09 all B (ilf_type(B,binary_relation_type)-> (all C (ilf_type(C,binary_relation_type)-> (B=C->C=B)))).
% 1.89/2.09 all B (ilf_type(B,binary_relation_type)->B=B).
% 1.89/2.09 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)))))))).
% 1.89/2.09 all B (ilf_type(B,set_type)->subset(B,B)).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 1.89/2.09 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)))))))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 1.89/2.09 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))))).
% 1.89/2.09 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 1.89/2.09 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)))))))))).
% 1.89/2.09 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 1.89/2.09 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)))))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->domain(B,C,D)=domain_of(D)))))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->ilf_type(domain(B,C,D),subset_type(B))))))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->range(B,C,D)=range_of(D)))))).
% 1.89/2.09 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))->ilf_type(range(B,C,D),subset_type(C))))))).
% 1.89/2.09 all B ilf_type(B,set_type).
% 1.89/2.09 -(all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(C,B))-> (ilf_type(D,relation_type(C,empty_set))->D=empty_set))))))).
% 1.89/2.09 end_of_list.
% 1.89/2.09
% 1.89/2.09 -------> usable clausifies to:
% 1.89/2.09
% 1.89/2.09 list(usable).
% 1.89/2.09 0 [] A=A.
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -subset(B,empty_set)|B=empty_set.
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)|domain_of(B)!=empty_set|B=empty_set.
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)|range_of(B)!=empty_set|B=empty_set.
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|subset(domain_of(D),B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|subset(range_of(D),C).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -member(B,empty_set).
% 1.89/2.09 0 [] empty(empty_set).
% 1.89/2.09 0 [] type(empty_set,set_type).
% 1.89/2.09 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)).
% 1.89/2.09 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))).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type($f1(B,C),relation_type(C,B)).
% 1.89/2.09 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).
% 1.89/2.09 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).
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B=C|ilf_type($f3(B,C),set_type).
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B=C|ilf_type($f2(B,C),set_type).
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B=C|member(ordered_pair($f3(B,C),$f2(B,C)),B)|member(ordered_pair($f3(B,C),$f2(B,C)),C).
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B=C| -member(ordered_pair($f3(B,C),$f2(B,C)),B)| -member(ordered_pair($f3(B,C),$f2(B,C)),C).
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)|ilf_type(domain_of(B),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)|ilf_type(range_of(B),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(B,binary_relation_type)|relation_like(B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|ilf_type(B,binary_relation_type)| -relation_like(B).
% 1.89/2.09 0 [] ilf_type($c1,binary_relation_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(C,subset_type(B))|ilf_type(C,member_type(power_set(B))).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(C,subset_type(B))| -ilf_type(C,member_type(power_set(B))).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|ilf_type($f4(B),subset_type(B)).
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|B!=C|C=B.
% 1.89/2.09 0 [] -ilf_type(B,binary_relation_type)|B=B.
% 1.89/2.09 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).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|ilf_type($f5(B,C),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|member($f5(B,C),B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)| -member($f5(B,C),C).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|subset(B,B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f6(B),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|empty(B)|member($f6(B),B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(B,power_set(C))| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f7(B,C),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f7(B,C),B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f7(B,C),C).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 1.89/2.09 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f8(B),member_type(B)).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f10(B,C),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f9(B,C),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|C=ordered_pair($f10(B,C),$f9(B,C)).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f11(B),set_type).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f11(B),B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f11(B)!=ordered_pair(D,E).
% 1.89/2.09 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 1.89/2.09 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 1.89/2.09 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).
% 1.89/2.09 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)).
% 1.89/2.09 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).
% 1.89/2.09 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)).
% 1.89/2.09 0 [] ilf_type(B,set_type).
% 1.89/2.09 0 [] ilf_type($c4,set_type).
% 1.89/2.09 0 [] ilf_type($c3,set_type).
% 1.89/2.09 0 [] ilf_type($c2,relation_type($c3,$c4)).
% 1.89/2.09 0 [] ilf_type($c2,relation_type($c3,empty_set)).
% 1.89/2.09 0 [] $c2!=empty_set.
% 1.89/2.09 end_of_list.
% 1.89/2.09
% 1.89/2.09 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.89/2.09
% 1.89/2.09 This ia a non-Horn set with equality. The strategy will be
% 1.89/2.09 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.89/2.09 deletion, with positive clauses in sos and nonpositive
% 1.89/2.09 clauses in usable.
% 1.89/2.09
% 1.89/2.09 dependent: set(knuth_bendix).
% 1.89/2.09 dependent: set(anl_eq).
% 1.89/2.09 dependent: set(para_from).
% 1.89/2.09 dependent: set(para_into).
% 1.89/2.09 dependent: clear(para_from_right).
% 1.89/2.09 dependent: clear(para_into_right).
% 1.89/2.09 dependent: set(para_from_vars).
% 1.89/2.09 dependent: set(eq_units_both_ways).
% 1.89/2.09 dependent: set(dynamic_demod_all).
% 1.89/2.09 dependent: set(dynamic_demod).
% 1.89/2.09 dependent: set(order_eq).
% 1.89/2.09 dependent: set(back_demod).
% 1.89/2.09 dependent: set(lrpo).
% 1.89/2.09 dependent: set(hyper_res).
% 1.89/2.09 dependent: set(unit_deletion).
% 1.89/2.09 dependent: set(factor).
% 1.89/2.09
% 1.89/2.09 ------------> process usable:
% 1.89/2.09 ** KEPT (pick-wt=9): 1 [] -ilf_type(A,set_type)| -subset(A,empty_set)|A=empty_set.
% 1.89/2.09 ** KEPT (pick-wt=10): 2 [] -ilf_type(A,binary_relation_type)|domain_of(A)!=empty_set|A=empty_set.
% 1.89/2.09 ** KEPT (pick-wt=10): 3 [] -ilf_type(A,binary_relation_type)|range_of(A)!=empty_set|A=empty_set.
% 1.89/2.09 ** KEPT (pick-wt=15): 4 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|subset(domain_of(C),A).
% 1.89/2.09 ** KEPT (pick-wt=15): 5 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|subset(range_of(C),B).
% 1.89/2.10 ** KEPT (pick-wt=6): 6 [] -ilf_type(A,set_type)| -member(A,empty_set).
% 1.89/2.10 ** KEPT (pick-wt=17): 7 [] -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)).
% 1.89/2.10 ** KEPT (pick-wt=17): 8 [] -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))).
% 1.89/2.10 ** KEPT (pick-wt=13): 9 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type($f1(A,B),relation_type(B,A)).
% 1.89/2.10 ** KEPT (pick-wt=25): 10 [] -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).
% 1.89/2.10 ** KEPT (pick-wt=25): 11 [] -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).
% 1.89/2.10 ** KEPT (pick-wt=14): 12 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A=B|ilf_type($f3(A,B),set_type).
% 1.89/2.10 ** KEPT (pick-wt=14): 13 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A=B|ilf_type($f2(A,B),set_type).
% 1.89/2.10 ** KEPT (pick-wt=27): 14 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A=B|member(ordered_pair($f3(A,B),$f2(A,B)),A)|member(ordered_pair($f3(A,B),$f2(A,B)),B).
% 1.89/2.10 ** KEPT (pick-wt=27): 15 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A=B| -member(ordered_pair($f3(A,B),$f2(A,B)),A)| -member(ordered_pair($f3(A,B),$f2(A,B)),B).
% 1.89/2.10 ** KEPT (pick-wt=7): 16 [] -ilf_type(A,binary_relation_type)|ilf_type(domain_of(A),set_type).
% 1.89/2.10 ** KEPT (pick-wt=11): 17 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 1.89/2.10 ** KEPT (pick-wt=7): 18 [] -ilf_type(A,binary_relation_type)|ilf_type(range_of(A),set_type).
% 1.89/2.10 ** KEPT (pick-wt=11): 19 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 1.89/2.10 ** KEPT (pick-wt=8): 20 [] -ilf_type(A,set_type)| -ilf_type(A,binary_relation_type)|relation_like(A).
% 1.89/2.10 ** KEPT (pick-wt=8): 21 [] -ilf_type(A,set_type)|ilf_type(A,binary_relation_type)| -relation_like(A).
% 1.89/2.10 ** 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))).
% 1.89/2.10 ** KEPT (pick-wt=15): 23 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,subset_type(A))| -ilf_type(B,member_type(power_set(A))).
% 1.89/2.10 ** KEPT (pick-wt=8): 24 [] -ilf_type(A,set_type)|ilf_type($f4(A),subset_type(A)).
% 1.89/2.10 ** KEPT (pick-wt=12): 25 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|A!=B|B=A.
% 1.89/2.10 ** KEPT (pick-wt=6): 26 [] -ilf_type(A,binary_relation_type)|A=A.
% 1.89/2.10 ** KEPT (pick-wt=18): 27 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -subset(A,B)| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 1.89/2.10 ** KEPT (pick-wt=14): 28 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|ilf_type($f5(A,B),set_type).
% 1.89/2.10 ** KEPT (pick-wt=14): 29 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|member($f5(A,B),A).
% 1.89/2.10 ** KEPT (pick-wt=14): 30 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)| -member($f5(A,B),B).
% 1.89/2.10 ** KEPT (pick-wt=6): 31 [] -ilf_type(A,set_type)|subset(A,A).
% 1.89/2.10 ** KEPT (pick-wt=11): 32 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 1.89/2.10 ** KEPT (pick-wt=9): 33 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f6(A),set_type).
% 1.89/2.10 ** KEPT (pick-wt=9): 34 [] -ilf_type(A,set_type)|empty(A)|member($f6(A),A).
% 1.89/2.10 ** KEPT (pick-wt=19): 35 [] -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).
% 1.89/2.10 ** KEPT (pick-wt=15): 36 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f7(A,B),set_type).
% 1.89/2.10 ** KEPT (pick-wt=15): 37 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f7(A,B),A).
% 1.89/2.10 ** KEPT (pick-wt=15): 38 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f7(A,B),B).
% 1.89/2.10 ** KEPT (pick-wt=6): 39 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 1.89/2.10 ** KEPT (pick-wt=7): 40 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 1.89/2.10 ** KEPT (pick-wt=15): 41 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 1.89/2.10 ** KEPT (pick-wt=15): 42 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)|ilf_type(A,member_type(B))| -member(A,B).
% 1.89/2.10 ** KEPT (pick-wt=10): 43 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f8(A),member_type(A)).
% 1.89/2.10 ** KEPT (pick-wt=16): 44 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f10(A,B),set_type).
% 1.89/2.10 ** KEPT (pick-wt=16): 45 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f9(A,B),set_type).
% 1.89/2.10 ** KEPT (pick-wt=20): 47 [copy,46,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.
% 1.89/2.10 ** KEPT (pick-wt=9): 48 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f11(A),set_type).
% 1.89/2.10 ** KEPT (pick-wt=9): 49 [] -ilf_type(A,set_type)|relation_like(A)|member($f11(A),A).
% 1.99/2.20 ** KEPT (pick-wt=17): 50 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f11(A)!=ordered_pair(B,C).
% 1.99/2.20 ** KEPT (pick-wt=7): 51 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 1.99/2.20 ** KEPT (pick-wt=14): 52 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 1.99/2.20 ** KEPT (pick-wt=18): 53 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|domain(A,B,C)=domain_of(C).
% 1.99/2.20 ** KEPT (pick-wt=18): 54 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(domain(A,B,C),subset_type(A)).
% 1.99/2.20 ** KEPT (pick-wt=18): 55 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|range(A,B,C)=range_of(C).
% 1.99/2.20 ** KEPT (pick-wt=18): 56 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(range(A,B,C),subset_type(B)).
% 1.99/2.20 ** KEPT (pick-wt=3): 58 [copy,57,flip.1] empty_set!=$c2.
% 1.99/2.20
% 1.99/2.20 ------------> process sos:
% 1.99/2.20 ** KEPT (pick-wt=3): 93 [] A=A.
% 1.99/2.20 ** KEPT (pick-wt=2): 94 [] empty(empty_set).
% 1.99/2.20 ** KEPT (pick-wt=3): 95 [] type(empty_set,set_type).
% 1.99/2.20 ** KEPT (pick-wt=3): 96 [] ilf_type($c1,binary_relation_type).
% 1.99/2.20 ** KEPT (pick-wt=3): 97 [] ilf_type(A,set_type).
% 1.99/2.20 Following clause subsumed by 97 during input processing: 0 [] ilf_type($c4,set_type).
% 1.99/2.20 Following clause subsumed by 97 during input processing: 0 [] ilf_type($c3,set_type).
% 1.99/2.20 ** KEPT (pick-wt=5): 98 [] ilf_type($c2,relation_type($c3,$c4)).
% 1.99/2.20 ** KEPT (pick-wt=5): 99 [] ilf_type($c2,relation_type($c3,empty_set)).
% 1.99/2.20 Following clause subsumed by 93 during input processing: 0 [copy,93,flip.1] A=A.
% 1.99/2.20 93 back subsumes 26.
% 1.99/2.20 97 back subsumes 82.
% 1.99/2.20 97 back subsumes 81.
% 1.99/2.20 97 back subsumes 76.
% 1.99/2.20 97 back subsumes 67.
% 1.99/2.20 97 back subsumes 66.
% 1.99/2.20 97 back subsumes 48.
% 1.99/2.20 97 back subsumes 45.
% 1.99/2.20 97 back subsumes 44.
% 1.99/2.20 97 back subsumes 40.
% 1.99/2.20 97 back subsumes 36.
% 1.99/2.20 97 back subsumes 33.
% 1.99/2.20 97 back subsumes 28.
% 1.99/2.20 97 back subsumes 19.
% 1.99/2.20 97 back subsumes 18.
% 1.99/2.20 97 back subsumes 17.
% 1.99/2.20 97 back subsumes 16.
% 1.99/2.20 97 back subsumes 13.
% 1.99/2.20 97 back subsumes 12.
% 1.99/2.20
% 1.99/2.20 ======= end of input processing =======
% 1.99/2.20
% 1.99/2.20 =========== start of search ===========
% 1.99/2.20
% 1.99/2.20 -------- PROOF --------
% 1.99/2.20
% 1.99/2.20 ----> UNIT CONFLICT at 0.11 sec ----> 649 [binary,647.1,58.1] $F.
% 1.99/2.20
% 1.99/2.20 Length of proof is 9. Level of proof is 5.
% 1.99/2.20
% 1.99/2.20 ---------------- PROOF ----------------
% 1.99/2.20 % SZS status Theorem
% 1.99/2.20 % SZS output start Refutation
% See solution above
% 1.99/2.20 ------------ end of proof -------------
% 1.99/2.20
% 1.99/2.20
% 1.99/2.20 Search stopped by max_proofs option.
% 1.99/2.20
% 1.99/2.20
% 1.99/2.20 Search stopped by max_proofs option.
% 1.99/2.20
% 1.99/2.20 ============ end of search ============
% 1.99/2.20
% 1.99/2.20 -------------- statistics -------------
% 1.99/2.20 clauses given 33
% 1.99/2.20 clauses generated 1345
% 1.99/2.20 clauses kept 638
% 1.99/2.20 clauses forward subsumed 752
% 1.99/2.20 clauses back subsumed 57
% 1.99/2.20 Kbytes malloced 3906
% 1.99/2.20
% 1.99/2.20 ----------- times (seconds) -----------
% 1.99/2.20 user CPU time 0.11 (0 hr, 0 min, 0 sec)
% 1.99/2.20 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.20 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.99/2.20
% 1.99/2.20 That finishes the proof of the theorem.
% 1.99/2.20
% 1.99/2.20 Process 969 finished Wed Jul 27 10:36:53 2022
% 1.99/2.20 Otter interrupted
% 1.99/2.20 PROOF FOUND
%------------------------------------------------------------------------------