%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET677+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:14:03 EDT 2022
% Result : Theorem 2.14s 2.32s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 8 unt; 0 nHn; 15 RR)
% Number of literals : 44 ( 13 equ; 29 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 20 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(B,A))
| ~ subset(identity_relation_of(B),C)
| B = domain(B,A,C) ),
file('SET677+3.p',unknown),
[] ).
cnf(2,plain,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(B,A))
| ~ subset(identity_relation_of(B),C)
| domain(B,A,C) = B ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.5')] ).
cnf(5,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| ~ subset(identity_relation_of(B),C)
| B = range(A,B,C) ),
file('SET677+3.p',unknown),
[] ).
cnf(6,plain,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(A,B))
| ~ subset(identity_relation_of(B),C)
| range(A,B,C) = B ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.5')] ).
cnf(11,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(B,identity_relation_of_type(A))
| ilf_type(B,relation_type(A,A)) ),
file('SET677+3.p',unknown),
[] ).
cnf(65,axiom,
( dollar_c3 != domain(dollar_c3,dollar_c3,dollar_c2)
| dollar_c3 != range(dollar_c3,dollar_c3,dollar_c2) ),
file('SET677+3.p',unknown),
[] ).
cnf(66,plain,
( domain(dollar_c3,dollar_c3,dollar_c2) != dollar_c3
| range(dollar_c3,dollar_c3,dollar_c2) != dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[65])])]),
[iquote('copy,65,flip.1,flip.2')] ).
cnf(67,plain,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,relation_type(A,A))
| ~ subset(identity_relation_of(A),B)
| domain(A,A,B) = A ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.2')] ).
cnf(70,plain,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,relation_type(A,A))
| ~ subset(identity_relation_of(A),B)
| range(A,A,B) = A ),
inference(factor,[status(thm)],[6]),
[iquote('factor,6.1.2')] ).
cnf(117,axiom,
A = A,
file('SET677+3.p',unknown),
[] ).
cnf(119,axiom,
ilf_type(A,set_type),
file('SET677+3.p',unknown),
[] ).
cnf(120,axiom,
ilf_type(dollar_c2,identity_relation_of_type(dollar_c3)),
file('SET677+3.p',unknown),
[] ).
cnf(121,axiom,
subset(identity_relation_of(dollar_c3),dollar_c2),
file('SET677+3.p',unknown),
[] ).
cnf(152,plain,
ilf_type(dollar_c2,relation_type(dollar_c3,dollar_c3)),
inference(hyper,[status(thm)],[120,11,119,119]),
[iquote('hyper,120,11,119,119')] ).
cnf(236,plain,
range(dollar_c3,dollar_c3,dollar_c2) = dollar_c3,
inference(hyper,[status(thm)],[152,70,119,121]),
[iquote('hyper,152,70,119,121')] ).
cnf(239,plain,
domain(dollar_c3,dollar_c3,dollar_c2) = dollar_c3,
inference(hyper,[status(thm)],[152,67,119,121]),
[iquote('hyper,152,67,119,121')] ).
cnf(243,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[66]),239,236]),117,117]),
[iquote('back_demod,66,demod,239,236,unit_del,117,117')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET677+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n026.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 10:45:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.14/2.30 ----- Otter 3.3f, August 2004 -----
% 2.14/2.30 The process was started by sandbox on n026.cluster.edu,
% 2.14/2.30 Wed Jul 27 10:45:24 2022
% 2.14/2.30 The command was "./otter". The process ID is 32070.
% 2.14/2.30
% 2.14/2.30 set(prolog_style_variables).
% 2.14/2.30 set(auto).
% 2.14/2.30 dependent: set(auto1).
% 2.14/2.30 dependent: set(process_input).
% 2.14/2.30 dependent: clear(print_kept).
% 2.14/2.30 dependent: clear(print_new_demod).
% 2.14/2.30 dependent: clear(print_back_demod).
% 2.14/2.30 dependent: clear(print_back_sub).
% 2.14/2.30 dependent: set(control_memory).
% 2.14/2.30 dependent: assign(max_mem, 12000).
% 2.14/2.30 dependent: assign(pick_given_ratio, 4).
% 2.14/2.30 dependent: assign(stats_level, 1).
% 2.14/2.30 dependent: assign(max_seconds, 10800).
% 2.14/2.30 clear(print_given).
% 2.14/2.30
% 2.14/2.30 formula_list(usable).
% 2.14/2.30 all A (A=A).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(C,B))-> (subset(identity_relation_of(C),D)->C=domain(C,B,D)&subset(C,range(C,B,D)))))))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,relation_type(B,C))-> (subset(identity_relation_of(C),D)->subset(C,domain(B,C,D))&C=range(B,C,D))))))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (all D (ilf_type(D,set_type)-> (member(ordered_pair(C,D),identity_relation_of(B))<->member(C,B)&C=D)))))).
% 2.14/2.30 all B (ilf_type(B,set_type)->ilf_type(identity_relation_of(B),binary_relation_type)).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (ilf_type(C,identity_relation_of_type(B))<->ilf_type(C,relation_type(B,B)))))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,identity_relation_of_type(B)))).
% 2.14/2.30 all B (ilf_type(B,binary_relation_type)-> (all C (ilf_type(C,binary_relation_type)-> (subset(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)))))))))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (B=C<->subset(B,C)&subset(C,B))))).
% 2.14/2.30 all B (ilf_type(B,binary_relation_type)->ilf_type(domain_of(B),set_type)).
% 2.14/2.30 all B (ilf_type(B,binary_relation_type)->ilf_type(range_of(B),set_type)).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (ilf_type(B,binary_relation_type)<->relation_like(B)&ilf_type(B,set_type))).
% 2.14/2.30 exists B ilf_type(B,binary_relation_type).
% 2.14/2.30 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)))))))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (exists D ilf_type(D,relation_type(C,B)))))).
% 2.14/2.30 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))))))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 2.14/2.30 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)))))))).
% 2.14/2.30 all B (ilf_type(B,set_type)->subset(B,B)).
% 2.14/2.30 all B (ilf_type(B,binary_relation_type)->subset(B,B)).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 2.14/2.30 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)))))))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 2.14/2.30 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))))).
% 2.14/2.30 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 2.14/2.30 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)))))))))).
% 2.14/2.30 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)))))).
% 2.14/2.30 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 2.14/2.30 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 2.14/2.30 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)))))).
% 2.14/2.30 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))))))).
% 2.14/2.30 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)))))).
% 2.14/2.30 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))))))).
% 2.14/2.30 all B ilf_type(B,set_type).
% 2.14/2.30 -(all B (ilf_type(B,set_type)-> (all C (ilf_type(C,identity_relation_of_type(B))-> (subset(identity_relation_of(B),C)->B=domain(B,B,C)&B=range(B,B,C)))))).
% 2.14/2.30 end_of_list.
% 2.14/2.30
% 2.14/2.30 -------> usable clausifies to:
% 2.14/2.30
% 2.14/2.30 list(usable).
% 2.14/2.30 0 [] A=A.
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(C,B))| -subset(identity_relation_of(C),D)|C=domain(C,B,D).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(C,B))| -subset(identity_relation_of(C),D)|subset(C,range(C,B,D)).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))| -subset(identity_relation_of(C),D)|subset(C,domain(B,C,D)).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))| -subset(identity_relation_of(C),D)|C=range(B,C,D).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(ordered_pair(C,D),identity_relation_of(B))|member(C,B).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(ordered_pair(C,D),identity_relation_of(B))|C=D.
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,set_type)|member(ordered_pair(C,D),identity_relation_of(B))| -member(C,B)|C!=D.
% 2.14/2.30 0 [] -ilf_type(B,set_type)|ilf_type(identity_relation_of(B),binary_relation_type).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(C,identity_relation_of_type(B))|ilf_type(C,relation_type(B,B)).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(C,identity_relation_of_type(B))| -ilf_type(C,relation_type(B,B)).
% 2.14/2.30 0 [] -ilf_type(B,set_type)|ilf_type($f1(B),identity_relation_of_type(B)).
% 2.14/2.30 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)| -subset(B,C)| -ilf_type(D,set_type)| -ilf_type(E,set_type)| -member(ordered_pair(D,E),B)|member(ordered_pair(D,E),C).
% 2.14/2.30 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|subset(B,C)|ilf_type($f3(B,C),set_type).
% 2.14/2.30 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|subset(B,C)|ilf_type($f2(B,C),set_type).
% 2.14/2.30 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|subset(B,C)|member(ordered_pair($f3(B,C),$f2(B,C)),B).
% 2.14/2.30 0 [] -ilf_type(B,binary_relation_type)| -ilf_type(C,binary_relation_type)|subset(B,C)| -member(ordered_pair($f3(B,C),$f2(B,C)),C).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C|subset(B,C).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C|subset(C,B).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C| -subset(B,C)| -subset(C,B).
% 2.14/2.30 0 [] -ilf_type(B,binary_relation_type)|ilf_type(domain_of(B),set_type).
% 2.14/2.30 0 [] -ilf_type(B,binary_relation_type)|ilf_type(range_of(B),set_type).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(B,binary_relation_type)|relation_like(B).
% 2.14/2.30 0 [] -ilf_type(B,set_type)|ilf_type(B,binary_relation_type)| -relation_like(B).
% 2.14/2.30 0 [] ilf_type($c1,binary_relation_type).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|ilf_type(D,relation_type(B,C)).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(E,relation_type(B,C))|ilf_type(E,subset_type(cross_product(B,C))).
% 2.14/2.30 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type($f4(B,C),relation_type(C,B)).
% 2.14/2.30 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))).
% 2.14/2.30 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))).
% 2.14/2.30 0 [] -ilf_type(B,set_type)|ilf_type($f5(B),subset_type(B)).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -subset(B,C)| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|ilf_type($f6(B,C),set_type).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)|member($f6(B,C),B).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|subset(B,C)| -member($f6(B,C),C).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|subset(B,B).
% 2.14/2.31 0 [] -ilf_type(B,binary_relation_type)|subset(B,B).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 2.14/2.31 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).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f7(B,C),set_type).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f7(B,C),B).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f7(B,C),C).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 2.14/2.31 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f8(B),member_type(B)).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f10(B,C),set_type).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f9(B,C),set_type).
% 2.14/2.31 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)).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f11(B),set_type).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f11(B),B).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f11(B)!=ordered_pair(D,E).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f12(B),set_type).
% 2.14/2.31 0 [] -ilf_type(B,set_type)|empty(B)|member($f12(B),B).
% 2.14/2.31 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|domain(B,C,D)=domain_of(D).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|ilf_type(domain(B,C,D),subset_type(B)).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|range(B,C,D)=range_of(D).
% 2.14/2.31 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,relation_type(B,C))|ilf_type(range(B,C,D),subset_type(C)).
% 2.14/2.31 0 [] ilf_type(B,set_type).
% 2.14/2.31 0 [] ilf_type($c3,set_type).
% 2.14/2.31 0 [] ilf_type($c2,identity_relation_of_type($c3)).
% 2.14/2.31 0 [] subset(identity_relation_of($c3),$c2).
% 2.14/2.31 0 [] $c3!=domain($c3,$c3,$c2)|$c3!=range($c3,$c3,$c2).
% 2.14/2.31 end_of_list.
% 2.14/2.31
% 2.14/2.31 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 2.14/2.31
% 2.14/2.31 This ia a non-Horn set with equality. The strategy will be
% 2.14/2.31 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.14/2.31 deletion, with positive clauses in sos and nonpositive
% 2.14/2.31 clauses in usable.
% 2.14/2.31
% 2.14/2.31 dependent: set(knuth_bendix).
% 2.14/2.31 dependent: set(anl_eq).
% 2.14/2.31 dependent: set(para_from).
% 2.14/2.31 dependent: set(para_into).
% 2.14/2.31 dependent: clear(para_from_right).
% 2.14/2.31 dependent: clear(para_into_right).
% 2.14/2.31 dependent: set(para_from_vars).
% 2.14/2.31 dependent: set(eq_units_both_ways).
% 2.14/2.31 dependent: set(dynamic_demod_all).
% 2.14/2.31 dependent: set(dynamic_demod).
% 2.14/2.31 dependent: set(order_eq).
% 2.14/2.31 dependent: set(back_demod).
% 2.14/2.31 dependent: set(lrpo).
% 2.14/2.31 dependent: set(hyper_res).
% 2.14/2.31 dependent: set(unit_deletion).
% 2.14/2.31 dependent: set(factor).
% 2.14/2.31
% 2.14/2.31 ------------> process usable:
% 2.14/2.31 ** KEPT (pick-wt=21): 2 [copy,1,flip.5] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(B,A))| -subset(identity_relation_of(B),C)|domain(B,A,C)=B.
% 2.14/2.31 ** KEPT (pick-wt=21): 3 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(B,A))| -subset(identity_relation_of(B),C)|subset(B,range(B,A,C)).
% 2.14/2.32 ** KEPT (pick-wt=21): 4 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))| -subset(identity_relation_of(B),C)|subset(B,domain(A,B,C)).
% 2.14/2.32 ** KEPT (pick-wt=21): 6 [copy,5,flip.5] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))| -subset(identity_relation_of(B),C)|range(A,B,C)=B.
% 2.14/2.32 ** KEPT (pick-wt=18): 7 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(ordered_pair(B,C),identity_relation_of(A))|member(B,A).
% 2.14/2.32 ** KEPT (pick-wt=18): 8 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(ordered_pair(B,C),identity_relation_of(A))|B=C.
% 2.14/2.32 ** KEPT (pick-wt=21): 9 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(ordered_pair(B,C),identity_relation_of(A))| -member(B,A)|B!=C.
% 2.14/2.32 ** KEPT (pick-wt=7): 10 [] -ilf_type(A,set_type)|ilf_type(identity_relation_of(A),binary_relation_type).
% 2.14/2.32 ** KEPT (pick-wt=15): 11 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(B,identity_relation_of_type(A))|ilf_type(B,relation_type(A,A)).
% 2.14/2.32 ** KEPT (pick-wt=15): 12 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,identity_relation_of_type(A))| -ilf_type(B,relation_type(A,A)).
% 2.14/2.32 ** KEPT (pick-wt=8): 13 [] -ilf_type(A,set_type)|ilf_type($f1(A),identity_relation_of_type(A)).
% 2.14/2.32 ** KEPT (pick-wt=25): 14 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)| -subset(A,B)| -ilf_type(C,set_type)| -ilf_type(D,set_type)| -member(ordered_pair(C,D),A)|member(ordered_pair(C,D),B).
% 2.14/2.32 ** KEPT (pick-wt=14): 15 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|subset(A,B)|ilf_type($f3(A,B),set_type).
% 2.14/2.32 ** KEPT (pick-wt=14): 16 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|subset(A,B)|ilf_type($f2(A,B),set_type).
% 2.14/2.32 ** KEPT (pick-wt=18): 17 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|subset(A,B)|member(ordered_pair($f3(A,B),$f2(A,B)),A).
% 2.14/2.32 ** KEPT (pick-wt=18): 18 [] -ilf_type(A,binary_relation_type)| -ilf_type(B,binary_relation_type)|subset(A,B)| -member(ordered_pair($f3(A,B),$f2(A,B)),B).
% 2.14/2.32 ** KEPT (pick-wt=12): 19 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B|subset(A,B).
% 2.14/2.32 ** KEPT (pick-wt=12): 20 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B|subset(B,A).
% 2.14/2.32 ** KEPT (pick-wt=15): 21 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B| -subset(A,B)| -subset(B,A).
% 2.14/2.32 ** KEPT (pick-wt=7): 22 [] -ilf_type(A,binary_relation_type)|ilf_type(domain_of(A),set_type).
% 2.14/2.32 ** KEPT (pick-wt=7): 23 [] -ilf_type(A,binary_relation_type)|ilf_type(range_of(A),set_type).
% 2.14/2.32 ** KEPT (pick-wt=11): 24 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 2.14/2.32 ** KEPT (pick-wt=8): 25 [] -ilf_type(A,set_type)| -ilf_type(A,binary_relation_type)|relation_like(A).
% 2.14/2.32 ** KEPT (pick-wt=8): 26 [] -ilf_type(A,set_type)|ilf_type(A,binary_relation_type)| -relation_like(A).
% 2.14/2.32 ** KEPT (pick-wt=17): 27 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B)).
% 2.14/2.32 ** KEPT (pick-wt=17): 28 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(C,subset_type(cross_product(A,B))).
% 2.14/2.32 ** KEPT (pick-wt=13): 29 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type($f4(A,B),relation_type(B,A)).
% 2.14/2.32 ** KEPT (pick-wt=15): 30 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A))).
% 2.14/2.32 ** KEPT (pick-wt=15): 31 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,subset_type(A))| -ilf_type(B,member_type(power_set(A))).
% 2.14/2.32 ** KEPT (pick-wt=8): 32 [] -ilf_type(A,set_type)|ilf_type($f5(A),subset_type(A)).
% 2.14/2.32 ** KEPT (pick-wt=18): 33 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -subset(A,B)| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 2.14/2.32 ** KEPT (pick-wt=14): 34 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|ilf_type($f6(A,B),set_type).
% 2.14/2.32 ** KEPT (pick-wt=14): 35 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)|member($f6(A,B),A).
% 2.14/2.32 ** KEPT (pick-wt=14): 36 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|subset(A,B)| -member($f6(A,B),B).
% 2.14/2.32 ** KEPT (pick-wt=6): 37 [] -ilf_type(A,set_type)|subset(A,A).
% 2.14/2.32 ** KEPT (pick-wt=6): 38 [] -ilf_type(A,binary_relation_type)|subset(A,A).
% 2.14/2.32 ** KEPT (pick-wt=11): 39 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 2.14/2.32 ** KEPT (pick-wt=19): 40 [] -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).
% 2.14/2.32 ** KEPT (pick-wt=15): 41 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f7(A,B),set_type).
% 2.14/2.32 ** KEPT (pick-wt=15): 42 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f7(A,B),A).
% 2.14/2.32 ** KEPT (pick-wt=15): 43 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f7(A,B),B).
% 2.14/2.32 ** KEPT (pick-wt=6): 44 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 2.14/2.32 ** KEPT (pick-wt=7): 45 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 2.14/2.32 ** KEPT (pick-wt=15): 46 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 2.14/2.32 ** KEPT (pick-wt=15): 47 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)|ilf_type(A,member_type(B))| -member(A,B).
% 2.14/2.32 ** KEPT (pick-wt=10): 48 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f8(A),member_type(A)).
% 2.14/2.32 ** KEPT (pick-wt=16): 49 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f10(A,B),set_type).
% 2.14/2.32 ** KEPT (pick-wt=16): 50 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f9(A,B),set_type).
% 2.14/2.32 ** KEPT (pick-wt=20): 52 [copy,51,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.
% 2.14/2.32 ** KEPT (pick-wt=9): 53 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f11(A),set_type).
% 2.14/2.32 ** KEPT (pick-wt=9): 54 [] -ilf_type(A,set_type)|relation_like(A)|member($f11(A),A).
% 2.14/2.32 ** KEPT (pick-wt=17): 55 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f11(A)!=ordered_pair(B,C).
% 2.14/2.32 ** KEPT (pick-wt=14): 56 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 2.14/2.32 ** KEPT (pick-wt=11): 57 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 2.14/2.32 ** KEPT (pick-wt=9): 58 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f12(A),set_type).
% 2.14/2.32 ** KEPT (pick-wt=9): 59 [] -ilf_type(A,set_type)|empty(A)|member($f12(A),A).
% 2.14/2.32 ** KEPT (pick-wt=7): 60 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 2.14/2.32 ** KEPT (pick-wt=18): 61 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|domain(A,B,C)=domain_of(C).
% 2.14/2.32 ** KEPT (pick-wt=18): 62 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(domain(A,B,C),subset_type(A)).
% 2.14/2.32 ** KEPT (pick-wt=18): 63 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|range(A,B,C)=range_of(C).
% 2.14/2.32 ** KEPT (pick-wt=18): 64 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,relation_type(A,B))|ilf_type(range(A,B,C),subset_type(B)).
% 2.14/2.32 ** KEPT (pick-wt=12): 66 [copy,65,flip.1,flip.2] domain($c3,$c3,$c2)!=$c3|range($c3,$c3,$c2)!=$c3.
% 2.14/2.32
% 2.14/2.32 ------------> process sos:
% 2.14/2.32 ** KEPT (pick-wt=3): 117 [] A=A.
% 2.14/2.32 ** KEPT (pick-wt=3): 118 [] ilf_type($c1,binary_relation_type).
% 2.14/2.32 ** KEPT (pick-wt=3): 119 [] ilf_type(A,set_type).
% 2.14/2.32 Following clause subsumed by 119 during input processing: 0 [] ilf_type($c3,set_type).
% 2.14/2.32 ** KEPT (pick-wt=4): 120 [] ilf_type($c2,identity_relation_of_type($c3)).
% 2.14/2.32 ** KEPT (pick-wt=4): 121 [] subset(identity_relation_of($c3),$c2).
% 2.14/2.32 Following clause subsumed by 117 during input processing: 0 [copy,117,flip.1] A=A.
% 2.14/2.32 117 back subsumes 114.
% 2.14/2.32 117 back subsumes 83.
% 2.14/2.32 117 back subsumes 76.
% 2.14/2.32 119 back subsumes 102.
% 2.14/2.32 119 back subsumes 101.
% 2.14/2.32 119 back subsumes 96.
% 2.14/2.32 119 back subsumes 92.
% 2.14/2.32 119 back subsumes 84.
% 2.14/2.32 119 back subsumes 58.
% 2.14/2.32 119 back subsumes 53.
% 2.14/2.32 119 back subsumes 50.
% 2.14/2.32 119 back subsumes 49.
% 2.14/2.32 119 back subsumes 45.
% 2.14/2.32 119 back subsumes 41.
% 2.14/2.32 119 back subsumes 39.
% 2.14/2.32 119 back subsumes 34.
% 2.14/2.32 119 back subsumes 24.
% 2.14/2.32 119 back subsumes 23.
% 2.14/2.32 119 back subsumes 22.
% 2.14/2.32 119 back subsumes 16.
% 2.14/2.32 119 back subsumes 15.
% 2.14/2.32
% 2.14/2.32 ======= end of input processing =======
% 2.14/2.32
% 2.14/2.32 =========== start of search ===========
% 2.14/2.32
% 2.14/2.32 -------- PROOF --------
% 2.14/2.32
% 2.14/2.32 -----> EMPTY CLAUSE at 0.02 sec ----> 243 [back_demod,66,demod,239,236,unit_del,117,117] $F.
% 2.14/2.32
% 2.14/2.32 Length of proof is 8. Level of proof is 3.
% 2.14/2.32
% 2.14/2.32 ---------------- PROOF ----------------
% 2.14/2.32 % SZS status Theorem
% 2.14/2.32 % SZS output start Refutation
% See solution above
% 2.14/2.32 ------------ end of proof -------------
% 2.14/2.32
% 2.14/2.32
% 2.14/2.32 Search stopped by max_proofs option.
% 2.14/2.32
% 2.14/2.32
% 2.14/2.32 Search stopped by max_proofs option.
% 2.14/2.32
% 2.14/2.32 ============ end of search ============
% 2.14/2.32
% 2.14/2.32 -------------- statistics -------------
% 2.14/2.32 clauses given 13
% 2.14/2.32 clauses generated 258
% 2.14/2.32 clauses kept 233
% 2.14/2.32 clauses forward subsumed 88
% 2.14/2.32 clauses back subsumed 79
% 2.14/2.32 Kbytes malloced 1953
% 2.14/2.32
% 2.14/2.32 ----------- times (seconds) -----------
% 2.14/2.32 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 2.14/2.32 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.14/2.32 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.14/2.32
% 2.14/2.32 That finishes the proof of the theorem.
% 2.14/2.32
% 2.14/2.32 Process 32070 finished Wed Jul 27 10:45:26 2022
% 2.14/2.32 Otter interrupted
% 2.14/2.32 PROOF FOUND
%------------------------------------------------------------------------------