TSTP Solution File: SET679+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 1.87s 2.06s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 11 unt; 5 nHn; 14 RR)
% Number of literals : 35 ( 5 equ; 16 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ ilf_type(A,set_type)
| ~ member(A,empty_set) ),
file('SET679+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ 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 ),
file('SET679+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| not_e_qual(A,B)
| A = B ),
file('SET679+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ ilf_type(A,set_type)
| empty(A)
| member(dollar_f2(A),A) ),
file('SET679+3.p',unknown),
[] ).
cnf(43,axiom,
~ empty(dollar_c2),
file('SET679+3.p',unknown),
[] ).
cnf(44,axiom,
~ not_e_qual(identity_relation_of(dollar_c2),empty_set),
file('SET679+3.p',unknown),
[] ).
cnf(85,axiom,
A = A,
file('SET679+3.p',unknown),
[] ).
cnf(89,axiom,
ilf_type(A,set_type),
file('SET679+3.p',unknown),
[] ).
cnf(127,plain,
( empty(A)
| member(dollar_f2(A),A) ),
inference(hyper,[status(thm)],[89,17]),
[iquote('hyper,89,17')] ).
cnf(128,plain,
( not_e_qual(A,B)
| A = B ),
inference(hyper,[status(thm)],[89,14,89]),
[iquote('hyper,89,14,89')] ).
cnf(305,plain,
member(dollar_f2(dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[127,43]),
[iquote('hyper,127,43')] ).
cnf(338,plain,
member(ordered_pair(dollar_f2(dollar_c2),dollar_f2(dollar_c2)),identity_relation_of(dollar_c2)),
inference(hyper,[status(thm)],[305,6,89,89,89,85]),
[iquote('hyper,305,6,89,89,89,85')] ).
cnf(368,plain,
identity_relation_of(dollar_c2) = empty_set,
inference(hyper,[status(thm)],[128,44]),
[iquote('hyper,128,44')] ).
cnf(369,plain,
member(ordered_pair(dollar_f2(dollar_c2),dollar_f2(dollar_c2)),empty_set),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[338]),368]),
[iquote('back_demod,338,demod,368')] ).
cnf(370,plain,
~ not_e_qual(empty_set,empty_set),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),368]),
[iquote('back_demod,44,demod,368')] ).
cnf(473,plain,
( ~ member(A,B)
| not_e_qual(empty_set,B) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[128,3]),89]),
[iquote('para_from,128.2.1,3.2.2,unit_del,89')] ).
cnf(893,plain,
( ~ member(A,B)
| not_e_qual(C,B)
| not_e_qual(empty_set,C) ),
inference(para_into,[status(thm),theory(equality)],[473,128]),
[iquote('para_into,473.2.1,128.2.1')] ).
cnf(898,plain,
~ member(A,empty_set),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[893]),370]),
[iquote('factor,893.2.3,unit_del,370')] ).
cnf(899,plain,
$false,
inference(binary,[status(thm)],[898,369]),
[iquote('binary,898.1,369.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:45:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.78/1.99 ----- Otter 3.3f, August 2004 -----
% 1.78/1.99 The process was started by sandbox2 on n019.cluster.edu,
% 1.78/1.99 Wed Jul 27 10:45:07 2022
% 1.78/1.99 The command was "./otter". The process ID is 12502.
% 1.78/1.99
% 1.78/1.99 set(prolog_style_variables).
% 1.78/1.99 set(auto).
% 1.78/1.99 dependent: set(auto1).
% 1.78/1.99 dependent: set(process_input).
% 1.78/1.99 dependent: clear(print_kept).
% 1.78/1.99 dependent: clear(print_new_demod).
% 1.78/1.99 dependent: clear(print_back_demod).
% 1.78/1.99 dependent: clear(print_back_sub).
% 1.78/1.99 dependent: set(control_memory).
% 1.78/1.99 dependent: assign(max_mem, 12000).
% 1.78/1.99 dependent: assign(pick_given_ratio, 4).
% 1.78/1.99 dependent: assign(stats_level, 1).
% 1.78/1.99 dependent: assign(max_seconds, 10800).
% 1.78/1.99 clear(print_given).
% 1.78/1.99
% 1.78/1.99 formula_list(usable).
% 1.78/1.99 all A (A=A).
% 1.78/1.99 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (member(C,B)<->member(ordered_pair(C,C),identity_relation_of(B)))))).
% 1.78/1.99 all B (ilf_type(B,set_type)-> -member(B,empty_set)).
% 1.78/1.99 empty(empty_set).
% 1.78/1.99 type(empty_set,set_type).
% 1.78/1.99 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)))))).
% 1.78/1.99 all B (ilf_type(B,set_type)->ilf_type(identity_relation_of(B),binary_relation_type)).
% 1.78/1.99 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)))))))).
% 1.78/1.99 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)-> (not_e_qual(B,C)<->B!=C)))).
% 1.78/1.99 all B (ilf_type(B,set_type)-> (empty(B)<-> (all C (ilf_type(C,set_type)-> -member(C,B))))).
% 1.78/1.99 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(ordered_pair(B,C),set_type)))).
% 1.78/1.99 all B (ilf_type(B,set_type)-> (ilf_type(B,binary_relation_type)<->relation_like(B)&ilf_type(B,set_type))).
% 1.78/1.99 exists B ilf_type(B,binary_relation_type).
% 1.78/1.99 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)))))))))).
% 1.78/1.99 all B (empty(B)&ilf_type(B,set_type)->relation_like(B)).
% 1.78/1.99 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)))))).
% 1.78/1.99 all B (ilf_type(B,set_type)-> (all C (ilf_type(C,set_type)->ilf_type(cross_product(B,C),set_type)))).
% 1.78/1.99 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))))))).
% 1.78/1.99 all B (ilf_type(B,set_type)-> (exists C ilf_type(C,subset_type(B)))).
% 1.78/1.99 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)))))))).
% 1.78/1.99 all B (ilf_type(B,set_type)-> -empty(power_set(B))&ilf_type(power_set(B),set_type)).
% 1.78/1.99 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))))).
% 1.78/1.99 all B (-empty(B)&ilf_type(B,set_type)-> (exists C ilf_type(C,member_type(B)))).
% 1.78/1.99 all B ilf_type(B,set_type).
% 1.78/1.99 -(all B (-empty(B)&ilf_type(B,set_type)->not_e_qual(identity_relation_of(B),empty_set))).
% 1.78/1.99 end_of_list.
% 1.78/1.99
% 1.78/1.99 -------> usable clausifies to:
% 1.78/1.99
% 1.78/1.99 list(usable).
% 1.78/1.99 0 [] A=A.
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(C,B)|member(ordered_pair(C,C),identity_relation_of(B)).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(C,B)| -member(ordered_pair(C,C),identity_relation_of(B)).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -member(B,empty_set).
% 1.78/1.99 0 [] empty(empty_set).
% 1.78/1.99 0 [] type(empty_set,set_type).
% 1.78/1.99 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).
% 1.78/1.99 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.
% 1.78/1.99 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.
% 1.78/1.99 0 [] -ilf_type(B,set_type)|ilf_type(identity_relation_of(B),binary_relation_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B!=C| -ilf_type(D,set_type)|member(D,B)| -member(D,C).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C|ilf_type($f1(B,C),set_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C|member($f1(B,C),B)|member($f1(B,C),C).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|B=C| -member($f1(B,C),B)| -member($f1(B,C),C).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -not_e_qual(B,C)|B!=C.
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|not_e_qual(B,C)|B=C.
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -empty(B)| -ilf_type(C,set_type)| -member(C,B).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|empty(B)|ilf_type($f2(B),set_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|empty(B)|member($f2(B),B).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(ordered_pair(B,C),set_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(B,binary_relation_type)|relation_like(B).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|ilf_type(B,binary_relation_type)| -relation_like(B).
% 1.78/1.99 0 [] ilf_type($c1,binary_relation_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f4(B,C),set_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|ilf_type($f3(B,C),set_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -relation_like(B)| -ilf_type(C,set_type)| -member(C,B)|C=ordered_pair($f4(B,C),$f3(B,C)).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|relation_like(B)|ilf_type($f5(B),set_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|relation_like(B)|member($f5(B),B).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|relation_like(B)| -ilf_type(D,set_type)| -ilf_type(E,set_type)|$f5(B)!=ordered_pair(D,E).
% 1.78/1.99 0 [] -empty(B)| -ilf_type(B,set_type)|relation_like(B).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|ilf_type(cross_product(B,C),set_type).
% 1.78/1.99 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))).
% 1.78/1.99 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))).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|ilf_type($f6(B),subset_type(B)).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)| -member(B,power_set(C))| -ilf_type(D,set_type)| -member(D,B)|member(D,C).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|ilf_type($f7(B,C),set_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))|member($f7(B,C),B).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -ilf_type(C,set_type)|member(B,power_set(C))| -member($f7(B,C),C).
% 1.78/1.99 0 [] -ilf_type(B,set_type)| -empty(power_set(B)).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|ilf_type(power_set(B),set_type).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)| -ilf_type(B,member_type(C))|member(B,C).
% 1.78/1.99 0 [] -ilf_type(B,set_type)|empty(C)| -ilf_type(C,set_type)|ilf_type(B,member_type(C))| -member(B,C).
% 1.78/1.99 0 [] empty(B)| -ilf_type(B,set_type)|ilf_type($f8(B),member_type(B)).
% 1.78/1.99 0 [] ilf_type(B,set_type).
% 1.78/1.99 0 [] -empty($c2).
% 1.78/1.99 0 [] ilf_type($c2,set_type).
% 1.78/1.99 0 [] -not_e_qual(identity_relation_of($c2),empty_set).
% 1.78/1.99 end_of_list.
% 1.78/1.99
% 1.78/1.99 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.78/1.99
% 1.78/1.99 This ia a non-Horn set with equality. The strategy will be
% 1.78/1.99 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.78/1.99 deletion, with positive clauses in sos and nonpositive
% 1.78/1.99 clauses in usable.
% 1.78/1.99
% 1.78/1.99 dependent: set(knuth_bendix).
% 1.78/1.99 dependent: set(anl_eq).
% 1.78/1.99 dependent: set(para_from).
% 1.78/1.99 dependent: set(para_into).
% 1.78/1.99 dependent: clear(para_from_right).
% 1.78/1.99 dependent: clear(para_into_right).
% 1.78/1.99 dependent: set(para_from_vars).
% 1.78/1.99 dependent: set(eq_units_both_ways).
% 1.78/1.99 dependent: set(dynamic_demod_all).
% 1.78/1.99 dependent: set(dynamic_demod).
% 1.78/1.99 dependent: set(order_eq).
% 1.78/1.99 dependent: set(back_demod).
% 1.78/1.99 dependent: set(lrpo).
% 1.78/1.99 dependent: set(hyper_res).
% 1.78/1.99 dependent: set(unit_deletion).
% 1.78/1.99 dependent: set(factor).
% 1.78/1.99
% 1.78/1.99 ------------> process usable:
% 1.78/1.99 ** KEPT (pick-wt=15): 1 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -member(B,A)|member(ordered_pair(B,B),identity_relation_of(A)).
% 1.78/1.99 ** KEPT (pick-wt=15): 2 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(B,A)| -member(ordered_pair(B,B),identity_relation_of(A)).
% 1.78/1.99 ** KEPT (pick-wt=6): 3 [] -ilf_type(A,set_type)| -member(A,empty_set).
% 1.78/2.00 ** KEPT (pick-wt=18): 4 [] -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).
% 1.78/2.00 ** KEPT (pick-wt=18): 5 [] -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.
% 1.78/2.00 ** KEPT (pick-wt=21): 6 [] -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.
% 1.78/2.00 ** KEPT (pick-wt=7): 7 [] -ilf_type(A,set_type)|ilf_type(identity_relation_of(A),binary_relation_type).
% 1.78/2.00 ** KEPT (pick-wt=18): 8 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 1.78/2.00 ** KEPT (pick-wt=18): 9 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A!=B| -ilf_type(C,set_type)|member(C,A)| -member(C,B).
% 1.78/2.00 ** KEPT (pick-wt=14): 10 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B|ilf_type($f1(A,B),set_type).
% 1.78/2.00 ** KEPT (pick-wt=19): 11 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B|member($f1(A,B),A)|member($f1(A,B),B).
% 1.78/2.00 ** KEPT (pick-wt=19): 12 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|A=B| -member($f1(A,B),A)| -member($f1(A,B),B).
% 1.78/2.00 ** KEPT (pick-wt=12): 13 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -not_e_qual(A,B)|A!=B.
% 1.78/2.00 ** KEPT (pick-wt=12): 14 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|not_e_qual(A,B)|A=B.
% 1.78/2.00 ** KEPT (pick-wt=11): 15 [] -ilf_type(A,set_type)| -empty(A)| -ilf_type(B,set_type)| -member(B,A).
% 1.78/2.00 ** KEPT (pick-wt=9): 16 [] -ilf_type(A,set_type)|empty(A)|ilf_type($f2(A),set_type).
% 1.78/2.00 ** KEPT (pick-wt=9): 17 [] -ilf_type(A,set_type)|empty(A)|member($f2(A),A).
% 1.78/2.00 ** KEPT (pick-wt=11): 18 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(ordered_pair(A,B),set_type).
% 1.78/2.00 ** KEPT (pick-wt=8): 19 [] -ilf_type(A,set_type)| -ilf_type(A,binary_relation_type)|relation_like(A).
% 1.78/2.00 ** KEPT (pick-wt=8): 20 [] -ilf_type(A,set_type)|ilf_type(A,binary_relation_type)| -relation_like(A).
% 1.78/2.00 ** KEPT (pick-wt=16): 21 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f4(A,B),set_type).
% 1.78/2.00 ** KEPT (pick-wt=16): 22 [] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ilf_type($f3(A,B),set_type).
% 1.78/2.00 ** KEPT (pick-wt=20): 24 [copy,23,flip.5] -ilf_type(A,set_type)| -relation_like(A)| -ilf_type(B,set_type)| -member(B,A)|ordered_pair($f4(A,B),$f3(A,B))=B.
% 1.78/2.00 ** KEPT (pick-wt=9): 25 [] -ilf_type(A,set_type)|relation_like(A)|ilf_type($f5(A),set_type).
% 1.78/2.00 ** KEPT (pick-wt=9): 26 [] -ilf_type(A,set_type)|relation_like(A)|member($f5(A),A).
% 1.78/2.00 ** KEPT (pick-wt=17): 27 [] -ilf_type(A,set_type)|relation_like(A)| -ilf_type(B,set_type)| -ilf_type(C,set_type)|$f5(A)!=ordered_pair(B,C).
% 1.78/2.00 ** KEPT (pick-wt=7): 28 [] -empty(A)| -ilf_type(A,set_type)|relation_like(A).
% 1.78/2.00 ** KEPT (pick-wt=14): 29 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C).
% 1.78/2.00 ** KEPT (pick-wt=11): 30 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(cross_product(A,B),set_type).
% 1.78/2.00 ** 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))).
% 1.78/2.00 ** KEPT (pick-wt=15): 32 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|ilf_type(B,subset_type(A))| -ilf_type(B,member_type(power_set(A))).
% 1.78/2.00 ** KEPT (pick-wt=8): 33 [] -ilf_type(A,set_type)|ilf_type($f6(A),subset_type(A)).
% 1.78/2.00 ** KEPT (pick-wt=19): 34 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)| -member(A,power_set(B))| -ilf_type(C,set_type)| -member(C,A)|member(C,B).
% 1.78/2.00 ** KEPT (pick-wt=15): 35 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|ilf_type($f7(A,B),set_type).
% 1.78/2.00 ** KEPT (pick-wt=15): 36 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))|member($f7(A,B),A).
% 1.78/2.00 ** KEPT (pick-wt=15): 37 [] -ilf_type(A,set_type)| -ilf_type(B,set_type)|member(A,power_set(B))| -member($f7(A,B),B).
% 1.78/2.00 ** KEPT (pick-wt=6): 38 [] -ilf_type(A,set_type)| -empty(power_set(A)).
% 1.78/2.00 ** KEPT (pick-wt=7): 39 [] -ilf_type(A,set_type)|ilf_type(power_set(A),set_type).
% 1.78/2.00 ** KEPT (pick-wt=15): 40 [] -ilf_type(A,set_type)|empty(B)| -ilf_type(B,set_type)| -ilf_type(A,member_type(B))|member(A,B).
% 1.87/2.06 ** 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).
% 1.87/2.06 ** KEPT (pick-wt=10): 42 [] empty(A)| -ilf_type(A,set_type)|ilf_type($f8(A),member_type(A)).
% 1.87/2.06 ** KEPT (pick-wt=2): 43 [] -empty($c2).
% 1.87/2.06 ** KEPT (pick-wt=4): 44 [] -not_e_qual(identity_relation_of($c2),empty_set).
% 1.87/2.06
% 1.87/2.06 ------------> process sos:
% 1.87/2.06 ** KEPT (pick-wt=3): 85 [] A=A.
% 1.87/2.06 ** KEPT (pick-wt=2): 86 [] empty(empty_set).
% 1.87/2.06 ** KEPT (pick-wt=3): 87 [] type(empty_set,set_type).
% 1.87/2.06 ** KEPT (pick-wt=3): 88 [] ilf_type($c1,binary_relation_type).
% 1.87/2.06 ** KEPT (pick-wt=3): 89 [] ilf_type(A,set_type).
% 1.87/2.06 Following clause subsumed by 89 during input processing: 0 [] ilf_type($c2,set_type).
% 1.87/2.06 Following clause subsumed by 85 during input processing: 0 [copy,85,flip.1] A=A.
% 1.87/2.06 85 back subsumes 83.
% 1.87/2.06 85 back subsumes 62.
% 1.87/2.06 85 back subsumes 60.
% 1.87/2.06 85 back subsumes 59.
% 1.87/2.06 85 back subsumes 58.
% 1.87/2.06 85 back subsumes 51.
% 1.87/2.06 89 back subsumes 78.
% 1.87/2.06 89 back subsumes 72.
% 1.87/2.06 89 back subsumes 66.
% 1.87/2.06 89 back subsumes 65.
% 1.87/2.06 89 back subsumes 64.
% 1.87/2.06 89 back subsumes 39.
% 1.87/2.06 89 back subsumes 35.
% 1.87/2.06 89 back subsumes 30.
% 1.87/2.06 89 back subsumes 25.
% 1.87/2.06 89 back subsumes 22.
% 1.87/2.06 89 back subsumes 21.
% 1.87/2.06 89 back subsumes 18.
% 1.87/2.06 89 back subsumes 16.
% 1.87/2.06 89 back subsumes 10.
% 1.87/2.06
% 1.87/2.06 ======= end of input processing =======
% 1.87/2.06
% 1.87/2.06 =========== start of search ===========
% 1.87/2.06
% 1.87/2.06 -------- PROOF --------
% 1.87/2.06
% 1.87/2.06 ----> UNIT CONFLICT at 0.07 sec ----> 899 [binary,898.1,369.1] $F.
% 1.87/2.06
% 1.87/2.06 Length of proof is 10. Level of proof is 4.
% 1.87/2.06
% 1.87/2.06 ---------------- PROOF ----------------
% 1.87/2.06 % SZS status Theorem
% 1.87/2.06 % SZS output start Refutation
% See solution above
% 1.87/2.06 ------------ end of proof -------------
% 1.87/2.06
% 1.87/2.06
% 1.87/2.06 Search stopped by max_proofs option.
% 1.87/2.06
% 1.87/2.06
% 1.87/2.06 Search stopped by max_proofs option.
% 1.87/2.06
% 1.87/2.06 ============ end of search ============
% 1.87/2.06
% 1.87/2.06 -------------- statistics -------------
% 1.87/2.06 clauses given 50
% 1.87/2.06 clauses generated 1321
% 1.87/2.06 clauses kept 896
% 1.87/2.06 clauses forward subsumed 457
% 1.87/2.06 clauses back subsumed 347
% 1.87/2.06 Kbytes malloced 1953
% 1.87/2.06
% 1.87/2.06 ----------- times (seconds) -----------
% 1.87/2.06 user CPU time 0.07 (0 hr, 0 min, 0 sec)
% 1.87/2.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.06 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.87/2.06
% 1.87/2.06 That finishes the proof of the theorem.
% 1.87/2.06
% 1.87/2.06 Process 12502 finished Wed Jul 27 10:45:08 2022
% 1.87/2.06 Otter interrupted
% 1.87/2.06 PROOF FOUND
%------------------------------------------------------------------------------