%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU326+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:15:40 EDT 2022
% Result : Theorem 1.95s 2.14s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 14 unt; 2 nHn; 14 RR)
% Number of literals : 35 ( 20 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(41,axiom,
( ~ element(A,powerset(powerset(B)))
| element(complements_of_subsets(B,A),powerset(powerset(B))) ),
file('SEU326+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ element(A,powerset(powerset(B)))
| complements_of_subsets(B,complements_of_subsets(B,A)) = A ),
file('SEU326+1.p',unknown),
[] ).
cnf(46,axiom,
( dollar_c2 != empty_set
| complements_of_subsets(dollar_c3,dollar_c2) != empty_set ),
file('SEU326+1.p',unknown),
[] ).
cnf(47,plain,
( empty_set != dollar_c2
| complements_of_subsets(dollar_c3,dollar_c2) != empty_set ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[46])]),
[iquote('copy,46,flip.1')] ).
cnf(52,axiom,
( ~ element(A,powerset(powerset(B)))
| A = empty_set
| complements_of_subsets(B,A) != empty_set ),
file('SEU326+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU326+1.p',unknown),
[] ).
cnf(60,axiom,
A = A,
file('SEU326+1.p',unknown),
[] ).
cnf(62,axiom,
empty(empty_set),
file('SEU326+1.p',unknown),
[] ).
cnf(74,axiom,
element(dollar_f3(A),powerset(A)),
file('SEU326+1.p',unknown),
[] ).
cnf(75,axiom,
empty(dollar_f3(A)),
file('SEU326+1.p',unknown),
[] ).
cnf(77,axiom,
element(dollar_c2,powerset(powerset(dollar_c3))),
file('SEU326+1.p',unknown),
[] ).
cnf(78,axiom,
( complements_of_subsets(dollar_c3,dollar_c2) = empty_set
| dollar_c2 = empty_set ),
file('SEU326+1.p',unknown),
[] ).
cnf(79,plain,
( complements_of_subsets(dollar_c3,dollar_c2) = empty_set
| empty_set = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[78])]),
[iquote('copy,78,flip.2')] ).
cnf(110,plain,
dollar_f3(A) = empty_set,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[75,57,62])]),
[iquote('hyper,75,57,62,flip.1')] ).
cnf(111,plain,
element(empty_set,powerset(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[74]),110]),
[iquote('back_demod,74,demod,110')] ).
cnf(166,plain,
empty_set = dollar_c2,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[79,52,77])]),
[iquote('hyper,79,52,77,factor_simp')] ).
cnf(194,plain,
element(dollar_c2,powerset(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[111]),166]),
[iquote('back_demod,111,demod,166')] ).
cnf(216,plain,
( ~ element(A,powerset(powerset(B)))
| A = dollar_c2
| complements_of_subsets(B,A) != dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[52]),166,166]),
[iquote('back_demod,52,demod,166,166')] ).
cnf(217,plain,
complements_of_subsets(dollar_c3,dollar_c2) != dollar_c2,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),166,166]),60]),
[iquote('back_demod,47,demod,166,166,unit_del,60')] ).
cnf(265,plain,
complements_of_subsets(A,complements_of_subsets(A,dollar_c2)) = dollar_c2,
inference(hyper,[status(thm)],[194,43]),
[iquote('hyper,194,43')] ).
cnf(267,plain,
element(complements_of_subsets(A,dollar_c2),powerset(powerset(A))),
inference(hyper,[status(thm)],[194,41]),
[iquote('hyper,194,41')] ).
cnf(1356,plain,
complements_of_subsets(A,dollar_c2) = dollar_c2,
inference(hyper,[status(thm)],[216,267,265]),
[iquote('hyper,216,267,265')] ).
cnf(1358,plain,
$false,
inference(binary,[status(thm)],[1356,217]),
[iquote('binary,1356.1,217.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU326+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n021.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 07:45:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.78/1.98 ----- Otter 3.3f, August 2004 -----
% 1.78/1.98 The process was started by sandbox2 on n021.cluster.edu,
% 1.78/1.98 Wed Jul 27 07:45:23 2022
% 1.78/1.98 The command was "./otter". The process ID is 5802.
% 1.78/1.98
% 1.78/1.98 set(prolog_style_variables).
% 1.78/1.98 set(auto).
% 1.78/1.98 dependent: set(auto1).
% 1.78/1.98 dependent: set(process_input).
% 1.78/1.98 dependent: clear(print_kept).
% 1.78/1.98 dependent: clear(print_new_demod).
% 1.78/1.98 dependent: clear(print_back_demod).
% 1.78/1.98 dependent: clear(print_back_sub).
% 1.78/1.98 dependent: set(control_memory).
% 1.78/1.98 dependent: assign(max_mem, 12000).
% 1.78/1.98 dependent: assign(pick_given_ratio, 4).
% 1.78/1.98 dependent: assign(stats_level, 1).
% 1.78/1.98 dependent: assign(max_seconds, 10800).
% 1.78/1.98 clear(print_given).
% 1.78/1.98
% 1.78/1.98 formula_list(usable).
% 1.78/1.98 all A (A=A).
% 1.78/1.98 all A B (in(A,B)-> -in(B,A)).
% 1.78/1.98 all A (v1_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)))).
% 1.78/1.98 all A (v2_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)))).
% 1.78/1.98 all A (v3_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)&v1_rat_1(B)))).
% 1.78/1.98 all A (v4_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)&v1_int_1(B)&v1_rat_1(B)))).
% 1.78/1.98 all A (v5_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&natural(B)&v1_xreal_0(B)&v1_int_1(B)&v1_rat_1(B)))).
% 1.78/1.98 all A (empty(A)->v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 1.78/1.98 all A (v1_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)))).
% 1.78/1.98 all A (v2_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)))).
% 1.78/1.98 all A (v3_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)))).
% 1.78/1.98 all A (v4_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)))).
% 1.78/1.98 all A (v5_membered(A)->v4_membered(A)).
% 1.78/1.98 all A (v5_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)))).
% 1.78/1.98 all A (v4_membered(A)->v3_membered(A)).
% 1.78/1.98 all A (v3_membered(A)->v2_membered(A)).
% 1.78/1.98 all A (v2_membered(A)->v1_membered(A)).
% 1.78/1.98 $T.
% 1.78/1.98 $T.
% 1.78/1.98 all A B (element(B,powerset(powerset(A)))->element(complements_of_subsets(A,B),powerset(powerset(A)))).
% 1.78/1.98 $T.
% 1.78/1.98 all A exists B element(B,A).
% 1.78/1.98 all A (-empty(powerset(A))).
% 1.78/1.98 empty(empty_set).
% 1.78/1.98 v1_membered(empty_set).
% 1.78/1.98 v2_membered(empty_set).
% 1.78/1.98 v3_membered(empty_set).
% 1.78/1.98 v4_membered(empty_set).
% 1.78/1.98 v5_membered(empty_set).
% 1.78/1.98 all A B (element(B,powerset(powerset(A)))->complements_of_subsets(A,complements_of_subsets(A,B))=B).
% 1.78/1.98 exists A (-empty(A)&v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 1.78/1.98 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.78/1.98 all A exists B (element(B,powerset(A))&empty(B)).
% 1.78/1.98 all A B subset(A,A).
% 1.78/1.98 -(all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set)& -(complements_of_subsets(A,B)!=empty_set&B=empty_set))).
% 1.78/1.98 all A B (in(A,B)->element(A,B)).
% 1.78/1.98 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.78/1.98 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.78/1.98 all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set)).
% 1.78/1.98 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.78/1.98 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.78/1.98 all A (empty(A)->A=empty_set).
% 1.78/1.98 all A B (-(in(A,B)&empty(B))).
% 1.78/1.98 all A B (-(empty(A)&A!=B&empty(B))).
% 1.78/1.98 end_of_list.
% 1.78/1.98
% 1.78/1.98 -------> usable clausifies to:
% 1.78/1.98
% 1.78/1.98 list(usable).
% 1.78/1.98 0 [] A=A.
% 1.78/1.98 0 [] -in(A,B)| -in(B,A).
% 1.78/1.98 0 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 0 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 0 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.78/1.98 0 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 0 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.78/1.98 0 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.78/1.98 0 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 0 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.78/1.98 0 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 1.78/1.98 0 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,A)|natural(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.78/1.98 0 [] -empty(A)|v1_membered(A).
% 1.78/1.98 0 [] -empty(A)|v2_membered(A).
% 1.78/1.98 0 [] -empty(A)|v3_membered(A).
% 1.78/1.98 0 [] -empty(A)|v4_membered(A).
% 1.78/1.98 0 [] -empty(A)|v5_membered(A).
% 1.78/1.98 0 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 0 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 0 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.78/1.98 0 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 0 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.78/1.98 0 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.78/1.98 0 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 0 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.78/1.98 0 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.78/1.98 0 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.78/1.98 0 [] -v5_membered(A)|v4_membered(A).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.78/1.98 0 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 1.78/1.98 0 [] -v4_membered(A)|v3_membered(A).
% 1.78/1.98 0 [] -v3_membered(A)|v2_membered(A).
% 1.78/1.98 0 [] -v2_membered(A)|v1_membered(A).
% 1.78/1.98 0 [] $T.
% 1.78/1.98 0 [] $T.
% 1.78/1.98 0 [] -element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))).
% 1.78/1.98 0 [] $T.
% 1.78/1.98 0 [] element($f1(A),A).
% 1.78/1.98 0 [] -empty(powerset(A)).
% 1.78/1.98 0 [] empty(empty_set).
% 1.78/1.98 0 [] v1_membered(empty_set).
% 1.78/1.98 0 [] v2_membered(empty_set).
% 1.78/1.98 0 [] v3_membered(empty_set).
% 1.78/1.98 0 [] v4_membered(empty_set).
% 1.78/1.98 0 [] v5_membered(empty_set).
% 1.78/1.98 0 [] -element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B.
% 1.78/1.98 0 [] -empty($c1).
% 1.78/1.98 0 [] v1_membered($c1).
% 1.78/1.98 0 [] v2_membered($c1).
% 1.78/1.98 0 [] v3_membered($c1).
% 1.78/1.98 0 [] v4_membered($c1).
% 1.78/1.98 0 [] v5_membered($c1).
% 1.78/1.98 0 [] empty(A)|element($f2(A),powerset(A)).
% 1.78/1.98 0 [] empty(A)| -empty($f2(A)).
% 1.78/1.98 0 [] element($f3(A),powerset(A)).
% 1.78/1.98 0 [] empty($f3(A)).
% 1.78/1.98 0 [] subset(A,A).
% 1.78/1.98 0 [] element($c2,powerset(powerset($c3))).
% 1.78/1.98 0 [] $c2!=empty_set|complements_of_subsets($c3,$c2)!=empty_set.
% 1.78/1.98 0 [] complements_of_subsets($c3,$c2)=empty_set|$c2=empty_set.
% 1.78/1.98 0 [] -in(A,B)|element(A,B).
% 1.78/1.98 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.78/1.98 0 [] -element(A,powerset(B))|subset(A,B).
% 1.78/1.98 0 [] element(A,powerset(B))| -subset(A,B).
% 1.78/1.98 0 [] -element(B,powerset(powerset(A)))|B=empty_set|complements_of_subsets(A,B)!=empty_set.
% 1.78/1.98 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.78/1.98 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.78/1.98 0 [] -empty(A)|A=empty_set.
% 1.78/1.98 0 [] -in(A,B)| -empty(B).
% 1.78/1.98 0 [] -empty(A)|A=B| -empty(B).
% 1.78/1.98 end_of_list.
% 1.78/1.98
% 1.78/1.98 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.78/1.98
% 1.78/1.98 This ia a non-Horn set with equality. The strategy will be
% 1.78/1.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.78/1.98 deletion, with positive clauses in sos and nonpositive
% 1.78/1.98 clauses in usable.
% 1.78/1.98
% 1.78/1.98 dependent: set(knuth_bendix).
% 1.78/1.98 dependent: set(anl_eq).
% 1.78/1.98 dependent: set(para_from).
% 1.78/1.98 dependent: set(para_into).
% 1.78/1.98 dependent: clear(para_from_right).
% 1.78/1.98 dependent: clear(para_into_right).
% 1.78/1.98 dependent: set(para_from_vars).
% 1.78/1.98 dependent: set(eq_units_both_ways).
% 1.78/1.98 dependent: set(dynamic_demod_all).
% 1.78/1.98 dependent: set(dynamic_demod).
% 1.78/1.98 dependent: set(order_eq).
% 1.78/1.98 dependent: set(back_demod).
% 1.78/1.98 dependent: set(lrpo).
% 1.78/1.98 dependent: set(hyper_res).
% 1.78/1.98 dependent: set(unit_deletion).
% 1.78/1.98 dependent: set(factor).
% 1.78/1.98
% 1.78/1.98 ------------> process usable:
% 1.78/1.98 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.78/1.98 ** KEPT (pick-wt=7): 2 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 3 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 4 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 5 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 6 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 7 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 8 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 9 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 10 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 11 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 12 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 13 [] -v5_membered(A)| -element(B,A)|natural(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 14 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 15 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 16 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.78/1.98 ** KEPT (pick-wt=4): 17 [] -empty(A)|v1_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=4): 18 [] -empty(A)|v2_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=4): 19 [] -empty(A)|v3_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=4): 20 [] -empty(A)|v4_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=4): 21 [] -empty(A)|v5_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=8): 22 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 23 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 24 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 25 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 26 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 27 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 28 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 29 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 30 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 31 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=4): 32 [] -v5_membered(A)|v4_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=8): 33 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 34 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 35 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 36 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=8): 37 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 1.78/1.98 ** KEPT (pick-wt=4): 38 [] -v4_membered(A)|v3_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=4): 39 [] -v3_membered(A)|v2_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=4): 40 [] -v2_membered(A)|v1_membered(A).
% 1.78/1.98 ** KEPT (pick-wt=12): 41 [] -element(A,powerset(powerset(B)))|element(complements_of_subsets(B,A),powerset(powerset(B))).
% 1.78/1.98 ** KEPT (pick-wt=3): 42 [] -empty(powerset(A)).
% 1.78/1.98 ** KEPT (pick-wt=12): 43 [] -element(A,powerset(powerset(B)))|complements_of_subsets(B,complements_of_subsets(B,A))=A.
% 1.78/1.98 ** KEPT (pick-wt=2): 44 [] -empty($c1).
% 1.78/1.98 ** KEPT (pick-wt=5): 45 [] empty(A)| -empty($f2(A)).
% 1.78/1.98 ** KEPT (pick-wt=8): 47 [copy,46,flip.1] empty_set!=$c2|complements_of_subsets($c3,$c2)!=empty_set.
% 1.78/1.98 ** KEPT (pick-wt=6): 48 [] -in(A,B)|element(A,B).
% 1.78/1.98 ** KEPT (pick-wt=8): 49 [] -element(A,B)|empty(B)|in(A,B).
% 1.78/1.98 ** KEPT (pick-wt=7): 50 [] -element(A,powerset(B))|subset(A,B).
% 1.78/1.98 ** KEPT (pick-wt=7): 51 [] element(A,powerset(B))| -subset(A,B).
% 1.78/1.98 ** KEPT (pick-wt=13): 52 [] -element(A,powerset(powerset(B)))|A=empty_set|complements_of_subsets(B,A)!=empty_set.
% 1.78/1.98 ** KEPT (pick-wt=10): 53 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.78/1.98 ** KEPT (pick-wt=9): 54 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.78/1.98 ** KEPT (pick-wt=5): 55 [] -empty(A)|A=empty_set.
% 1.78/1.98 ** KEPT (pick-wt=5): 56 [] -in(A,B)| -empty(B).
% 1.78/1.98 ** KEPT (pick-wt=7): 57 [] -empty(A)|A=B| -empty(B).
% 1.78/1.98
% 1.78/1.98 ------------> process sos:
% 1.78/1.98 ** KEPT (pick-wt=3): 60 [] A=A.
% 1.78/1.98 ** KEPT (pick-wt=4): 61 [] element($f1(A),A).
% 1.78/1.98 ** KEPT (pick-wt=2): 62 [] empty(empty_set).
% 1.78/1.98 ** KEPT (pick-wt=2): 63 [] v1_membered(empty_set).
% 1.78/1.98 ** KEPT (pick-wt=2): 64 [] v2_membered(empty_set).
% 1.78/1.98 ** KEPT (pick-wt=2): 65 [] v3_membered(empty_set).
% 1.78/1.98 ** KEPT (pick-wt=2): 66 [] v4_membered(empty_set).
% 1.78/1.98 ** KEPT (pick-wt=2): 67 [] v5_membered(empty_set).
% 1.78/1.98 ** KEPT (pick-wt=2): 68 [] v1_membered($c1).
% 1.78/1.98 ** KEPT (pick-wt=2): 69 [] v2_membered($c1).
% 1.78/1.98 ** KEPT (pick-wt=2): 70 [] v3_membered($c1).
% 1.78/1.98 ** KEPT (pick-wt=2): 71 [] v4_membered($c1).
% 1.78/1.98 ** KEPT (pick-wt=2): 72 [] v5_membered($c1).
% 1.78/1.98 ** KEPT (pick-wt=7): 73 [] empty(A)|element($f2(A),powerset(A)).
% 1.78/1.98 ** KEPT (pick-wt=5): 74 [] element($f3(A),powerset(A)).
% 1.78/1.98 ** KEPT (pick-wt=3): 75 [] empty($f3(A)).
% 1.78/1.98 ** KEPT (pick-wt=3): 76 [] subset(A,A).
% 1.78/1.98 ** KEPT (pick-wt=5): 77 [] element($c2,powerset(powerset($c3))).
% 1.95/2.14 ** KEPT (pick-wt=8): 79 [copy,78,flip.2] complements_of_subsets($c3,$c2)=empty_set|empty_set=$c2.
% 1.95/2.14 Following clause subsumed by 60 during input processing: 0 [copy,60,flip.1] A=A.
% 1.95/2.14 60 back subsumes 59.
% 1.95/2.14
% 1.95/2.14 ======= end of input processing =======
% 1.95/2.14
% 1.95/2.14 =========== start of search ===========
% 1.95/2.14
% 1.95/2.14 -------- PROOF --------
% 1.95/2.14
% 1.95/2.14 ----> UNIT CONFLICT at 0.16 sec ----> 1358 [binary,1356.1,217.1] $F.
% 1.95/2.14
% 1.95/2.14 Length of proof is 11. Level of proof is 5.
% 1.95/2.14
% 1.95/2.14 ---------------- PROOF ----------------
% 1.95/2.14 % SZS status Theorem
% 1.95/2.14 % SZS output start Refutation
% See solution above
% 1.95/2.14 ------------ end of proof -------------
% 1.95/2.14
% 1.95/2.14
% 1.95/2.14 Search stopped by max_proofs option.
% 1.95/2.14
% 1.95/2.14
% 1.95/2.14 Search stopped by max_proofs option.
% 1.95/2.14
% 1.95/2.14 ============ end of search ============
% 1.95/2.14
% 1.95/2.14 -------------- statistics -------------
% 1.95/2.14 clauses given 201
% 1.95/2.14 clauses generated 5982
% 1.95/2.14 clauses kept 1345
% 1.95/2.14 clauses forward subsumed 4830
% 1.95/2.14 clauses back subsumed 144
% 1.95/2.14 Kbytes malloced 3906
% 1.95/2.14
% 1.95/2.14 ----------- times (seconds) -----------
% 1.95/2.14 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 1.95/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.14
% 1.95/2.14 That finishes the proof of the theorem.
% 1.95/2.14
% 1.95/2.14 Process 5802 finished Wed Jul 27 07:45:25 2022
% 1.95/2.14 Otter interrupted
% 1.95/2.14 PROOF FOUND
%------------------------------------------------------------------------------