%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU354+1 : TPTP v8.1.0. Released v3.3.0.
% 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 13:15:49 EDT 2022
% Result : Theorem 2.05s 2.24s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 23 ( 15 unt; 2 nHn; 15 RR)
% Number of literals : 32 ( 15 equ; 10 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; 2 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(42,axiom,
( ~ element(A,B)
| proper_element(A,B)
| A = union(B) ),
file('SEU354+1.p',unknown),
[] ).
cnf(47,axiom,
~ proper_element(dollar_f4(A),powerset(A)),
file('SEU354+1.p',unknown),
[] ).
cnf(55,axiom,
( proper_element(dollar_c2,powerset(dollar_c3))
| dollar_c2 != dollar_c3 ),
file('SEU354+1.p',unknown),
[] ).
cnf(56,plain,
( proper_element(dollar_c2,powerset(dollar_c3))
| dollar_c3 != dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[55])]),
[iquote('copy,55,flip.2')] ).
cnf(57,axiom,
( ~ proper_element(dollar_c2,powerset(dollar_c3))
| dollar_c2 = dollar_c3 ),
file('SEU354+1.p',unknown),
[] ).
cnf(58,plain,
( ~ proper_element(dollar_c2,powerset(dollar_c3))
| dollar_c3 = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[57])]),
[iquote('copy,57,flip.2')] ).
cnf(64,axiom,
A = A,
file('SEU354+1.p',unknown),
[] ).
cnf(81,axiom,
element(dollar_f4(A),powerset(A)),
file('SEU354+1.p',unknown),
[] ).
cnf(82,axiom,
k1_pcomps_1(A) = powerset(A),
file('SEU354+1.p',unknown),
[] ).
cnf(84,plain,
powerset(A) = k1_pcomps_1(A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[82])]),
[iquote('copy,82,flip.1')] ).
cnf(86,axiom,
element(dollar_c2,powerset(dollar_c3)),
file('SEU354+1.p',unknown),
[] ).
cnf(87,plain,
element(dollar_c2,k1_pcomps_1(dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[86]),84]),
[iquote('copy,86,demod,84')] ).
cnf(88,axiom,
union(powerset(A)) = A,
file('SEU354+1.p',unknown),
[] ).
cnf(90,plain,
union(k1_pcomps_1(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[88]),84]),
[iquote('copy,88,demod,84')] ).
cnf(91,plain,
element(dollar_f4(A),k1_pcomps_1(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[81]),84]),
[iquote('back_demod,81,demod,84')] ).
cnf(95,plain,
( ~ proper_element(dollar_c2,k1_pcomps_1(dollar_c3))
| dollar_c3 = dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),84]),
[iquote('back_demod,58,demod,84')] ).
cnf(96,plain,
( proper_element(dollar_c2,k1_pcomps_1(dollar_c3))
| dollar_c3 != dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),84]),
[iquote('back_demod,56,demod,84')] ).
cnf(102,plain,
~ proper_element(dollar_f4(A),k1_pcomps_1(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),84]),
[iquote('back_demod,47,demod,84')] ).
cnf(168,plain,
( proper_element(dollar_c2,k1_pcomps_1(dollar_c3))
| dollar_c3 = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[87,42]),90])]),
[iquote('hyper,87,42,demod,90,flip.2')] ).
cnf(210,plain,
dollar_f4(A) = A,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[91,42]),90]),102]),
[iquote('hyper,91,42,demod,90,unit_del,102')] ).
cnf(212,plain,
~ proper_element(A,k1_pcomps_1(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[102]),210]),
[iquote('back_demod,102,demod,210')] ).
cnf(1705,plain,
dollar_c3 = dollar_c2,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[168,95])]),
[iquote('hyper,168,95,factor_simp')] ).
cnf(1763,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),1705,1705]),212,64]),
[iquote('back_demod,96,demod,1705,1705,unit_del,212,64')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU354+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % 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 07:34:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.10 ----- Otter 3.3f, August 2004 -----
% 1.89/2.10 The process was started by sandbox2 on n019.cluster.edu,
% 1.89/2.10 Wed Jul 27 07:34:37 2022
% 1.89/2.10 The command was "./otter". The process ID is 20200.
% 1.89/2.10
% 1.89/2.10 set(prolog_style_variables).
% 1.89/2.10 set(auto).
% 1.89/2.10 dependent: set(auto1).
% 1.89/2.10 dependent: set(process_input).
% 1.89/2.10 dependent: clear(print_kept).
% 1.89/2.10 dependent: clear(print_new_demod).
% 1.89/2.10 dependent: clear(print_back_demod).
% 1.89/2.10 dependent: clear(print_back_sub).
% 1.89/2.10 dependent: set(control_memory).
% 1.89/2.10 dependent: assign(max_mem, 12000).
% 1.89/2.10 dependent: assign(pick_given_ratio, 4).
% 1.89/2.10 dependent: assign(stats_level, 1).
% 1.89/2.10 dependent: assign(max_seconds, 10800).
% 1.89/2.10 clear(print_given).
% 1.89/2.10
% 1.89/2.10 formula_list(usable).
% 1.89/2.10 all A (A=A).
% 1.89/2.10 all A B (in(A,B)-> -in(B,A)).
% 1.89/2.10 all A (v1_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)))).
% 1.89/2.10 all A (v2_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)))).
% 1.89/2.10 all A (v3_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)&v1_rat_1(B)))).
% 1.89/2.10 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)))).
% 1.89/2.10 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)))).
% 1.89/2.10 all A (empty(A)->v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 1.89/2.10 all A (v1_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)))).
% 1.89/2.10 all A (v2_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)))).
% 1.89/2.10 all A (v3_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)))).
% 1.89/2.10 all A (v4_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)))).
% 1.89/2.10 all A (v5_membered(A)->v4_membered(A)).
% 1.89/2.10 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)))).
% 1.89/2.10 all A (v4_membered(A)->v3_membered(A)).
% 1.89/2.10 all A (v3_membered(A)->v2_membered(A)).
% 1.89/2.10 all A (v2_membered(A)->v1_membered(A)).
% 1.89/2.10 all A B (element(B,A)-> (proper_element(B,A)<->B!=union(A))).
% 1.89/2.10 all A element(k1_pcomps_1(A),powerset(powerset(A))).
% 1.89/2.10 $T.
% 1.89/2.10 $T.
% 1.89/2.10 $T.
% 1.89/2.10 all A B (element(B,powerset(powerset(A)))->element(union_of_subsets(A,B),powerset(A))).
% 1.89/2.10 $T.
% 1.89/2.10 all A exists B element(B,A).
% 1.89/2.10 all A (-empty(powerset(A))).
% 1.89/2.10 empty(empty_set).
% 1.89/2.10 v1_membered(empty_set).
% 1.89/2.10 v2_membered(empty_set).
% 1.89/2.10 v3_membered(empty_set).
% 1.89/2.10 v4_membered(empty_set).
% 1.89/2.10 v5_membered(empty_set).
% 1.89/2.10 exists A (-empty(A)&v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 1.89/2.10 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.89/2.10 all A exists B (element(B,powerset(A))&empty(B)).
% 1.89/2.10 all A exists B (element(B,powerset(A))& -proper_element(B,powerset(A))).
% 1.89/2.10 all A (k1_pcomps_1(A)=powerset(A)).
% 1.89/2.10 all A B (element(B,powerset(powerset(A)))->union_of_subsets(A,B)=union(B)).
% 1.89/2.10 all A B subset(A,A).
% 1.89/2.10 all A B (in(A,B)->element(A,B)).
% 1.89/2.10 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.89/2.10 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.89/2.10 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.89/2.10 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.89/2.10 -(all A B (element(B,powerset(A))-> (proper_element(B,powerset(A))<->B!=A))).
% 1.89/2.10 all A (empty(A)->A=empty_set).
% 1.89/2.10 all A B (-(in(A,B)&empty(B))).
% 1.89/2.10 all A B (-(empty(A)&A!=B&empty(B))).
% 1.89/2.10 all A (union(powerset(A))=A).
% 1.89/2.10 end_of_list.
% 1.89/2.10
% 1.89/2.10 -------> usable clausifies to:
% 1.89/2.10
% 1.89/2.10 list(usable).
% 1.89/2.10 0 [] A=A.
% 1.89/2.10 0 [] -in(A,B)| -in(B,A).
% 1.89/2.10 0 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 0 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 0 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.89/2.10 0 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 0 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.89/2.10 0 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.89/2.10 0 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 0 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.89/2.10 0 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 1.89/2.10 0 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,A)|natural(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.89/2.10 0 [] -empty(A)|v1_membered(A).
% 1.89/2.10 0 [] -empty(A)|v2_membered(A).
% 1.89/2.10 0 [] -empty(A)|v3_membered(A).
% 1.89/2.10 0 [] -empty(A)|v4_membered(A).
% 1.89/2.10 0 [] -empty(A)|v5_membered(A).
% 1.89/2.10 0 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.89/2.10 0 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.89/2.10 0 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.89/2.10 0 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.89/2.10 0 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.89/2.10 0 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.89/2.10 0 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.89/2.10 0 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.89/2.10 0 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.89/2.10 0 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.89/2.10 0 [] -v5_membered(A)|v4_membered(A).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.89/2.10 0 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 1.89/2.10 0 [] -v4_membered(A)|v3_membered(A).
% 1.89/2.10 0 [] -v3_membered(A)|v2_membered(A).
% 1.89/2.10 0 [] -v2_membered(A)|v1_membered(A).
% 1.89/2.10 0 [] -element(B,A)| -proper_element(B,A)|B!=union(A).
% 1.89/2.10 0 [] -element(B,A)|proper_element(B,A)|B=union(A).
% 1.89/2.10 0 [] element(k1_pcomps_1(A),powerset(powerset(A))).
% 1.89/2.10 0 [] $T.
% 1.89/2.10 0 [] $T.
% 1.89/2.10 0 [] $T.
% 1.89/2.10 0 [] -element(B,powerset(powerset(A)))|element(union_of_subsets(A,B),powerset(A)).
% 1.89/2.10 0 [] $T.
% 1.89/2.10 0 [] element($f1(A),A).
% 1.89/2.10 0 [] -empty(powerset(A)).
% 1.89/2.10 0 [] empty(empty_set).
% 1.89/2.10 0 [] v1_membered(empty_set).
% 1.89/2.10 0 [] v2_membered(empty_set).
% 1.89/2.10 0 [] v3_membered(empty_set).
% 1.89/2.10 0 [] v4_membered(empty_set).
% 1.89/2.10 0 [] v5_membered(empty_set).
% 1.89/2.10 0 [] -empty($c1).
% 1.89/2.10 0 [] v1_membered($c1).
% 1.89/2.10 0 [] v2_membered($c1).
% 1.89/2.10 0 [] v3_membered($c1).
% 1.89/2.10 0 [] v4_membered($c1).
% 1.89/2.10 0 [] v5_membered($c1).
% 1.89/2.10 0 [] empty(A)|element($f2(A),powerset(A)).
% 1.89/2.10 0 [] empty(A)| -empty($f2(A)).
% 1.89/2.10 0 [] element($f3(A),powerset(A)).
% 1.89/2.10 0 [] empty($f3(A)).
% 1.89/2.10 0 [] element($f4(A),powerset(A)).
% 1.89/2.10 0 [] -proper_element($f4(A),powerset(A)).
% 1.89/2.10 0 [] k1_pcomps_1(A)=powerset(A).
% 1.89/2.10 0 [] -element(B,powerset(powerset(A)))|union_of_subsets(A,B)=union(B).
% 1.89/2.10 0 [] subset(A,A).
% 1.89/2.10 0 [] -in(A,B)|element(A,B).
% 1.89/2.10 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.89/2.10 0 [] -element(A,powerset(B))|subset(A,B).
% 1.89/2.10 0 [] element(A,powerset(B))| -subset(A,B).
% 1.89/2.10 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.89/2.10 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.89/2.10 0 [] element($c2,powerset($c3)).
% 1.89/2.10 0 [] proper_element($c2,powerset($c3))|$c2!=$c3.
% 1.89/2.10 0 [] -proper_element($c2,powerset($c3))|$c2=$c3.
% 1.89/2.10 0 [] -empty(A)|A=empty_set.
% 1.89/2.10 0 [] -in(A,B)| -empty(B).
% 1.89/2.10 0 [] -empty(A)|A=B| -empty(B).
% 1.89/2.10 0 [] union(powerset(A))=A.
% 1.89/2.10 end_of_list.
% 1.89/2.10
% 1.89/2.10 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.89/2.10
% 1.89/2.10 This ia a non-Horn set with equality. The strategy will be
% 1.89/2.10 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.89/2.10 deletion, with positive clauses in sos and nonpositive
% 1.89/2.10 clauses in usable.
% 1.89/2.10
% 1.89/2.10 dependent: set(knuth_bendix).
% 1.89/2.10 dependent: set(anl_eq).
% 1.89/2.10 dependent: set(para_from).
% 1.89/2.10 dependent: set(para_into).
% 1.89/2.10 dependent: clear(para_from_right).
% 1.89/2.10 dependent: clear(para_into_right).
% 1.89/2.10 dependent: set(para_from_vars).
% 1.89/2.10 dependent: set(eq_units_both_ways).
% 1.89/2.10 dependent: set(dynamic_demod_all).
% 1.89/2.10 dependent: set(dynamic_demod).
% 1.89/2.10 dependent: set(order_eq).
% 1.89/2.10 dependent: set(back_demod).
% 1.89/2.10 dependent: set(lrpo).
% 1.89/2.10 dependent: set(hyper_res).
% 1.89/2.10 dependent: set(unit_deletion).
% 1.89/2.10 dependent: set(factor).
% 1.89/2.10
% 1.89/2.10 ------------> process usable:
% 1.89/2.10 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.89/2.10 ** KEPT (pick-wt=7): 2 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 3 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 4 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 5 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 6 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 7 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 8 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 9 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 10 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 1.94/2.10 ** KEPT (pick-wt=7): 11 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.94/2.10 ** KEPT (pick-wt=7): 12 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.94/2.10 ** KEPT (pick-wt=7): 13 [] -v5_membered(A)| -element(B,A)|natural(B).
% 1.94/2.10 ** KEPT (pick-wt=7): 14 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.94/2.10 ** KEPT (pick-wt=7): 15 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 1.94/2.10 ** KEPT (pick-wt=7): 16 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.94/2.10 ** KEPT (pick-wt=4): 17 [] -empty(A)|v1_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=4): 18 [] -empty(A)|v2_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=4): 19 [] -empty(A)|v3_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=4): 20 [] -empty(A)|v4_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=4): 21 [] -empty(A)|v5_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=8): 22 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 23 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 24 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 25 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 26 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 27 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 28 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 29 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 30 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 31 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=4): 32 [] -v5_membered(A)|v4_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=8): 33 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 34 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 35 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 36 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=8): 37 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 1.94/2.10 ** KEPT (pick-wt=4): 38 [] -v4_membered(A)|v3_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=4): 39 [] -v3_membered(A)|v2_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=4): 40 [] -v2_membered(A)|v1_membered(A).
% 1.94/2.10 ** KEPT (pick-wt=10): 41 [] -element(A,B)| -proper_element(A,B)|A!=union(B).
% 1.94/2.10 ** KEPT (pick-wt=10): 42 [] -element(A,B)|proper_element(A,B)|A=union(B).
% 1.94/2.10 ** KEPT (pick-wt=11): 43 [] -element(A,powerset(powerset(B)))|element(union_of_subsets(B,A),powerset(B)).
% 1.94/2.10 ** KEPT (pick-wt=3): 44 [] -empty(powerset(A)).
% 1.94/2.10 ** KEPT (pick-wt=2): 45 [] -empty($c1).
% 1.94/2.10 ** KEPT (pick-wt=5): 46 [] empty(A)| -empty($f2(A)).
% 1.94/2.10 ** KEPT (pick-wt=5): 47 [] -proper_element($f4(A),powerset(A)).
% 1.94/2.10 ** KEPT (pick-wt=11): 48 [] -element(A,powerset(powerset(B)))|union_of_subsets(B,A)=union(A).
% 1.94/2.10 ** KEPT (pick-wt=6): 49 [] -in(A,B)|element(A,B).
% 1.94/2.10 ** KEPT (pick-wt=8): 50 [] -element(A,B)|empty(B)|in(A,B).
% 1.94/2.10 ** KEPT (pick-wt=7): 51 [] -element(A,powerset(B))|subset(A,B).
% 1.94/2.10 ** KEPT (pick-wt=7): 52 [] element(A,powerset(B))| -subset(A,B).
% 1.94/2.10 ** KEPT (pick-wt=10): 53 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.94/2.10 ** KEPT (pick-wt=9): 54 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.94/2.10 ** KEPT (pick-wt=7): 56 [copy,55,flip.2] proper_element($c2,powerset($c3))|$c3!=$c2.
% 1.94/2.10 ** KEPT (pick-wt=7): 58 [copy,57,flip.2] -proper_element($c2,powerset($c3))|$c3=$c2.
% 1.94/2.10 ** KEPT (pick-wt=5): 59 [] -empty(A)|A=empty_set.
% 1.94/2.10 ** KEPT (pick-wt=5): 60 [] -in(A,B)| -empty(B).
% 1.94/2.10 ** KEPT (pick-wt=7): 61 [] -empty(A)|A=B| -empty(B).
% 1.94/2.10
% 1.94/2.10 ------------> process sos:
% 1.94/2.10 ** KEPT (pick-wt=3): 64 [] A=A.
% 1.94/2.10 ** KEPT (pick-wt=6): 65 [] element(k1_pcomps_1(A),powerset(powerset(A))).
% 1.94/2.10 ** KEPT (pick-wt=4): 66 [] element($f1(A),A).
% 1.94/2.10 ** KEPT (pick-wt=2): 67 [] empty(empty_set).
% 1.94/2.10 ** KEPT (pick-wt=2): 68 [] v1_membered(empty_set).
% 1.94/2.10 ** KEPT (pick-wt=2): 69 [] v2_membered(empty_set).
% 1.94/2.10 ** KEPT (pick-wt=2): 70 [] v3_membered(empty_set).
% 1.94/2.10 ** KEPT (pick-wt=2): 71 [] v4_membered(empty_set).
% 1.94/2.10 ** KEPT (pick-wt=2): 72 [] v5_membered(empty_set).
% 1.94/2.10 ** KEPT (pick-wt=2): 73 [] v1_membered($c1).
% 1.94/2.10 ** KEPT (pick-wt=2): 74 [] v2_membered($c1).
% 1.94/2.10 ** KEPT (pick-wt=2): 75 [] v3_membered($c1).
% 2.05/2.24 ** KEPT (pick-wt=2): 76 [] v4_membered($c1).
% 2.05/2.24 ** KEPT (pick-wt=2): 77 [] v5_membered($c1).
% 2.05/2.24 ** KEPT (pick-wt=7): 78 [] empty(A)|element($f2(A),powerset(A)).
% 2.05/2.24 ** KEPT (pick-wt=5): 79 [] element($f3(A),powerset(A)).
% 2.05/2.24 ** KEPT (pick-wt=3): 80 [] empty($f3(A)).
% 2.05/2.24 ** KEPT (pick-wt=5): 81 [] element($f4(A),powerset(A)).
% 2.05/2.24 ** KEPT (pick-wt=5): 83 [copy,82,flip.1] powerset(A)=k1_pcomps_1(A).
% 2.05/2.24 ---> New Demodulator: 84 [new_demod,83] powerset(A)=k1_pcomps_1(A).
% 2.05/2.24 ** KEPT (pick-wt=3): 85 [] subset(A,A).
% 2.05/2.24 ** KEPT (pick-wt=4): 87 [copy,86,demod,84] element($c2,k1_pcomps_1($c3)).
% 2.05/2.24 ** KEPT (pick-wt=5): 89 [copy,88,demod,84] union(k1_pcomps_1(A))=A.
% 2.05/2.24 ---> New Demodulator: 90 [new_demod,89] union(k1_pcomps_1(A))=A.
% 2.05/2.24 Following clause subsumed by 64 during input processing: 0 [copy,64,flip.1] A=A.
% 2.05/2.24 64 back subsumes 63.
% 2.05/2.24 >>>> Starting back demodulation with 84.
% 2.05/2.24 >> back demodulating 81 with 84.
% 2.05/2.24 >> back demodulating 79 with 84.
% 2.05/2.24 >> back demodulating 78 with 84.
% 2.05/2.24 >> back demodulating 65 with 84.
% 2.05/2.24 >> back demodulating 58 with 84.
% 2.05/2.24 >> back demodulating 56 with 84.
% 2.05/2.24 >> back demodulating 54 with 84.
% 2.05/2.24 >> back demodulating 53 with 84.
% 2.05/2.24 >> back demodulating 52 with 84.
% 2.05/2.24 >> back demodulating 51 with 84.
% 2.05/2.24 >> back demodulating 48 with 84.
% 2.05/2.24 >> back demodulating 47 with 84.
% 2.05/2.24 >> back demodulating 44 with 84.
% 2.05/2.24 >> back demodulating 43 with 84.
% 2.05/2.24 >> back demodulating 37 with 84.
% 2.05/2.24 >> back demodulating 36 with 84.
% 2.05/2.24 >> back demodulating 35 with 84.
% 2.05/2.24 >> back demodulating 34 with 84.
% 2.05/2.24 >> back demodulating 33 with 84.
% 2.05/2.24 >> back demodulating 31 with 84.
% 2.05/2.24 >> back demodulating 30 with 84.
% 2.05/2.24 >> back demodulating 29 with 84.
% 2.05/2.24 >> back demodulating 28 with 84.
% 2.05/2.24 >> back demodulating 27 with 84.
% 2.05/2.24 >> back demodulating 26 with 84.
% 2.05/2.24 >> back demodulating 25 with 84.
% 2.05/2.24 >> back demodulating 24 with 84.
% 2.05/2.24 >> back demodulating 23 with 84.
% 2.05/2.24 >> back demodulating 22 with 84.
% 2.05/2.24 >>>> Starting back demodulation with 90.
% 2.05/2.24
% 2.05/2.24 ======= end of input processing =======
% 2.05/2.24
% 2.05/2.24 =========== start of search ===========
% 2.05/2.24
% 2.05/2.24 -------- PROOF --------
% 2.05/2.24
% 2.05/2.24 -----> EMPTY CLAUSE at 0.14 sec ----> 1763 [back_demod,96,demod,1705,1705,unit_del,212,64] $F.
% 2.05/2.24
% 2.05/2.24 Length of proof is 13. Level of proof is 4.
% 2.05/2.24
% 2.05/2.24 ---------------- PROOF ----------------
% 2.05/2.24 % SZS status Theorem
% 2.05/2.24 % SZS output start Refutation
% See solution above
% 2.05/2.24 ------------ end of proof -------------
% 2.05/2.24
% 2.05/2.24
% 2.05/2.24 Search stopped by max_proofs option.
% 2.05/2.24
% 2.05/2.24
% 2.05/2.24 Search stopped by max_proofs option.
% 2.05/2.24
% 2.05/2.24 ============ end of search ============
% 2.05/2.24
% 2.05/2.24 -------------- statistics -------------
% 2.05/2.24 clauses given 274
% 2.05/2.24 clauses generated 4954
% 2.05/2.24 clauses kept 1750
% 2.05/2.24 clauses forward subsumed 3498
% 2.05/2.24 clauses back subsumed 31
% 2.05/2.24 Kbytes malloced 3906
% 2.05/2.24
% 2.05/2.24 ----------- times (seconds) -----------
% 2.05/2.24 user CPU time 0.14 (0 hr, 0 min, 0 sec)
% 2.05/2.24 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.05/2.24 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.05/2.24
% 2.05/2.24 That finishes the proof of the theorem.
% 2.05/2.24
% 2.05/2.24 Process 20200 finished Wed Jul 27 07:34:38 2022
% 2.05/2.24 Otter interrupted
% 2.05/2.24 PROOF FOUND
%------------------------------------------------------------------------------