TSTP Solution File: SEU325+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU325+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 12.34s 12.58s
% Output : Refutation 12.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of clauses : 39 ( 25 unt; 3 nHn; 30 RR)
% Number of literals : 64 ( 13 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(41,axiom,
( ~ one_sorted_str(A)
| cast_as_carrier_subset(A) = the_carrier(A) ),
file('SEU325+1.p',unknown),
[] ).
cnf(42,plain,
( ~ one_sorted_str(A)
| the_carrier(A) = cast_as_carrier_subset(A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[41])]),
[iquote('copy,41,flip.2')] ).
cnf(47,axiom,
( ~ one_sorted_str(A)
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ is_a_cover_of_carrier(A,B)
| cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ),
file('SEU325+1.p',unknown),
[] ).
cnf(48,plain,
( ~ one_sorted_str(A)
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ is_a_cover_of_carrier(A,B)
| union_of_subsets(the_carrier(A),B) = cast_as_carrier_subset(A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[47])]),
[iquote('copy,47,flip.4')] ).
cnf(52,axiom,
( ~ element(A,powerset(powerset(B)))
| element(union_of_subsets(B,A),powerset(B)) ),
file('SEU325+1.p',unknown),
[] ).
cnf(53,axiom,
( empty_carrier(A)
| ~ one_sorted_str(A)
| ~ empty(the_carrier(A)) ),
file('SEU325+1.p',unknown),
[] ).
cnf(59,axiom,
( empty_carrier(A)
| ~ one_sorted_str(A)
| element(dollar_f7(A),powerset(the_carrier(A))) ),
file('SEU325+1.p',unknown),
[] ).
cnf(60,axiom,
( empty_carrier(A)
| ~ one_sorted_str(A)
| ~ empty(dollar_f7(A)) ),
file('SEU325+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ element(A,powerset(powerset(B)))
| union_of_subsets(B,A) = union(A) ),
file('SEU325+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
file('SEU325+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ in(A,B)
| ~ element(B,powerset(C))
| element(A,C) ),
file('SEU325+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ in(A,B)
| ~ element(B,powerset(C))
| ~ empty(C) ),
file('SEU325+1.p',unknown),
[] ).
cnf(68,axiom,
~ empty_carrier(dollar_c5),
file('SEU325+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU325+1.p',unknown),
[] ).
cnf(79,axiom,
element(dollar_f4(A),A),
file('SEU325+1.p',unknown),
[] ).
cnf(80,axiom,
empty(empty_set),
file('SEU325+1.p',unknown),
[] ).
cnf(92,axiom,
element(dollar_f6(A),powerset(A)),
file('SEU325+1.p',unknown),
[] ).
cnf(93,axiom,
empty(dollar_f6(A)),
file('SEU325+1.p',unknown),
[] ).
cnf(96,axiom,
one_sorted_str(dollar_c5),
file('SEU325+1.p',unknown),
[] ).
cnf(98,axiom,
is_a_cover_of_carrier(dollar_c5,dollar_c4),
file('SEU325+1.p',unknown),
[] ).
cnf(99,axiom,
dollar_c4 = empty_set,
file('SEU325+1.p',unknown),
[] ).
cnf(101,plain,
empty_set = dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[99])]),
[iquote('copy,99,flip.1')] ).
cnf(107,plain,
empty(dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[80]),101]),
[iquote('back_demod,80,demod,101')] ).
cnf(226,plain,
element(dollar_f7(dollar_c5),powerset(the_carrier(dollar_c5))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[96,59]),68]),
[iquote('hyper,96,59,unit_del,68')] ).
cnf(229,plain,
the_carrier(dollar_c5) = cast_as_carrier_subset(dollar_c5),
inference(hyper,[status(thm)],[96,42]),
[iquote('hyper,96,42')] ).
cnf(231,plain,
element(dollar_f7(dollar_c5),powerset(cast_as_carrier_subset(dollar_c5))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[226]),229]),
[iquote('back_demod,226,demod,229')] ).
cnf(362,plain,
( empty(A)
| in(dollar_f4(A),A) ),
inference(hyper,[status(thm)],[79,63]),
[iquote('hyper,79,63')] ).
cnf(406,plain,
dollar_f6(A) = dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[93,71,107])]),
[iquote('hyper,93,71,107,flip.1')] ).
cnf(407,plain,
element(dollar_c4,powerset(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[92]),406]),
[iquote('back_demod,92,demod,406')] ).
cnf(812,plain,
union_of_subsets(A,dollar_c4) = union(dollar_c4),
inference(hyper,[status(thm)],[407,61]),
[iquote('hyper,407,61')] ).
cnf(814,plain,
union_of_subsets(cast_as_carrier_subset(dollar_c5),dollar_c4) = cast_as_carrier_subset(dollar_c5),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[407,48,96,98]),229]),
[iquote('hyper,407,48,96,98,demod,229')] ).
cnf(1127,plain,
~ empty(cast_as_carrier_subset(dollar_c5)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[229,53]),68,96]),
[iquote('para_from,228.1.1,53.3.1,unit_del,68,96')] ).
cnf(1959,plain,
in(dollar_f4(dollar_f7(dollar_c5)),dollar_f7(dollar_c5)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[362,60,96]),68]),
[iquote('hyper,362,60,96,unit_del,68')] ).
cnf(1979,plain,
element(union(dollar_c4),powerset(A)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[812,52]),407]),
[iquote('para_from,812.1.1,52.2.1,unit_del,407')] ).
cnf(2162,plain,
element(dollar_f4(dollar_f7(dollar_c5)),cast_as_carrier_subset(dollar_c5)),
inference(hyper,[status(thm)],[1959,66,231]),
[iquote('hyper,1959,66,231')] ).
cnf(2164,plain,
in(dollar_f4(dollar_f7(dollar_c5)),cast_as_carrier_subset(dollar_c5)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[2162,63]),1127]),
[iquote('hyper,2162,63,unit_del,1127')] ).
cnf(2172,plain,
union(dollar_c4) = cast_as_carrier_subset(dollar_c5),
inference(para_into,[status(thm),theory(equality)],[814,812]),
[iquote('para_into,814.1.1,812.1.1')] ).
cnf(2200,plain,
element(cast_as_carrier_subset(dollar_c5),powerset(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1979]),2172]),
[iquote('back_demod,1979,demod,2172')] ).
cnf(2290,plain,
$false,
inference(hyper,[status(thm)],[2200,67,2164,107]),
[iquote('hyper,2200,67,2164,107')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU325+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 07:41:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.16 ----- Otter 3.3f, August 2004 -----
% 1.95/2.16 The process was started by sandbox on n005.cluster.edu,
% 1.95/2.16 Wed Jul 27 07:41:05 2022
% 1.95/2.16 The command was "./otter". The process ID is 23315.
% 1.95/2.16
% 1.95/2.16 set(prolog_style_variables).
% 1.95/2.16 set(auto).
% 1.95/2.16 dependent: set(auto1).
% 1.95/2.16 dependent: set(process_input).
% 1.95/2.16 dependent: clear(print_kept).
% 1.95/2.16 dependent: clear(print_new_demod).
% 1.95/2.16 dependent: clear(print_back_demod).
% 1.95/2.16 dependent: clear(print_back_sub).
% 1.95/2.16 dependent: set(control_memory).
% 1.95/2.16 dependent: assign(max_mem, 12000).
% 1.95/2.16 dependent: assign(pick_given_ratio, 4).
% 1.95/2.16 dependent: assign(stats_level, 1).
% 1.95/2.16 dependent: assign(max_seconds, 10800).
% 1.95/2.16 clear(print_given).
% 1.95/2.16
% 1.95/2.16 formula_list(usable).
% 1.95/2.16 all A (A=A).
% 1.95/2.16 all A B (in(A,B)-> -in(B,A)).
% 1.95/2.16 all A (v1_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)))).
% 1.95/2.16 all A (v2_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)))).
% 1.95/2.16 all A (v3_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)&v1_rat_1(B)))).
% 1.95/2.16 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)))).
% 1.95/2.16 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)))).
% 1.95/2.16 all A (empty(A)->v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 1.95/2.16 all A (v1_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)))).
% 1.95/2.16 all A (v2_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)))).
% 1.95/2.16 all A (v3_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)))).
% 1.95/2.16 all A (v4_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)))).
% 1.95/2.16 all A (v5_membered(A)->v4_membered(A)).
% 1.95/2.16 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)))).
% 1.95/2.16 all A (v4_membered(A)->v3_membered(A)).
% 1.95/2.16 all A (v3_membered(A)->v2_membered(A)).
% 1.95/2.16 all A (v2_membered(A)->v1_membered(A)).
% 1.95/2.16 all A (one_sorted_str(A)->cast_as_carrier_subset(A)=the_carrier(A)).
% 1.95/2.16 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 1.95/2.16 all A (one_sorted_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> (is_a_cover_of_carrier(A,B)<->cast_as_carrier_subset(A)=union_of_subsets(the_carrier(A),B))))).
% 1.95/2.16 $T.
% 1.95/2.16 $T.
% 1.95/2.16 all A (one_sorted_str(A)->element(cast_as_carrier_subset(A),powerset(the_carrier(A)))).
% 1.95/2.16 $T.
% 1.95/2.16 all A B (element(B,powerset(powerset(A)))->element(union_of_subsets(A,B),powerset(A))).
% 1.95/2.16 $T.
% 1.95/2.16 $T.
% 1.95/2.16 $T.
% 1.95/2.16 exists A one_sorted_str(A).
% 1.95/2.16 all A exists B element(B,A).
% 1.95/2.16 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 1.95/2.16 all A (-empty(powerset(A))).
% 1.95/2.16 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(cast_as_carrier_subset(A))).
% 1.95/2.16 empty(empty_set).
% 1.95/2.16 v1_membered(empty_set).
% 1.95/2.16 v2_membered(empty_set).
% 1.95/2.16 v3_membered(empty_set).
% 1.95/2.16 v4_membered(empty_set).
% 1.95/2.16 v5_membered(empty_set).
% 1.95/2.16 exists A (-empty(A)&v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 1.95/2.16 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.95/2.16 all A exists B (element(B,powerset(A))&empty(B)).
% 1.95/2.16 exists A (one_sorted_str(A)& -empty_carrier(A)).
% 1.95/2.16 all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 1.95/2.16 all A B (element(B,powerset(powerset(A)))->union_of_subsets(A,B)=union(B)).
% 1.95/2.16 all A B subset(A,A).
% 1.95/2.16 all A B (in(A,B)->element(A,B)).
% 1.95/2.16 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.95/2.16 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.95/2.16 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.95/2.16 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.95/2.16 -(all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (element(B,powerset(powerset(the_carrier(A))))-> -(is_a_cover_of_carrier(A,B)&B=empty_set))))).
% 1.95/2.16 all A (empty(A)->A=empty_set).
% 1.95/2.16 all A B (-(in(A,B)&empty(B))).
% 1.95/2.16 all A B (-(empty(A)&A!=B&empty(B))).
% 1.95/2.16 end_of_list.
% 1.95/2.16
% 1.95/2.16 -------> usable clausifies to:
% 1.95/2.16
% 1.95/2.16 list(usable).
% 1.95/2.16 0 [] A=A.
% 1.95/2.16 0 [] -in(A,B)| -in(B,A).
% 1.95/2.16 0 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.16 0 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.16 0 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.95/2.16 0 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.16 0 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.95/2.17 0 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.95/2.17 0 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.17 0 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.95/2.17 0 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 1.95/2.17 0 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,A)|natural(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.95/2.17 0 [] -empty(A)|v1_membered(A).
% 1.95/2.17 0 [] -empty(A)|v2_membered(A).
% 1.95/2.17 0 [] -empty(A)|v3_membered(A).
% 1.95/2.17 0 [] -empty(A)|v4_membered(A).
% 1.95/2.17 0 [] -empty(A)|v5_membered(A).
% 1.95/2.17 0 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 0 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 0 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.95/2.17 0 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 0 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.95/2.17 0 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.95/2.17 0 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 0 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.95/2.17 0 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.95/2.17 0 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.95/2.17 0 [] -v5_membered(A)|v4_membered(A).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.95/2.17 0 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 1.95/2.17 0 [] -v4_membered(A)|v3_membered(A).
% 1.95/2.17 0 [] -v3_membered(A)|v2_membered(A).
% 1.95/2.17 0 [] -v2_membered(A)|v1_membered(A).
% 1.95/2.17 0 [] -one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A).
% 1.95/2.17 0 [] B!=union(A)| -in(C,B)|in(C,$f1(A,B,C)).
% 1.95/2.17 0 [] B!=union(A)| -in(C,B)|in($f1(A,B,C),A).
% 1.95/2.17 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 1.95/2.17 0 [] B=union(A)|in($f3(A,B),B)|in($f3(A,B),$f2(A,B)).
% 1.95/2.17 0 [] B=union(A)|in($f3(A,B),B)|in($f2(A,B),A).
% 1.95/2.17 0 [] B=union(A)| -in($f3(A,B),B)| -in($f3(A,B),X1)| -in(X1,A).
% 1.95/2.17 0 [] -one_sorted_str(A)| -element(B,powerset(powerset(the_carrier(A))))| -is_a_cover_of_carrier(A,B)|cast_as_carrier_subset(A)=union_of_subsets(the_carrier(A),B).
% 1.95/2.17 0 [] -one_sorted_str(A)| -element(B,powerset(powerset(the_carrier(A))))|is_a_cover_of_carrier(A,B)|cast_as_carrier_subset(A)!=union_of_subsets(the_carrier(A),B).
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] -element(B,powerset(powerset(A)))|element(union_of_subsets(A,B),powerset(A)).
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] $T.
% 1.95/2.17 0 [] one_sorted_str($c1).
% 1.95/2.17 0 [] element($f4(A),A).
% 1.95/2.17 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 1.95/2.17 0 [] -empty(powerset(A)).
% 1.95/2.17 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(cast_as_carrier_subset(A)).
% 1.95/2.17 0 [] empty(empty_set).
% 1.95/2.17 0 [] v1_membered(empty_set).
% 1.95/2.17 0 [] v2_membered(empty_set).
% 1.95/2.17 0 [] v3_membered(empty_set).
% 1.95/2.17 0 [] v4_membered(empty_set).
% 1.95/2.17 0 [] v5_membered(empty_set).
% 1.95/2.17 0 [] -empty($c2).
% 1.95/2.17 0 [] v1_membered($c2).
% 1.95/2.17 0 [] v2_membered($c2).
% 1.95/2.17 0 [] v3_membered($c2).
% 1.95/2.17 0 [] v4_membered($c2).
% 1.95/2.17 0 [] v5_membered($c2).
% 1.95/2.17 0 [] empty(A)|element($f5(A),powerset(A)).
% 1.95/2.17 0 [] empty(A)| -empty($f5(A)).
% 1.95/2.17 0 [] element($f6(A),powerset(A)).
% 1.95/2.17 0 [] empty($f6(A)).
% 1.95/2.17 0 [] one_sorted_str($c3).
% 1.95/2.17 0 [] -empty_carrier($c3).
% 1.95/2.17 0 [] empty_carrier(A)| -one_sorted_str(A)|element($f7(A),powerset(the_carrier(A))).
% 1.95/2.17 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f7(A)).
% 1.95/2.17 0 [] -element(B,powerset(powerset(A)))|union_of_subsets(A,B)=union(B).
% 1.95/2.17 0 [] subset(A,A).
% 1.95/2.17 0 [] -in(A,B)|element(A,B).
% 1.95/2.17 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.95/2.17 0 [] -element(A,powerset(B))|subset(A,B).
% 1.95/2.17 0 [] element(A,powerset(B))| -subset(A,B).
% 1.95/2.17 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.95/2.17 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.95/2.17 0 [] -empty_carrier($c5).
% 1.95/2.17 0 [] one_sorted_str($c5).
% 1.95/2.17 0 [] element($c4,powerset(powerset(the_carrier($c5)))).
% 1.95/2.17 0 [] is_a_cover_of_carrier($c5,$c4).
% 1.95/2.17 0 [] $c4=empty_set.
% 1.95/2.17 0 [] -empty(A)|A=empty_set.
% 1.95/2.17 0 [] -in(A,B)| -empty(B).
% 1.95/2.17 0 [] -empty(A)|A=B| -empty(B).
% 1.95/2.17 end_of_list.
% 1.95/2.17
% 1.95/2.17 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.95/2.17
% 1.95/2.17 This ia a non-Horn set with equality. The strategy will be
% 1.95/2.17 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.95/2.17 deletion, with positive clauses in sos and nonpositive
% 1.95/2.17 clauses in usable.
% 1.95/2.17
% 1.95/2.17 dependent: set(knuth_bendix).
% 1.95/2.17 dependent: set(anl_eq).
% 1.95/2.17 dependent: set(para_from).
% 1.95/2.17 dependent: set(para_into).
% 1.95/2.17 dependent: clear(para_from_right).
% 1.95/2.17 dependent: clear(para_into_right).
% 1.95/2.17 dependent: set(para_from_vars).
% 1.95/2.17 dependent: set(eq_units_both_ways).
% 1.95/2.17 dependent: set(dynamic_demod_all).
% 1.95/2.17 dependent: set(dynamic_demod).
% 1.95/2.17 dependent: set(order_eq).
% 1.95/2.17 dependent: set(back_demod).
% 1.95/2.17 dependent: set(lrpo).
% 1.95/2.17 dependent: set(hyper_res).
% 1.95/2.17 dependent: set(unit_deletion).
% 1.95/2.17 dependent: set(factor).
% 1.95/2.17
% 1.95/2.17 ------------> process usable:
% 1.95/2.17 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.95/2.17 ** KEPT (pick-wt=7): 2 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 3 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 4 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 5 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 6 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 7 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 8 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 9 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 10 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 11 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 12 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 13 [] -v5_membered(A)| -element(B,A)|natural(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 14 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 15 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 1.95/2.17 ** KEPT (pick-wt=7): 16 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 1.95/2.17 ** KEPT (pick-wt=4): 17 [] -empty(A)|v1_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=4): 18 [] -empty(A)|v2_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=4): 19 [] -empty(A)|v3_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=4): 20 [] -empty(A)|v4_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=4): 21 [] -empty(A)|v5_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=8): 22 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 23 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 24 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 25 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 26 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 27 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 28 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 29 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 30 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 31 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=4): 32 [] -v5_membered(A)|v4_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=8): 33 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 34 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 35 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 36 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=8): 37 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 1.95/2.17 ** KEPT (pick-wt=4): 38 [] -v4_membered(A)|v3_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=4): 39 [] -v3_membered(A)|v2_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=4): 40 [] -v2_membered(A)|v1_membered(A).
% 1.95/2.17 ** KEPT (pick-wt=7): 42 [copy,41,flip.2] -one_sorted_str(A)|the_carrier(A)=cast_as_carrier_subset(A).
% 1.95/2.17 ** KEPT (pick-wt=13): 43 [] A!=union(B)| -in(C,A)|in(C,$f1(B,A,C)).
% 1.95/2.17 ** KEPT (pick-wt=13): 44 [] A!=union(B)| -in(C,A)|in($f1(B,A,C),B).
% 1.95/2.17 ** KEPT (pick-wt=13): 45 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 1.95/2.17 ** KEPT (pick-wt=17): 46 [] A=union(B)| -in($f3(B,A),A)| -in($f3(B,A),C)| -in(C,B).
% 12.34/12.58 ** KEPT (pick-wt=18): 48 [copy,47,flip.4] -one_sorted_str(A)| -element(B,powerset(powerset(the_carrier(A))))| -is_a_cover_of_carrier(A,B)|union_of_subsets(the_carrier(A),B)=cast_as_carrier_subset(A).
% 12.34/12.58 ** KEPT (pick-wt=18): 50 [copy,49,flip.4] -one_sorted_str(A)| -element(B,powerset(powerset(the_carrier(A))))|is_a_cover_of_carrier(A,B)|union_of_subsets(the_carrier(A),B)!=cast_as_carrier_subset(A).
% 12.34/12.58 ** KEPT (pick-wt=8): 51 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 12.34/12.58 ** KEPT (pick-wt=11): 52 [] -element(A,powerset(powerset(B)))|element(union_of_subsets(B,A),powerset(B)).
% 12.34/12.58 ** KEPT (pick-wt=7): 53 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 12.34/12.58 ** KEPT (pick-wt=3): 54 [] -empty(powerset(A)).
% 12.34/12.58 ** KEPT (pick-wt=7): 55 [] empty_carrier(A)| -one_sorted_str(A)| -empty(cast_as_carrier_subset(A)).
% 12.34/12.58 ** KEPT (pick-wt=2): 56 [] -empty($c2).
% 12.34/12.58 ** KEPT (pick-wt=5): 57 [] empty(A)| -empty($f5(A)).
% 12.34/12.58 ** KEPT (pick-wt=2): 58 [] -empty_carrier($c3).
% 12.34/12.58 ** KEPT (pick-wt=10): 59 [] empty_carrier(A)| -one_sorted_str(A)|element($f7(A),powerset(the_carrier(A))).
% 12.34/12.58 ** KEPT (pick-wt=7): 60 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f7(A)).
% 12.34/12.58 ** KEPT (pick-wt=11): 61 [] -element(A,powerset(powerset(B)))|union_of_subsets(B,A)=union(A).
% 12.34/12.58 ** KEPT (pick-wt=6): 62 [] -in(A,B)|element(A,B).
% 12.34/12.58 ** KEPT (pick-wt=8): 63 [] -element(A,B)|empty(B)|in(A,B).
% 12.34/12.58 ** KEPT (pick-wt=7): 64 [] -element(A,powerset(B))|subset(A,B).
% 12.34/12.58 ** KEPT (pick-wt=7): 65 [] element(A,powerset(B))| -subset(A,B).
% 12.34/12.58 ** KEPT (pick-wt=10): 66 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 12.34/12.58 ** KEPT (pick-wt=9): 67 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 12.34/12.58 ** KEPT (pick-wt=2): 68 [] -empty_carrier($c5).
% 12.34/12.58 ** KEPT (pick-wt=5): 69 [] -empty(A)|A=empty_set.
% 12.34/12.58 ** KEPT (pick-wt=5): 70 [] -in(A,B)| -empty(B).
% 12.34/12.58 ** KEPT (pick-wt=7): 71 [] -empty(A)|A=B| -empty(B).
% 12.34/12.58
% 12.34/12.58 ------------> process sos:
% 12.34/12.58 ** KEPT (pick-wt=3): 75 [] A=A.
% 12.34/12.58 ** KEPT (pick-wt=16): 76 [] A=union(B)|in($f3(B,A),A)|in($f3(B,A),$f2(B,A)).
% 12.34/12.58 ** KEPT (pick-wt=14): 77 [] A=union(B)|in($f3(B,A),A)|in($f2(B,A),B).
% 12.34/12.58 ** KEPT (pick-wt=2): 78 [] one_sorted_str($c1).
% 12.34/12.58 ** KEPT (pick-wt=4): 79 [] element($f4(A),A).
% 12.34/12.58 ** KEPT (pick-wt=2): 80 [] empty(empty_set).
% 12.34/12.58 ** KEPT (pick-wt=2): 81 [] v1_membered(empty_set).
% 12.34/12.58 ** KEPT (pick-wt=2): 82 [] v2_membered(empty_set).
% 12.34/12.58 ** KEPT (pick-wt=2): 83 [] v3_membered(empty_set).
% 12.34/12.58 ** KEPT (pick-wt=2): 84 [] v4_membered(empty_set).
% 12.34/12.58 ** KEPT (pick-wt=2): 85 [] v5_membered(empty_set).
% 12.34/12.58 ** KEPT (pick-wt=2): 86 [] v1_membered($c2).
% 12.34/12.58 ** KEPT (pick-wt=2): 87 [] v2_membered($c2).
% 12.34/12.58 ** KEPT (pick-wt=2): 88 [] v3_membered($c2).
% 12.34/12.58 ** KEPT (pick-wt=2): 89 [] v4_membered($c2).
% 12.34/12.58 ** KEPT (pick-wt=2): 90 [] v5_membered($c2).
% 12.34/12.58 ** KEPT (pick-wt=7): 91 [] empty(A)|element($f5(A),powerset(A)).
% 12.34/12.58 ** KEPT (pick-wt=5): 92 [] element($f6(A),powerset(A)).
% 12.34/12.58 ** KEPT (pick-wt=3): 93 [] empty($f6(A)).
% 12.34/12.58 ** KEPT (pick-wt=2): 94 [] one_sorted_str($c3).
% 12.34/12.58 ** KEPT (pick-wt=3): 95 [] subset(A,A).
% 12.34/12.58 ** KEPT (pick-wt=2): 96 [] one_sorted_str($c5).
% 12.34/12.58 ** KEPT (pick-wt=6): 97 [] element($c4,powerset(powerset(the_carrier($c5)))).
% 12.34/12.58 ** KEPT (pick-wt=3): 98 [] is_a_cover_of_carrier($c5,$c4).
% 12.34/12.58 ** KEPT (pick-wt=3): 100 [copy,99,flip.1] empty_set=$c4.
% 12.34/12.58 ---> New Demodulator: 101 [new_demod,100] empty_set=$c4.
% 12.34/12.58 Following clause subsumed by 75 during input processing: 0 [copy,75,flip.1] A=A.
% 12.34/12.58 75 back subsumes 74.
% 12.34/12.58 >>>> Starting back demodulation with 101.
% 12.34/12.58 >> back demodulating 85 with 101.
% 12.34/12.58 >> back demodulating 84 with 101.
% 12.34/12.58 >> back demodulating 83 with 101.
% 12.34/12.58 >> back demodulating 82 with 101.
% 12.34/12.58 >> back demodulating 81 with 101.
% 12.34/12.58 >> back demodulating 80 with 101.
% 12.34/12.58 >> back demodulating 69 with 101.
% 12.34/12.58
% 12.34/12.58 ======= end of input processing =======
% 12.34/12.58
% 12.34/12.58 =========== start of search ===========
% 12.34/12.58
% 12.34/12.58
% 12.34/12.58 Resetting weight limit to 7.
% 12.34/12.58
% 12.34/12.58
% 12.34/12.58 Resetting weight limit to 7.
% 12.34/12.58
% 12.34/12.58 sos_size=1698
% 12.34/12.58
% 12.34/12.58
% 12.34/12.58 Resetting weight limit to 6.
% 12.34/12.58
% 12.34/12.58
% 12.34/12.58 Resetting weight limit to 6.
% 12.34/12.58
% 12.34/12.58 sos_size=1799
% 12.34/12.58
% 12.34/12.58 -- HEY sandbox, WE HAVE A PROOF!! --
% 12.34/12.58
% 12.34/12.58 -----> EMPTY CLAUSE at 10.42 sec ----> 2290 [hyper,2200,67,2164,107] $F.
% 12.34/12.58
% 12.34/12.58 Length of proof is 19. Level of proof is 7.
% 12.34/12.58
% 12.34/12.58 ---------------- PROOF ----------------
% 12.34/12.58 % SZS status Theorem
% 12.34/12.58 % SZS output start Refutation
% See solution above
% 12.34/12.58 ------------ end of proof -------------
% 12.34/12.58
% 12.34/12.58
% 12.34/12.58 Search stopped by max_proofs option.
% 12.34/12.58
% 12.34/12.58
% 12.34/12.58 Search stopped by max_proofs option.
% 12.34/12.58
% 12.34/12.58 ============ end of search ============
% 12.34/12.58
% 12.34/12.58 -------------- statistics -------------
% 12.34/12.58 clauses given 408
% 12.34/12.58 clauses generated 69653
% 12.34/12.58 clauses kept 2276
% 12.34/12.58 clauses forward subsumed 3941
% 12.34/12.58 clauses back subsumed 125
% 12.34/12.58 Kbytes malloced 7812
% 12.34/12.58
% 12.34/12.58 ----------- times (seconds) -----------
% 12.34/12.58 user CPU time 10.42 (0 hr, 0 min, 10 sec)
% 12.34/12.58 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 12.34/12.58 wall-clock time 12 (0 hr, 0 min, 12 sec)
% 12.34/12.58
% 12.34/12.58 That finishes the proof of the theorem.
% 12.34/12.58
% 12.34/12.58 Process 23315 finished Wed Jul 27 07:41:17 2022
% 12.34/12.58 Otter interrupted
% 12.34/12.58 PROOF FOUND
%------------------------------------------------------------------------------