%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU308+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:15:35 EDT 2022
% Result : Theorem 2.20s 2.41s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 13 unt; 0 nHn; 15 RR)
% Number of literals : 24 ( 11 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(66,axiom,
( ~ element(A,powerset(B))
| ~ element(C,powerset(B))
| subset_difference(B,A,C) = set_difference(A,C) ),
file('SEU308+1.p',unknown),
[] ).
cnf(72,axiom,
( element(A,powerset(B))
| ~ subset(A,B) ),
file('SEU308+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ one_sorted_str(A)
| cast_as_carrier_subset(A) = the_carrier(A) ),
file('SEU308+1.p',unknown),
[] ).
cnf(74,plain,
( ~ one_sorted_str(A)
| the_carrier(A) = cast_as_carrier_subset(A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[73])]),
[iquote('copy,73,flip.2')] ).
cnf(75,axiom,
subset_complement(the_carrier(dollar_c4),dollar_c3) != subset_difference(the_carrier(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3),
file('SEU308+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ element(A,powerset(B))
| subset_complement(B,A) = set_difference(B,A) ),
file('SEU308+1.p',unknown),
[] ).
cnf(81,axiom,
A = A,
file('SEU308+1.p',unknown),
[] ).
cnf(97,axiom,
subset(A,A),
file('SEU308+1.p',unknown),
[] ).
cnf(103,axiom,
one_sorted_str(dollar_c4),
file('SEU308+1.p',unknown),
[] ).
cnf(104,axiom,
element(dollar_c3,powerset(the_carrier(dollar_c4))),
file('SEU308+1.p',unknown),
[] ).
cnf(116,plain,
the_carrier(dollar_c4) = cast_as_carrier_subset(dollar_c4),
inference(hyper,[status(thm)],[103,74]),
[iquote('hyper,103,74')] ).
cnf(118,plain,
element(dollar_c3,powerset(cast_as_carrier_subset(dollar_c4))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[104]),116]),
[iquote('back_demod,104,demod,116')] ).
cnf(119,plain,
subset_complement(cast_as_carrier_subset(dollar_c4),dollar_c3) != subset_difference(cast_as_carrier_subset(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[75]),116,116]),
[iquote('back_demod,75,demod,116,116')] ).
cnf(122,plain,
element(A,powerset(A)),
inference(hyper,[status(thm)],[97,72]),
[iquote('hyper,97,72')] ).
cnf(280,plain,
subset_complement(cast_as_carrier_subset(dollar_c4),dollar_c3) = set_difference(cast_as_carrier_subset(dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[118,76]),
[iquote('hyper,118,76')] ).
cnf(292,plain,
set_difference(cast_as_carrier_subset(dollar_c4),dollar_c3) = subset_difference(cast_as_carrier_subset(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[118,66,122])]),
[iquote('hyper,118,66,122,flip.1')] ).
cnf(306,plain,
subset_difference(cast_as_carrier_subset(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3) != subset_difference(cast_as_carrier_subset(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[119]),280,292]),
[iquote('back_demod,119,demod,280,292')] ).
cnf(307,plain,
$false,
inference(binary,[status(thm)],[306,81]),
[iquote('binary,306.1,81.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU308+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 07:45:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.20/2.40 ----- Otter 3.3f, August 2004 -----
% 2.20/2.40 The process was started by sandbox2 on n015.cluster.edu,
% 2.20/2.40 Wed Jul 27 07:45:42 2022
% 2.20/2.40 The command was "./otter". The process ID is 11247.
% 2.20/2.40
% 2.20/2.40 set(prolog_style_variables).
% 2.20/2.40 set(auto).
% 2.20/2.40 dependent: set(auto1).
% 2.20/2.40 dependent: set(process_input).
% 2.20/2.40 dependent: clear(print_kept).
% 2.20/2.40 dependent: clear(print_new_demod).
% 2.20/2.40 dependent: clear(print_back_demod).
% 2.20/2.40 dependent: clear(print_back_sub).
% 2.20/2.40 dependent: set(control_memory).
% 2.20/2.40 dependent: assign(max_mem, 12000).
% 2.20/2.40 dependent: assign(pick_given_ratio, 4).
% 2.20/2.40 dependent: assign(stats_level, 1).
% 2.20/2.40 dependent: assign(max_seconds, 10800).
% 2.20/2.40 clear(print_given).
% 2.20/2.40
% 2.20/2.40 formula_list(usable).
% 2.20/2.40 all A (A=A).
% 2.20/2.40 all A B (in(A,B)-> -in(B,A)).
% 2.20/2.40 $T.
% 2.20/2.40 all A (v5_membered(A)->v4_membered(A)).
% 2.20/2.40 all A (v4_membered(A)->v3_membered(A)).
% 2.20/2.40 all A (v3_membered(A)->v2_membered(A)).
% 2.20/2.40 all A (v2_membered(A)->v1_membered(A)).
% 2.20/2.40 exists A (-empty(A)&v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 2.20/2.40 all A (v1_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)))).
% 2.20/2.40 all A (v2_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)))).
% 2.20/2.40 all A (v3_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)&v1_rat_1(B)))).
% 2.20/2.40 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)))).
% 2.20/2.40 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)))).
% 2.20/2.40 empty(empty_set).
% 2.20/2.40 v1_membered(empty_set).
% 2.20/2.40 v2_membered(empty_set).
% 2.20/2.40 v3_membered(empty_set).
% 2.20/2.40 v4_membered(empty_set).
% 2.20/2.40 v5_membered(empty_set).
% 2.20/2.40 all A (v1_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)))).
% 2.20/2.40 all A (v2_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)))).
% 2.20/2.40 all A (v3_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)))).
% 2.20/2.40 all A (v4_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)))).
% 2.20/2.40 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)))).
% 2.20/2.40 all A B (v1_membered(A)->v1_membered(set_difference(A,B))).
% 2.20/2.40 all A B (v2_membered(A)->v1_membered(set_difference(A,B))&v2_membered(set_difference(A,B))).
% 2.20/2.40 all A B (v3_membered(A)->v1_membered(set_difference(A,B))&v2_membered(set_difference(A,B))&v3_membered(set_difference(A,B))).
% 2.20/2.40 all A B (v4_membered(A)->v1_membered(set_difference(A,B))&v2_membered(set_difference(A,B))&v3_membered(set_difference(A,B))&v4_membered(set_difference(A,B))).
% 2.20/2.40 all A B (v5_membered(A)->v1_membered(set_difference(A,B))&v2_membered(set_difference(A,B))&v3_membered(set_difference(A,B))&v4_membered(set_difference(A,B))&v5_membered(set_difference(A,B))).
% 2.20/2.40 all A B (in(A,B)->element(A,B)).
% 2.20/2.40 all A (set_difference(A,empty_set)=A).
% 2.20/2.40 all A (set_difference(empty_set,A)=empty_set).
% 2.20/2.40 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.20/2.40 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.20/2.40 all A B subset(A,A).
% 2.20/2.40 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.20/2.40 all A exists B (element(B,powerset(A))&empty(B)).
% 2.20/2.40 all A (empty(A)->v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 2.20/2.40 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.20/2.40 all A (empty(A)->A=empty_set).
% 2.20/2.40 all A B (-(in(A,B)&empty(B))).
% 2.20/2.40 all A B (-(empty(A)&A!=B&empty(B))).
% 2.20/2.40 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 2.20/2.40 exists A one_sorted_str(A).
% 2.20/2.40 all A exists B element(B,A).
% 2.20/2.40 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_difference(A,B,C)=set_difference(B,C)).
% 2.20/2.40 $T.
% 2.20/2.40 all A (one_sorted_str(A)->element(cast_as_carrier_subset(A),powerset(the_carrier(A)))).
% 2.20/2.40 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 2.20/2.40 $T.
% 2.20/2.40 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_difference(A,B,C),powerset(A))).
% 2.20/2.40 $T.
% 2.20/2.40 $T.
% 2.20/2.40 $T.
% 2.20/2.40 all A (-empty(powerset(A))).
% 2.20/2.40 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.20/2.40 all A (one_sorted_str(A)->cast_as_carrier_subset(A)=the_carrier(A)).
% 2.20/2.40 -(all A (one_sorted_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset_complement(the_carrier(A),B)=subset_difference(the_carrier(A),cast_as_carrier_subset(A),B))))).
% 2.20/2.40 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 2.20/2.40 end_of_list.
% 2.20/2.40
% 2.20/2.40 -------> usable clausifies to:
% 2.20/2.40
% 2.20/2.40 list(usable).
% 2.20/2.40 0 [] A=A.
% 2.20/2.40 0 [] -in(A,B)| -in(B,A).
% 2.20/2.40 0 [] $T.
% 2.20/2.40 0 [] -v5_membered(A)|v4_membered(A).
% 2.20/2.40 0 [] -v4_membered(A)|v3_membered(A).
% 2.20/2.40 0 [] -v3_membered(A)|v2_membered(A).
% 2.20/2.40 0 [] -v2_membered(A)|v1_membered(A).
% 2.20/2.40 0 [] -empty($c1).
% 2.20/2.40 0 [] v1_membered($c1).
% 2.20/2.40 0 [] v2_membered($c1).
% 2.20/2.40 0 [] v3_membered($c1).
% 2.20/2.40 0 [] v4_membered($c1).
% 2.20/2.40 0 [] v5_membered($c1).
% 2.20/2.40 0 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 0 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 0 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.20/2.40 0 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 0 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.20/2.40 0 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.20/2.40 0 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 0 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.20/2.40 0 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 2.20/2.40 0 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,A)|natural(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.20/2.40 0 [] empty(empty_set).
% 2.20/2.40 0 [] v1_membered(empty_set).
% 2.20/2.40 0 [] v2_membered(empty_set).
% 2.20/2.40 0 [] v3_membered(empty_set).
% 2.20/2.40 0 [] v4_membered(empty_set).
% 2.20/2.40 0 [] v5_membered(empty_set).
% 2.20/2.40 0 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 0 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 0 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.20/2.40 0 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 0 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.20/2.40 0 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.20/2.40 0 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 0 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.20/2.40 0 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.20/2.40 0 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 2.20/2.40 0 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 2.20/2.40 0 [] -v1_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v2_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v2_membered(A)|v2_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v3_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v3_membered(A)|v2_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v3_membered(A)|v3_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v4_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v4_membered(A)|v2_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v4_membered(A)|v3_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v4_membered(A)|v4_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v5_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v5_membered(A)|v2_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v5_membered(A)|v3_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v5_membered(A)|v4_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -v5_membered(A)|v5_membered(set_difference(A,B)).
% 2.20/2.40 0 [] -in(A,B)|element(A,B).
% 2.20/2.40 0 [] set_difference(A,empty_set)=A.
% 2.20/2.40 0 [] set_difference(empty_set,A)=empty_set.
% 2.20/2.40 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.20/2.40 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.20/2.40 0 [] subset(A,A).
% 2.20/2.40 0 [] empty(A)|element($f1(A),powerset(A)).
% 2.20/2.40 0 [] empty(A)| -empty($f1(A)).
% 2.20/2.40 0 [] element($f2(A),powerset(A)).
% 2.20/2.40 0 [] empty($f2(A)).
% 2.20/2.40 0 [] -empty(A)|v1_membered(A).
% 2.20/2.40 0 [] -empty(A)|v2_membered(A).
% 2.20/2.40 0 [] -empty(A)|v3_membered(A).
% 2.20/2.40 0 [] -empty(A)|v4_membered(A).
% 2.20/2.40 0 [] -empty(A)|v5_membered(A).
% 2.20/2.40 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.20/2.40 0 [] -empty(A)|A=empty_set.
% 2.20/2.40 0 [] -in(A,B)| -empty(B).
% 2.20/2.40 0 [] -empty(A)|A=B| -empty(B).
% 2.20/2.40 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 2.20/2.40 0 [] one_sorted_str($c2).
% 2.20/2.40 0 [] element($f3(A),A).
% 2.20/2.40 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_difference(A,B,C)=set_difference(B,C).
% 2.20/2.40 0 [] $T.
% 2.20/2.40 0 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 2.20/2.40 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 2.20/2.40 0 [] $T.
% 2.20/2.40 0 [] -element(B,powerset(A))| -element(C,powerset(A))|element(subset_difference(A,B,C),powerset(A)).
% 2.20/2.40 0 [] $T.
% 2.20/2.40 0 [] $T.
% 2.20/2.40 0 [] $T.
% 2.20/2.40 0 [] -empty(powerset(A)).
% 2.20/2.40 0 [] -element(A,powerset(B))|subset(A,B).
% 2.20/2.40 0 [] element(A,powerset(B))| -subset(A,B).
% 2.20/2.40 0 [] -one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A).
% 2.20/2.40 0 [] one_sorted_str($c4).
% 2.20/2.40 0 [] element($c3,powerset(the_carrier($c4))).
% 2.20/2.40 0 [] subset_complement(the_carrier($c4),$c3)!=subset_difference(the_carrier($c4),cast_as_carrier_subset($c4),$c3).
% 2.20/2.40 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 2.20/2.40 end_of_list.
% 2.20/2.40
% 2.20/2.40 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.20/2.40
% 2.20/2.40 This ia a non-Horn set with equality. The strategy will be
% 2.20/2.40 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.20/2.40 deletion, with positive clauses in sos and nonpositive
% 2.20/2.40 clauses in usable.
% 2.20/2.40
% 2.20/2.40 dependent: set(knuth_bendix).
% 2.20/2.40 dependent: set(anl_eq).
% 2.20/2.40 dependent: set(para_from).
% 2.20/2.40 dependent: set(para_into).
% 2.20/2.40 dependent: clear(para_from_right).
% 2.20/2.40 dependent: clear(para_into_right).
% 2.20/2.40 dependent: set(para_from_vars).
% 2.20/2.40 dependent: set(eq_units_both_ways).
% 2.20/2.40 dependent: set(dynamic_demod_all).
% 2.20/2.40 dependent: set(dynamic_demod).
% 2.20/2.40 dependent: set(order_eq).
% 2.20/2.40 dependent: set(back_demod).
% 2.20/2.40 dependent: set(lrpo).
% 2.20/2.40 dependent: set(hyper_res).
% 2.20/2.40 dependent: set(unit_deletion).
% 2.20/2.40 dependent: set(factor).
% 2.20/2.40
% 2.20/2.40 ------------> process usable:
% 2.20/2.40 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.20/2.40 ** KEPT (pick-wt=4): 2 [] -v5_membered(A)|v4_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=4): 3 [] -v4_membered(A)|v3_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=4): 4 [] -v3_membered(A)|v2_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=4): 5 [] -v2_membered(A)|v1_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=2): 6 [] -empty($c1).
% 2.20/2.40 ** KEPT (pick-wt=7): 7 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 8 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 9 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 10 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 11 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 12 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 13 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 14 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 15 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 16 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 17 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 18 [] -v5_membered(A)| -element(B,A)|natural(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 19 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 20 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 21 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 22 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 23 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 24 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 25 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 26 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 27 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 28 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 29 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 30 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 31 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 32 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 33 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 34 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 35 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=8): 36 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 2.20/2.40 ** KEPT (pick-wt=6): 37 [] -v1_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 38 [] -v2_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 39 [] -v2_membered(A)|v2_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 40 [] -v3_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 41 [] -v3_membered(A)|v2_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 42 [] -v3_membered(A)|v3_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 43 [] -v4_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 44 [] -v4_membered(A)|v2_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 45 [] -v4_membered(A)|v3_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 46 [] -v4_membered(A)|v4_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 47 [] -v5_membered(A)|v1_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 48 [] -v5_membered(A)|v2_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 49 [] -v5_membered(A)|v3_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 50 [] -v5_membered(A)|v4_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 51 [] -v5_membered(A)|v5_membered(set_difference(A,B)).
% 2.20/2.40 ** KEPT (pick-wt=6): 52 [] -in(A,B)|element(A,B).
% 2.20/2.40 ** KEPT (pick-wt=10): 53 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.20/2.40 ** KEPT (pick-wt=9): 54 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.20/2.40 ** KEPT (pick-wt=5): 55 [] empty(A)| -empty($f1(A)).
% 2.20/2.40 ** KEPT (pick-wt=4): 56 [] -empty(A)|v1_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=4): 57 [] -empty(A)|v2_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=4): 58 [] -empty(A)|v3_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=4): 59 [] -empty(A)|v4_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=4): 60 [] -empty(A)|v5_membered(A).
% 2.20/2.40 ** KEPT (pick-wt=8): 61 [] -element(A,B)|empty(B)|in(A,B).
% 2.20/2.40 ** KEPT (pick-wt=5): 62 [] -empty(A)|A=empty_set.
% 2.20/2.40 ** KEPT (pick-wt=5): 63 [] -in(A,B)| -empty(B).
% 2.20/2.40 ** KEPT (pick-wt=7): 64 [] -empty(A)|A=B| -empty(B).
% 2.20/2.40 ** KEPT (pick-wt=11): 65 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 2.20/2.40 ** KEPT (pick-wt=16): 66 [] -element(A,powerset(B))| -element(C,powerset(B))|subset_difference(B,A,C)=set_difference(A,C).
% 2.20/2.40 ** KEPT (pick-wt=8): 67 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 2.20/2.40 ** KEPT (pick-wt=10): 68 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 2.20/2.40 ** KEPT (pick-wt=15): 69 [] -element(A,powerset(B))| -element(C,powerset(B))|element(subset_difference(B,A,C),powerset(B)).
% 2.20/2.40 ** KEPT (pick-wt=3): 70 [] -empty(powerset(A)).
% 2.20/2.40 ** KEPT (pick-wt=7): 71 [] -element(A,powerset(B))|subset(A,B).
% 2.20/2.40 ** KEPT (pick-wt=7): 72 [] element(A,powerset(B))| -subset(A,B).
% 2.20/2.40 ** KEPT (pick-wt=7): 74 [copy,73,flip.2] -one_sorted_str(A)|the_carrier(A)=cast_as_carrier_subset(A).
% 2.20/2.40 ** KEPT (pick-wt=11): 75 [] subset_complement(the_carrier($c4),$c3)!=subset_difference(the_carrier($c4),cast_as_carrier_subset($c4),$c3).
% 2.20/2.40 ** KEPT (pick-wt=11): 76 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 2.20/2.40
% 2.20/2.40 ------------> process sos:
% 2.20/2.40 ** KEPT (pick-wt=3): 81 [] A=A.
% 2.20/2.40 ** KEPT (pick-wt=2): 82 [] v1_membered($c1).
% 2.20/2.40 ** KEPT (pick-wt=2): 83 [] v2_membered($c1).
% 2.20/2.40 ** KEPT (pick-wt=2): 84 [] v3_membered($c1).
% 2.20/2.40 ** KEPT (pick-wt=2): 85 [] v4_membered($c1).
% 2.20/2.40 ** KEPT (pick-wt=2): 86 [] v5_membered($c1).
% 2.20/2.40 ** KEPT (pick-wt=2): 87 [] empty(empty_set).
% 2.20/2.40 ** KEPT (pick-wt=2): 88 [] v1_membered(empty_set).
% 2.20/2.40 ** KEPT (pick-wt=2): 89 [] v2_membered(empty_set).
% 2.20/2.40 ** KEPT (pick-wt=2): 90 [] v3_membered(empty_set).
% 2.20/2.40 ** KEPT (pick-wt=2): 91 [] v4_membered(empty_set).
% 2.20/2.40 ** KEPT (pick-wt=2): 92 [] v5_membered(empty_set).
% 2.20/2.40 ** KEPT (pick-wt=5): 93 [] set_difference(A,empty_set)=A.
% 2.20/2.40 ---> New Demodulator: 94 [new_demod,93] set_difference(A,empty_set)=A.
% 2.20/2.40 ** KEPT (pick-wt=5): 95 [] set_difference(empty_set,A)=empty_set.
% 2.20/2.40 ---> New Demodulator: 96 [new_demod,95] set_difference(empty_set,A)=empty_set.
% 2.20/2.40 ** KEPT (pick-wt=3): 97 [] subset(A,A).
% 2.20/2.40 ** KEPT (pick-wt=7): 98 [] empty(A)|element($f1(A),powerset(A)).
% 2.20/2.40 ** KEPT (pick-wt=5): 99 [] element($f2(A),powerset(A)).
% 2.20/2.40 ** KEPT (pick-wt=3): 100 [] empty($f2(A)).
% 2.20/2.41 ** KEPT (pick-wt=2): 101 [] one_sorted_str($c2).
% 2.20/2.41 ** KEPT (pick-wt=4): 102 [] element($f3(A),A).
% 2.20/2.41 ** KEPT (pick-wt=2): 103 [] one_sorted_str($c4).
% 2.20/2.41 ** KEPT (pick-wt=5): 104 [] element($c3,powerset(the_carrier($c4))).
% 2.20/2.41 Following clause subsumed by 81 during input processing: 0 [copy,81,flip.1] A=A.
% 2.20/2.41 81 back subsumes 78.
% 2.20/2.41 >>>> Starting back demodulation with 94.
% 2.20/2.41 >>>> Starting back demodulation with 96.
% 2.20/2.41
% 2.20/2.41 ======= end of input processing =======
% 2.20/2.41
% 2.20/2.41 =========== start of search ===========
% 2.20/2.41
% 2.20/2.41 -------- PROOF --------
% 2.20/2.41
% 2.20/2.41 ----> UNIT CONFLICT at 0.01 sec ----> 307 [binary,306.1,81.1] $F.
% 2.20/2.41
% 2.20/2.41 Length of proof is 8. Level of proof is 5.
% 2.20/2.41
% 2.20/2.41 ---------------- PROOF ----------------
% 2.20/2.41 % SZS status Theorem
% 2.20/2.41 % SZS output start Refutation
% See solution above
% 2.20/2.41 ------------ end of proof -------------
% 2.20/2.41
% 2.20/2.41
% 2.20/2.41 Search stopped by max_proofs option.
% 2.20/2.41
% 2.20/2.41
% 2.20/2.41 Search stopped by max_proofs option.
% 2.20/2.41
% 2.20/2.41 ============ end of search ============
% 2.20/2.41
% 2.20/2.41 -------------- statistics -------------
% 2.20/2.41 clauses given 51
% 2.20/2.41 clauses generated 564
% 2.20/2.41 clauses kept 270
% 2.20/2.41 clauses forward subsumed 412
% 2.20/2.41 clauses back subsumed 3
% 2.20/2.41 Kbytes malloced 1953
% 2.20/2.41
% 2.20/2.41 ----------- times (seconds) -----------
% 2.20/2.41 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.20/2.41 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.20/2.41 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.20/2.41
% 2.20/2.41 That finishes the proof of the theorem.
% 2.20/2.41
% 2.20/2.41 Process 11247 finished Wed Jul 27 07:45:44 2022
% 2.20/2.41 Otter interrupted
% 2.20/2.41 PROOF FOUND
%------------------------------------------------------------------------------