%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU307+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:15:34 EDT 2022
% Result : Theorem 2.03s 2.25s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 12 unt; 0 nHn; 16 RR)
% Number of literals : 25 ( 9 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(83,axiom,
( ~ element(A,powerset(B))
| ~ element(C,powerset(B))
| subset_intersection2(B,A,C) = set_intersection2(A,C) ),
file('SEU307+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ element(A,powerset(B))
| subset(A,B) ),
file('SEU307+1.p',unknown),
[] ).
cnf(88,axiom,
( element(A,powerset(B))
| ~ subset(A,B) ),
file('SEU307+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ one_sorted_str(A)
| cast_as_carrier_subset(A) = the_carrier(A) ),
file('SEU307+1.p',unknown),
[] ).
cnf(90,plain,
( ~ one_sorted_str(A)
| the_carrier(A) = cast_as_carrier_subset(A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[89])]),
[iquote('copy,89,flip.2')] ).
cnf(91,axiom,
subset_intersection2(the_carrier(dollar_c4),dollar_c3,cast_as_carrier_subset(dollar_c4)) != dollar_c3,
file('SEU307+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
file('SEU307+1.p',unknown),
[] ).
cnf(118,axiom,
subset(A,A),
file('SEU307+1.p',unknown),
[] ).
cnf(121,axiom,
one_sorted_str(dollar_c4),
file('SEU307+1.p',unknown),
[] ).
cnf(122,axiom,
element(dollar_c3,powerset(the_carrier(dollar_c4))),
file('SEU307+1.p',unknown),
[] ).
cnf(144,plain,
the_carrier(dollar_c4) = cast_as_carrier_subset(dollar_c4),
inference(hyper,[status(thm)],[121,90]),
[iquote('hyper,121,90')] ).
cnf(146,plain,
element(dollar_c3,powerset(cast_as_carrier_subset(dollar_c4))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[122]),144]),
[iquote('back_demod,122,demod,144')] ).
cnf(147,plain,
subset_intersection2(cast_as_carrier_subset(dollar_c4),dollar_c3,cast_as_carrier_subset(dollar_c4)) != dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[91]),144]),
[iquote('back_demod,91,demod,144')] ).
cnf(157,plain,
element(A,powerset(A)),
inference(hyper,[status(thm)],[118,88]),
[iquote('hyper,118,88')] ).
cnf(364,plain,
subset(dollar_c3,cast_as_carrier_subset(dollar_c4)),
inference(hyper,[status(thm)],[146,87]),
[iquote('hyper,146,87')] ).
cnf(380,plain,
set_intersection2(dollar_c3,cast_as_carrier_subset(dollar_c4)) = subset_intersection2(cast_as_carrier_subset(dollar_c4),dollar_c3,cast_as_carrier_subset(dollar_c4)),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[146,83,157])]),
[iquote('hyper,146,83,157,flip.1')] ).
cnf(412,plain,
subset_intersection2(cast_as_carrier_subset(dollar_c4),dollar_c3,cast_as_carrier_subset(dollar_c4)) = dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[364,92]),380]),
[iquote('hyper,364,92,demod,380')] ).
cnf(414,plain,
$false,
inference(binary,[status(thm)],[412,147]),
[iquote('binary,412.1,147.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU307+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 07:26:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.03/2.24 ----- Otter 3.3f, August 2004 -----
% 2.03/2.24 The process was started by sandbox2 on n007.cluster.edu,
% 2.03/2.24 Wed Jul 27 07:26:46 2022
% 2.03/2.24 The command was "./otter". The process ID is 10525.
% 2.03/2.24
% 2.03/2.24 set(prolog_style_variables).
% 2.03/2.24 set(auto).
% 2.03/2.24 dependent: set(auto1).
% 2.03/2.24 dependent: set(process_input).
% 2.03/2.24 dependent: clear(print_kept).
% 2.03/2.24 dependent: clear(print_new_demod).
% 2.03/2.24 dependent: clear(print_back_demod).
% 2.03/2.24 dependent: clear(print_back_sub).
% 2.03/2.24 dependent: set(control_memory).
% 2.03/2.24 dependent: assign(max_mem, 12000).
% 2.03/2.24 dependent: assign(pick_given_ratio, 4).
% 2.03/2.24 dependent: assign(stats_level, 1).
% 2.03/2.24 dependent: assign(max_seconds, 10800).
% 2.03/2.24 clear(print_given).
% 2.03/2.24
% 2.03/2.24 formula_list(usable).
% 2.03/2.24 all A (A=A).
% 2.03/2.24 all A B (in(A,B)-> -in(B,A)).
% 2.03/2.24 $T.
% 2.03/2.24 all A (v5_membered(A)->v4_membered(A)).
% 2.03/2.24 all A (v4_membered(A)->v3_membered(A)).
% 2.03/2.24 all A (v3_membered(A)->v2_membered(A)).
% 2.03/2.24 all A (v2_membered(A)->v1_membered(A)).
% 2.03/2.24 exists A (-empty(A)&v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 2.03/2.24 all A (v1_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)))).
% 2.03/2.24 all A (v2_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)))).
% 2.03/2.24 all A (v3_membered(A)-> (all B (element(B,A)->v1_xcmplx_0(B)&v1_xreal_0(B)&v1_rat_1(B)))).
% 2.03/2.24 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)))).
% 2.03/2.24 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)))).
% 2.03/2.24 empty(empty_set).
% 2.03/2.24 v1_membered(empty_set).
% 2.03/2.24 v2_membered(empty_set).
% 2.03/2.24 v3_membered(empty_set).
% 2.03/2.24 v4_membered(empty_set).
% 2.03/2.24 v5_membered(empty_set).
% 2.03/2.24 all A (v1_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)))).
% 2.03/2.24 all A (v2_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)))).
% 2.03/2.24 all A (v3_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)))).
% 2.03/2.24 all A (v4_membered(A)-> (all B (element(B,powerset(A))->v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)))).
% 2.03/2.24 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)))).
% 2.03/2.24 all A B (v1_membered(A)->v1_membered(set_intersection2(A,B))).
% 2.03/2.24 all A B (v1_membered(A)->v1_membered(set_intersection2(B,A))).
% 2.03/2.24 all A B (v2_membered(A)->v1_membered(set_intersection2(A,B))&v2_membered(set_intersection2(A,B))).
% 2.03/2.24 all A B (v2_membered(A)->v1_membered(set_intersection2(B,A))&v2_membered(set_intersection2(B,A))).
% 2.03/2.24 all A B (v3_membered(A)->v1_membered(set_intersection2(A,B))&v2_membered(set_intersection2(A,B))&v3_membered(set_intersection2(A,B))).
% 2.03/2.24 all A B (v3_membered(A)->v1_membered(set_intersection2(B,A))&v2_membered(set_intersection2(B,A))&v3_membered(set_intersection2(B,A))).
% 2.03/2.24 all A B (v4_membered(A)->v1_membered(set_intersection2(A,B))&v2_membered(set_intersection2(A,B))&v3_membered(set_intersection2(A,B))&v4_membered(set_intersection2(A,B))).
% 2.03/2.24 all A B (v4_membered(A)->v1_membered(set_intersection2(B,A))&v2_membered(set_intersection2(B,A))&v3_membered(set_intersection2(B,A))&v4_membered(set_intersection2(B,A))).
% 2.03/2.24 all A B (v5_membered(A)->v1_membered(set_intersection2(A,B))&v2_membered(set_intersection2(A,B))&v3_membered(set_intersection2(A,B))&v4_membered(set_intersection2(A,B))&v5_membered(set_intersection2(A,B))).
% 2.03/2.24 all A B (v5_membered(A)->v1_membered(set_intersection2(B,A))&v2_membered(set_intersection2(B,A))&v3_membered(set_intersection2(B,A))&v4_membered(set_intersection2(B,A))&v5_membered(set_intersection2(B,A))).
% 2.03/2.24 all A B (in(A,B)->element(A,B)).
% 2.03/2.24 all A (set_intersection2(A,empty_set)=empty_set).
% 2.03/2.24 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.03/2.24 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.03/2.24 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.03/2.24 all A exists B (element(B,powerset(A))&empty(B)).
% 2.03/2.24 all A (empty(A)->v1_membered(A)&v2_membered(A)&v3_membered(A)&v4_membered(A)&v5_membered(A)).
% 2.03/2.24 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.03/2.24 all A (empty(A)->A=empty_set).
% 2.03/2.24 all A B (-(in(A,B)&empty(B))).
% 2.03/2.24 all A B (-(empty(A)&A!=B&empty(B))).
% 2.03/2.24 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.03/2.24 all A B (set_intersection2(A,A)=A).
% 2.03/2.24 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_intersection2(A,B,C)=subset_intersection2(A,C,B)).
% 2.03/2.24 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_intersection2(A,B,B)=B).
% 2.03/2.24 all A B subset(A,A).
% 2.03/2.24 exists A one_sorted_str(A).
% 2.03/2.24 all A exists B element(B,A).
% 2.03/2.24 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_intersection2(A,B,C)=set_intersection2(B,C)).
% 2.03/2.24 $T.
% 2.03/2.24 all A (one_sorted_str(A)->element(cast_as_carrier_subset(A),powerset(the_carrier(A)))).
% 2.03/2.24 $T.
% 2.03/2.24 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_intersection2(A,B,C),powerset(A))).
% 2.03/2.24 $T.
% 2.03/2.24 $T.
% 2.03/2.24 $T.
% 2.03/2.24 all A (-empty(powerset(A))).
% 2.03/2.24 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.03/2.24 all A (one_sorted_str(A)->cast_as_carrier_subset(A)=the_carrier(A)).
% 2.03/2.24 -(all A (one_sorted_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A))=B)))).
% 2.03/2.24 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 2.03/2.24 end_of_list.
% 2.03/2.24
% 2.03/2.24 -------> usable clausifies to:
% 2.03/2.24
% 2.03/2.24 list(usable).
% 2.03/2.24 0 [] A=A.
% 2.03/2.24 0 [] -in(A,B)| -in(B,A).
% 2.03/2.24 0 [] $T.
% 2.03/2.24 0 [] -v5_membered(A)|v4_membered(A).
% 2.03/2.24 0 [] -v4_membered(A)|v3_membered(A).
% 2.03/2.24 0 [] -v3_membered(A)|v2_membered(A).
% 2.03/2.24 0 [] -v2_membered(A)|v1_membered(A).
% 2.03/2.24 0 [] -empty($c1).
% 2.03/2.24 0 [] v1_membered($c1).
% 2.03/2.24 0 [] v2_membered($c1).
% 2.03/2.24 0 [] v3_membered($c1).
% 2.03/2.24 0 [] v4_membered($c1).
% 2.03/2.24 0 [] v5_membered($c1).
% 2.03/2.24 0 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 0 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 0 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.03/2.24 0 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 0 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.03/2.24 0 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.03/2.24 0 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 0 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.03/2.24 0 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 2.03/2.24 0 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,A)|natural(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.03/2.24 0 [] empty(empty_set).
% 2.03/2.24 0 [] v1_membered(empty_set).
% 2.03/2.24 0 [] v2_membered(empty_set).
% 2.03/2.24 0 [] v3_membered(empty_set).
% 2.03/2.24 0 [] v4_membered(empty_set).
% 2.03/2.24 0 [] v5_membered(empty_set).
% 2.03/2.24 0 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 0 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 0 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.03/2.24 0 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 0 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.03/2.24 0 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.03/2.24 0 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 0 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.03/2.24 0 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.03/2.24 0 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 2.03/2.24 0 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 2.03/2.24 0 [] -v1_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v1_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v2_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v2_membered(A)|v2_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v2_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v2_membered(A)|v2_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v3_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v3_membered(A)|v2_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v3_membered(A)|v3_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v3_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v3_membered(A)|v2_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v3_membered(A)|v3_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v4_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v4_membered(A)|v2_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v4_membered(A)|v3_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v4_membered(A)|v4_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v4_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v4_membered(A)|v2_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v4_membered(A)|v3_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v4_membered(A)|v4_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v5_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v5_membered(A)|v2_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v5_membered(A)|v3_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v5_membered(A)|v4_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v5_membered(A)|v5_membered(set_intersection2(A,B)).
% 2.03/2.24 0 [] -v5_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v5_membered(A)|v2_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v5_membered(A)|v3_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v5_membered(A)|v4_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -v5_membered(A)|v5_membered(set_intersection2(B,A)).
% 2.03/2.24 0 [] -in(A,B)|element(A,B).
% 2.03/2.24 0 [] set_intersection2(A,empty_set)=empty_set.
% 2.03/2.24 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.03/2.24 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.03/2.24 0 [] empty(A)|element($f1(A),powerset(A)).
% 2.03/2.24 0 [] empty(A)| -empty($f1(A)).
% 2.03/2.24 0 [] element($f2(A),powerset(A)).
% 2.03/2.24 0 [] empty($f2(A)).
% 2.03/2.24 0 [] -empty(A)|v1_membered(A).
% 2.03/2.24 0 [] -empty(A)|v2_membered(A).
% 2.03/2.24 0 [] -empty(A)|v3_membered(A).
% 2.03/2.24 0 [] -empty(A)|v4_membered(A).
% 2.03/2.24 0 [] -empty(A)|v5_membered(A).
% 2.03/2.24 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.03/2.24 0 [] -empty(A)|A=empty_set.
% 2.03/2.24 0 [] -in(A,B)| -empty(B).
% 2.03/2.24 0 [] -empty(A)|A=B| -empty(B).
% 2.03/2.24 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.03/2.24 0 [] set_intersection2(A,A)=A.
% 2.03/2.24 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_intersection2(A,B,C)=subset_intersection2(A,C,B).
% 2.03/2.24 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_intersection2(A,B,B)=B.
% 2.03/2.24 0 [] subset(A,A).
% 2.03/2.24 0 [] one_sorted_str($c2).
% 2.03/2.24 0 [] element($f3(A),A).
% 2.03/2.24 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_intersection2(A,B,C)=set_intersection2(B,C).
% 2.03/2.24 0 [] $T.
% 2.03/2.24 0 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 2.03/2.24 0 [] $T.
% 2.03/2.24 0 [] -element(B,powerset(A))| -element(C,powerset(A))|element(subset_intersection2(A,B,C),powerset(A)).
% 2.03/2.24 0 [] $T.
% 2.03/2.24 0 [] $T.
% 2.03/2.24 0 [] $T.
% 2.03/2.24 0 [] -empty(powerset(A)).
% 2.03/2.24 0 [] -element(A,powerset(B))|subset(A,B).
% 2.03/2.24 0 [] element(A,powerset(B))| -subset(A,B).
% 2.03/2.24 0 [] -one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A).
% 2.03/2.24 0 [] one_sorted_str($c4).
% 2.03/2.24 0 [] element($c3,powerset(the_carrier($c4))).
% 2.03/2.24 0 [] subset_intersection2(the_carrier($c4),$c3,cast_as_carrier_subset($c4))!=$c3.
% 2.03/2.24 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.03/2.24 end_of_list.
% 2.03/2.24
% 2.03/2.24 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.03/2.24
% 2.03/2.24 This ia a non-Horn set with equality. The strategy will be
% 2.03/2.24 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.03/2.24 deletion, with positive clauses in sos and nonpositive
% 2.03/2.24 clauses in usable.
% 2.03/2.24
% 2.03/2.24 dependent: set(knuth_bendix).
% 2.03/2.24 dependent: set(anl_eq).
% 2.03/2.24 dependent: set(para_from).
% 2.03/2.24 dependent: set(para_into).
% 2.03/2.24 dependent: clear(para_from_right).
% 2.03/2.24 dependent: clear(para_into_right).
% 2.03/2.24 dependent: set(para_from_vars).
% 2.03/2.24 dependent: set(eq_units_both_ways).
% 2.03/2.24 dependent: set(dynamic_demod_all).
% 2.03/2.24 dependent: set(dynamic_demod).
% 2.03/2.24 dependent: set(order_eq).
% 2.03/2.24 dependent: set(back_demod).
% 2.03/2.24 dependent: set(lrpo).
% 2.03/2.24 dependent: set(hyper_res).
% 2.03/2.24 dependent: set(unit_deletion).
% 2.03/2.24 dependent: set(factor).
% 2.03/2.24
% 2.03/2.24 ------------> process usable:
% 2.03/2.24 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.03/2.24 ** KEPT (pick-wt=4): 2 [] -v5_membered(A)|v4_membered(A).
% 2.03/2.24 ** KEPT (pick-wt=4): 3 [] -v4_membered(A)|v3_membered(A).
% 2.03/2.24 ** KEPT (pick-wt=4): 4 [] -v3_membered(A)|v2_membered(A).
% 2.03/2.24 ** KEPT (pick-wt=4): 5 [] -v2_membered(A)|v1_membered(A).
% 2.03/2.24 ** KEPT (pick-wt=2): 6 [] -empty($c1).
% 2.03/2.24 ** KEPT (pick-wt=7): 7 [] -v1_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 8 [] -v2_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 9 [] -v2_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 10 [] -v3_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 11 [] -v3_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 12 [] -v3_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 13 [] -v4_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 14 [] -v4_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 15 [] -v4_membered(A)| -element(B,A)|v1_int_1(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 16 [] -v4_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 17 [] -v5_membered(A)| -element(B,A)|v1_xcmplx_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 18 [] -v5_membered(A)| -element(B,A)|natural(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 19 [] -v5_membered(A)| -element(B,A)|v1_xreal_0(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 20 [] -v5_membered(A)| -element(B,A)|v1_int_1(B).
% 2.03/2.24 ** KEPT (pick-wt=7): 21 [] -v5_membered(A)| -element(B,A)|v1_rat_1(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 22 [] -v1_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 23 [] -v2_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 24 [] -v2_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 25 [] -v3_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 26 [] -v3_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 27 [] -v3_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 28 [] -v4_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 29 [] -v4_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 30 [] -v4_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 31 [] -v4_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 32 [] -v5_membered(A)| -element(B,powerset(A))|v1_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 33 [] -v5_membered(A)| -element(B,powerset(A))|v2_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 34 [] -v5_membered(A)| -element(B,powerset(A))|v3_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 35 [] -v5_membered(A)| -element(B,powerset(A))|v4_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=8): 36 [] -v5_membered(A)| -element(B,powerset(A))|v5_membered(B).
% 2.03/2.24 ** KEPT (pick-wt=6): 37 [] -v1_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 38 [] -v1_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 39 [] -v2_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 40 [] -v2_membered(A)|v2_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 41 [] -v2_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 42 [] -v2_membered(A)|v2_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 43 [] -v3_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 44 [] -v3_membered(A)|v2_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 45 [] -v3_membered(A)|v3_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 46 [] -v3_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 47 [] -v3_membered(A)|v2_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 48 [] -v3_membered(A)|v3_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 49 [] -v4_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 50 [] -v4_membered(A)|v2_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 51 [] -v4_membered(A)|v3_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 52 [] -v4_membered(A)|v4_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 53 [] -v4_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 54 [] -v4_membered(A)|v2_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 55 [] -v4_membered(A)|v3_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 56 [] -v4_membered(A)|v4_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 57 [] -v5_membered(A)|v1_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 58 [] -v5_membered(A)|v2_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 59 [] -v5_membered(A)|v3_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 60 [] -v5_membered(A)|v4_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 61 [] -v5_membered(A)|v5_membered(set_intersection2(A,B)).
% 2.03/2.24 ** KEPT (pick-wt=6): 62 [] -v5_membered(A)|v1_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 63 [] -v5_membered(A)|v2_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 64 [] -v5_membered(A)|v3_membered(set_intersection2(B,A)).
% 2.03/2.24 ** KEPT (pick-wt=6): 65 [] -v5_membered(A)|v4_membered(set_intersection2(B,A)).
% 2.03/2.25 ** KEPT (pick-wt=6): 66 [] -v5_membered(A)|v5_membered(set_intersection2(B,A)).
% 2.03/2.25 ** KEPT (pick-wt=6): 67 [] -in(A,B)|element(A,B).
% 2.03/2.25 ** KEPT (pick-wt=10): 68 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.03/2.25 ** KEPT (pick-wt=9): 69 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.03/2.25 ** KEPT (pick-wt=5): 70 [] empty(A)| -empty($f1(A)).
% 2.03/2.25 ** KEPT (pick-wt=4): 71 [] -empty(A)|v1_membered(A).
% 2.03/2.25 ** KEPT (pick-wt=4): 72 [] -empty(A)|v2_membered(A).
% 2.03/2.25 ** KEPT (pick-wt=4): 73 [] -empty(A)|v3_membered(A).
% 2.03/2.25 ** KEPT (pick-wt=4): 74 [] -empty(A)|v4_membered(A).
% 2.03/2.25 ** KEPT (pick-wt=4): 75 [] -empty(A)|v5_membered(A).
% 2.03/2.25 ** KEPT (pick-wt=8): 76 [] -element(A,B)|empty(B)|in(A,B).
% 2.03/2.25 ** KEPT (pick-wt=5): 77 [] -empty(A)|A=empty_set.
% 2.03/2.25 ** KEPT (pick-wt=5): 78 [] -in(A,B)| -empty(B).
% 2.03/2.25 ** KEPT (pick-wt=7): 79 [] -empty(A)|A=B| -empty(B).
% 2.03/2.25 ** KEPT (pick-wt=17): 80 [] -element(A,powerset(B))| -element(C,powerset(B))|subset_intersection2(B,A,C)=subset_intersection2(B,C,A).
% 2.03/2.25 ** KEPT (pick-wt=10): 82 [copy,81,factor_simp] -element(A,powerset(B))|subset_intersection2(B,A,A)=A.
% 2.03/2.25 ** KEPT (pick-wt=16): 83 [] -element(A,powerset(B))| -element(C,powerset(B))|subset_intersection2(B,A,C)=set_intersection2(A,C).
% 2.03/2.25 ** KEPT (pick-wt=8): 84 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 2.03/2.25 ** KEPT (pick-wt=15): 85 [] -element(A,powerset(B))| -element(C,powerset(B))|element(subset_intersection2(B,A,C),powerset(B)).
% 2.03/2.25 ** KEPT (pick-wt=3): 86 [] -empty(powerset(A)).
% 2.03/2.25 ** KEPT (pick-wt=7): 87 [] -element(A,powerset(B))|subset(A,B).
% 2.03/2.25 ** KEPT (pick-wt=7): 88 [] element(A,powerset(B))| -subset(A,B).
% 2.03/2.25 ** KEPT (pick-wt=7): 90 [copy,89,flip.2] -one_sorted_str(A)|the_carrier(A)=cast_as_carrier_subset(A).
% 2.03/2.25 ** KEPT (pick-wt=8): 91 [] subset_intersection2(the_carrier($c4),$c3,cast_as_carrier_subset($c4))!=$c3.
% 2.03/2.25 ** KEPT (pick-wt=8): 92 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.03/2.25
% 2.03/2.25 ------------> process sos:
% 2.03/2.25 ** KEPT (pick-wt=3): 98 [] A=A.
% 2.03/2.25 ** KEPT (pick-wt=2): 99 [] v1_membered($c1).
% 2.03/2.25 ** KEPT (pick-wt=2): 100 [] v2_membered($c1).
% 2.03/2.25 ** KEPT (pick-wt=2): 101 [] v3_membered($c1).
% 2.03/2.25 ** KEPT (pick-wt=2): 102 [] v4_membered($c1).
% 2.03/2.25 ** KEPT (pick-wt=2): 103 [] v5_membered($c1).
% 2.03/2.25 ** KEPT (pick-wt=2): 104 [] empty(empty_set).
% 2.03/2.25 ** KEPT (pick-wt=2): 105 [] v1_membered(empty_set).
% 2.03/2.25 ** KEPT (pick-wt=2): 106 [] v2_membered(empty_set).
% 2.03/2.25 ** KEPT (pick-wt=2): 107 [] v3_membered(empty_set).
% 2.03/2.25 ** KEPT (pick-wt=2): 108 [] v4_membered(empty_set).
% 2.03/2.25 ** KEPT (pick-wt=2): 109 [] v5_membered(empty_set).
% 2.03/2.25 ** KEPT (pick-wt=5): 110 [] set_intersection2(A,empty_set)=empty_set.
% 2.03/2.25 ---> New Demodulator: 111 [new_demod,110] set_intersection2(A,empty_set)=empty_set.
% 2.03/2.25 ** KEPT (pick-wt=7): 112 [] empty(A)|element($f1(A),powerset(A)).
% 2.03/2.25 ** KEPT (pick-wt=5): 113 [] element($f2(A),powerset(A)).
% 2.03/2.25 ** KEPT (pick-wt=3): 114 [] empty($f2(A)).
% 2.03/2.25 ** KEPT (pick-wt=7): 115 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.03/2.25 ** KEPT (pick-wt=5): 116 [] set_intersection2(A,A)=A.
% 2.03/2.25 ---> New Demodulator: 117 [new_demod,116] set_intersection2(A,A)=A.
% 2.03/2.25 ** KEPT (pick-wt=3): 118 [] subset(A,A).
% 2.03/2.25 ** KEPT (pick-wt=2): 119 [] one_sorted_str($c2).
% 2.03/2.25 ** KEPT (pick-wt=4): 120 [] element($f3(A),A).
% 2.03/2.25 ** KEPT (pick-wt=2): 121 [] one_sorted_str($c4).
% 2.03/2.25 ** KEPT (pick-wt=5): 122 [] element($c3,powerset(the_carrier($c4))).
% 2.03/2.25 Following clause subsumed by 98 during input processing: 0 [copy,98,flip.1] A=A.
% 2.03/2.25 98 back subsumes 95.
% 2.03/2.25 98 back subsumes 94.
% 2.03/2.25 >>>> Starting back demodulation with 111.
% 2.03/2.25 Following clause subsumed by 115 during input processing: 0 [copy,115,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.03/2.25 >>>> Starting back demodulation with 117.
% 2.03/2.25 >> back demodulating 96 with 117.
% 2.03/2.25
% 2.03/2.25 ======= end of input processing =======
% 2.03/2.25
% 2.03/2.25 =========== start of search ===========
% 2.03/2.25
% 2.03/2.25 -------- PROOF --------
% 2.03/2.25
% 2.03/2.25 ----> UNIT CONFLICT at 0.02 sec ----> 414 [binary,412.1,147.1] $F.
% 2.03/2.25
% 2.03/2.25 Length of proof is 8. Level of proof is 5.
% 2.03/2.25
% 2.03/2.25 ---------------- PROOF ----------------
% 2.03/2.25 % SZS status Theorem
% 2.03/2.25 % SZS output start Refutation
% See solution above
% 2.03/2.25 ------------ end of proof -------------
% 2.03/2.25
% 2.03/2.25
% 2.03/2.25 Search stopped by max_proofs option.
% 2.03/2.25
% 2.03/2.25
% 2.03/2.25 Search stopped by max_proofs option.
% 2.03/2.25
% 2.03/2.25 ============ end of search ============
% 2.03/2.25
% 2.03/2.25 -------------- statistics -------------
% 2.03/2.25 clauses given 72
% 2.03/2.25 clauses generated 1155
% 2.03/2.25 clauses kept 382
% 2.03/2.25 clauses forward subsumed 905
% 2.03/2.25 clauses back subsumed 4
% 2.03/2.25 Kbytes malloced 1953
% 2.03/2.25
% 2.03/2.25 ----------- times (seconds) -----------
% 2.03/2.25 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 2.03/2.25 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.03/2.25 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.03/2.25
% 2.03/2.25 That finishes the proof of the theorem.
% 2.03/2.25
% 2.03/2.25 Process 10525 finished Wed Jul 27 07:26:48 2022
% 2.03/2.25 Otter interrupted
% 2.03/2.25 PROOF FOUND
%------------------------------------------------------------------------------