TSTP Solution File: SEU304+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:15:33 EDT 2022
% Result : Theorem 2.14s 2.36s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of clauses : 23 ( 16 unt; 5 nHn; 23 RR)
% Number of literals : 50 ( 8 equ; 25 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( empty_carrier(A)
| ~ meet_commutative(A)
| ~ meet_semilatt_str(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| meet_commut(A,B,C) = meet_commut(A,C,B) ),
file('SEU304+1.p',unknown),
[] ).
cnf(9,axiom,
( empty_carrier(A)
| ~ join_semilatt_str(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| below(A,B,C)
| join(A,B,C) != C ),
file('SEU304+1.p',unknown),
[] ).
cnf(10,axiom,
( empty_carrier(A)
| ~ latt_str(A)
| ~ meet_absorbing(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| join(A,meet(A,B,C),C) = C ),
file('SEU304+1.p',unknown),
[] ).
cnf(17,axiom,
( empty_carrier(A)
| ~ meet_commutative(A)
| ~ meet_semilatt_str(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| element(meet_commut(A,B,C),the_carrier(A)) ),
file('SEU304+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ latt_str(A)
| meet_semilatt_str(A) ),
file('SEU304+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ latt_str(A)
| join_semilatt_str(A) ),
file('SEU304+1.p',unknown),
[] ).
cnf(35,axiom,
( empty_carrier(A)
| ~ meet_commutative(A)
| ~ meet_semilatt_str(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| meet_commut(A,B,C) = meet(A,B,C) ),
file('SEU304+1.p',unknown),
[] ).
cnf(39,axiom,
~ empty_carrier(dollar_c8),
file('SEU304+1.p',unknown),
[] ).
cnf(40,axiom,
~ below(dollar_c8,meet_commut(dollar_c8,dollar_c7,dollar_c6),dollar_c7),
file('SEU304+1.p',unknown),
[] ).
cnf(78,axiom,
meet_commutative(dollar_c8),
file('SEU304+1.p',unknown),
[] ).
cnf(79,axiom,
meet_absorbing(dollar_c8),
file('SEU304+1.p',unknown),
[] ).
cnf(80,axiom,
latt_str(dollar_c8),
file('SEU304+1.p',unknown),
[] ).
cnf(81,axiom,
element(dollar_c7,the_carrier(dollar_c8)),
file('SEU304+1.p',unknown),
[] ).
cnf(82,axiom,
element(dollar_c6,the_carrier(dollar_c8)),
file('SEU304+1.p',unknown),
[] ).
cnf(114,plain,
join_semilatt_str(dollar_c8),
inference(hyper,[status(thm)],[80,21]),
[iquote('hyper,80,21')] ).
cnf(115,plain,
meet_semilatt_str(dollar_c8),
inference(hyper,[status(thm)],[80,20]),
[iquote('hyper,80,20')] ).
cnf(269,plain,
meet_commut(dollar_c8,dollar_c7,dollar_c6) = meet(dollar_c8,dollar_c7,dollar_c6),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[82,35,78,115,81]),39]),
[iquote('hyper,82,35,78,115,81,unit_del,39')] ).
cnf(273,plain,
meet_commut(dollar_c8,dollar_c6,dollar_c7) = meet(dollar_c8,dollar_c6,dollar_c7),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[82,35,78,115,81]),39]),
[iquote('hyper,82,35,78,115,81,unit_del,39')] ).
cnf(278,plain,
element(meet(dollar_c8,dollar_c6,dollar_c7),the_carrier(dollar_c8)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[82,17,78,115,81]),273]),39]),
[iquote('hyper,82,17,78,115,81,demod,273,unit_del,39')] ).
cnf(288,plain,
join(dollar_c8,meet(dollar_c8,dollar_c6,dollar_c7),dollar_c7) = dollar_c7,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[82,10,80,79,81]),39]),
[iquote('hyper,82,10,80,79,81,unit_del,39')] ).
cnf(309,plain,
meet(dollar_c8,dollar_c7,dollar_c6) = meet(dollar_c8,dollar_c6,dollar_c7),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[82,5,78,115,81]),269,273]),39]),
[iquote('hyper,82,5,78,115,81,demod,269,273,unit_del,39')] ).
cnf(312,plain,
~ below(dollar_c8,meet(dollar_c8,dollar_c6,dollar_c7),dollar_c7),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),269,309]),
[iquote('back_demod,40,demod,269,309')] ).
cnf(1087,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[288,9,114,278,81]),39,312]),
[iquote('hyper,288,9,114,278,81,unit_del,39,312')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:44:30 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.65/2.21 ----- Otter 3.3f, August 2004 -----
% 1.65/2.21 The process was started by sandbox on n013.cluster.edu,
% 1.65/2.21 Wed Jul 27 07:44:30 2022
% 1.65/2.21 The command was "./otter". The process ID is 361.
% 1.65/2.21
% 1.65/2.21 set(prolog_style_variables).
% 1.65/2.21 set(auto).
% 1.65/2.21 dependent: set(auto1).
% 1.65/2.21 dependent: set(process_input).
% 1.65/2.21 dependent: clear(print_kept).
% 1.65/2.21 dependent: clear(print_new_demod).
% 1.65/2.21 dependent: clear(print_back_demod).
% 1.65/2.21 dependent: clear(print_back_sub).
% 1.65/2.21 dependent: set(control_memory).
% 1.65/2.21 dependent: assign(max_mem, 12000).
% 1.65/2.21 dependent: assign(pick_given_ratio, 4).
% 1.65/2.21 dependent: assign(stats_level, 1).
% 1.65/2.21 dependent: assign(max_seconds, 10800).
% 1.65/2.21 clear(print_given).
% 1.65/2.21
% 1.65/2.21 formula_list(usable).
% 1.65/2.21 all A (A=A).
% 1.65/2.21 all A B (in(A,B)-> -in(B,A)).
% 1.65/2.21 all A (preboolean(A)->cup_closed(A)&diff_closed(A)).
% 1.65/2.21 all A (cup_closed(A)&diff_closed(A)->preboolean(A)).
% 1.65/2.21 all A B C (-empty_carrier(A)&meet_commutative(A)&meet_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->meet_commut(A,B,C)=meet_commut(A,C,B)).
% 1.65/2.21 all A (-empty_carrier(A)&join_semilatt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))->join(A,B,C)=apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C)))))).
% 1.65/2.21 all A (-empty_carrier(A)&meet_semilatt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))->meet(A,B,C)=apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C)))))).
% 1.65/2.21 all A (-empty_carrier(A)&join_semilatt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (below(A,B,C)<->join(A,B,C)=C)))))).
% 1.65/2.21 all A (-empty_carrier(A)&latt_str(A)-> (meet_absorbing(A)<-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))->join(A,meet(A,B,C),C)=C)))))).
% 1.65/2.21 $T.
% 1.65/2.21 all A B C (-empty_carrier(A)&join_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(join(A,B,C),the_carrier(A))).
% 1.65/2.21 $T.
% 1.65/2.21 $T.
% 1.65/2.21 all A B C D E F (-empty(A)& -empty(B)&function(D)&quasi_total(D,cartesian_product2(A,B),C)&relation_of2(D,cartesian_product2(A,B),C)&element(E,A)&element(F,B)->element(apply_binary_as_element(A,B,C,D,E,F),C)).
% 1.65/2.21 all A B C (-empty_carrier(A)&meet_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(meet(A,B,C),the_carrier(A))).
% 1.65/2.21 $T.
% 1.65/2.21 all A B C (-empty_carrier(A)&meet_commutative(A)&meet_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(meet_commut(A,B,C),the_carrier(A))).
% 1.65/2.21 all A (meet_semilatt_str(A)->one_sorted_str(A)).
% 1.65/2.21 $T.
% 1.65/2.21 all A (join_semilatt_str(A)->one_sorted_str(A)).
% 1.65/2.21 all A (latt_str(A)->meet_semilatt_str(A)&join_semilatt_str(A)).
% 1.65/2.21 $T.
% 1.65/2.21 $T.
% 1.65/2.21 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 1.65/2.21 all A (meet_semilatt_str(A)->function(the_L_meet(A))&quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))&relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))).
% 1.65/2.21 $T.
% 1.65/2.21 all A (join_semilatt_str(A)->function(the_L_join(A))&quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))&relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))).
% 1.65/2.21 exists A meet_semilatt_str(A).
% 1.65/2.21 exists A one_sorted_str(A).
% 1.65/2.21 exists A join_semilatt_str(A).
% 1.65/2.21 exists A latt_str(A).
% 1.65/2.21 all A B exists C relation_of2(C,A,B).
% 1.65/2.21 all A exists B element(B,A).
% 1.65/2.21 all A B exists C relation_of2_as_subset(C,A,B).
% 1.65/2.21 all A (-empty(powerset(A))&cup_closed(powerset(A))&diff_closed(powerset(A))&preboolean(powerset(A))).
% 1.65/2.21 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 1.65/2.21 exists A (one_sorted_str(A)& -empty_carrier(A)).
% 1.65/2.21 all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 1.65/2.21 all A B C D E F (-empty(A)& -empty(B)&function(D)&quasi_total(D,cartesian_product2(A,B),C)&relation_of2(D,cartesian_product2(A,B),C)&element(E,A)&element(F,B)->apply_binary_as_element(A,B,C,D,E,F)=apply_binary(D,E,F)).
% 1.65/2.21 all A B C (-empty_carrier(A)&meet_commutative(A)&meet_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->meet_commut(A,B,C)=meet(A,B,C)).
% 1.65/2.21 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 1.65/2.21 all A B subset(A,A).
% 1.65/2.21 all A B (in(A,B)->element(A,B)).
% 1.65/2.21 -(all A (-empty_carrier(A)&meet_commutative(A)&meet_absorbing(A)&latt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))->below(A,meet_commut(A,B,C),B))))))).
% 1.65/2.21 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.65/2.21 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.65/2.21 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.65/2.21 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.65/2.21 all A (empty(A)->A=empty_set).
% 1.65/2.21 all A B (-(in(A,B)&empty(B))).
% 1.65/2.21 all A B (-(empty(A)&A!=B&empty(B))).
% 1.65/2.21 end_of_list.
% 1.65/2.21
% 1.65/2.21 -------> usable clausifies to:
% 1.65/2.21
% 1.65/2.21 list(usable).
% 1.65/2.21 0 [] A=A.
% 1.65/2.21 0 [] -in(A,B)| -in(B,A).
% 1.65/2.21 0 [] -preboolean(A)|cup_closed(A).
% 1.65/2.21 0 [] -preboolean(A)|diff_closed(A).
% 1.65/2.21 0 [] -cup_closed(A)| -diff_closed(A)|preboolean(A).
% 1.65/2.21 0 [] empty_carrier(A)| -meet_commutative(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|meet_commut(A,B,C)=meet_commut(A,C,B).
% 1.65/2.21 0 [] empty_carrier(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|join(A,B,C)=apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C).
% 1.65/2.21 0 [] empty_carrier(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|meet(A,B,C)=apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C).
% 1.65/2.21 0 [] empty_carrier(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))| -below(A,B,C)|join(A,B,C)=C.
% 1.65/2.21 0 [] empty_carrier(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|below(A,B,C)|join(A,B,C)!=C.
% 1.65/2.21 0 [] empty_carrier(A)| -latt_str(A)| -meet_absorbing(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|join(A,meet(A,B,C),C)=C.
% 1.65/2.21 0 [] empty_carrier(A)| -latt_str(A)|meet_absorbing(A)|element($f2(A),the_carrier(A)).
% 1.65/2.21 0 [] empty_carrier(A)| -latt_str(A)|meet_absorbing(A)|element($f1(A),the_carrier(A)).
% 1.65/2.21 0 [] empty_carrier(A)| -latt_str(A)|meet_absorbing(A)|join(A,meet(A,$f2(A),$f1(A)),$f1(A))!=$f1(A).
% 2.06/2.21 0 [] $T.
% 2.06/2.21 0 [] empty_carrier(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|element(join(A,B,C),the_carrier(A)).
% 2.06/2.21 0 [] $T.
% 2.06/2.21 0 [] $T.
% 2.06/2.21 0 [] empty(A)|empty(B)| -function(D)| -quasi_total(D,cartesian_product2(A,B),C)| -relation_of2(D,cartesian_product2(A,B),C)| -element(E,A)| -element(F,B)|element(apply_binary_as_element(A,B,C,D,E,F),C).
% 2.06/2.21 0 [] empty_carrier(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|element(meet(A,B,C),the_carrier(A)).
% 2.06/2.21 0 [] $T.
% 2.06/2.21 0 [] empty_carrier(A)| -meet_commutative(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|element(meet_commut(A,B,C),the_carrier(A)).
% 2.06/2.21 0 [] -meet_semilatt_str(A)|one_sorted_str(A).
% 2.06/2.21 0 [] $T.
% 2.06/2.21 0 [] -join_semilatt_str(A)|one_sorted_str(A).
% 2.06/2.21 0 [] -latt_str(A)|meet_semilatt_str(A).
% 2.06/2.21 0 [] -latt_str(A)|join_semilatt_str(A).
% 2.06/2.21 0 [] $T.
% 2.06/2.21 0 [] $T.
% 2.06/2.21 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 2.06/2.21 0 [] -meet_semilatt_str(A)|function(the_L_meet(A)).
% 2.06/2.21 0 [] -meet_semilatt_str(A)|quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 2.06/2.21 0 [] -meet_semilatt_str(A)|relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 2.06/2.21 0 [] $T.
% 2.06/2.21 0 [] -join_semilatt_str(A)|function(the_L_join(A)).
% 2.06/2.21 0 [] -join_semilatt_str(A)|quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 2.06/2.21 0 [] -join_semilatt_str(A)|relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 2.06/2.21 0 [] meet_semilatt_str($c1).
% 2.06/2.21 0 [] one_sorted_str($c2).
% 2.06/2.21 0 [] join_semilatt_str($c3).
% 2.06/2.21 0 [] latt_str($c4).
% 2.06/2.21 0 [] relation_of2($f3(A,B),A,B).
% 2.06/2.21 0 [] element($f4(A),A).
% 2.06/2.21 0 [] relation_of2_as_subset($f5(A,B),A,B).
% 2.06/2.21 0 [] -empty(powerset(A)).
% 2.06/2.21 0 [] cup_closed(powerset(A)).
% 2.06/2.21 0 [] diff_closed(powerset(A)).
% 2.06/2.21 0 [] preboolean(powerset(A)).
% 2.06/2.21 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 2.06/2.21 0 [] one_sorted_str($c5).
% 2.06/2.21 0 [] -empty_carrier($c5).
% 2.06/2.21 0 [] empty_carrier(A)| -one_sorted_str(A)|element($f6(A),powerset(the_carrier(A))).
% 2.06/2.22 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f6(A)).
% 2.06/2.22 0 [] empty(A)|empty(B)| -function(D)| -quasi_total(D,cartesian_product2(A,B),C)| -relation_of2(D,cartesian_product2(A,B),C)| -element(E,A)| -element(F,B)|apply_binary_as_element(A,B,C,D,E,F)=apply_binary(D,E,F).
% 2.06/2.22 0 [] empty_carrier(A)| -meet_commutative(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|meet_commut(A,B,C)=meet(A,B,C).
% 2.06/2.22 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 2.06/2.22 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 2.06/2.22 0 [] subset(A,A).
% 2.06/2.22 0 [] -in(A,B)|element(A,B).
% 2.06/2.22 0 [] -empty_carrier($c8).
% 2.06/2.22 0 [] meet_commutative($c8).
% 2.06/2.22 0 [] meet_absorbing($c8).
% 2.06/2.22 0 [] latt_str($c8).
% 2.06/2.22 0 [] element($c7,the_carrier($c8)).
% 2.06/2.22 0 [] element($c6,the_carrier($c8)).
% 2.06/2.22 0 [] -below($c8,meet_commut($c8,$c7,$c6),$c7).
% 2.06/2.22 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.06/2.22 0 [] -element(A,powerset(B))|subset(A,B).
% 2.06/2.22 0 [] element(A,powerset(B))| -subset(A,B).
% 2.06/2.22 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.06/2.22 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.06/2.22 0 [] -empty(A)|A=empty_set.
% 2.06/2.22 0 [] -in(A,B)| -empty(B).
% 2.06/2.22 0 [] -empty(A)|A=B| -empty(B).
% 2.06/2.22 end_of_list.
% 2.06/2.22
% 2.06/2.22 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 2.06/2.22
% 2.06/2.22 This ia a non-Horn set with equality. The strategy will be
% 2.06/2.22 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.06/2.22 deletion, with positive clauses in sos and nonpositive
% 2.06/2.22 clauses in usable.
% 2.06/2.22
% 2.06/2.22 dependent: set(knuth_bendix).
% 2.06/2.22 dependent: set(anl_eq).
% 2.06/2.22 dependent: set(para_from).
% 2.06/2.22 dependent: set(para_into).
% 2.06/2.22 dependent: clear(para_from_right).
% 2.06/2.22 dependent: clear(para_into_right).
% 2.06/2.22 dependent: set(para_from_vars).
% 2.06/2.22 dependent: set(eq_units_both_ways).
% 2.06/2.22 dependent: set(dynamic_demod_all).
% 2.06/2.22 dependent: set(dynamic_demod).
% 2.06/2.22 dependent: set(order_eq).
% 2.06/2.22 dependent: set(back_demod).
% 2.06/2.22 dependent: set(lrpo).
% 2.06/2.22 dependent: set(hyper_res).
% 2.06/2.22 dependent: set(unit_deletion).
% 2.06/2.22 dependent: set(factor).
% 2.06/2.22
% 2.06/2.22 ------------> process usable:
% 2.06/2.22 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.06/2.22 ** KEPT (pick-wt=4): 2 [] -preboolean(A)|cup_closed(A).
% 2.06/2.22 ** KEPT (pick-wt=4): 3 [] -preboolean(A)|diff_closed(A).
% 2.06/2.22 ** KEPT (pick-wt=6): 4 [] -cup_closed(A)| -diff_closed(A)|preboolean(A).
% 2.06/2.22 ** KEPT (pick-wt=23): 5 [] empty_carrier(A)| -meet_commutative(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|meet_commut(A,B,C)=meet_commut(A,C,B).
% 2.06/2.22 ** KEPT (pick-wt=28): 6 [] empty_carrier(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|join(A,B,C)=apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C).
% 2.06/2.22 ** KEPT (pick-wt=28): 7 [] empty_carrier(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|meet(A,B,C)=apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C).
% 2.06/2.22 ** KEPT (pick-wt=22): 8 [] empty_carrier(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))| -below(A,B,C)|join(A,B,C)=C.
% 2.06/2.22 ** KEPT (pick-wt=22): 9 [] empty_carrier(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|below(A,B,C)|join(A,B,C)!=C.
% 2.06/2.22 ** KEPT (pick-wt=23): 10 [] empty_carrier(A)| -latt_str(A)| -meet_absorbing(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|join(A,meet(A,B,C),C)=C.
% 2.06/2.22 ** KEPT (pick-wt=11): 11 [] empty_carrier(A)| -latt_str(A)|meet_absorbing(A)|element($f2(A),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=11): 12 [] empty_carrier(A)| -latt_str(A)|meet_absorbing(A)|element($f1(A),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=19): 13 [] empty_carrier(A)| -latt_str(A)|meet_absorbing(A)|join(A,meet(A,$f2(A),$f1(A)),$f1(A))!=$f1(A).
% 2.06/2.22 ** KEPT (pick-wt=19): 14 [] empty_carrier(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|element(join(A,B,C),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=33): 15 [] empty(A)|empty(B)| -function(C)| -quasi_total(C,cartesian_product2(A,B),D)| -relation_of2(C,cartesian_product2(A,B),D)| -element(E,A)| -element(F,B)|element(apply_binary_as_element(A,B,D,C,E,F),D).
% 2.06/2.22 ** KEPT (pick-wt=19): 16 [] empty_carrier(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|element(meet(A,B,C),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=21): 17 [] empty_carrier(A)| -meet_commutative(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|element(meet_commut(A,B,C),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=4): 18 [] -meet_semilatt_str(A)|one_sorted_str(A).
% 2.06/2.22 ** KEPT (pick-wt=4): 19 [] -join_semilatt_str(A)|one_sorted_str(A).
% 2.06/2.22 ** KEPT (pick-wt=4): 20 [] -latt_str(A)|meet_semilatt_str(A).
% 2.06/2.22 ** KEPT (pick-wt=4): 21 [] -latt_str(A)|join_semilatt_str(A).
% 2.06/2.22 ** KEPT (pick-wt=10): 22 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 2.06/2.22 ** KEPT (pick-wt=5): 23 [] -meet_semilatt_str(A)|function(the_L_meet(A)).
% 2.06/2.22 ** KEPT (pick-wt=12): 24 [] -meet_semilatt_str(A)|quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=12): 25 [] -meet_semilatt_str(A)|relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=5): 26 [] -join_semilatt_str(A)|function(the_L_join(A)).
% 2.06/2.22 ** KEPT (pick-wt=12): 27 [] -join_semilatt_str(A)|quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=12): 28 [] -join_semilatt_str(A)|relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=3): 29 [] -empty(powerset(A)).
% 2.06/2.22 ** KEPT (pick-wt=7): 30 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 2.06/2.22 ** KEPT (pick-wt=2): 31 [] -empty_carrier($c5).
% 2.06/2.22 ** KEPT (pick-wt=10): 32 [] empty_carrier(A)| -one_sorted_str(A)|element($f6(A),powerset(the_carrier(A))).
% 2.06/2.22 ** KEPT (pick-wt=7): 33 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f6(A)).
% 2.06/2.22 ** KEPT (pick-wt=36): 34 [] empty(A)|empty(B)| -function(C)| -quasi_total(C,cartesian_product2(A,B),D)| -relation_of2(C,cartesian_product2(A,B),D)| -element(E,A)| -element(F,B)|apply_binary_as_element(A,B,D,C,E,F)=apply_binary(C,E,F).
% 2.06/2.22 ** KEPT (pick-wt=23): 35 [] empty_carrier(A)| -meet_commutative(A)| -meet_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|meet_commut(A,B,C)=meet(A,B,C).
% 2.06/2.22 ** KEPT (pick-wt=8): 36 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 2.06/2.22 ** KEPT (pick-wt=8): 37 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 2.06/2.22 ** KEPT (pick-wt=6): 38 [] -in(A,B)|element(A,B).
% 2.06/2.22 ** KEPT (pick-wt=2): 39 [] -empty_carrier($c8).
% 2.06/2.22 ** KEPT (pick-wt=7): 40 [] -below($c8,meet_commut($c8,$c7,$c6),$c7).
% 2.06/2.22 ** KEPT (pick-wt=8): 41 [] -element(A,B)|empty(B)|in(A,B).
% 2.06/2.22 ** KEPT (pick-wt=7): 42 [] -element(A,powerset(B))|subset(A,B).
% 2.06/2.22 ** KEPT (pick-wt=7): 43 [] element(A,powerset(B))| -subset(A,B).
% 2.06/2.22 ** KEPT (pick-wt=10): 44 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.06/2.22 ** KEPT (pick-wt=9): 45 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.06/2.22 ** KEPT (pick-wt=5): 46 [] -empty(A)|A=empty_set.
% 2.06/2.22 ** KEPT (pick-wt=5): 47 [] -in(A,B)| -empty(B).
% 2.06/2.22 ** KEPT (pick-wt=7): 48 [] -empty(A)|A=B| -empty(B).
% 2.06/2.22
% 2.06/2.22 ------------> process sos:
% 2.06/2.22 ** KEPT (pick-wt=3): 65 [] A=A.
% 2.06/2.22 ** KEPT (pick-wt=2): 66 [] meet_semilatt_str($c1).
% 2.06/2.22 ** KEPT (pick-wt=2): 67 [] one_sorted_str($c2).
% 2.06/2.22 ** KEPT (pick-wt=2): 68 [] join_semilatt_str($c3).
% 2.06/2.22 ** KEPT (pick-wt=2): 69 [] latt_str($c4).
% 2.06/2.22 ** KEPT (pick-wt=6): 70 [] relation_of2($f3(A,B),A,B).
% 2.06/2.22 ** KEPT (pick-wt=4): 71 [] element($f4(A),A).
% 2.06/2.22 ** KEPT (pick-wt=6): 72 [] relation_of2_as_subset($f5(A,B),A,B).
% 2.06/2.22 ** KEPT (pick-wt=3): 73 [] cup_closed(powerset(A)).
% 2.06/2.22 ** KEPT (pick-wt=3): 74 [] diff_closed(powerset(A)).
% 2.06/2.22 ** KEPT (pick-wt=3): 75 [] preboolean(powerset(A)).
% 2.06/2.22 ** KEPT (pick-wt=2): 76 [] one_sorted_str($c5).
% 2.06/2.22 ** KEPT (pick-wt=3): 77 [] subset(A,A).
% 2.06/2.22 ** KEPT (pick-wt=2): 78 [] meet_commutative($c8).
% 2.06/2.22 ** KEPT (pick-wt=2): 79 [] meet_absorbing($c8).
% 2.06/2.22 ** KEPT (pick-wt=2): 80 [] latt_str($c8).
% 2.06/2.22 ** KEPT (pick-wt=4): 81 [] element($c7,the_carrier($c8)).
% 2.06/2.22 ** KEPT (pick-wt=4): 82 [] element($c6,the_carrier($c8)).
% 2.06/2.22 Following clause subsumed by 65 during input processing: 0 [copy,65,flip.1] A=A.
% 2.06/2.22 65 back subsumes 64.
% 2.06/2.22 65 back subsumes 50.
% 2.06/2.22
% 2.06/2.22 ======= end of input processing =======
% 2.14/2.36
% 2.14/2.36 =========== start of search ===========
% 2.14/2.36
% 2.14/2.36
% 2.14/2.36 Resetting weight limit to 7.
% 2.14/2.36
% 2.14/2.36
% 2.14/2.36 Resetting weight limit to 7.
% 2.14/2.36
% 2.14/2.36 sos_size=704
% 2.14/2.36
% 2.14/2.36 -------- PROOF --------
% 2.14/2.36
% 2.14/2.36 -----> EMPTY CLAUSE at 0.15 sec ----> 1087 [hyper,288,9,114,278,81,unit_del,39,312] $F.
% 2.14/2.36
% 2.14/2.36 Length of proof is 8. Level of proof is 4.
% 2.14/2.36
% 2.14/2.36 ---------------- PROOF ----------------
% 2.14/2.36 % SZS status Theorem
% 2.14/2.36 % SZS output start Refutation
% See solution above
% 2.14/2.36 ------------ end of proof -------------
% 2.14/2.36
% 2.14/2.36
% 2.14/2.36 Search stopped by max_proofs option.
% 2.14/2.36
% 2.14/2.36
% 2.14/2.36 Search stopped by max_proofs option.
% 2.14/2.36
% 2.14/2.36 ============ end of search ============
% 2.14/2.36
% 2.14/2.36 -------------- statistics -------------
% 2.14/2.36 clauses given 341
% 2.14/2.36 clauses generated 8997
% 2.14/2.36 clauses kept 990
% 2.14/2.36 clauses forward subsumed 1172
% 2.14/2.36 clauses back subsumed 21
% 2.14/2.36 Kbytes malloced 4882
% 2.14/2.36
% 2.14/2.36 ----------- times (seconds) -----------
% 2.14/2.36 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 2.14/2.36 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.14/2.36 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.14/2.36
% 2.14/2.36 That finishes the proof of the theorem.
% 2.14/2.36
% 2.14/2.36 Process 361 finished Wed Jul 27 07:44:32 2022
% 2.14/2.36 Otter interrupted
% 2.14/2.36 PROOF FOUND
%------------------------------------------------------------------------------