TSTP Solution File: SEU305+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU305+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 1.86s 2.07s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 16 ( 13 unt; 3 nHn; 16 RR)
% Number of literals : 31 ( 8 equ; 14 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( empty_carrier(A)
| ~ join_commutative(A)
| ~ join_semilatt_str(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| join_commut(A,B,C) = join_commut(A,C,B) ),
file('SEU305+1.p',unknown),
[] ).
cnf(7,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('SEU305+1.p',unknown),
[] ).
cnf(23,axiom,
( empty_carrier(A)
| ~ join_commutative(A)
| ~ join_semilatt_str(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| join_commut(A,B,C) = join(A,B,C) ),
file('SEU305+1.p',unknown),
[] ).
cnf(27,axiom,
~ empty_carrier(dollar_c6),
file('SEU305+1.p',unknown),
[] ).
cnf(28,axiom,
dollar_c5 != dollar_c4,
file('SEU305+1.p',unknown),
[] ).
cnf(61,axiom,
join_commutative(dollar_c6),
file('SEU305+1.p',unknown),
[] ).
cnf(62,axiom,
join_semilatt_str(dollar_c6),
file('SEU305+1.p',unknown),
[] ).
cnf(63,axiom,
element(dollar_c5,the_carrier(dollar_c6)),
file('SEU305+1.p',unknown),
[] ).
cnf(64,axiom,
element(dollar_c4,the_carrier(dollar_c6)),
file('SEU305+1.p',unknown),
[] ).
cnf(65,axiom,
below(dollar_c6,dollar_c5,dollar_c4),
file('SEU305+1.p',unknown),
[] ).
cnf(66,axiom,
below(dollar_c6,dollar_c4,dollar_c5),
file('SEU305+1.p',unknown),
[] ).
cnf(161,plain,
join_commut(dollar_c6,dollar_c5,dollar_c4) = join(dollar_c6,dollar_c5,dollar_c4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[64,23,61,62,63]),27]),
[iquote('hyper,64,23,61,62,63,unit_del,27')] ).
cnf(165,plain,
join_commut(dollar_c6,dollar_c4,dollar_c5) = join(dollar_c6,dollar_c4,dollar_c5),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[64,23,61,62,63]),27]),
[iquote('hyper,64,23,61,62,63,unit_del,27')] ).
cnf(181,plain,
join(dollar_c6,dollar_c5,dollar_c4) = join(dollar_c6,dollar_c4,dollar_c5),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[64,5,61,62,63]),161,165]),27]),
[iquote('hyper,64,5,61,62,63,demod,161,165,unit_del,27')] ).
cnf(202,plain,
join(dollar_c6,dollar_c4,dollar_c5) = dollar_c4,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[65,7,62,63,64]),181]),27]),
[iquote('hyper,65,7,62,63,64,demod,181,unit_del,27')] ).
cnf(219,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[66,7,62,64,63]),202]),27,28]),
[iquote('hyper,66,7,62,64,63,demod,202,unit_del,27,28')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU305+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % 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 07:12:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.86/2.07 ----- Otter 3.3f, August 2004 -----
% 1.86/2.07 The process was started by sandbox2 on n007.cluster.edu,
% 1.86/2.07 Wed Jul 27 07:12:46 2022
% 1.86/2.07 The command was "./otter". The process ID is 7821.
% 1.86/2.07
% 1.86/2.07 set(prolog_style_variables).
% 1.86/2.07 set(auto).
% 1.86/2.07 dependent: set(auto1).
% 1.86/2.07 dependent: set(process_input).
% 1.86/2.07 dependent: clear(print_kept).
% 1.86/2.07 dependent: clear(print_new_demod).
% 1.86/2.07 dependent: clear(print_back_demod).
% 1.86/2.07 dependent: clear(print_back_sub).
% 1.86/2.07 dependent: set(control_memory).
% 1.86/2.07 dependent: assign(max_mem, 12000).
% 1.86/2.07 dependent: assign(pick_given_ratio, 4).
% 1.86/2.07 dependent: assign(stats_level, 1).
% 1.86/2.07 dependent: assign(max_seconds, 10800).
% 1.86/2.07 clear(print_given).
% 1.86/2.07
% 1.86/2.07 formula_list(usable).
% 1.86/2.07 all A (A=A).
% 1.86/2.07 all A B (in(A,B)-> -in(B,A)).
% 1.86/2.07 all A (preboolean(A)->cup_closed(A)&diff_closed(A)).
% 1.86/2.07 all A (cup_closed(A)&diff_closed(A)->preboolean(A)).
% 1.86/2.07 all A B C (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->join_commut(A,B,C)=join_commut(A,C,B)).
% 1.86/2.07 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)))))).
% 1.86/2.07 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)))))).
% 1.86/2.07 $T.
% 1.86/2.07 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))).
% 1.86/2.07 $T.
% 1.86/2.07 $T.
% 1.86/2.07 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)).
% 1.86/2.07 $T.
% 1.86/2.07 all A B C (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->element(join_commut(A,B,C),the_carrier(A))).
% 1.86/2.07 $T.
% 1.86/2.07 all A (join_semilatt_str(A)->one_sorted_str(A)).
% 1.86/2.07 $T.
% 1.86/2.07 $T.
% 1.86/2.07 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 1.86/2.07 $T.
% 1.86/2.07 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))).
% 1.86/2.07 exists A one_sorted_str(A).
% 1.86/2.07 exists A join_semilatt_str(A).
% 1.86/2.07 all A B exists C relation_of2(C,A,B).
% 1.86/2.07 all A exists B element(B,A).
% 1.86/2.07 all A B exists C relation_of2_as_subset(C,A,B).
% 1.86/2.07 all A (-empty(powerset(A))&cup_closed(powerset(A))&diff_closed(powerset(A))&preboolean(powerset(A))).
% 1.86/2.07 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 1.86/2.07 exists A (one_sorted_str(A)& -empty_carrier(A)).
% 1.86/2.07 all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 1.86/2.07 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)).
% 1.86/2.07 all A B C (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)&element(B,the_carrier(A))&element(C,the_carrier(A))->join_commut(A,B,C)=join(A,B,C)).
% 1.86/2.07 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 1.86/2.07 all A B subset(A,A).
% 1.86/2.07 all A B (in(A,B)->element(A,B)).
% 1.86/2.07 -(all A (-empty_carrier(A)&join_commutative(A)&join_semilatt_str(A)-> (all B (element(B,the_carrier(A))-> (all C (element(C,the_carrier(A))-> (below(A,B,C)&below(A,C,B)->B=C))))))).
% 1.86/2.07 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.86/2.07 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.86/2.07 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.86/2.07 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.86/2.07 all A (empty(A)->A=empty_set).
% 1.86/2.07 all A B (-(in(A,B)&empty(B))).
% 1.86/2.07 all A B (-(empty(A)&A!=B&empty(B))).
% 1.86/2.07 end_of_list.
% 1.86/2.07
% 1.86/2.07 -------> usable clausifies to:
% 1.86/2.07
% 1.86/2.07 list(usable).
% 1.86/2.07 0 [] A=A.
% 1.86/2.07 0 [] -in(A,B)| -in(B,A).
% 1.86/2.07 0 [] -preboolean(A)|cup_closed(A).
% 1.86/2.07 0 [] -preboolean(A)|diff_closed(A).
% 1.86/2.07 0 [] -cup_closed(A)| -diff_closed(A)|preboolean(A).
% 1.86/2.07 0 [] empty_carrier(A)| -join_commutative(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|join_commut(A,B,C)=join_commut(A,C,B).
% 1.86/2.07 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).
% 1.86/2.07 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.
% 1.86/2.07 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.
% 1.86/2.07 0 [] $T.
% 1.86/2.07 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)).
% 1.86/2.07 0 [] $T.
% 1.86/2.07 0 [] $T.
% 1.86/2.07 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).
% 1.86/2.07 0 [] $T.
% 1.86/2.07 0 [] empty_carrier(A)| -join_commutative(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|element(join_commut(A,B,C),the_carrier(A)).
% 1.86/2.07 0 [] $T.
% 1.86/2.07 0 [] -join_semilatt_str(A)|one_sorted_str(A).
% 1.86/2.07 0 [] $T.
% 1.86/2.07 0 [] $T.
% 1.86/2.07 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 1.86/2.07 0 [] $T.
% 1.86/2.07 0 [] -join_semilatt_str(A)|function(the_L_join(A)).
% 1.86/2.07 0 [] -join_semilatt_str(A)|quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 1.86/2.07 0 [] -join_semilatt_str(A)|relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 1.86/2.07 0 [] one_sorted_str($c1).
% 1.86/2.07 0 [] join_semilatt_str($c2).
% 1.86/2.07 0 [] relation_of2($f1(A,B),A,B).
% 1.86/2.07 0 [] element($f2(A),A).
% 1.86/2.07 0 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.86/2.07 0 [] -empty(powerset(A)).
% 1.86/2.07 0 [] cup_closed(powerset(A)).
% 1.86/2.07 0 [] diff_closed(powerset(A)).
% 1.86/2.07 0 [] preboolean(powerset(A)).
% 1.86/2.07 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 1.86/2.07 0 [] one_sorted_str($c3).
% 1.86/2.07 0 [] -empty_carrier($c3).
% 1.86/2.07 0 [] empty_carrier(A)| -one_sorted_str(A)|element($f4(A),powerset(the_carrier(A))).
% 1.86/2.07 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f4(A)).
% 1.86/2.07 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).
% 1.86/2.07 0 [] empty_carrier(A)| -join_commutative(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|join_commut(A,B,C)=join(A,B,C).
% 1.86/2.07 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 1.86/2.07 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 1.86/2.07 0 [] subset(A,A).
% 1.86/2.07 0 [] -in(A,B)|element(A,B).
% 1.86/2.07 0 [] -empty_carrier($c6).
% 1.86/2.07 0 [] join_commutative($c6).
% 1.86/2.07 0 [] join_semilatt_str($c6).
% 1.86/2.07 0 [] element($c5,the_carrier($c6)).
% 1.86/2.07 0 [] element($c4,the_carrier($c6)).
% 1.86/2.07 0 [] below($c6,$c5,$c4).
% 1.86/2.07 0 [] below($c6,$c4,$c5).
% 1.86/2.07 0 [] $c5!=$c4.
% 1.86/2.07 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.86/2.07 0 [] -element(A,powerset(B))|subset(A,B).
% 1.86/2.07 0 [] element(A,powerset(B))| -subset(A,B).
% 1.86/2.07 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.86/2.07 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.86/2.07 0 [] -empty(A)|A=empty_set.
% 1.86/2.07 0 [] -in(A,B)| -empty(B).
% 1.86/2.07 0 [] -empty(A)|A=B| -empty(B).
% 1.86/2.07 end_of_list.
% 1.86/2.07
% 1.86/2.07 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.86/2.07
% 1.86/2.07 This ia a non-Horn set with equality. The strategy will be
% 1.86/2.07 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.86/2.07 deletion, with positive clauses in sos and nonpositive
% 1.86/2.07 clauses in usable.
% 1.86/2.07
% 1.86/2.07 dependent: set(knuth_bendix).
% 1.86/2.07 dependent: set(anl_eq).
% 1.86/2.07 dependent: set(para_from).
% 1.86/2.07 dependent: set(para_into).
% 1.86/2.07 dependent: clear(para_from_right).
% 1.86/2.07 dependent: clear(para_into_right).
% 1.86/2.07 dependent: set(para_from_vars).
% 1.86/2.07 dependent: set(eq_units_both_ways).
% 1.86/2.07 dependent: set(dynamic_demod_all).
% 1.86/2.07 dependent: set(dynamic_demod).
% 1.86/2.07 dependent: set(order_eq).
% 1.86/2.07 dependent: set(back_demod).
% 1.86/2.07 dependent: set(lrpo).
% 1.86/2.07 dependent: set(hyper_res).
% 1.86/2.07 dependent: set(unit_deletion).
% 1.86/2.07 dependent: set(factor).
% 1.86/2.07
% 1.86/2.07 ------------> process usable:
% 1.86/2.07 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.86/2.07 ** KEPT (pick-wt=4): 2 [] -preboolean(A)|cup_closed(A).
% 1.86/2.07 ** KEPT (pick-wt=4): 3 [] -preboolean(A)|diff_closed(A).
% 1.86/2.07 ** KEPT (pick-wt=6): 4 [] -cup_closed(A)| -diff_closed(A)|preboolean(A).
% 1.86/2.07 ** KEPT (pick-wt=23): 5 [] empty_carrier(A)| -join_commutative(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|join_commut(A,B,C)=join_commut(A,C,B).
% 1.86/2.07 ** 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).
% 1.86/2.07 ** KEPT (pick-wt=22): 7 [] 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.
% 1.86/2.07 ** 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.
% 1.86/2.07 ** KEPT (pick-wt=19): 9 [] 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)).
% 1.86/2.07 ** KEPT (pick-wt=33): 10 [] 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).
% 1.86/2.07 ** KEPT (pick-wt=21): 11 [] empty_carrier(A)| -join_commutative(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|element(join_commut(A,B,C),the_carrier(A)).
% 1.86/2.07 ** KEPT (pick-wt=4): 12 [] -join_semilatt_str(A)|one_sorted_str(A).
% 1.86/2.07 ** KEPT (pick-wt=10): 13 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 1.86/2.07 ** KEPT (pick-wt=5): 14 [] -join_semilatt_str(A)|function(the_L_join(A)).
% 1.86/2.07 ** KEPT (pick-wt=12): 15 [] -join_semilatt_str(A)|quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 1.86/2.07 ** KEPT (pick-wt=12): 16 [] -join_semilatt_str(A)|relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)).
% 1.86/2.07 ** KEPT (pick-wt=3): 17 [] -empty(powerset(A)).
% 1.86/2.07 ** KEPT (pick-wt=7): 18 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 1.86/2.07 ** KEPT (pick-wt=2): 19 [] -empty_carrier($c3).
% 1.86/2.07 ** KEPT (pick-wt=10): 20 [] empty_carrier(A)| -one_sorted_str(A)|element($f4(A),powerset(the_carrier(A))).
% 1.86/2.07 ** KEPT (pick-wt=7): 21 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f4(A)).
% 1.86/2.07 ** KEPT (pick-wt=36): 22 [] empty(A)|empty(B)| -function(C)| -quasi_total(C,cartesian_product2(A,B),D)| -relation_of2(C,cartesian_product2(A,B),D)| -element(E,A)| -element(F,B)|apply_binary_as_element(A,B,D,C,E,F)=apply_binary(C,E,F).
% 1.86/2.07 ** KEPT (pick-wt=23): 23 [] empty_carrier(A)| -join_commutative(A)| -join_semilatt_str(A)| -element(B,the_carrier(A))| -element(C,the_carrier(A))|join_commut(A,B,C)=join(A,B,C).
% 1.86/2.07 ** KEPT (pick-wt=8): 24 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 1.86/2.07 ** KEPT (pick-wt=8): 25 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 1.86/2.07 ** KEPT (pick-wt=6): 26 [] -in(A,B)|element(A,B).
% 1.86/2.07 ** KEPT (pick-wt=2): 27 [] -empty_carrier($c6).
% 1.86/2.07 ** KEPT (pick-wt=3): 28 [] $c5!=$c4.
% 1.86/2.07 ** KEPT (pick-wt=8): 29 [] -element(A,B)|empty(B)|in(A,B).
% 1.86/2.07 ** KEPT (pick-wt=7): 30 [] -element(A,powerset(B))|subset(A,B).
% 1.86/2.07 ** KEPT (pick-wt=7): 31 [] element(A,powerset(B))| -subset(A,B).
% 1.86/2.07 ** KEPT (pick-wt=10): 32 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.86/2.07 ** KEPT (pick-wt=9): 33 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.86/2.07 ** KEPT (pick-wt=5): 34 [] -empty(A)|A=empty_set.
% 1.86/2.07 ** KEPT (pick-wt=5): 35 [] -in(A,B)| -empty(B).
% 1.86/2.07 ** KEPT (pick-wt=7): 36 [] -empty(A)|A=B| -empty(B).
% 1.86/2.07
% 1.86/2.07 ------------> process sos:
% 1.86/2.07 ** KEPT (pick-wt=3): 50 [] A=A.
% 1.86/2.07 ** KEPT (pick-wt=2): 51 [] one_sorted_str($c1).
% 1.86/2.07 ** KEPT (pick-wt=2): 52 [] join_semilatt_str($c2).
% 1.86/2.07 ** KEPT (pick-wt=6): 53 [] relation_of2($f1(A,B),A,B).
% 1.86/2.07 ** KEPT (pick-wt=4): 54 [] element($f2(A),A).
% 1.86/2.07 ** KEPT (pick-wt=6): 55 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.86/2.07 ** KEPT (pick-wt=3): 56 [] cup_closed(powerset(A)).
% 1.86/2.07 ** KEPT (pick-wt=3): 57 [] diff_closed(powerset(A)).
% 1.86/2.07 ** KEPT (pick-wt=3): 58 [] preboolean(powerset(A)).
% 1.86/2.07 ** KEPT (pick-wt=2): 59 [] one_sorted_str($c3).
% 1.86/2.07 ** KEPT (pick-wt=3): 60 [] subset(A,A).
% 1.86/2.07 ** KEPT (pick-wt=2): 61 [] join_commutative($c6).
% 1.86/2.07 ** KEPT (pick-wt=2): 62 [] join_semilatt_str($c6).
% 1.86/2.07 ** KEPT (pick-wt=4): 63 [] element($c5,the_carrier($c6)).
% 1.86/2.07 ** KEPT (pick-wt=4): 64 [] element($c4,the_carrier($c6)).
% 1.86/2.07 ** KEPT (pick-wt=4): 65 [] below($c6,$c5,$c4).
% 1.86/2.07 ** KEPT (pick-wt=4): 66 [] below($c6,$c4,$c5).
% 1.86/2.07 Following clause subsumed by 50 during input processing: 0 [copy,50,flip.1] A=A.
% 1.86/2.07 50 back subsumes 49.
% 1.86/2.07 50 back subsumes 38.
% 1.86/2.07
% 1.86/2.07 ======= end of input processing =======
% 1.86/2.07
% 1.86/2.07 =========== start of search ===========
% 1.86/2.07
% 1.86/2.07 -------- PROOF --------
% 1.86/2.07
% 1.86/2.07 -----> EMPTY CLAUSE at 0.01 sec ----> 219 [hyper,66,7,62,64,63,demod,202,unit_del,27,28] $F.
% 1.86/2.07
% 1.86/2.07 Length of proof is 4. Level of proof is 3.
% 1.86/2.07
% 1.86/2.07 ---------------- PROOF ----------------
% 1.86/2.07 % SZS status Theorem
% 1.86/2.07 % SZS output start Refutation
% See solution above
% 1.86/2.07 ------------ end of proof -------------
% 1.86/2.07
% 1.86/2.07
% 1.86/2.07 Search stopped by max_proofs option.
% 1.86/2.07
% 1.86/2.07
% 1.86/2.07 Search stopped by max_proofs option.
% 1.86/2.07
% 1.86/2.07 ============ end of search ============
% 1.86/2.07
% 1.86/2.07 -------------- statistics -------------
% 1.86/2.07 clauses given 21
% 1.86/2.07 clauses generated 193
% 1.86/2.07 clauses kept 182
% 1.86/2.07 clauses forward subsumed 85
% 1.86/2.07 clauses back subsumed 2
% 1.86/2.07 Kbytes malloced 1953
% 1.86/2.07
% 1.86/2.07 ----------- times (seconds) -----------
% 1.86/2.07 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.86/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.07 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.86/2.07
% 1.86/2.07 That finishes the proof of the theorem.
% 1.86/2.07
% 1.86/2.07 Process 7821 finished Wed Jul 27 07:12:47 2022
% 1.86/2.07 Otter interrupted
% 1.86/2.07 PROOF FOUND
%------------------------------------------------------------------------------