%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU373+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:15:55 EDT 2022
% Result : Theorem 2.02s 2.21s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 14 RR)
% Number of literals : 26 ( 0 equ; 13 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ rel_str(A)
| ~ rel_str(B)
| ~ subrelstr(B,A)
| subset(the_carrier(B),the_carrier(A)) ),
file('SEU373+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ one_sorted_str(A)
| ~ net_str(B,A)
| ~ net_str(C,A)
| ~ subnetstr(C,A,B)
| subrelstr(C,B) ),
file('SEU373+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ one_sorted_str(A)
| ~ net_str(B,A)
| rel_str(B) ),
file('SEU373+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ one_sorted_str(A)
| ~ net_str(B,A)
| ~ subnetstr(C,A,B)
| net_str(C,A) ),
file('SEU373+1.p',unknown),
[] ).
cnf(35,axiom,
~ subset(the_carrier(dollar_c11),the_carrier(dollar_c12)),
file('SEU373+1.p',unknown),
[] ).
cnf(86,axiom,
one_sorted_str(dollar_c13),
file('SEU373+1.p',unknown),
[] ).
cnf(87,axiom,
net_str(dollar_c12,dollar_c13),
file('SEU373+1.p',unknown),
[] ).
cnf(88,axiom,
subnetstr(dollar_c11,dollar_c13,dollar_c12),
file('SEU373+1.p',unknown),
[] ).
cnf(181,plain,
rel_str(dollar_c12),
inference(hyper,[status(thm)],[87,15,86]),
[iquote('hyper,87,15,86')] ).
cnf(191,plain,
net_str(dollar_c11,dollar_c13),
inference(hyper,[status(thm)],[88,17,86,87]),
[iquote('hyper,88,17,86,87')] ).
cnf(208,plain,
rel_str(dollar_c11),
inference(hyper,[status(thm)],[191,15,86]),
[iquote('hyper,191,15,86')] ).
cnf(211,plain,
subrelstr(dollar_c11,dollar_c12),
inference(hyper,[status(thm)],[191,9,86,87,88]),
[iquote('hyper,191,9,86,87,88')] ).
cnf(238,plain,
subset(the_carrier(dollar_c11),the_carrier(dollar_c12)),
inference(hyper,[status(thm)],[211,6,181,208]),
[iquote('hyper,211,6,181,208')] ).
cnf(239,plain,
$false,
inference(binary,[status(thm)],[238,35]),
[iquote('binary,238.1,35.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU373+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 08:09:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.02/2.20 ----- Otter 3.3f, August 2004 -----
% 2.02/2.20 The process was started by sandbox on n027.cluster.edu,
% 2.02/2.20 Wed Jul 27 08:09:06 2022
% 2.02/2.20 The command was "./otter". The process ID is 9574.
% 2.02/2.20
% 2.02/2.20 set(prolog_style_variables).
% 2.02/2.20 set(auto).
% 2.02/2.20 dependent: set(auto1).
% 2.02/2.20 dependent: set(process_input).
% 2.02/2.20 dependent: clear(print_kept).
% 2.02/2.20 dependent: clear(print_new_demod).
% 2.02/2.20 dependent: clear(print_back_demod).
% 2.02/2.20 dependent: clear(print_back_sub).
% 2.02/2.20 dependent: set(control_memory).
% 2.02/2.20 dependent: assign(max_mem, 12000).
% 2.02/2.20 dependent: assign(pick_given_ratio, 4).
% 2.02/2.20 dependent: assign(stats_level, 1).
% 2.02/2.20 dependent: assign(max_seconds, 10800).
% 2.02/2.20 clear(print_given).
% 2.02/2.20
% 2.02/2.20 formula_list(usable).
% 2.02/2.20 all A (A=A).
% 2.02/2.20 all A B (in(A,B)-> -in(B,A)).
% 2.02/2.20 all A (empty(A)->function(A)).
% 2.02/2.20 all A (empty(A)->relation(A)).
% 2.02/2.20 all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 2.02/2.20 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.02/2.20 all A (rel_str(A)-> (all B (rel_str(B)-> (subrelstr(B,A)<->subset(the_carrier(B),the_carrier(A))&subset(the_InternalRel(B),the_InternalRel(A)))))).
% 2.02/2.20 all A (one_sorted_str(A)-> (all B (net_str(B,A)-> (all C (net_str(C,A)-> (subnetstr(C,A,B)<->subrelstr(C,B)&the_mapping(A,C)=relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)))))))).
% 2.02/2.20 $T.
% 2.02/2.20 $T.
% 2.02/2.20 $T.
% 2.02/2.20 all A B (relation(A)->relation(relation_dom_restriction(A,B))).
% 2.02/2.20 all A B C D (relation_of2(C,A,B)->relation_of2_as_subset(relation_dom_restr_as_relation_of(A,B,C,D),A,B)).
% 2.02/2.20 all A (rel_str(A)->one_sorted_str(A)).
% 2.02/2.20 $T.
% 2.02/2.20 all A (one_sorted_str(A)-> (all B (net_str(B,A)->rel_str(B)))).
% 2.02/2.20 $T.
% 2.02/2.20 $T.
% 2.02/2.20 all A (rel_str(A)-> (all B (subrelstr(B,A)->rel_str(B)))).
% 2.02/2.20 all A B (one_sorted_str(A)&net_str(B,A)-> (all C (subnetstr(C,A,B)->net_str(C,A)))).
% 2.02/2.20 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 2.02/2.20 all A (rel_str(A)->relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))).
% 2.02/2.20 $T.
% 2.02/2.20 all A B (one_sorted_str(A)&net_str(B,A)->function(the_mapping(A,B))&quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A))&relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A))).
% 2.02/2.20 exists A rel_str(A).
% 2.02/2.20 exists A one_sorted_str(A).
% 2.02/2.20 all A (one_sorted_str(A)-> (exists B net_str(B,A))).
% 2.02/2.20 all A B exists C relation_of2(C,A,B).
% 2.02/2.20 all A exists B element(B,A).
% 2.02/2.20 all A (rel_str(A)-> (exists B subrelstr(B,A))).
% 2.02/2.20 all A B (one_sorted_str(A)&net_str(B,A)-> (exists C subnetstr(C,A,B))).
% 2.02/2.20 all A B exists C relation_of2_as_subset(C,A,B).
% 2.02/2.20 empty(empty_set).
% 2.02/2.20 relation(empty_set).
% 2.02/2.20 relation_empty_yielding(empty_set).
% 2.02/2.20 all A B (relation(A)&relation_empty_yielding(A)->relation(relation_dom_restriction(A,B))&relation_empty_yielding(relation_dom_restriction(A,B))).
% 2.02/2.20 all A (-empty(powerset(A))).
% 2.02/2.20 all A B (relation(A)&function(A)->relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))).
% 2.02/2.20 empty(empty_set).
% 2.02/2.20 relation(empty_set).
% 2.02/2.20 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 2.02/2.20 exists A (relation(A)&function(A)).
% 2.02/2.20 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.02/2.20 exists A (empty(A)&relation(A)).
% 2.02/2.20 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.02/2.20 exists A (relation(A)&empty(A)&function(A)).
% 2.02/2.20 exists A (-empty(A)&relation(A)).
% 2.02/2.20 all A exists B (element(B,powerset(A))&empty(B)).
% 2.02/2.20 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.02/2.20 exists A (relation(A)&relation_empty_yielding(A)).
% 2.02/2.20 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.02/2.20 all A B C D (relation_of2(C,A,B)->relation_dom_restr_as_relation_of(A,B,C,D)=relation_dom_restriction(C,D)).
% 2.02/2.20 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 2.02/2.20 all A B subset(A,A).
% 2.02/2.20 -(all A (one_sorted_str(A)-> (all B (net_str(B,A)-> (all C (subnetstr(C,A,B)->subset(the_carrier(C),the_carrier(B)))))))).
% 2.02/2.20 all A B (in(A,B)->element(A,B)).
% 2.02/2.20 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.02/2.20 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.02/2.20 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.02/2.20 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.02/2.20 all A (empty(A)->A=empty_set).
% 2.02/2.20 all A B (-(in(A,B)&empty(B))).
% 2.02/2.20 all A B (-(empty(A)&A!=B&empty(B))).
% 2.02/2.20 end_of_list.
% 2.02/2.20
% 2.02/2.20 -------> usable clausifies to:
% 2.02/2.20
% 2.02/2.20 list(usable).
% 2.02/2.20 0 [] A=A.
% 2.02/2.20 0 [] -in(A,B)| -in(B,A).
% 2.02/2.20 0 [] -empty(A)|function(A).
% 2.02/2.20 0 [] -empty(A)|relation(A).
% 2.02/2.20 0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 2.02/2.20 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.02/2.20 0 [] -rel_str(A)| -rel_str(B)| -subrelstr(B,A)|subset(the_carrier(B),the_carrier(A)).
% 2.02/2.20 0 [] -rel_str(A)| -rel_str(B)| -subrelstr(B,A)|subset(the_InternalRel(B),the_InternalRel(A)).
% 2.02/2.20 0 [] -rel_str(A)| -rel_str(B)|subrelstr(B,A)| -subset(the_carrier(B),the_carrier(A))| -subset(the_InternalRel(B),the_InternalRel(A)).
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)| -net_str(C,A)| -subnetstr(C,A,B)|subrelstr(C,B).
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)| -net_str(C,A)| -subnetstr(C,A,B)|the_mapping(A,C)=relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)).
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)| -net_str(C,A)|subnetstr(C,A,B)| -subrelstr(C,B)|the_mapping(A,C)!=relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)).
% 2.02/2.20 0 [] $T.
% 2.02/2.20 0 [] $T.
% 2.02/2.20 0 [] $T.
% 2.02/2.20 0 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 2.02/2.20 0 [] -relation_of2(C,A,B)|relation_of2_as_subset(relation_dom_restr_as_relation_of(A,B,C,D),A,B).
% 2.02/2.20 0 [] -rel_str(A)|one_sorted_str(A).
% 2.02/2.20 0 [] $T.
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)|rel_str(B).
% 2.02/2.20 0 [] $T.
% 2.02/2.20 0 [] $T.
% 2.02/2.20 0 [] -rel_str(A)| -subrelstr(B,A)|rel_str(B).
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)| -subnetstr(C,A,B)|net_str(C,A).
% 2.02/2.20 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 2.02/2.20 0 [] -rel_str(A)|relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)).
% 2.02/2.20 0 [] $T.
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)|function(the_mapping(A,B)).
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)|quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)|relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 2.02/2.20 0 [] rel_str($c1).
% 2.02/2.20 0 [] one_sorted_str($c2).
% 2.02/2.20 0 [] -one_sorted_str(A)|net_str($f1(A),A).
% 2.02/2.20 0 [] relation_of2($f2(A,B),A,B).
% 2.02/2.20 0 [] element($f3(A),A).
% 2.02/2.20 0 [] -rel_str(A)|subrelstr($f4(A),A).
% 2.02/2.20 0 [] -one_sorted_str(A)| -net_str(B,A)|subnetstr($f5(A,B),A,B).
% 2.02/2.20 0 [] relation_of2_as_subset($f6(A,B),A,B).
% 2.02/2.20 0 [] empty(empty_set).
% 2.02/2.20 0 [] relation(empty_set).
% 2.02/2.20 0 [] relation_empty_yielding(empty_set).
% 2.02/2.20 0 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 2.02/2.20 0 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 2.02/2.20 0 [] -empty(powerset(A)).
% 2.02/2.20 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 2.02/2.20 0 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 2.02/2.20 0 [] empty(empty_set).
% 2.02/2.20 0 [] relation(empty_set).
% 2.02/2.20 0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 2.02/2.20 0 [] relation($c3).
% 2.02/2.20 0 [] function($c3).
% 2.02/2.20 0 [] relation($c4).
% 2.02/2.20 0 [] relation_empty_yielding($c4).
% 2.02/2.20 0 [] function($c4).
% 2.02/2.20 0 [] empty($c5).
% 2.02/2.20 0 [] relation($c5).
% 2.02/2.20 0 [] empty(A)|element($f7(A),powerset(A)).
% 2.02/2.20 0 [] empty(A)| -empty($f7(A)).
% 2.02/2.20 0 [] relation($c6).
% 2.02/2.20 0 [] empty($c6).
% 2.02/2.20 0 [] function($c6).
% 2.02/2.20 0 [] -empty($c7).
% 2.02/2.20 0 [] relation($c7).
% 2.02/2.20 0 [] element($f8(A),powerset(A)).
% 2.02/2.20 0 [] empty($f8(A)).
% 2.02/2.20 0 [] relation($c8).
% 2.02/2.20 0 [] function($c8).
% 2.02/2.20 0 [] one_to_one($c8).
% 2.02/2.20 0 [] relation($c9).
% 2.02/2.20 0 [] relation_empty_yielding($c9).
% 2.02/2.20 0 [] relation($c10).
% 2.02/2.20 0 [] relation_empty_yielding($c10).
% 2.02/2.20 0 [] function($c10).
% 2.02/2.20 0 [] -relation_of2(C,A,B)|relation_dom_restr_as_relation_of(A,B,C,D)=relation_dom_restriction(C,D).
% 2.02/2.20 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 2.02/2.20 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 2.02/2.20 0 [] subset(A,A).
% 2.02/2.20 0 [] one_sorted_str($c13).
% 2.02/2.20 0 [] net_str($c12,$c13).
% 2.02/2.20 0 [] subnetstr($c11,$c13,$c12).
% 2.02/2.20 0 [] -subset(the_carrier($c11),the_carrier($c12)).
% 2.02/2.20 0 [] -in(A,B)|element(A,B).
% 2.02/2.20 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.02/2.20 0 [] -element(A,powerset(B))|subset(A,B).
% 2.02/2.20 0 [] element(A,powerset(B))| -subset(A,B).
% 2.02/2.20 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.02/2.20 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.02/2.20 0 [] -empty(A)|A=empty_set.
% 2.02/2.20 0 [] -in(A,B)| -empty(B).
% 2.02/2.20 0 [] -empty(A)|A=B| -empty(B).
% 2.02/2.20 end_of_list.
% 2.02/2.20
% 2.02/2.20 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 2.02/2.20
% 2.02/2.20 This ia a non-Horn set with equality. The strategy will be
% 2.02/2.20 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.02/2.20 deletion, with positive clauses in sos and nonpositive
% 2.02/2.20 clauses in usable.
% 2.02/2.20
% 2.02/2.20 dependent: set(knuth_bendix).
% 2.02/2.20 dependent: set(anl_eq).
% 2.02/2.20 dependent: set(para_from).
% 2.02/2.20 dependent: set(para_into).
% 2.02/2.20 dependent: clear(para_from_right).
% 2.02/2.20 dependent: clear(para_into_right).
% 2.02/2.20 dependent: set(para_from_vars).
% 2.02/2.20 dependent: set(eq_units_both_ways).
% 2.02/2.20 dependent: set(dynamic_demod_all).
% 2.02/2.20 dependent: set(dynamic_demod).
% 2.02/2.20 dependent: set(order_eq).
% 2.02/2.20 dependent: set(back_demod).
% 2.02/2.20 dependent: set(lrpo).
% 2.02/2.20 dependent: set(hyper_res).
% 2.02/2.20 dependent: set(unit_deletion).
% 2.02/2.20 dependent: set(factor).
% 2.02/2.20
% 2.02/2.20 ------------> process usable:
% 2.02/2.20 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.02/2.20 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 2.02/2.20 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 2.02/2.20 ** KEPT (pick-wt=8): 4 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 2.02/2.20 ** KEPT (pick-wt=8): 5 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.02/2.20 ** KEPT (pick-wt=12): 6 [] -rel_str(A)| -rel_str(B)| -subrelstr(B,A)|subset(the_carrier(B),the_carrier(A)).
% 2.02/2.20 ** KEPT (pick-wt=12): 7 [] -rel_str(A)| -rel_str(B)| -subrelstr(B,A)|subset(the_InternalRel(B),the_InternalRel(A)).
% 2.02/2.20 ** KEPT (pick-wt=17): 8 [] -rel_str(A)| -rel_str(B)|subrelstr(B,A)| -subset(the_carrier(B),the_carrier(A))| -subset(the_InternalRel(B),the_InternalRel(A)).
% 2.02/2.20 ** KEPT (pick-wt=15): 9 [] -one_sorted_str(A)| -net_str(B,A)| -net_str(C,A)| -subnetstr(C,A,B)|subrelstr(C,B).
% 2.02/2.20 ** KEPT (pick-wt=26): 10 [] -one_sorted_str(A)| -net_str(B,A)| -net_str(C,A)| -subnetstr(C,A,B)|the_mapping(A,C)=relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)).
% 2.02/2.20 ** KEPT (pick-wt=29): 11 [] -one_sorted_str(A)| -net_str(B,A)| -net_str(C,A)|subnetstr(C,A,B)| -subrelstr(C,B)|the_mapping(A,C)!=relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)).
% 2.02/2.20 ** KEPT (pick-wt=6): 12 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 2.02/2.20 ** KEPT (pick-wt=12): 13 [] -relation_of2(A,B,C)|relation_of2_as_subset(relation_dom_restr_as_relation_of(B,C,A,D),B,C).
% 2.02/2.20 ** KEPT (pick-wt=4): 14 [] -rel_str(A)|one_sorted_str(A).
% 2.02/2.20 ** KEPT (pick-wt=7): 15 [] -one_sorted_str(A)| -net_str(B,A)|rel_str(B).
% 2.02/2.20 ** KEPT (pick-wt=7): 16 [] -rel_str(A)| -subrelstr(B,A)|rel_str(B).
% 2.02/2.20 ** KEPT (pick-wt=12): 17 [] -one_sorted_str(A)| -net_str(B,A)| -subnetstr(C,A,B)|net_str(C,A).
% 2.02/2.20 ** KEPT (pick-wt=10): 18 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 2.02/2.20 ** KEPT (pick-wt=9): 19 [] -rel_str(A)|relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)).
% 2.02/2.20 ** KEPT (pick-wt=9): 20 [] -one_sorted_str(A)| -net_str(B,A)|function(the_mapping(A,B)).
% 2.02/2.20 ** KEPT (pick-wt=13): 21 [] -one_sorted_str(A)| -net_str(B,A)|quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 2.02/2.20 ** KEPT (pick-wt=13): 22 [] -one_sorted_str(A)| -net_str(B,A)|relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A)).
% 2.02/2.20 ** KEPT (pick-wt=6): 23 [] -one_sorted_str(A)|net_str($f1(A),A).
% 2.02/2.20 ** KEPT (pick-wt=6): 24 [] -rel_str(A)|subrelstr($f4(A),A).
% 2.02/2.20 ** KEPT (pick-wt=11): 25 [] -one_sorted_str(A)| -net_str(B,A)|subnetstr($f5(A,B),A,B).
% 2.02/2.20 Following clause subsumed by 12 during input processing: 0 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 2.02/2.20 ** KEPT (pick-wt=8): 26 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 2.02/2.20 ** KEPT (pick-wt=3): 27 [] -empty(powerset(A)).
% 2.02/2.20 Following clause subsumed by 12 during input processing: 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 2.02/2.20 ** KEPT (pick-wt=8): 28 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 2.02/2.20 ** KEPT (pick-wt=8): 29 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 2.02/2.20 ** KEPT (pick-wt=5): 30 [] empty(A)| -empty($f7(A)).
% 2.02/2.20 ** KEPT (pick-wt=2): 31 [] -empty($c7).
% 2.02/2.20 ** KEPT (pick-wt=13): 32 [] -relation_of2(A,B,C)|relation_dom_restr_as_relation_of(B,C,A,D)=relation_dom_restriction(A,D).
% 2.02/2.21 ** KEPT (pick-wt=8): 33 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 2.02/2.21 ** KEPT (pick-wt=8): 34 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 2.02/2.21 ** KEPT (pick-wt=5): 35 [] -subset(the_carrier($c11),the_carrier($c12)).
% 2.02/2.21 ** KEPT (pick-wt=6): 36 [] -in(A,B)|element(A,B).
% 2.02/2.21 ** KEPT (pick-wt=8): 37 [] -element(A,B)|empty(B)|in(A,B).
% 2.02/2.21 ** KEPT (pick-wt=7): 38 [] -element(A,powerset(B))|subset(A,B).
% 2.02/2.21 ** KEPT (pick-wt=7): 39 [] element(A,powerset(B))| -subset(A,B).
% 2.02/2.21 ** KEPT (pick-wt=10): 40 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.02/2.21 ** KEPT (pick-wt=9): 41 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.02/2.21 ** KEPT (pick-wt=5): 42 [] -empty(A)|A=empty_set.
% 2.02/2.21 ** KEPT (pick-wt=5): 43 [] -in(A,B)| -empty(B).
% 2.02/2.21 ** KEPT (pick-wt=7): 44 [] -empty(A)|A=B| -empty(B).
% 2.02/2.21
% 2.02/2.21 ------------> process sos:
% 2.02/2.21 ** KEPT (pick-wt=3): 54 [] A=A.
% 2.02/2.21 ** KEPT (pick-wt=2): 55 [] rel_str($c1).
% 2.02/2.21 ** KEPT (pick-wt=2): 56 [] one_sorted_str($c2).
% 2.02/2.21 ** KEPT (pick-wt=6): 57 [] relation_of2($f2(A,B),A,B).
% 2.02/2.21 ** KEPT (pick-wt=4): 58 [] element($f3(A),A).
% 2.02/2.21 ** KEPT (pick-wt=6): 59 [] relation_of2_as_subset($f6(A,B),A,B).
% 2.02/2.21 ** KEPT (pick-wt=2): 60 [] empty(empty_set).
% 2.02/2.21 ** KEPT (pick-wt=2): 61 [] relation(empty_set).
% 2.02/2.21 ** KEPT (pick-wt=2): 62 [] relation_empty_yielding(empty_set).
% 2.02/2.21 Following clause subsumed by 60 during input processing: 0 [] empty(empty_set).
% 2.02/2.21 Following clause subsumed by 61 during input processing: 0 [] relation(empty_set).
% 2.02/2.21 ** KEPT (pick-wt=2): 63 [] relation($c3).
% 2.02/2.21 ** KEPT (pick-wt=2): 64 [] function($c3).
% 2.02/2.21 ** KEPT (pick-wt=2): 65 [] relation($c4).
% 2.02/2.21 ** KEPT (pick-wt=2): 66 [] relation_empty_yielding($c4).
% 2.02/2.21 ** KEPT (pick-wt=2): 67 [] function($c4).
% 2.02/2.21 ** KEPT (pick-wt=2): 68 [] empty($c5).
% 2.02/2.21 ** KEPT (pick-wt=2): 69 [] relation($c5).
% 2.02/2.21 ** KEPT (pick-wt=7): 70 [] empty(A)|element($f7(A),powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=2): 71 [] relation($c6).
% 2.02/2.21 ** KEPT (pick-wt=2): 72 [] empty($c6).
% 2.02/2.21 ** KEPT (pick-wt=2): 73 [] function($c6).
% 2.02/2.21 ** KEPT (pick-wt=2): 74 [] relation($c7).
% 2.02/2.21 ** KEPT (pick-wt=5): 75 [] element($f8(A),powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 76 [] empty($f8(A)).
% 2.02/2.21 ** KEPT (pick-wt=2): 77 [] relation($c8).
% 2.02/2.21 ** KEPT (pick-wt=2): 78 [] function($c8).
% 2.02/2.21 ** KEPT (pick-wt=2): 79 [] one_to_one($c8).
% 2.02/2.21 ** KEPT (pick-wt=2): 80 [] relation($c9).
% 2.02/2.21 ** KEPT (pick-wt=2): 81 [] relation_empty_yielding($c9).
% 2.02/2.21 ** KEPT (pick-wt=2): 82 [] relation($c10).
% 2.02/2.21 ** KEPT (pick-wt=2): 83 [] relation_empty_yielding($c10).
% 2.02/2.21 ** KEPT (pick-wt=2): 84 [] function($c10).
% 2.02/2.21 ** KEPT (pick-wt=3): 85 [] subset(A,A).
% 2.02/2.21 ** KEPT (pick-wt=2): 86 [] one_sorted_str($c13).
% 2.02/2.21 ** KEPT (pick-wt=3): 87 [] net_str($c12,$c13).
% 2.02/2.21 ** KEPT (pick-wt=4): 88 [] subnetstr($c11,$c13,$c12).
% 2.02/2.21 Following clause subsumed by 54 during input processing: 0 [copy,54,flip.1] A=A.
% 2.02/2.21 54 back subsumes 53.
% 2.02/2.21 85 back subsumes 47.
% 2.02/2.21 85 back subsumes 46.
% 2.02/2.21
% 2.02/2.21 ======= end of input processing =======
% 2.02/2.21
% 2.02/2.21 =========== start of search ===========
% 2.02/2.21
% 2.02/2.21 -------- PROOF --------
% 2.02/2.21
% 2.02/2.21 ----> UNIT CONFLICT at 0.01 sec ----> 239 [binary,238.1,35.1] $F.
% 2.02/2.21
% 2.02/2.21 Length of proof is 5. Level of proof is 3.
% 2.02/2.21
% 2.02/2.21 ---------------- PROOF ----------------
% 2.02/2.21 % SZS status Theorem
% 2.02/2.21 % SZS output start Refutation
% See solution above
% 2.02/2.21 ------------ end of proof -------------
% 2.02/2.21
% 2.02/2.21
% 2.02/2.21 Search stopped by max_proofs option.
% 2.02/2.21
% 2.02/2.21
% 2.02/2.21 Search stopped by max_proofs option.
% 2.02/2.21
% 2.02/2.21 ============ end of search ============
% 2.02/2.21
% 2.02/2.21 -------------- statistics -------------
% 2.02/2.21 clauses given 52
% 2.02/2.21 clauses generated 256
% 2.02/2.21 clauses kept 233
% 2.02/2.21 clauses forward subsumed 128
% 2.02/2.21 clauses back subsumed 6
% 2.02/2.21 Kbytes malloced 1953
% 2.02/2.21
% 2.02/2.21 ----------- times (seconds) -----------
% 2.02/2.21 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.02/2.21 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.21 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.02/2.21
% 2.02/2.21 That finishes the proof of the theorem.
% 2.02/2.21
% 2.02/2.21 Process 9574 finished Wed Jul 27 08:09:08 2022
% 2.02/2.21 Otter interrupted
% 2.02/2.21 PROOF FOUND
%------------------------------------------------------------------------------