TSTP Solution File: NUM409+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:08:15 EDT 2022
% Result : Theorem 2.13s 2.29s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 17 unt; 0 nHn; 21 RR)
% Number of literals : 39 ( 4 equ; 16 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 13 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ empty(A)
| function(A) ),
file('NUM409+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ empty(A)
| ordinal(A) ),
file('NUM409+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ relation(A)
| ~ function(A)
| transfinite_se_quence(A)
| ~ ordinal(relation_dom(A)) ),
file('NUM409+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ relation(A)
| ~ function(A)
| ~ transfinite_se_quence(A)
| transfinite_se_quence_of(A,B)
| ~ subset(relation_rng(A),B) ),
file('NUM409+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ empty(A)
| empty(relation_dom(A)) ),
file('NUM409+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ empty(A)
| empty(relation_rng(A)) ),
file('NUM409+1.p',unknown),
[] ).
cnf(37,axiom,
~ transfinite_se_quence_of(empty_set,dollar_c15),
file('NUM409+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('NUM409+1.p',unknown),
[] ).
cnf(54,axiom,
empty(empty_set),
file('NUM409+1.p',unknown),
[] ).
cnf(67,axiom,
empty(dollar_c3),
file('NUM409+1.p',unknown),
[] ).
cnf(68,axiom,
relation(dollar_c3),
file('NUM409+1.p',unknown),
[] ).
cnf(99,axiom,
subset(empty_set,A),
file('NUM409+1.p',unknown),
[] ).
cnf(162,plain,
empty_set = dollar_c3,
inference(hyper,[status(thm)],[67,44,54]),
[iquote('hyper,67,44,54')] ).
cnf(164,plain,
empty(relation_rng(dollar_c3)),
inference(hyper,[status(thm)],[67,28]),
[iquote('hyper,67,28')] ).
cnf(166,plain,
empty(relation_dom(dollar_c3)),
inference(hyper,[status(thm)],[67,26]),
[iquote('hyper,67,26')] ).
cnf(167,plain,
ordinal(dollar_c3),
inference(hyper,[status(thm)],[67,10]),
[iquote('hyper,67,10')] ).
cnf(170,plain,
function(dollar_c3),
inference(hyper,[status(thm)],[67,2]),
[iquote('hyper,67,2')] ).
cnf(192,plain,
subset(dollar_c3,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[99]),162]),
[iquote('back_demod,99,demod,162')] ).
cnf(198,plain,
~ transfinite_se_quence_of(dollar_c3,dollar_c15),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),162]),
[iquote('back_demod,37,demod,162')] ).
cnf(333,plain,
relation_rng(dollar_c3) = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[164,44,67])]),
[iquote('hyper,164,44,67,flip.1')] ).
cnf(376,plain,
relation_dom(dollar_c3) = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[166,44,67])]),
[iquote('hyper,166,44,67,flip.1')] ).
cnf(538,plain,
( ~ transfinite_se_quence(dollar_c3)
| transfinite_se_quence_of(dollar_c3,A) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[333,18]),68,170,192]),
[iquote('para_from,333.1.1,18.5.1,unit_del,68,170,192')] ).
cnf(544,plain,
transfinite_se_quence(dollar_c3),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[376,16]),68,170,167]),
[iquote('para_from,376.1.1,16.4.1,unit_del,68,170,167')] ).
cnf(929,plain,
transfinite_se_quence_of(dollar_c3,A),
inference(hyper,[status(thm)],[538,544]),
[iquote('hyper,538,544')] ).
cnf(930,plain,
$false,
inference(binary,[status(thm)],[929,198]),
[iquote('binary,929.1,198.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 09:59:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.16 ----- Otter 3.3f, August 2004 -----
% 1.96/2.16 The process was started by sandbox2 on n014.cluster.edu,
% 1.96/2.16 Wed Jul 27 09:59:24 2022
% 1.96/2.16 The command was "./otter". The process ID is 10953.
% 1.96/2.16
% 1.96/2.16 set(prolog_style_variables).
% 1.96/2.16 set(auto).
% 1.96/2.16 dependent: set(auto1).
% 1.96/2.16 dependent: set(process_input).
% 1.96/2.16 dependent: clear(print_kept).
% 1.96/2.16 dependent: clear(print_new_demod).
% 1.96/2.16 dependent: clear(print_back_demod).
% 1.96/2.16 dependent: clear(print_back_sub).
% 1.96/2.16 dependent: set(control_memory).
% 1.96/2.16 dependent: assign(max_mem, 12000).
% 1.96/2.16 dependent: assign(pick_given_ratio, 4).
% 1.96/2.16 dependent: assign(stats_level, 1).
% 1.96/2.16 dependent: assign(max_seconds, 10800).
% 1.96/2.16 clear(print_given).
% 1.96/2.16
% 1.96/2.16 formula_list(usable).
% 1.96/2.16 all A (A=A).
% 1.96/2.16 all A B (in(A,B)-> -in(B,A)).
% 1.96/2.16 all A (empty(A)->function(A)).
% 1.96/2.16 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 1.96/2.16 all A (empty(A)->relation(A)).
% 1.96/2.16 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.96/2.16 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 1.96/2.16 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.96/2.16 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.96/2.16 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 1.96/2.16 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.96/2.16 all A (relation(A)&function(A)-> (transfinite_se_quence(A)<->ordinal(relation_dom(A)))).
% 1.96/2.16 all A B (relation(B)&function(B)&transfinite_se_quence(B)-> (transfinite_se_quence_of(B,A)<->subset(relation_rng(B),A))).
% 1.96/2.16 all A B (transfinite_se_quence_of(B,A)->relation(B)&function(B)&transfinite_se_quence(B)).
% 1.96/2.16 all A exists B transfinite_se_quence_of(B,A).
% 1.96/2.16 all A exists B element(B,A).
% 1.96/2.16 empty(empty_set).
% 1.96/2.16 relation(empty_set).
% 1.96/2.16 relation_empty_yielding(empty_set).
% 1.96/2.16 empty(empty_set).
% 1.96/2.16 all A B (-empty(ordered_pair(A,B))).
% 1.96/2.16 relation(empty_set).
% 1.96/2.16 relation_empty_yielding(empty_set).
% 1.96/2.16 function(empty_set).
% 1.96/2.16 one_to_one(empty_set).
% 1.96/2.16 empty(empty_set).
% 1.96/2.16 epsilon_transitive(empty_set).
% 1.96/2.16 epsilon_connected(empty_set).
% 1.96/2.16 ordinal(empty_set).
% 1.96/2.16 empty(empty_set).
% 1.96/2.16 relation(empty_set).
% 1.96/2.16 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.96/2.16 all A (relation(A)&relation_non_empty(A)&function(A)->with_non_empty_elements(relation_rng(A))).
% 1.96/2.16 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 1.96/2.16 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.96/2.16 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 1.96/2.16 exists A (relation(A)&function(A)).
% 1.96/2.16 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.96/2.16 exists A (empty(A)&relation(A)).
% 1.96/2.16 exists A empty(A).
% 1.96/2.16 exists A (relation(A)&empty(A)&function(A)).
% 1.96/2.16 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.96/2.16 exists A (-empty(A)&relation(A)).
% 1.96/2.16 exists A (-empty(A)).
% 1.96/2.16 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.96/2.16 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.96/2.16 exists A (relation(A)&relation_empty_yielding(A)).
% 1.96/2.16 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 1.96/2.16 exists A (relation(A)&function(A)&transfinite_se_quence(A)).
% 1.96/2.16 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 1.96/2.16 all A B subset(A,A).
% 1.96/2.16 all A B (in(A,B)->element(A,B)).
% 1.96/2.16 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.96/2.16 all A subset(empty_set,A).
% 1.96/2.16 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.96/2.16 -(all A transfinite_se_quence_of(empty_set,A)).
% 1.96/2.16 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.96/2.16 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.96/2.16 all A (relation(A)-> (relation_dom(A)=empty_set<->relation_rng(A)=empty_set)).
% 1.96/2.16 all A (empty(A)->A=empty_set).
% 1.96/2.16 all A B (-(in(A,B)&empty(B))).
% 1.96/2.16 all A B (-(empty(A)&A!=B&empty(B))).
% 1.96/2.16 end_of_list.
% 1.96/2.16
% 1.96/2.16 -------> usable clausifies to:
% 1.96/2.16
% 1.96/2.16 list(usable).
% 1.96/2.16 0 [] A=A.
% 1.96/2.16 0 [] -in(A,B)| -in(B,A).
% 1.96/2.16 0 [] -empty(A)|function(A).
% 1.96/2.16 0 [] -ordinal(A)|epsilon_transitive(A).
% 1.96/2.16 0 [] -ordinal(A)|epsilon_connected(A).
% 1.96/2.16 0 [] -empty(A)|relation(A).
% 1.96/2.16 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.96/2.16 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 1.96/2.16 0 [] -empty(A)|epsilon_transitive(A).
% 1.96/2.16 0 [] -empty(A)|epsilon_connected(A).
% 1.96/2.16 0 [] -empty(A)|ordinal(A).
% 1.96/2.16 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.96/2.16 0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f1(A,B,C)),A).
% 1.96/2.16 0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.96/2.16 0 [] -relation(A)|B=relation_dom(A)|in($f3(A,B),B)|in(ordered_pair($f3(A,B),$f2(A,B)),A).
% 1.96/2.16 0 [] -relation(A)|B=relation_dom(A)| -in($f3(A,B),B)| -in(ordered_pair($f3(A,B),X1),A).
% 1.96/2.16 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.96/2.16 0 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|ordinal(relation_dom(A)).
% 1.96/2.16 0 [] -relation(A)| -function(A)|transfinite_se_quence(A)| -ordinal(relation_dom(A)).
% 1.96/2.16 0 [] -relation(B)| -function(B)| -transfinite_se_quence(B)| -transfinite_se_quence_of(B,A)|subset(relation_rng(B),A).
% 1.96/2.16 0 [] -relation(B)| -function(B)| -transfinite_se_quence(B)|transfinite_se_quence_of(B,A)| -subset(relation_rng(B),A).
% 1.96/2.16 0 [] -transfinite_se_quence_of(B,A)|relation(B).
% 1.96/2.16 0 [] -transfinite_se_quence_of(B,A)|function(B).
% 1.96/2.16 0 [] -transfinite_se_quence_of(B,A)|transfinite_se_quence(B).
% 1.96/2.16 0 [] transfinite_se_quence_of($f4(A),A).
% 1.96/2.16 0 [] element($f5(A),A).
% 1.96/2.16 0 [] empty(empty_set).
% 1.96/2.16 0 [] relation(empty_set).
% 1.96/2.16 0 [] relation_empty_yielding(empty_set).
% 1.96/2.16 0 [] empty(empty_set).
% 1.96/2.16 0 [] -empty(ordered_pair(A,B)).
% 1.96/2.16 0 [] relation(empty_set).
% 1.96/2.16 0 [] relation_empty_yielding(empty_set).
% 1.96/2.16 0 [] function(empty_set).
% 1.96/2.16 0 [] one_to_one(empty_set).
% 1.96/2.16 0 [] empty(empty_set).
% 1.96/2.16 0 [] epsilon_transitive(empty_set).
% 1.96/2.16 0 [] epsilon_connected(empty_set).
% 1.96/2.16 0 [] ordinal(empty_set).
% 1.96/2.16 0 [] empty(empty_set).
% 1.96/2.16 0 [] relation(empty_set).
% 1.96/2.16 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.96/2.16 0 [] -relation(A)| -relation_non_empty(A)| -function(A)|with_non_empty_elements(relation_rng(A)).
% 1.96/2.16 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.96/2.16 0 [] -empty(A)|empty(relation_dom(A)).
% 1.96/2.16 0 [] -empty(A)|relation(relation_dom(A)).
% 1.96/2.16 0 [] -empty(A)|empty(relation_rng(A)).
% 1.96/2.16 0 [] -empty(A)|relation(relation_rng(A)).
% 1.96/2.16 0 [] relation($c1).
% 1.96/2.16 0 [] function($c1).
% 1.96/2.16 0 [] epsilon_transitive($c2).
% 1.96/2.16 0 [] epsilon_connected($c2).
% 1.96/2.16 0 [] ordinal($c2).
% 1.96/2.16 0 [] empty($c3).
% 1.96/2.16 0 [] relation($c3).
% 1.96/2.16 0 [] empty($c4).
% 1.96/2.16 0 [] relation($c5).
% 1.96/2.16 0 [] empty($c5).
% 1.96/2.16 0 [] function($c5).
% 1.96/2.16 0 [] relation($c6).
% 1.96/2.16 0 [] function($c6).
% 1.96/2.16 0 [] one_to_one($c6).
% 1.96/2.16 0 [] empty($c6).
% 1.96/2.16 0 [] epsilon_transitive($c6).
% 1.96/2.16 0 [] epsilon_connected($c6).
% 1.96/2.16 0 [] ordinal($c6).
% 1.96/2.16 0 [] -empty($c7).
% 1.96/2.16 0 [] relation($c7).
% 1.96/2.16 0 [] -empty($c8).
% 1.96/2.16 0 [] relation($c9).
% 1.96/2.16 0 [] function($c9).
% 1.96/2.16 0 [] one_to_one($c9).
% 1.96/2.16 0 [] -empty($c10).
% 1.96/2.16 0 [] epsilon_transitive($c10).
% 1.96/2.16 0 [] epsilon_connected($c10).
% 1.96/2.16 0 [] ordinal($c10).
% 1.96/2.16 0 [] relation($c11).
% 1.96/2.16 0 [] relation_empty_yielding($c11).
% 1.96/2.16 0 [] relation($c12).
% 1.96/2.16 0 [] relation_empty_yielding($c12).
% 1.96/2.16 0 [] function($c12).
% 1.96/2.16 0 [] relation($c13).
% 1.96/2.16 0 [] function($c13).
% 1.96/2.16 0 [] transfinite_se_quence($c13).
% 1.96/2.16 0 [] relation($c14).
% 1.96/2.16 0 [] relation_non_empty($c14).
% 1.96/2.16 0 [] function($c14).
% 1.96/2.16 0 [] subset(A,A).
% 1.96/2.16 0 [] -in(A,B)|element(A,B).
% 1.96/2.16 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.96/2.16 0 [] subset(empty_set,A).
% 1.96/2.16 0 [] -element(A,powerset(B))|subset(A,B).
% 1.96/2.16 0 [] element(A,powerset(B))| -subset(A,B).
% 1.96/2.16 0 [] -transfinite_se_quence_of(empty_set,$c15).
% 1.96/2.16 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.96/2.16 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.96/2.16 0 [] -relation(A)|relation_dom(A)!=empty_set|relation_rng(A)=empty_set.
% 1.96/2.16 0 [] -relation(A)|relation_dom(A)=empty_set|relation_rng(A)!=empty_set.
% 1.96/2.16 0 [] -empty(A)|A=empty_set.
% 1.96/2.16 0 [] -in(A,B)| -empty(B).
% 1.96/2.16 0 [] -empty(A)|A=B| -empty(B).
% 1.96/2.16 end_of_list.
% 1.96/2.16
% 1.96/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.96/2.16
% 1.96/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.96/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.96/2.16 deletion, with positive clauses in sos and nonpositive
% 1.96/2.16 clauses in usable.
% 1.96/2.16
% 1.96/2.16 dependent: set(knuth_bendix).
% 1.96/2.16 dependent: set(anl_eq).
% 1.96/2.16 dependent: set(para_from).
% 1.96/2.16 dependent: set(para_into).
% 1.96/2.16 dependent: clear(para_from_right).
% 1.96/2.16 dependent: clear(para_into_right).
% 1.96/2.16 dependent: set(para_from_vars).
% 1.96/2.16 dependent: set(eq_units_both_ways).
% 1.96/2.16 dependent: set(dynamic_demod_all).
% 1.96/2.16 dependent: set(dynamic_demod).
% 1.96/2.16 dependent: set(order_eq).
% 1.96/2.16 dependent: set(back_demod).
% 1.96/2.16 dependent: set(lrpo).
% 1.96/2.16 dependent: set(hyper_res).
% 1.96/2.16 dependent: set(unit_deletion).
% 1.96/2.16 dependent: set(factor).
% 1.96/2.16
% 1.96/2.16 ------------> process usable:
% 1.96/2.16 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.96/2.16 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.96/2.16 ** KEPT (pick-wt=4): 3 [] -ordinal(A)|epsilon_transitive(A).
% 1.96/2.16 ** KEPT (pick-wt=4): 4 [] -ordinal(A)|epsilon_connected(A).
% 1.96/2.16 ** KEPT (pick-wt=4): 5 [] -empty(A)|relation(A).
% 1.96/2.16 ** KEPT (pick-wt=8): 6 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.96/2.16 ** KEPT (pick-wt=6): 7 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 1.96/2.16 ** KEPT (pick-wt=4): 8 [] -empty(A)|epsilon_transitive(A).
% 1.96/2.16 ** KEPT (pick-wt=4): 9 [] -empty(A)|epsilon_connected(A).
% 1.96/2.16 ** KEPT (pick-wt=4): 10 [] -empty(A)|ordinal(A).
% 1.96/2.16 ** KEPT (pick-wt=17): 11 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f1(A,B,C)),A).
% 1.96/2.16 ** KEPT (pick-wt=14): 12 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.96/2.16 ** KEPT (pick-wt=20): 13 [] -relation(A)|B=relation_dom(A)|in($f3(A,B),B)|in(ordered_pair($f3(A,B),$f2(A,B)),A).
% 1.96/2.16 ** KEPT (pick-wt=18): 14 [] -relation(A)|B=relation_dom(A)| -in($f3(A,B),B)| -in(ordered_pair($f3(A,B),C),A).
% 1.96/2.16 ** KEPT (pick-wt=9): 15 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|ordinal(relation_dom(A)).
% 1.96/2.16 ** KEPT (pick-wt=9): 16 [] -relation(A)| -function(A)|transfinite_se_quence(A)| -ordinal(relation_dom(A)).
% 1.96/2.16 ** KEPT (pick-wt=13): 17 [] -relation(A)| -function(A)| -transfinite_se_quence(A)| -transfinite_se_quence_of(A,B)|subset(relation_rng(A),B).
% 1.96/2.16 ** KEPT (pick-wt=13): 18 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|transfinite_se_quence_of(A,B)| -subset(relation_rng(A),B).
% 1.96/2.16 ** KEPT (pick-wt=5): 19 [] -transfinite_se_quence_of(A,B)|relation(A).
% 1.96/2.16 ** KEPT (pick-wt=5): 20 [] -transfinite_se_quence_of(A,B)|function(A).
% 1.96/2.16 ** KEPT (pick-wt=5): 21 [] -transfinite_se_quence_of(A,B)|transfinite_se_quence(A).
% 1.96/2.16 ** KEPT (pick-wt=4): 22 [] -empty(ordered_pair(A,B)).
% 1.96/2.16 ** KEPT (pick-wt=7): 23 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.96/2.16 ** KEPT (pick-wt=9): 24 [] -relation(A)| -relation_non_empty(A)| -function(A)|with_non_empty_elements(relation_rng(A)).
% 1.96/2.16 ** KEPT (pick-wt=7): 25 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.96/2.16 ** KEPT (pick-wt=5): 26 [] -empty(A)|empty(relation_dom(A)).
% 1.96/2.16 ** KEPT (pick-wt=5): 27 [] -empty(A)|relation(relation_dom(A)).
% 1.96/2.16 ** KEPT (pick-wt=5): 28 [] -empty(A)|empty(relation_rng(A)).
% 1.96/2.16 ** KEPT (pick-wt=5): 29 [] -empty(A)|relation(relation_rng(A)).
% 1.96/2.16 ** KEPT (pick-wt=2): 30 [] -empty($c7).
% 1.96/2.16 ** KEPT (pick-wt=2): 31 [] -empty($c8).
% 1.96/2.16 ** KEPT (pick-wt=2): 32 [] -empty($c10).
% 1.96/2.16 ** KEPT (pick-wt=6): 33 [] -in(A,B)|element(A,B).
% 1.96/2.16 ** KEPT (pick-wt=8): 34 [] -element(A,B)|empty(B)|in(A,B).
% 1.96/2.16 ** KEPT (pick-wt=7): 35 [] -element(A,powerset(B))|subset(A,B).
% 1.96/2.16 ** KEPT (pick-wt=7): 36 [] element(A,powerset(B))| -subset(A,B).
% 1.96/2.16 ** KEPT (pick-wt=3): 37 [] -transfinite_se_quence_of(empty_set,$c15).
% 1.96/2.16 ** KEPT (pick-wt=10): 38 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.96/2.16 ** KEPT (pick-wt=9): 39 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.96/2.16 ** KEPT (pick-wt=10): 40 [] -relation(A)|relation_dom(A)!=empty_set|relation_rng(A)=empty_set.
% 1.96/2.16 ** KEPT (pick-wt=10): 41 [] -relation(A)|relation_dom(A)=empty_set|relation_rng(A)!=empty_set.
% 1.96/2.16 ** KEPT (pick-wt=5): 42 [] -empty(A)|A=empty_set.
% 1.96/2.16 ** KEPT (pick-wt=5): 43 [] -in(A,B)| -empty(B).
% 1.96/2.16 ** KEPT (pick-wt=7): 44 [] -empty(A)|A=B| -empty(B).
% 1.96/2.16
% 1.96/2.16 ------------> process sos:
% 1.96/2.16 ** KEPT (pick-wt=3): 47 [] A=A.
% 1.96/2.16 ** KEPT (pick-wt=7): 48 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.96/2.16 ** KEPT (pick-wt=10): 50 [copy,49,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.96/2.16 ---> New Demodulator: 51 [new_demod,50] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.96/2.16 ** KEPT (pick-wt=4): 52 [] transfinite_se_quence_of($f4(A),A).
% 1.96/2.16 ** KEPT (pick-wt=4): 53 [] element($f5(A),A).
% 1.96/2.16 ** KEPT (pick-wt=2): 54 [] empty(empty_set).
% 1.96/2.16 ** KEPT (pick-wt=2): 55 [] relation(empty_set).
% 1.96/2.16 ** KEPT (pick-wt=2): 56 [] relation_empty_yielding(empty_set).
% 1.96/2.16 Following clause subsumed by 54 during input processing: 0 [] empty(empty_set).
% 1.96/2.16 Following clause subsumed by 55 during input processing: 0 [] relation(empty_set).
% 1.96/2.16 Following clause subsumed by 56 during input processing: 0 [] relation_empty_yielding(empty_set).
% 2.13/2.29 ** KEPT (pick-wt=2): 57 [] function(empty_set).
% 2.13/2.29 ** KEPT (pick-wt=2): 58 [] one_to_one(empty_set).
% 2.13/2.29 Following clause subsumed by 54 during input processing: 0 [] empty(empty_set).
% 2.13/2.29 ** KEPT (pick-wt=2): 59 [] epsilon_transitive(empty_set).
% 2.13/2.29 ** KEPT (pick-wt=2): 60 [] epsilon_connected(empty_set).
% 2.13/2.29 ** KEPT (pick-wt=2): 61 [] ordinal(empty_set).
% 2.13/2.29 Following clause subsumed by 54 during input processing: 0 [] empty(empty_set).
% 2.13/2.29 Following clause subsumed by 55 during input processing: 0 [] relation(empty_set).
% 2.13/2.29 ** KEPT (pick-wt=2): 62 [] relation($c1).
% 2.13/2.29 ** KEPT (pick-wt=2): 63 [] function($c1).
% 2.13/2.29 ** KEPT (pick-wt=2): 64 [] epsilon_transitive($c2).
% 2.13/2.29 ** KEPT (pick-wt=2): 65 [] epsilon_connected($c2).
% 2.13/2.29 ** KEPT (pick-wt=2): 66 [] ordinal($c2).
% 2.13/2.29 ** KEPT (pick-wt=2): 67 [] empty($c3).
% 2.13/2.29 ** KEPT (pick-wt=2): 68 [] relation($c3).
% 2.13/2.29 ** KEPT (pick-wt=2): 69 [] empty($c4).
% 2.13/2.29 ** KEPT (pick-wt=2): 70 [] relation($c5).
% 2.13/2.29 ** KEPT (pick-wt=2): 71 [] empty($c5).
% 2.13/2.29 ** KEPT (pick-wt=2): 72 [] function($c5).
% 2.13/2.29 ** KEPT (pick-wt=2): 73 [] relation($c6).
% 2.13/2.29 ** KEPT (pick-wt=2): 74 [] function($c6).
% 2.13/2.29 ** KEPT (pick-wt=2): 75 [] one_to_one($c6).
% 2.13/2.29 ** KEPT (pick-wt=2): 76 [] empty($c6).
% 2.13/2.29 ** KEPT (pick-wt=2): 77 [] epsilon_transitive($c6).
% 2.13/2.29 ** KEPT (pick-wt=2): 78 [] epsilon_connected($c6).
% 2.13/2.29 ** KEPT (pick-wt=2): 79 [] ordinal($c6).
% 2.13/2.29 ** KEPT (pick-wt=2): 80 [] relation($c7).
% 2.13/2.29 ** KEPT (pick-wt=2): 81 [] relation($c9).
% 2.13/2.29 ** KEPT (pick-wt=2): 82 [] function($c9).
% 2.13/2.29 ** KEPT (pick-wt=2): 83 [] one_to_one($c9).
% 2.13/2.29 ** KEPT (pick-wt=2): 84 [] epsilon_transitive($c10).
% 2.13/2.29 ** KEPT (pick-wt=2): 85 [] epsilon_connected($c10).
% 2.13/2.29 ** KEPT (pick-wt=2): 86 [] ordinal($c10).
% 2.13/2.29 ** KEPT (pick-wt=2): 87 [] relation($c11).
% 2.13/2.29 ** KEPT (pick-wt=2): 88 [] relation_empty_yielding($c11).
% 2.13/2.29 ** KEPT (pick-wt=2): 89 [] relation($c12).
% 2.13/2.29 ** KEPT (pick-wt=2): 90 [] relation_empty_yielding($c12).
% 2.13/2.29 ** KEPT (pick-wt=2): 91 [] function($c12).
% 2.13/2.29 ** KEPT (pick-wt=2): 92 [] relation($c13).
% 2.13/2.29 ** KEPT (pick-wt=2): 93 [] function($c13).
% 2.13/2.29 ** KEPT (pick-wt=2): 94 [] transfinite_se_quence($c13).
% 2.13/2.29 ** KEPT (pick-wt=2): 95 [] relation($c14).
% 2.13/2.29 ** KEPT (pick-wt=2): 96 [] relation_non_empty($c14).
% 2.13/2.29 ** KEPT (pick-wt=2): 97 [] function($c14).
% 2.13/2.29 ** KEPT (pick-wt=3): 98 [] subset(A,A).
% 2.13/2.29 ** KEPT (pick-wt=3): 99 [] subset(empty_set,A).
% 2.13/2.29 Following clause subsumed by 47 during input processing: 0 [copy,47,flip.1] A=A.
% 2.13/2.29 47 back subsumes 46.
% 2.13/2.29 Following clause subsumed by 48 during input processing: 0 [copy,48,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.13/2.29 >>>> Starting back demodulation with 51.
% 2.13/2.29
% 2.13/2.29 ======= end of input processing =======
% 2.13/2.29
% 2.13/2.29 =========== start of search ===========
% 2.13/2.29
% 2.13/2.29
% 2.13/2.29 Resetting weight limit to 8.
% 2.13/2.29
% 2.13/2.29
% 2.13/2.29 Resetting weight limit to 8.
% 2.13/2.29
% 2.13/2.29 sos_size=694
% 2.13/2.29
% 2.13/2.29 -------- PROOF --------
% 2.13/2.29
% 2.13/2.29 ----> UNIT CONFLICT at 0.13 sec ----> 930 [binary,929.1,198.1] $F.
% 2.13/2.29
% 2.13/2.29 Length of proof is 12. Level of proof is 4.
% 2.13/2.29
% 2.13/2.29 ---------------- PROOF ----------------
% 2.13/2.29 % SZS status Theorem
% 2.13/2.29 % SZS output start Refutation
% See solution above
% 2.13/2.29 ------------ end of proof -------------
% 2.13/2.29
% 2.13/2.29
% 2.13/2.29 Search stopped by max_proofs option.
% 2.13/2.29
% 2.13/2.29
% 2.13/2.29 Search stopped by max_proofs option.
% 2.13/2.29
% 2.13/2.29 ============ end of search ============
% 2.13/2.29
% 2.13/2.29 -------------- statistics -------------
% 2.13/2.29 clauses given 102
% 2.13/2.29 clauses generated 1594
% 2.13/2.29 clauses kept 911
% 2.13/2.29 clauses forward subsumed 782
% 2.13/2.29 clauses back subsumed 23
% 2.13/2.29 Kbytes malloced 4882
% 2.13/2.29
% 2.13/2.29 ----------- times (seconds) -----------
% 2.13/2.29 user CPU time 0.13 (0 hr, 0 min, 0 sec)
% 2.13/2.29 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.13/2.29 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.13/2.29
% 2.13/2.29 That finishes the proof of the theorem.
% 2.13/2.29
% 2.13/2.29 Process 10953 finished Wed Jul 27 09:59:26 2022
% 2.13/2.29 Otter interrupted
% 2.13/2.29 PROOF FOUND
%------------------------------------------------------------------------------