%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU034+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:14:41 EDT 2022
% Result : Theorem 3.70s 3.89s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 20 ( 13 unt; 0 nHn; 9 RR)
% Number of literals : 45 ( 16 equ; 26 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ relation(A)
| ~ function(A)
| relation(function_inverse(A)) ),
file('SEU034+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ relation(A)
| ~ function(A)
| function(function_inverse(A)) ),
file('SEU034+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| relation_rng(A) != relation_dom(B)
| relation_composition(A,B) != A
| B = identity_relation(relation_dom(B)) ),
file('SEU034+1.p',unknown),
[] ).
cnf(28,plain,
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| relation_rng(A) != relation_dom(B)
| relation_composition(A,B) != A
| identity_relation(relation_dom(B)) = B ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[27])]),
[iquote('copy,27,flip.7')] ).
cnf(30,axiom,
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| relation_rng(A) = relation_dom(function_inverse(A)) ),
file('SEU034+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A)) ),
file('SEU034+1.p',unknown),
[] ).
cnf(35,plain,
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| identity_relation(relation_dom(A)) = relation_composition(A,function_inverse(A)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[34])]),
[iquote('copy,34,flip.4')] ).
cnf(38,axiom,
function_inverse(identity_relation(dollar_c9)) != identity_relation(dollar_c9),
file('SEU034+1.p',unknown),
[] ).
cnf(47,axiom,
A = A,
file('SEU034+1.p',unknown),
[] ).
cnf(48,axiom,
relation(identity_relation(A)),
file('SEU034+1.p',unknown),
[] ).
cnf(53,axiom,
function(identity_relation(A)),
file('SEU034+1.p',unknown),
[] ).
cnf(72,axiom,
one_to_one(identity_relation(A)),
file('SEU034+1.p',unknown),
[] ).
cnf(74,axiom,
relation_dom(identity_relation(A)) = A,
file('SEU034+1.p',unknown),
[] ).
cnf(76,axiom,
relation_rng(identity_relation(A)) = A,
file('SEU034+1.p',unknown),
[] ).
cnf(162,plain,
function(function_inverse(identity_relation(A))),
inference(hyper,[status(thm)],[53,6,48]),
[iquote('hyper,53,6,48')] ).
cnf(163,plain,
relation(function_inverse(identity_relation(A))),
inference(hyper,[status(thm)],[53,5,48]),
[iquote('hyper,53,5,48')] ).
cnf(276,plain,
relation_composition(identity_relation(A),function_inverse(identity_relation(A))) = identity_relation(A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[72,35,48,53]),74])]),
[iquote('hyper,72,35,48,53,demod,74,flip.1')] ).
cnf(281,plain,
relation_dom(function_inverse(identity_relation(A))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[72,30,48,53]),76])]),
[iquote('hyper,72,30,48,53,demod,76,flip.1')] ).
cnf(4520,plain,
function_inverse(identity_relation(A)) = identity_relation(A),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[276,28]),76,281,281]),48,53,163,162,47,47])]),
[iquote('para_from,276.1.1,28.6.1,demod,76,281,281,unit_del,48,53,163,162,47,47,flip.1')] ).
cnf(4522,plain,
$false,
inference(binary,[status(thm)],[4520,38]),
[iquote('binary,4520.1,38.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU034+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n009.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 07:53:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox2 on n009.cluster.edu,
% 1.75/1.96 Wed Jul 27 07:53:21 2022
% 1.75/1.96 The command was "./otter". The process ID is 31973.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 formula_list(usable).
% 1.75/1.96 all A (A=A).
% 1.75/1.96 all A B (in(A,B)-> -in(B,A)).
% 1.75/1.96 all A (empty(A)->function(A)).
% 1.75/1.96 all A (empty(A)->relation(A)).
% 1.75/1.96 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.75/1.96 all A (relation(A)&function(A)->relation(function_inverse(A))&function(function_inverse(A))).
% 1.75/1.96 all A B (relation(A)&relation(B)->relation(relation_composition(A,B))).
% 1.75/1.96 all A relation(identity_relation(A)).
% 1.75/1.96 all A exists B element(B,A).
% 1.75/1.96 all A B (empty(A)&relation(B)->empty(relation_composition(B,A))&relation(relation_composition(B,A))).
% 1.75/1.96 empty(empty_set).
% 1.75/1.96 relation(empty_set).
% 1.75/1.96 relation_empty_yielding(empty_set).
% 1.75/1.96 all A B (relation(A)&function(A)&relation(B)&function(B)->relation(relation_composition(A,B))&function(relation_composition(A,B))).
% 1.75/1.96 all A (-empty(powerset(A))).
% 1.75/1.96 empty(empty_set).
% 1.75/1.96 all A (relation(identity_relation(A))&function(identity_relation(A))).
% 1.75/1.96 empty(empty_set).
% 1.75/1.96 relation(empty_set).
% 1.75/1.96 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.75/1.96 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 1.75/1.96 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.75/1.96 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 1.75/1.96 all A B (empty(A)&relation(B)->empty(relation_composition(A,B))&relation(relation_composition(A,B))).
% 1.75/1.96 exists A (relation(A)&function(A)).
% 1.75/1.96 exists A (empty(A)&relation(A)).
% 1.75/1.96 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.75/1.96 exists A empty(A).
% 1.75/1.97 exists A (relation(A)&empty(A)&function(A)).
% 1.75/1.97 exists A (-empty(A)&relation(A)).
% 1.75/1.97 all A exists B (element(B,powerset(A))&empty(B)).
% 1.75/1.97 exists A (-empty(A)).
% 1.75/1.97 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.75/1.97 exists A (relation(A)&relation_empty_yielding(A)).
% 1.75/1.97 all A B subset(A,A).
% 1.75/1.97 all A B (in(A,B)->element(A,B)).
% 1.75/1.97 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.75/1.97 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.75/1.97 all A (relation(A)&function(A)-> (all B (relation(B)&function(B)-> (relation_rng(A)=relation_dom(B)&relation_composition(A,B)=A->B=identity_relation(relation_dom(B)))))).
% 1.75/1.97 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.75/1.97 all A one_to_one(identity_relation(A)).
% 1.75/1.97 all A (relation(A)&function(A)-> (one_to_one(A)->relation_rng(A)=relation_dom(function_inverse(A))&relation_dom(A)=relation_rng(function_inverse(A)))).
% 1.75/1.97 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.75/1.97 all A (relation(A)&function(A)-> (one_to_one(A)->relation_composition(A,function_inverse(A))=identity_relation(relation_dom(A))&relation_composition(function_inverse(A),A)=identity_relation(relation_rng(A)))).
% 1.75/1.97 -(all A (function_inverse(identity_relation(A))=identity_relation(A))).
% 1.75/1.97 all A (empty(A)->A=empty_set).
% 1.75/1.97 all A (relation_dom(identity_relation(A))=A&relation_rng(identity_relation(A))=A).
% 1.75/1.97 all A B (-(in(A,B)&empty(B))).
% 1.75/1.97 all A B (-(empty(A)&A!=B&empty(B))).
% 1.75/1.97 end_of_list.
% 1.75/1.97
% 1.75/1.97 -------> usable clausifies to:
% 1.75/1.97
% 1.75/1.97 list(usable).
% 1.75/1.97 0 [] A=A.
% 1.75/1.97 0 [] -in(A,B)| -in(B,A).
% 1.75/1.97 0 [] -empty(A)|function(A).
% 1.75/1.97 0 [] -empty(A)|relation(A).
% 1.75/1.97 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.75/1.97 0 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 1.75/1.97 0 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 1.75/1.97 0 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 1.75/1.97 0 [] relation(identity_relation(A)).
% 1.75/1.97 0 [] element($f1(A),A).
% 1.75/1.97 0 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 1.75/1.97 0 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 1.75/1.97 0 [] empty(empty_set).
% 1.75/1.97 0 [] relation(empty_set).
% 1.75/1.97 0 [] relation_empty_yielding(empty_set).
% 1.75/1.97 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 1.75/1.97 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 1.75/1.97 0 [] -empty(powerset(A)).
% 1.75/1.97 0 [] empty(empty_set).
% 1.75/1.97 0 [] relation(identity_relation(A)).
% 1.75/1.97 0 [] function(identity_relation(A)).
% 1.75/1.97 0 [] empty(empty_set).
% 1.75/1.97 0 [] relation(empty_set).
% 1.75/1.97 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.75/1.97 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.75/1.97 0 [] -empty(A)|empty(relation_dom(A)).
% 1.75/1.97 0 [] -empty(A)|relation(relation_dom(A)).
% 1.75/1.97 0 [] -empty(A)|empty(relation_rng(A)).
% 1.75/1.97 0 [] -empty(A)|relation(relation_rng(A)).
% 1.75/1.97 0 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 1.75/1.97 0 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 1.75/1.97 0 [] relation($c1).
% 1.75/1.97 0 [] function($c1).
% 1.75/1.97 0 [] empty($c2).
% 1.75/1.97 0 [] relation($c2).
% 1.75/1.97 0 [] empty(A)|element($f2(A),powerset(A)).
% 1.75/1.97 0 [] empty(A)| -empty($f2(A)).
% 1.75/1.97 0 [] empty($c3).
% 1.75/1.97 0 [] relation($c4).
% 1.75/1.97 0 [] empty($c4).
% 1.75/1.97 0 [] function($c4).
% 1.75/1.97 0 [] -empty($c5).
% 1.75/1.97 0 [] relation($c5).
% 1.75/1.97 0 [] element($f3(A),powerset(A)).
% 1.75/1.97 0 [] empty($f3(A)).
% 1.75/1.97 0 [] -empty($c6).
% 1.75/1.97 0 [] relation($c7).
% 1.75/1.97 0 [] function($c7).
% 1.75/1.97 0 [] one_to_one($c7).
% 1.75/1.97 0 [] relation($c8).
% 1.75/1.97 0 [] relation_empty_yielding($c8).
% 1.75/1.97 0 [] subset(A,A).
% 1.75/1.97 0 [] -in(A,B)|element(A,B).
% 1.75/1.97 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.75/1.97 0 [] -element(A,powerset(B))|subset(A,B).
% 1.75/1.97 0 [] element(A,powerset(B))| -subset(A,B).
% 1.75/1.97 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation_rng(A)!=relation_dom(B)|relation_composition(A,B)!=A|B=identity_relation(relation_dom(B)).
% 1.75/1.97 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.75/1.97 0 [] one_to_one(identity_relation(A)).
% 1.75/1.97 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(A)=relation_dom(function_inverse(A)).
% 1.75/1.97 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation_dom(A)=relation_rng(function_inverse(A)).
% 1.75/1.97 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.75/1.97 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation_composition(A,function_inverse(A))=identity_relation(relation_dom(A)).
% 1.75/1.97 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation_composition(function_inverse(A),A)=identity_relation(relation_rng(A)).
% 1.75/1.97 0 [] function_inverse(identity_relation($c9))!=identity_relation($c9).
% 1.75/1.97 0 [] -empty(A)|A=empty_set.
% 1.75/1.97 0 [] relation_dom(identity_relation(A))=A.
% 1.75/1.97 0 [] relation_rng(identity_relation(A))=A.
% 1.75/1.97 0 [] -in(A,B)| -empty(B).
% 1.75/1.97 0 [] -empty(A)|A=B| -empty(B).
% 1.75/1.97 end_of_list.
% 1.75/1.97
% 1.75/1.97 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.75/1.97
% 1.75/1.97 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.97 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.97 deletion, with positive clauses in sos and nonpositive
% 1.75/1.97 clauses in usable.
% 1.75/1.97
% 1.75/1.97 dependent: set(knuth_bendix).
% 1.75/1.97 dependent: set(anl_eq).
% 1.75/1.97 dependent: set(para_from).
% 1.75/1.97 dependent: set(para_into).
% 1.75/1.97 dependent: clear(para_from_right).
% 1.75/1.97 dependent: clear(para_into_right).
% 1.75/1.97 dependent: set(para_from_vars).
% 1.75/1.97 dependent: set(eq_units_both_ways).
% 1.75/1.97 dependent: set(dynamic_demod_all).
% 1.75/1.97 dependent: set(dynamic_demod).
% 1.75/1.97 dependent: set(order_eq).
% 1.75/1.97 dependent: set(back_demod).
% 1.75/1.97 dependent: set(lrpo).
% 1.75/1.97 dependent: set(hyper_res).
% 1.75/1.97 dependent: set(unit_deletion).
% 1.75/1.97 dependent: set(factor).
% 1.75/1.97
% 1.75/1.97 ------------> process usable:
% 1.75/1.97 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.75/1.97 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.75/1.97 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 1.75/1.97 ** KEPT (pick-wt=8): 4 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.75/1.97 ** KEPT (pick-wt=7): 5 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 1.75/1.97 ** KEPT (pick-wt=7): 6 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 1.75/1.97 ** KEPT (pick-wt=8): 7 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 1.75/1.97 ** KEPT (pick-wt=8): 8 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 1.75/1.97 ** KEPT (pick-wt=8): 9 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 1.75/1.97 Following clause subsumed by 7 during input processing: 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 1.75/1.97 ** KEPT (pick-wt=12): 10 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 1.75/1.97 ** KEPT (pick-wt=3): 11 [] -empty(powerset(A)).
% 1.75/1.97 ** KEPT (pick-wt=7): 12 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.75/1.97 ** KEPT (pick-wt=7): 13 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.75/1.97 ** KEPT (pick-wt=5): 14 [] -empty(A)|empty(relation_dom(A)).
% 1.75/1.97 ** KEPT (pick-wt=5): 15 [] -empty(A)|relation(relation_dom(A)).
% 1.75/1.97 ** KEPT (pick-wt=5): 16 [] -empty(A)|empty(relation_rng(A)).
% 1.75/1.97 ** KEPT (pick-wt=5): 17 [] -empty(A)|relation(relation_rng(A)).
% 1.75/1.97 ** KEPT (pick-wt=8): 18 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 1.75/1.97 ** KEPT (pick-wt=8): 19 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 1.75/1.97 ** KEPT (pick-wt=5): 20 [] empty(A)| -empty($f2(A)).
% 1.75/1.97 ** KEPT (pick-wt=2): 21 [] -empty($c5).
% 1.75/1.97 ** KEPT (pick-wt=2): 22 [] -empty($c6).
% 1.75/1.97 ** KEPT (pick-wt=6): 23 [] -in(A,B)|element(A,B).
% 1.75/1.97 ** KEPT (pick-wt=8): 24 [] -element(A,B)|empty(B)|in(A,B).
% 1.75/1.97 ** KEPT (pick-wt=7): 25 [] -element(A,powerset(B))|subset(A,B).
% 1.75/1.97 ** KEPT (pick-wt=7): 26 [] element(A,powerset(B))| -subset(A,B).
% 1.75/1.97 ** KEPT (pick-wt=23): 28 [copy,27,flip.7] -relation(A)| -function(A)| -relation(B)| -function(B)|relation_rng(A)!=relation_dom(B)|relation_composition(A,B)!=A|identity_relation(relation_dom(B))=B.
% 1.75/1.97 ** KEPT (pick-wt=10): 29 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.75/1.97 ** KEPT (pick-wt=12): 30 [] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(A)=relation_dom(function_inverse(A)).
% 1.75/1.97 ** KEPT (pick-wt=12): 32 [copy,31,flip.4] -relation(A)| -function(A)| -one_to_one(A)|relation_rng(function_inverse(A))=relation_dom(A).
% 1.75/1.97 ** KEPT (pick-wt=9): 33 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.75/1.97 ** KEPT (pick-wt=14): 35 [copy,34,flip.4] -relation(A)| -function(A)| -one_to_one(A)|identity_relation(relation_dom(A))=relation_composition(A,function_inverse(A)).
% 1.75/1.97 ** KEPT (pick-wt=14): 37 [copy,36,flip.4] -relation(A)| -function(A)| -one_to_one(A)|identity_relation(relation_rng(A))=relation_composition(function_inverse(A),A).
% 1.75/1.97 ** KEPT (pick-wt=6): 38 [] function_inverse(identity_relation($c9))!=identity_relation($c9).
% 1.75/1.97 ** KEPT (pick-wt=5): 39 [] -empty(A)|A=empty_set.
% 1.75/1.97 ** KEPT (pick-wt=5): 40 [] -in(A,B)| -empty(B).
% 1.75/1.97 ** KEPT (pick-wt=7): 41 [] -empty(A)|A=B| -empty(B).
% 1.75/1.97
% 1.75/1.97 ------------> process sos:
% 1.75/1.97 ** KEPT (pick-wt=3): 47 [] A=A.
% 1.75/1.97 ** KEPT (pick-wt=3): 48 [] relation(identity_relation(A)).
% 1.75/1.97 ** KEPT (pick-wt=4): 49 [] element($f1(A),A).
% 1.75/1.97 ** KEPT (pick-wt=2): 50 [] empty(empty_set).
% 1.75/1.97 ** KEPT (pick-wt=2): 51 [] relation(empty_set).
% 1.75/1.97 ** KEPT (pick-wt=2): 52 [] relation_empty_yielding(empty_set).
% 1.75/1.97 Following clause subsumed by 50 during input processing: 0 [] empty(empty_set).
% 1.75/1.97 Following clause subsumed by 48 during input processing: 0 [] relation(identity_relation(A)).
% 1.75/1.97 ** KEPT (pick-wt=3): 53 [] function(identity_relation(A)).
% 1.75/1.97 Following clause subsumed by 50 during input processing: 0 [] empty(empty_set).
% 1.75/1.97 Following clause subsumed by 51 during input processing: 0 [] relation(empty_set).
% 1.75/1.97 ** KEPT (pick-wt=2): 54 [] relation($c1).
% 1.75/1.97 ** KEPT (pick-wt=2): 55 [] function($c1).
% 1.75/1.97 ** KEPT (pick-wt=2): 56 [] empty($c2).
% 1.75/1.97 ** KEPT (pick-wt=2): 57 [] relation($c2).
% 1.75/1.97 ** KEPT (pick-wt=7): 58 [] empty(A)|element($f2(A),powerset(A)).
% 1.75/1.97 ** KEPT (pick-wt=2): 59 [] empty($c3).
% 1.75/1.97 ** KEPT (pick-wt=2): 60 [] relation($c4).
% 1.75/1.97 ** KEPT (pick-wt=2): 61 [] empty($c4).
% 1.75/1.97 ** KEPT (pick-wt=2): 62 [] function($c4).
% 1.75/1.97 ** KEPT (pick-wt=2): 63 [] relation($c5).
% 1.75/1.97 ** KEPT (pick-wt=5): 64 [] element($f3(A),powerset(A)).
% 1.75/1.97 ** KEPT (pick-wt=3): 65 [] empty($f3(A)).
% 1.75/1.97 ** KEPT (pick-wt=2): 66 [] relation($c7).
% 1.75/1.97 ** KEPT (pick-wt=2): 67 [] function($c7).
% 1.75/1.97 ** KEPT (pick-wt=2): 68 [] one_to_one($c7).
% 1.75/1.97 ** KEPT (pick-wt=2): 69 [] relation($c8).
% 1.75/1.97 ** KEPT (pick-wt=2): 70 [] relation_empty_yielding($c8).
% 1.75/1.97 ** KEPT (pick-wt=3): 71 [] subset(A,A).
% 1.75/1.97 ** KEPT (pick-wt=3): 72 [] one_to_one(identity_relation(A)).
% 1.75/1.97 ** KEPT (pick-wt=5): 73 [] relation_dom(identity_relation(A))=A.
% 1.75/1.97 ---> New Demodulator: 74 [new_demod,73] relation_dom(identity_relation(A))=A.
% 1.75/1.97 ** KEPT (pick-wt=5): 75 [] relation_rng(identity_relation(A))=A.
% 1.75/1.97 ---> New Demodulator: 76 [new_demod,75] relation_rng(identity_relation(A))=A.
% 1.75/1.97 Following clause subsumed by 47 during input processing: 0 [copy,47,flip.1] A=A.
% 3.70/3.89 47 back subsumes 46.
% 3.70/3.89 >>>> Starting back demodulation with 74.
% 3.70/3.89 >>>> Starting back demodulation with 76.
% 3.70/3.89
% 3.70/3.89 ======= end of input processing =======
% 3.70/3.89
% 3.70/3.89 =========== start of search ===========
% 3.70/3.89
% 3.70/3.89
% 3.70/3.89 Resetting weight limit to 6.
% 3.70/3.89
% 3.70/3.89
% 3.70/3.89 Resetting weight limit to 6.
% 3.70/3.89
% 3.70/3.89 sos_size=3295
% 3.70/3.89
% 3.70/3.89 -------- PROOF --------
% 3.70/3.89
% 3.70/3.89 ----> UNIT CONFLICT at 1.93 sec ----> 4522 [binary,4520.1,38.1] $F.
% 3.70/3.89
% 3.70/3.89 Length of proof is 7. Level of proof is 3.
% 3.70/3.89
% 3.70/3.89 ---------------- PROOF ----------------
% 3.70/3.89 % SZS status Theorem
% 3.70/3.89 % SZS output start Refutation
% See solution above
% 3.70/3.89 ------------ end of proof -------------
% 3.70/3.89
% 3.70/3.89
% 3.70/3.89 Search stopped by max_proofs option.
% 3.70/3.89
% 3.70/3.89
% 3.70/3.89 Search stopped by max_proofs option.
% 3.70/3.89
% 3.70/3.89 ============ end of search ============
% 3.70/3.89
% 3.70/3.89 -------------- statistics -------------
% 3.70/3.89 clauses given 381
% 3.70/3.89 clauses generated 185488
% 3.70/3.89 clauses kept 4469
% 3.70/3.89 clauses forward subsumed 4694
% 3.70/3.89 clauses back subsumed 45
% 3.70/3.89 Kbytes malloced 4882
% 3.70/3.89
% 3.70/3.89 ----------- times (seconds) -----------
% 3.70/3.89 user CPU time 1.93 (0 hr, 0 min, 1 sec)
% 3.70/3.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.70/3.89 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.70/3.89
% 3.70/3.89 That finishes the proof of the theorem.
% 3.70/3.89
% 3.70/3.89 Process 31973 finished Wed Jul 27 07:53:24 2022
% 3.70/3.89 Otter interrupted
% 3.70/3.89 PROOF FOUND
%------------------------------------------------------------------------------