TSTP Solution File: SEU062+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 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 13:14:43 EDT 2022
% Result : Theorem 2.11s 2.31s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 18 ( 10 unt; 3 nHn; 14 RR)
% Number of literals : 29 ( 7 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( subset(A,B)
| ~ in(dollar_f1(A,B),B) ),
file('SEU062+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ relation(A)
| in(B,relation_rng(A))
| relation_inverse_image(A,singleton(B)) = empty_set ),
file('SEU062+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(A,dollar_c10)
| relation_inverse_image(dollar_c9,singleton(A)) != empty_set ),
file('SEU062+1.p',unknown),
[] ).
cnf(18,axiom,
~ subset(dollar_c10,relation_rng(dollar_c9)),
file('SEU062+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU062+1.p',unknown),
[] ).
cnf(30,axiom,
A = A,
file('SEU062+1.p',unknown),
[] ).
cnf(31,axiom,
( subset(A,B)
| in(dollar_f1(A,B),A) ),
file('SEU062+1.p',unknown),
[] ).
cnf(33,axiom,
empty(empty_set),
file('SEU062+1.p',unknown),
[] ).
cnf(38,axiom,
empty(dollar_c2),
file('SEU062+1.p',unknown),
[] ).
cnf(54,axiom,
relation(dollar_c9),
file('SEU062+1.p',unknown),
[] ).
cnf(62,plain,
in(dollar_f1(dollar_c10,relation_rng(dollar_c9)),dollar_c10),
inference(hyper,[status(thm)],[31,18]),
[iquote('hyper,31,18')] ).
cnf(66,plain,
empty_set = dollar_c2,
inference(hyper,[status(thm)],[38,27,33]),
[iquote('hyper,38,27,33')] ).
cnf(75,plain,
( ~ in(A,dollar_c10)
| relation_inverse_image(dollar_c9,singleton(A)) != dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),66]),
[iquote('back_demod,17,demod,66')] ).
cnf(76,plain,
( ~ relation(A)
| in(B,relation_rng(A))
| relation_inverse_image(A,singleton(B)) = dollar_c2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),66]),
[iquote('back_demod,16,demod,66')] ).
cnf(247,plain,
( ~ in(A,dollar_c10)
| in(A,relation_rng(dollar_c9)) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[76,75]),30,54]),
[iquote('para_from,76.3.1,75.2.1,unit_del,30,54')] ).
cnf(690,plain,
in(dollar_f1(dollar_c10,relation_rng(dollar_c9)),relation_rng(dollar_c9)),
inference(hyper,[status(thm)],[247,62]),
[iquote('hyper,247,62')] ).
cnf(1726,plain,
subset(dollar_c10,relation_rng(dollar_c9)),
inference(hyper,[status(thm)],[690,6]),
[iquote('hyper,690,6')] ).
cnf(1727,plain,
$false,
inference(binary,[status(thm)],[1726,18]),
[iquote('binary,1726.1,18.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 08:08:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.87/2.08 ----- Otter 3.3f, August 2004 -----
% 1.87/2.08 The process was started by sandbox2 on n027.cluster.edu,
% 1.87/2.08 Wed Jul 27 08:08:36 2022
% 1.87/2.08 The command was "./otter". The process ID is 7137.
% 1.87/2.08
% 1.87/2.08 set(prolog_style_variables).
% 1.87/2.08 set(auto).
% 1.87/2.08 dependent: set(auto1).
% 1.87/2.08 dependent: set(process_input).
% 1.87/2.08 dependent: clear(print_kept).
% 1.87/2.08 dependent: clear(print_new_demod).
% 1.87/2.08 dependent: clear(print_back_demod).
% 1.87/2.08 dependent: clear(print_back_sub).
% 1.87/2.08 dependent: set(control_memory).
% 1.87/2.08 dependent: assign(max_mem, 12000).
% 1.87/2.08 dependent: assign(pick_given_ratio, 4).
% 1.87/2.08 dependent: assign(stats_level, 1).
% 1.87/2.08 dependent: assign(max_seconds, 10800).
% 1.87/2.08 clear(print_given).
% 1.87/2.08
% 1.87/2.08 formula_list(usable).
% 1.87/2.08 all A (A=A).
% 1.87/2.08 all A B (in(A,B)-> -in(B,A)).
% 1.87/2.08 all A (empty(A)->function(A)).
% 1.87/2.08 all A (empty(A)->relation(A)).
% 1.87/2.08 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.87/2.08 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.87/2.08 all A exists B element(B,A).
% 1.87/2.08 empty(empty_set).
% 1.87/2.08 relation(empty_set).
% 1.87/2.08 relation_empty_yielding(empty_set).
% 1.87/2.08 all A (-empty(powerset(A))).
% 1.87/2.08 empty(empty_set).
% 1.87/2.08 all A (-empty(singleton(A))).
% 1.87/2.08 empty(empty_set).
% 1.87/2.08 relation(empty_set).
% 1.87/2.08 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 1.87/2.08 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 1.87/2.08 exists A (relation(A)&function(A)).
% 1.87/2.08 exists A (empty(A)&relation(A)).
% 1.87/2.08 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.87/2.08 exists A empty(A).
% 1.87/2.08 exists A (relation(A)&empty(A)&function(A)).
% 1.87/2.08 exists A (-empty(A)&relation(A)).
% 1.87/2.08 all A exists B (element(B,powerset(A))&empty(B)).
% 1.87/2.08 exists A (-empty(A)).
% 1.87/2.08 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.87/2.08 exists A (relation(A)&relation_empty_yielding(A)).
% 1.87/2.08 all A B subset(A,A).
% 1.87/2.08 all A B (relation(B)-> (in(A,relation_rng(B))<->relation_inverse_image(B,singleton(A))!=empty_set)).
% 1.87/2.08 -(all A B (relation(B)-> ((all C (-(in(C,A)&relation_inverse_image(B,singleton(C))=empty_set)))->subset(A,relation_rng(B))))).
% 1.87/2.08 all A B (in(A,B)->element(A,B)).
% 1.87/2.08 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.87/2.08 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.87/2.08 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.87/2.08 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.87/2.08 all A (empty(A)->A=empty_set).
% 1.87/2.08 all A B (-(in(A,B)&empty(B))).
% 1.87/2.08 all A B (-(empty(A)&A!=B&empty(B))).
% 1.87/2.08 end_of_list.
% 1.87/2.08
% 1.87/2.08 -------> usable clausifies to:
% 1.87/2.08
% 1.87/2.08 list(usable).
% 1.87/2.08 0 [] A=A.
% 1.87/2.08 0 [] -in(A,B)| -in(B,A).
% 1.87/2.08 0 [] -empty(A)|function(A).
% 1.87/2.08 0 [] -empty(A)|relation(A).
% 1.87/2.08 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.87/2.08 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.87/2.08 0 [] subset(A,B)|in($f1(A,B),A).
% 1.87/2.08 0 [] subset(A,B)| -in($f1(A,B),B).
% 1.87/2.08 0 [] element($f2(A),A).
% 1.87/2.08 0 [] empty(empty_set).
% 1.87/2.08 0 [] relation(empty_set).
% 1.87/2.08 0 [] relation_empty_yielding(empty_set).
% 1.87/2.08 0 [] -empty(powerset(A)).
% 1.87/2.08 0 [] empty(empty_set).
% 1.87/2.08 0 [] -empty(singleton(A)).
% 1.87/2.08 0 [] empty(empty_set).
% 1.87/2.08 0 [] relation(empty_set).
% 1.87/2.08 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.87/2.08 0 [] -empty(A)|empty(relation_rng(A)).
% 1.87/2.08 0 [] -empty(A)|relation(relation_rng(A)).
% 1.87/2.08 0 [] relation($c1).
% 1.87/2.08 0 [] function($c1).
% 1.87/2.08 0 [] empty($c2).
% 1.87/2.08 0 [] relation($c2).
% 1.87/2.08 0 [] empty(A)|element($f3(A),powerset(A)).
% 1.87/2.08 0 [] empty(A)| -empty($f3(A)).
% 1.87/2.08 0 [] empty($c3).
% 1.87/2.08 0 [] relation($c4).
% 1.87/2.08 0 [] empty($c4).
% 1.87/2.08 0 [] function($c4).
% 1.87/2.08 0 [] -empty($c5).
% 1.87/2.08 0 [] relation($c5).
% 1.87/2.08 0 [] element($f4(A),powerset(A)).
% 1.87/2.08 0 [] empty($f4(A)).
% 1.87/2.08 0 [] -empty($c6).
% 1.87/2.08 0 [] relation($c7).
% 1.87/2.08 0 [] function($c7).
% 1.87/2.08 0 [] one_to_one($c7).
% 1.87/2.08 0 [] relation($c8).
% 1.87/2.08 0 [] relation_empty_yielding($c8).
% 1.87/2.08 0 [] subset(A,A).
% 1.87/2.08 0 [] -relation(B)| -in(A,relation_rng(B))|relation_inverse_image(B,singleton(A))!=empty_set.
% 1.87/2.08 0 [] -relation(B)|in(A,relation_rng(B))|relation_inverse_image(B,singleton(A))=empty_set.
% 1.87/2.08 0 [] relation($c9).
% 1.87/2.08 0 [] -in(C,$c10)|relation_inverse_image($c9,singleton(C))!=empty_set.
% 1.87/2.08 0 [] -subset($c10,relation_rng($c9)).
% 1.87/2.08 0 [] -in(A,B)|element(A,B).
% 1.87/2.08 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.87/2.08 0 [] -element(A,powerset(B))|subset(A,B).
% 1.87/2.08 0 [] element(A,powerset(B))| -subset(A,B).
% 1.87/2.08 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.87/2.08 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.87/2.08 0 [] -empty(A)|A=empty_set.
% 1.87/2.08 0 [] -in(A,B)| -empty(B).
% 1.87/2.08 0 [] -empty(A)|A=B| -empty(B).
% 1.87/2.08 end_of_list.
% 1.87/2.08
% 1.87/2.08 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.11/2.30
% 2.11/2.30 This ia a non-Horn set with equality. The strategy will be
% 2.11/2.30 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.11/2.30 deletion, with positive clauses in sos and nonpositive
% 2.11/2.30 clauses in usable.
% 2.11/2.30
% 2.11/2.30 dependent: set(knuth_bendix).
% 2.11/2.30 dependent: set(anl_eq).
% 2.11/2.30 dependent: set(para_from).
% 2.11/2.30 dependent: set(para_into).
% 2.11/2.30 dependent: clear(para_from_right).
% 2.11/2.30 dependent: clear(para_into_right).
% 2.11/2.30 dependent: set(para_from_vars).
% 2.11/2.30 dependent: set(eq_units_both_ways).
% 2.11/2.30 dependent: set(dynamic_demod_all).
% 2.11/2.30 dependent: set(dynamic_demod).
% 2.11/2.30 dependent: set(order_eq).
% 2.11/2.30 dependent: set(back_demod).
% 2.11/2.30 dependent: set(lrpo).
% 2.11/2.30 dependent: set(hyper_res).
% 2.11/2.30 dependent: set(unit_deletion).
% 2.11/2.30 dependent: set(factor).
% 2.11/2.30
% 2.11/2.30 ------------> process usable:
% 2.11/2.30 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.11/2.30 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 2.11/2.30 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 2.11/2.30 ** KEPT (pick-wt=8): 4 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.11/2.30 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.11/2.30 ** KEPT (pick-wt=8): 6 [] subset(A,B)| -in($f1(A,B),B).
% 2.11/2.30 ** KEPT (pick-wt=3): 7 [] -empty(powerset(A)).
% 2.11/2.30 ** KEPT (pick-wt=3): 8 [] -empty(singleton(A)).
% 2.11/2.30 ** KEPT (pick-wt=7): 9 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.11/2.30 ** KEPT (pick-wt=5): 10 [] -empty(A)|empty(relation_rng(A)).
% 2.11/2.30 ** KEPT (pick-wt=5): 11 [] -empty(A)|relation(relation_rng(A)).
% 2.11/2.30 ** KEPT (pick-wt=5): 12 [] empty(A)| -empty($f3(A)).
% 2.11/2.30 ** KEPT (pick-wt=2): 13 [] -empty($c5).
% 2.11/2.30 ** KEPT (pick-wt=2): 14 [] -empty($c6).
% 2.11/2.30 ** KEPT (pick-wt=12): 15 [] -relation(A)| -in(B,relation_rng(A))|relation_inverse_image(A,singleton(B))!=empty_set.
% 2.11/2.30 ** KEPT (pick-wt=12): 16 [] -relation(A)|in(B,relation_rng(A))|relation_inverse_image(A,singleton(B))=empty_set.
% 2.11/2.30 ** KEPT (pick-wt=9): 17 [] -in(A,$c10)|relation_inverse_image($c9,singleton(A))!=empty_set.
% 2.11/2.30 ** KEPT (pick-wt=4): 18 [] -subset($c10,relation_rng($c9)).
% 2.11/2.30 ** KEPT (pick-wt=6): 19 [] -in(A,B)|element(A,B).
% 2.11/2.30 ** KEPT (pick-wt=8): 20 [] -element(A,B)|empty(B)|in(A,B).
% 2.11/2.30 ** KEPT (pick-wt=7): 21 [] -element(A,powerset(B))|subset(A,B).
% 2.11/2.30 ** KEPT (pick-wt=7): 22 [] element(A,powerset(B))| -subset(A,B).
% 2.11/2.30 ** KEPT (pick-wt=10): 23 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.11/2.30 ** KEPT (pick-wt=9): 24 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.11/2.30 ** KEPT (pick-wt=5): 25 [] -empty(A)|A=empty_set.
% 2.11/2.30 ** KEPT (pick-wt=5): 26 [] -in(A,B)| -empty(B).
% 2.11/2.30 ** KEPT (pick-wt=7): 27 [] -empty(A)|A=B| -empty(B).
% 2.11/2.30
% 2.11/2.30 ------------> process sos:
% 2.11/2.30 ** KEPT (pick-wt=3): 30 [] A=A.
% 2.11/2.30 ** KEPT (pick-wt=8): 31 [] subset(A,B)|in($f1(A,B),A).
% 2.11/2.30 ** KEPT (pick-wt=4): 32 [] element($f2(A),A).
% 2.11/2.30 ** KEPT (pick-wt=2): 33 [] empty(empty_set).
% 2.11/2.30 ** KEPT (pick-wt=2): 34 [] relation(empty_set).
% 2.11/2.30 ** KEPT (pick-wt=2): 35 [] relation_empty_yielding(empty_set).
% 2.11/2.30 Following clause subsumed by 33 during input processing: 0 [] empty(empty_set).
% 2.11/2.30 Following clause subsumed by 33 during input processing: 0 [] empty(empty_set).
% 2.11/2.30 Following clause subsumed by 34 during input processing: 0 [] relation(empty_set).
% 2.11/2.30 ** KEPT (pick-wt=2): 36 [] relation($c1).
% 2.11/2.30 ** KEPT (pick-wt=2): 37 [] function($c1).
% 2.11/2.30 ** KEPT (pick-wt=2): 38 [] empty($c2).
% 2.11/2.30 ** KEPT (pick-wt=2): 39 [] relation($c2).
% 2.11/2.30 ** KEPT (pick-wt=7): 40 [] empty(A)|element($f3(A),powerset(A)).
% 2.11/2.30 ** KEPT (pick-wt=2): 41 [] empty($c3).
% 2.11/2.30 ** KEPT (pick-wt=2): 42 [] relation($c4).
% 2.11/2.30 ** KEPT (pick-wt=2): 43 [] empty($c4).
% 2.11/2.30 ** KEPT (pick-wt=2): 44 [] function($c4).
% 2.11/2.30 ** KEPT (pick-wt=2): 45 [] relation($c5).
% 2.11/2.30 ** KEPT (pick-wt=5): 46 [] element($f4(A),powerset(A)).
% 2.11/2.30 ** KEPT (pick-wt=3): 47 [] empty($f4(A)).
% 2.11/2.30 ** KEPT (pick-wt=2): 48 [] relation($c7).
% 2.11/2.30 ** KEPT (pick-wt=2): 49 [] function($c7).
% 2.11/2.30 ** KEPT (pick-wt=2): 50 [] one_to_one($c7).
% 2.11/2.30 ** KEPT (pick-wt=2): 51 [] relation($c8).
% 2.11/2.30 ** KEPT (pick-wt=2): 52 [] relation_empty_yielding($c8).
% 2.11/2.30 ** KEPT (pick-wt=3): 53 [] subset(A,A).
% 2.11/2.30 ** KEPT (pick-wt=2): 54 [] relation($c9).
% 2.11/2.30 Following clause subsumed by 30 during input processing: 0 [copy,30,flip.1] A=A.
% 2.11/2.30 30 back subsumes 29.
% 2.11/2.30
% 2.11/2.30 ======= end of input processing =======
% 2.11/2.30
% 2.11/2.30 =========== start of search ===========
% 2.11/2.30
% 2.11/2.30
% 2.11/2.30 Resetting weight limit to 8.
% 2.11/2.30
% 2.11/2.30
% 2.11/2.30 Resetting weight limit to 8.
% 2.11/2.31
% 2.11/2.31 sos_size=1268
% 2.11/2.31
% 2.11/2.31 -------- PROOF --------
% 2.11/2.31
% 2.11/2.31 ----> UNIT CONFLICT at 0.23 sec ----> 1727 [binary,1726.1,18.1] $F.
% 2.11/2.31
% 2.11/2.31 Length of proof is 7. Level of proof is 5.
% 2.11/2.31
% 2.11/2.31 ---------------- PROOF ----------------
% 2.11/2.31 % SZS status Theorem
% 2.11/2.31 % SZS output start Refutation
% See solution above
% 2.11/2.31 ------------ end of proof -------------
% 2.11/2.31
% 2.11/2.31
% 2.11/2.31 Search stopped by max_proofs option.
% 2.11/2.31
% 2.11/2.31
% 2.11/2.31 Search stopped by max_proofs option.
% 2.11/2.31
% 2.11/2.31 ============ end of search ============
% 2.11/2.31
% 2.11/2.31 -------------- statistics -------------
% 2.11/2.31 clauses given 177
% 2.11/2.31 clauses generated 7557
% 2.11/2.31 clauses kept 1716
% 2.11/2.31 clauses forward subsumed 4669
% 2.11/2.31 clauses back subsumed 220
% 2.11/2.31 Kbytes malloced 4882
% 2.11/2.31
% 2.11/2.31 ----------- times (seconds) -----------
% 2.11/2.31 user CPU time 0.23 (0 hr, 0 min, 0 sec)
% 2.11/2.31 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.11/2.31 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.11/2.31
% 2.11/2.31 That finishes the proof of the theorem.
% 2.11/2.31
% 2.11/2.31 Process 7137 finished Wed Jul 27 08:08:38 2022
% 2.11/2.31 Otter interrupted
% 2.11/2.31 PROOF FOUND
%------------------------------------------------------------------------------