TSTP Solution File: SEU010+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU010+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:14:40 EDT 2022
% Result : Theorem 2.10s 2.28s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 14 ( 7 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(29,axiom,
( relation_composition(identity_relation(relation_dom(dollar_c7)),dollar_c7) != dollar_c7
| relation_composition(dollar_c7,identity_relation(relation_rng(dollar_c7))) != dollar_c7 ),
file('SEU010+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ relation(A)
| ~ subset(relation_dom(A),B)
| relation_composition(identity_relation(B),A) = A ),
file('SEU010+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ relation(A)
| ~ subset(relation_rng(A),B)
| relation_composition(A,identity_relation(B)) = A ),
file('SEU010+1.p',unknown),
[] ).
cnf(36,axiom,
A = A,
file('SEU010+1.p',unknown),
[] ).
cnf(41,axiom,
subset(A,A),
file('SEU010+1.p',unknown),
[] ).
cnf(55,axiom,
relation(dollar_c7),
file('SEU010+1.p',unknown),
[] ).
cnf(128,plain,
relation_composition(dollar_c7,identity_relation(relation_rng(dollar_c7))) = dollar_c7,
inference(hyper,[status(thm)],[55,31,41]),
[iquote('hyper,55,31,41')] ).
cnf(130,plain,
relation_composition(identity_relation(relation_dom(dollar_c7)),dollar_c7) = dollar_c7,
inference(hyper,[status(thm)],[55,30,41]),
[iquote('hyper,55,30,41')] ).
cnf(141,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),130,128]),36,36]),
[iquote('back_demod,29,demod,130,128,unit_del,36,36')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU010+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 07:49:15 EDT 2022
% 0.14/0.33 % CPUTime :
% 2.10/2.28 ----- Otter 3.3f, August 2004 -----
% 2.10/2.28 The process was started by sandbox2 on n013.cluster.edu,
% 2.10/2.28 Wed Jul 27 07:49:15 2022
% 2.10/2.28 The command was "./otter". The process ID is 19425.
% 2.10/2.28
% 2.10/2.28 set(prolog_style_variables).
% 2.10/2.28 set(auto).
% 2.10/2.28 dependent: set(auto1).
% 2.10/2.28 dependent: set(process_input).
% 2.10/2.28 dependent: clear(print_kept).
% 2.10/2.28 dependent: clear(print_new_demod).
% 2.10/2.28 dependent: clear(print_back_demod).
% 2.10/2.28 dependent: clear(print_back_sub).
% 2.10/2.28 dependent: set(control_memory).
% 2.10/2.28 dependent: assign(max_mem, 12000).
% 2.10/2.28 dependent: assign(pick_given_ratio, 4).
% 2.10/2.28 dependent: assign(stats_level, 1).
% 2.10/2.28 dependent: assign(max_seconds, 10800).
% 2.10/2.28 clear(print_given).
% 2.10/2.28
% 2.10/2.28 formula_list(usable).
% 2.10/2.28 all A (A=A).
% 2.10/2.28 all A B (in(A,B)-> -in(B,A)).
% 2.10/2.28 empty(empty_set).
% 2.10/2.28 relation(empty_set).
% 2.10/2.28 empty(empty_set).
% 2.10/2.28 relation(empty_set).
% 2.10/2.28 relation_empty_yielding(empty_set).
% 2.10/2.28 empty(empty_set).
% 2.10/2.28 all A B (in(A,B)->element(A,B)).
% 2.10/2.28 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.10/2.28 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.10/2.28 all A exists B element(B,A).
% 2.10/2.28 all A (empty(A)->function(A)).
% 2.10/2.28 all A (-empty(powerset(A))).
% 2.10/2.28 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 2.10/2.28 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 2.10/2.28 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 2.10/2.28 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 2.10/2.28 all A B (empty(A)&relation(B)->empty(relation_composition(A,B))&relation(relation_composition(A,B))).
% 2.10/2.28 all A B (empty(A)&relation(B)->empty(relation_composition(B,A))&relation(relation_composition(B,A))).
% 2.10/2.28 all A (empty(A)->relation(A)).
% 2.10/2.28 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.10/2.28 all A (empty(A)->A=empty_set).
% 2.10/2.28 all A B (-(in(A,B)&empty(B))).
% 2.10/2.28 all A B (-(empty(A)&A!=B&empty(B))).
% 2.10/2.28 all A B subset(A,A).
% 2.10/2.28 all A B (relation(A)&relation(B)->relation(relation_composition(A,B))).
% 2.10/2.28 all A relation(identity_relation(A)).
% 2.10/2.28 all A B (relation(A)&function(A)&relation(B)&function(B)->relation(relation_composition(A,B))&function(relation_composition(A,B))).
% 2.10/2.28 all A (relation(identity_relation(A))&function(identity_relation(A))).
% 2.10/2.28 exists A (relation(A)&function(A)).
% 2.10/2.28 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.10/2.28 all A exists B (element(B,powerset(A))&empty(B)).
% 2.10/2.28 exists A (empty(A)&relation(A)).
% 2.10/2.28 exists A (-empty(A)&relation(A)).
% 2.10/2.28 exists A (relation(A)&relation_empty_yielding(A)).
% 2.10/2.28 exists A empty(A).
% 2.10/2.28 exists A (-empty(A)).
% 2.10/2.28 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.10/2.28 -(all A (relation(A)&function(A)->relation_composition(identity_relation(relation_dom(A)),A)=A&relation_composition(A,identity_relation(relation_rng(A)))=A)).
% 2.10/2.28 all A B (relation(B)-> (subset(relation_dom(B),A)->relation_composition(identity_relation(A),B)=B)).
% 2.10/2.28 all A B (relation(B)-> (subset(relation_rng(B),A)->relation_composition(B,identity_relation(A))=B)).
% 2.10/2.28 end_of_list.
% 2.10/2.28
% 2.10/2.28 -------> usable clausifies to:
% 2.10/2.28
% 2.10/2.28 list(usable).
% 2.10/2.28 0 [] A=A.
% 2.10/2.28 0 [] -in(A,B)| -in(B,A).
% 2.10/2.28 0 [] empty(empty_set).
% 2.10/2.28 0 [] relation(empty_set).
% 2.10/2.28 0 [] empty(empty_set).
% 2.10/2.28 0 [] relation(empty_set).
% 2.10/2.28 0 [] relation_empty_yielding(empty_set).
% 2.10/2.28 0 [] empty(empty_set).
% 2.10/2.28 0 [] -in(A,B)|element(A,B).
% 2.10/2.28 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.10/2.28 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.10/2.28 0 [] element($f1(A),A).
% 2.10/2.28 0 [] -empty(A)|function(A).
% 2.10/2.28 0 [] -empty(powerset(A)).
% 2.10/2.28 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 2.10/2.28 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.10/2.28 0 [] -empty(A)|empty(relation_dom(A)).
% 2.10/2.28 0 [] -empty(A)|relation(relation_dom(A)).
% 2.10/2.28 0 [] -empty(A)|empty(relation_rng(A)).
% 2.10/2.28 0 [] -empty(A)|relation(relation_rng(A)).
% 2.10/2.28 0 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 2.10/2.28 0 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 2.10/2.28 0 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 2.10/2.28 0 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 2.10/2.28 0 [] -empty(A)|relation(A).
% 2.10/2.28 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.10/2.28 0 [] -empty(A)|A=empty_set.
% 2.10/2.28 0 [] -in(A,B)| -empty(B).
% 2.10/2.28 0 [] -empty(A)|A=B| -empty(B).
% 2.10/2.28 0 [] subset(A,A).
% 2.10/2.28 0 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 2.10/2.28 0 [] relation(identity_relation(A)).
% 2.10/2.28 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 2.10/2.28 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 2.10/2.28 0 [] relation(identity_relation(A)).
% 2.10/2.28 0 [] function(identity_relation(A)).
% 2.10/2.28 0 [] relation($c1).
% 2.10/2.28 0 [] function($c1).
% 2.10/2.28 0 [] empty(A)|element($f2(A),powerset(A)).
% 2.10/2.28 0 [] empty(A)| -empty($f2(A)).
% 2.10/2.28 0 [] element($f3(A),powerset(A)).
% 2.10/2.28 0 [] empty($f3(A)).
% 2.10/2.28 0 [] empty($c2).
% 2.10/2.28 0 [] relation($c2).
% 2.10/2.28 0 [] -empty($c3).
% 2.10/2.28 0 [] relation($c3).
% 2.10/2.28 0 [] relation($c4).
% 2.10/2.28 0 [] relation_empty_yielding($c4).
% 2.10/2.28 0 [] empty($c5).
% 2.10/2.28 0 [] -empty($c6).
% 2.10/2.28 0 [] -element(A,powerset(B))|subset(A,B).
% 2.10/2.28 0 [] element(A,powerset(B))| -subset(A,B).
% 2.10/2.28 0 [] relation($c7).
% 2.10/2.28 0 [] function($c7).
% 2.10/2.28 0 [] relation_composition(identity_relation(relation_dom($c7)),$c7)!=$c7|relation_composition($c7,identity_relation(relation_rng($c7)))!=$c7.
% 2.10/2.28 0 [] -relation(B)| -subset(relation_dom(B),A)|relation_composition(identity_relation(A),B)=B.
% 2.10/2.28 0 [] -relation(B)| -subset(relation_rng(B),A)|relation_composition(B,identity_relation(A))=B.
% 2.10/2.28 end_of_list.
% 2.10/2.28
% 2.10/2.28 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.10/2.28
% 2.10/2.28 This ia a non-Horn set with equality. The strategy will be
% 2.10/2.28 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.10/2.28 deletion, with positive clauses in sos and nonpositive
% 2.10/2.28 clauses in usable.
% 2.10/2.28
% 2.10/2.28 dependent: set(knuth_bendix).
% 2.10/2.28 dependent: set(anl_eq).
% 2.10/2.28 dependent: set(para_from).
% 2.10/2.28 dependent: set(para_into).
% 2.10/2.28 dependent: clear(para_from_right).
% 2.10/2.28 dependent: clear(para_into_right).
% 2.10/2.28 dependent: set(para_from_vars).
% 2.10/2.28 dependent: set(eq_units_both_ways).
% 2.10/2.28 dependent: set(dynamic_demod_all).
% 2.10/2.28 dependent: set(dynamic_demod).
% 2.10/2.28 dependent: set(order_eq).
% 2.10/2.28 dependent: set(back_demod).
% 2.10/2.28 dependent: set(lrpo).
% 2.10/2.28 dependent: set(hyper_res).
% 2.10/2.28 dependent: set(unit_deletion).
% 2.10/2.28 dependent: set(factor).
% 2.10/2.28
% 2.10/2.28 ------------> process usable:
% 2.10/2.28 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.10/2.28 ** KEPT (pick-wt=6): 2 [] -in(A,B)|element(A,B).
% 2.10/2.28 ** KEPT (pick-wt=10): 3 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.10/2.28 ** KEPT (pick-wt=9): 4 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.10/2.28 ** KEPT (pick-wt=4): 5 [] -empty(A)|function(A).
% 2.10/2.28 ** KEPT (pick-wt=3): 6 [] -empty(powerset(A)).
% 2.10/2.28 ** KEPT (pick-wt=7): 7 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 2.10/2.28 ** KEPT (pick-wt=7): 8 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.10/2.28 ** KEPT (pick-wt=5): 9 [] -empty(A)|empty(relation_dom(A)).
% 2.10/2.28 ** KEPT (pick-wt=5): 10 [] -empty(A)|relation(relation_dom(A)).
% 2.10/2.28 ** KEPT (pick-wt=5): 11 [] -empty(A)|empty(relation_rng(A)).
% 2.10/2.28 ** KEPT (pick-wt=5): 12 [] -empty(A)|relation(relation_rng(A)).
% 2.10/2.28 ** KEPT (pick-wt=8): 13 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 2.10/2.28 ** KEPT (pick-wt=8): 14 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 2.10/2.28 ** KEPT (pick-wt=8): 15 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 2.10/2.28 ** KEPT (pick-wt=8): 16 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 2.10/2.28 ** KEPT (pick-wt=4): 17 [] -empty(A)|relation(A).
% 2.10/2.28 ** KEPT (pick-wt=8): 18 [] -element(A,B)|empty(B)|in(A,B).
% 2.10/2.28 ** KEPT (pick-wt=5): 19 [] -empty(A)|A=empty_set.
% 2.10/2.28 ** KEPT (pick-wt=5): 20 [] -in(A,B)| -empty(B).
% 2.10/2.28 ** KEPT (pick-wt=7): 21 [] -empty(A)|A=B| -empty(B).
% 2.10/2.28 ** KEPT (pick-wt=8): 22 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 2.10/2.28 Following clause subsumed by 22 during input processing: 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 2.10/2.28 ** KEPT (pick-wt=12): 23 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 2.10/2.28 ** KEPT (pick-wt=5): 24 [] empty(A)| -empty($f2(A)).
% 2.10/2.28 ** KEPT (pick-wt=2): 25 [] -empty($c3).
% 2.10/2.28 ** KEPT (pick-wt=2): 26 [] -empty($c6).
% 2.10/2.28 ** KEPT (pick-wt=7): 27 [] -element(A,powerset(B))|subset(A,B).
% 2.10/2.28 ** KEPT (pick-wt=7): 28 [] element(A,powerset(B))| -subset(A,B).
% 2.10/2.28 ** KEPT (pick-wt=14): 29 [] relation_composition(identity_relation(relation_dom($c7)),$c7)!=$c7|relation_composition($c7,identity_relation(relation_rng($c7)))!=$c7.
% 2.10/2.28 ** KEPT (pick-wt=12): 30 [] -relation(A)| -subset(relation_dom(A),B)|relation_composition(identity_relation(B),A)=A.
% 2.10/2.28 ** KEPT (pick-wt=12): 31 [] -relation(A)| -subset(relation_rng(A),B)|relation_composition(A,identity_relation(B))=A.
% 2.10/2.28
% 2.10/2.28 ------------> process sos:
% 2.10/2.28 ** KEPT (pick-wt=3): 36 [] A=A.
% 2.10/2.28 ** KEPT (pick-wt=2): 37 [] empty(empty_set).
% 2.10/2.28 ** KEPT (pick-wt=2): 38 [] relation(empty_set).
% 2.10/2.28 Following clause subsumed by 37 during input processing: 0 [] empty(empty_set).
% 2.10/2.28 Following clause subsumed by 38 during input processing: 0 [] relation(empty_set).
% 2.10/2.28 ** KEPT (pick-wt=2): 39 [] relation_empty_yielding(empty_set).
% 2.10/2.28 Following clause subsumed by 37 during input processing: 0 [] empty(empty_set).
% 2.10/2.28 ** KEPT (pick-wt=4): 40 [] element($f1(A),A).
% 2.10/2.28 ** KEPT (pick-wt=3): 41 [] subset(A,A).
% 2.10/2.28 ** KEPT (pick-wt=3): 42 [] relation(identity_relation(A)).
% 2.10/2.28 Following clause subsumed by 42 during input processing: 0 [] relation(identity_relation(A)).
% 2.10/2.28 ** KEPT (pick-wt=3): 43 [] function(identity_relation(A)).
% 2.10/2.28 ** KEPT (pick-wt=2): 44 [] relation($c1).
% 2.10/2.28 ** KEPT (pick-wt=2): 45 [] function($c1).
% 2.10/2.28 ** KEPT (pick-wt=7): 46 [] empty(A)|element($f2(A),powerset(A)).
% 2.10/2.28 ** KEPT (pick-wt=5): 47 [] element($f3(A),powerset(A)).
% 2.10/2.28 ** KEPT (pick-wt=3): 48 [] empty($f3(A)).
% 2.10/2.28 ** KEPT (pick-wt=2): 49 [] empty($c2).
% 2.10/2.28 ** KEPT (pick-wt=2): 50 [] relation($c2).
% 2.10/2.28 ** KEPT (pick-wt=2): 51 [] relation($c3).
% 2.10/2.28 ** KEPT (pick-wt=2): 52 [] relation($c4).
% 2.10/2.28 ** KEPT (pick-wt=2): 53 [] relation_empty_yielding($c4).
% 2.10/2.28 ** KEPT (pick-wt=2): 54 [] empty($c5).
% 2.10/2.28 ** KEPT (pick-wt=2): 55 [] relation($c7).
% 2.10/2.28 ** KEPT (pick-wt=2): 56 [] function($c7).
% 2.10/2.28 Following clause subsumed by 36 during input processing: 0 [copy,36,flip.1] A=A.
% 2.10/2.28 36 back subsumes 33.
% 2.10/2.28
% 2.10/2.28 ======= end of input processing =======
% 2.10/2.28
% 2.10/2.28 =========== start of search ===========
% 2.10/2.28
% 2.10/2.28 -------- PROOF --------
% 2.10/2.28
% 2.10/2.28 -----> EMPTY CLAUSE at 0.00 sec ----> 141 [back_demod,29,demod,130,128,unit_del,36,36] $F.
% 2.10/2.28
% 2.10/2.28 Length of proof is 2. Level of proof is 1.
% 2.10/2.28
% 2.10/2.28 ---------------- PROOF ----------------
% 2.10/2.28 % SZS status Theorem
% 2.10/2.28 % SZS output start Refutation
% See solution above
% 2.10/2.28 ------------ end of proof -------------
% 2.10/2.28
% 2.10/2.28
% 2.10/2.28 Search stopped by max_proofs option.
% 2.10/2.28
% 2.10/2.28
% 2.10/2.28 Search stopped by max_proofs option.
% 2.10/2.28
% 2.10/2.28 ============ end of search ============
% 2.10/2.28
% 2.10/2.28 -------------- statistics -------------
% 2.10/2.28 clauses given 15
% 2.10/2.28 clauses generated 157
% 2.10/2.28 clauses kept 128
% 2.10/2.28 clauses forward subsumed 102
% 2.10/2.28 clauses back subsumed 1
% 2.10/2.28 Kbytes malloced 976
% 2.10/2.28
% 2.10/2.28 ----------- times (seconds) -----------
% 2.10/2.28 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.10/2.28 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.10/2.28 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.10/2.28
% 2.10/2.28 That finishes the proof of the theorem.
% 2.10/2.28
% 2.10/2.28 Process 19425 finished Wed Jul 27 07:49:17 2022
% 2.10/2.28 Otter interrupted
% 2.10/2.28 PROOF FOUND
%------------------------------------------------------------------------------