TSTP Solution File: SEU047+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU047+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n005.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 13:14:42 EDT 2022

% Result   : Theorem 1.86s 2.08s
% Output   : Refutation 1.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    6
% Syntax   : Number of clauses     :    9 (   6 unt;   0 nHn;   8 RR)
%            Number of literals    :   14 (   7 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :    7 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(20,axiom,
    ( relation_rng_restriction(dollar_c10,relation_rng_restriction(dollar_c11,dollar_c9)) != relation_rng_restriction(dollar_c11,dollar_c9)
    | relation_rng_restriction(dollar_c11,relation_rng_restriction(dollar_c10,dollar_c9)) != relation_rng_restriction(dollar_c11,dollar_c9) ),
    file('SEU047+1.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ relation(A)
    | ~ subset(B,C)
    | relation_rng_restriction(C,relation_rng_restriction(B,A)) = relation_rng_restriction(B,A) ),
    file('SEU047+1.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ relation(A)
    | ~ subset(B,C)
    | relation_rng_restriction(B,relation_rng_restriction(C,A)) = relation_rng_restriction(B,A) ),
    file('SEU047+1.p',unknown),
    [] ).

cnf(25,axiom,
    A = A,
    file('SEU047+1.p',unknown),
    [] ).

cnf(48,axiom,
    relation(dollar_c9),
    file('SEU047+1.p',unknown),
    [] ).

cnf(50,axiom,
    subset(dollar_c11,dollar_c10),
    file('SEU047+1.p',unknown),
    [] ).

cnf(116,plain,
    relation_rng_restriction(dollar_c11,relation_rng_restriction(dollar_c10,dollar_c9)) = relation_rng_restriction(dollar_c11,dollar_c9),
    inference(hyper,[status(thm)],[50,22,48]),
    [iquote('hyper,50,22,48')] ).

cnf(128,plain,
    relation_rng_restriction(dollar_c10,relation_rng_restriction(dollar_c11,dollar_c9)) = relation_rng_restriction(dollar_c11,dollar_c9),
    inference(hyper,[status(thm)],[50,21,48]),
    [iquote('hyper,50,21,48')] ).

cnf(140,plain,
    $false,
    inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),128,116]),25,25]),
    [iquote('back_demod,20,demod,128,116,unit_del,25,25')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU047+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n005.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 07:59:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.86/2.08  ----- Otter 3.3f, August 2004 -----
% 1.86/2.08  The process was started by sandbox on n005.cluster.edu,
% 1.86/2.08  Wed Jul 27 07:59:35 2022
% 1.86/2.08  The command was "./otter".  The process ID is 19984.
% 1.86/2.08  
% 1.86/2.08  set(prolog_style_variables).
% 1.86/2.08  set(auto).
% 1.86/2.08     dependent: set(auto1).
% 1.86/2.08     dependent: set(process_input).
% 1.86/2.08     dependent: clear(print_kept).
% 1.86/2.08     dependent: clear(print_new_demod).
% 1.86/2.08     dependent: clear(print_back_demod).
% 1.86/2.08     dependent: clear(print_back_sub).
% 1.86/2.08     dependent: set(control_memory).
% 1.86/2.08     dependent: assign(max_mem, 12000).
% 1.86/2.08     dependent: assign(pick_given_ratio, 4).
% 1.86/2.08     dependent: assign(stats_level, 1).
% 1.86/2.08     dependent: assign(max_seconds, 10800).
% 1.86/2.08  clear(print_given).
% 1.86/2.08  
% 1.86/2.08  formula_list(usable).
% 1.86/2.08  all A (A=A).
% 1.86/2.08  all A B (in(A,B)-> -in(B,A)).
% 1.86/2.08  empty(empty_set).
% 1.86/2.08  relation(empty_set).
% 1.86/2.08  empty(empty_set).
% 1.86/2.08  relation(empty_set).
% 1.86/2.08  relation_empty_yielding(empty_set).
% 1.86/2.08  empty(empty_set).
% 1.86/2.08  all A B (in(A,B)->element(A,B)).
% 1.86/2.08  all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.86/2.08  all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.86/2.08  all A exists B element(B,A).
% 1.86/2.08  all A (empty(A)->function(A)).
% 1.86/2.08  all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.86/2.08  all A (-empty(powerset(A))).
% 1.86/2.08  all A (empty(A)->relation(A)).
% 1.86/2.08  all A B (element(A,B)->empty(B)|in(A,B)).
% 1.86/2.08  all A (empty(A)->A=empty_set).
% 1.86/2.08  all A B (-(in(A,B)&empty(B))).
% 1.86/2.08  all A B (-(empty(A)&A!=B&empty(B))).
% 1.86/2.08  all A B subset(A,A).
% 1.86/2.08  all A B (relation(B)->relation(relation_rng_restriction(A,B))).
% 1.86/2.08  all A B (relation(B)&function(B)->relation(relation_rng_restriction(A,B))&function(relation_rng_restriction(A,B))).
% 1.86/2.08  exists A (relation(A)&function(A)).
% 1.86/2.08  exists A (relation(A)&empty(A)&function(A)).
% 1.86/2.08  exists A (relation(A)&function(A)&one_to_one(A)).
% 1.86/2.08  all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.86/2.08  all A exists B (element(B,powerset(A))&empty(B)).
% 1.86/2.08  exists A (empty(A)&relation(A)).
% 1.86/2.08  exists A (-empty(A)&relation(A)).
% 1.86/2.08  exists A (relation(A)&relation_empty_yielding(A)).
% 1.86/2.08  exists A empty(A).
% 1.86/2.08  exists A (-empty(A)).
% 1.86/2.08  all A B (element(A,powerset(B))<->subset(A,B)).
% 1.86/2.08  -(all A B C (relation(C)&function(C)-> (subset(A,B)->relation_rng_restriction(B,relation_rng_restriction(A,C))=relation_rng_restriction(A,C)&relation_rng_restriction(A,relation_rng_restriction(B,C))=relation_rng_restriction(A,C)))).
% 1.86/2.08  all A B C (relation(C)-> (subset(A,B)->relation_rng_restriction(B,relation_rng_restriction(A,C))=relation_rng_restriction(A,C))).
% 1.86/2.08  all A B C (relation(C)-> (subset(A,B)->relation_rng_restriction(A,relation_rng_restriction(B,C))=relation_rng_restriction(A,C))).
% 1.86/2.08  end_of_list.
% 1.86/2.08  
% 1.86/2.08  -------> usable clausifies to:
% 1.86/2.08  
% 1.86/2.08  list(usable).
% 1.86/2.08  0 [] A=A.
% 1.86/2.08  0 [] -in(A,B)| -in(B,A).
% 1.86/2.08  0 [] empty(empty_set).
% 1.86/2.08  0 [] relation(empty_set).
% 1.86/2.08  0 [] empty(empty_set).
% 1.86/2.08  0 [] relation(empty_set).
% 1.86/2.08  0 [] relation_empty_yielding(empty_set).
% 1.86/2.08  0 [] empty(empty_set).
% 1.86/2.08  0 [] -in(A,B)|element(A,B).
% 1.86/2.08  0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.86/2.08  0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.86/2.08  0 [] element($f1(A),A).
% 1.86/2.08  0 [] -empty(A)|function(A).
% 1.86/2.08  0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.86/2.08  0 [] -empty(powerset(A)).
% 1.86/2.08  0 [] -empty(A)|relation(A).
% 1.86/2.08  0 [] -element(A,B)|empty(B)|in(A,B).
% 1.86/2.08  0 [] -empty(A)|A=empty_set.
% 1.86/2.08  0 [] -in(A,B)| -empty(B).
% 1.86/2.08  0 [] -empty(A)|A=B| -empty(B).
% 1.86/2.08  0 [] subset(A,A).
% 1.86/2.08  0 [] -relation(B)|relation(relation_rng_restriction(A,B)).
% 1.86/2.08  0 [] -relation(B)| -function(B)|relation(relation_rng_restriction(A,B)).
% 1.86/2.08  0 [] -relation(B)| -function(B)|function(relation_rng_restriction(A,B)).
% 1.86/2.08  0 [] relation($c1).
% 1.86/2.08  0 [] function($c1).
% 1.86/2.08  0 [] relation($c2).
% 1.86/2.08  0 [] empty($c2).
% 1.86/2.08  0 [] function($c2).
% 1.86/2.08  0 [] relation($c3).
% 1.86/2.08  0 [] function($c3).
% 1.86/2.08  0 [] one_to_one($c3).
% 1.86/2.08  0 [] empty(A)|element($f2(A),powerset(A)).
% 1.86/2.08  0 [] empty(A)| -empty($f2(A)).
% 1.86/2.08  0 [] element($f3(A),powerset(A)).
% 1.86/2.08  0 [] empty($f3(A)).
% 1.86/2.08  0 [] empty($c4).
% 1.86/2.08  0 [] relation($c4).
% 1.86/2.08  0 [] -empty($c5).
% 1.86/2.08  0 [] relation($c5).
% 1.86/2.08  0 [] relation($c6).
% 1.86/2.08  0 [] relation_empty_yielding($c6).
% 1.86/2.08  0 [] empty($c7).
% 1.86/2.08  0 [] -empty($c8).
% 1.86/2.08  0 [] -element(A,powerset(B))|subset(A,B).
% 1.86/2.08  0 [] element(A,powerset(B))| -subset(A,B).
% 1.86/2.08  0 [] relation($c9).
% 1.86/2.08  0 [] function($c9).
% 1.86/2.08  0 [] subset($c11,$c10).
% 1.86/2.08  0 [] relation_rng_restriction($c10,relation_rng_restriction($c11,$c9))!=relation_rng_restriction($c11,$c9)|relation_rng_restriction($c11,relation_rng_restriction($c10,$c9))!=relation_rng_restriction($c11,$c9).
% 1.86/2.08  0 [] -relation(C)| -subset(A,B)|relation_rng_restriction(B,relation_rng_restriction(A,C))=relation_rng_restriction(A,C).
% 1.86/2.08  0 [] -relation(C)| -subset(A,B)|relation_rng_restriction(A,relation_rng_restriction(B,C))=relation_rng_restriction(A,C).
% 1.86/2.08  end_of_list.
% 1.86/2.08  
% 1.86/2.08  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.86/2.08  
% 1.86/2.08  This ia a non-Horn set with equality.  The strategy will be
% 1.86/2.08  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.86/2.08  deletion, with positive clauses in sos and nonpositive
% 1.86/2.08  clauses in usable.
% 1.86/2.08  
% 1.86/2.08     dependent: set(knuth_bendix).
% 1.86/2.08     dependent: set(anl_eq).
% 1.86/2.08     dependent: set(para_from).
% 1.86/2.08     dependent: set(para_into).
% 1.86/2.08     dependent: clear(para_from_right).
% 1.86/2.08     dependent: clear(para_into_right).
% 1.86/2.08     dependent: set(para_from_vars).
% 1.86/2.08     dependent: set(eq_units_both_ways).
% 1.86/2.08     dependent: set(dynamic_demod_all).
% 1.86/2.08     dependent: set(dynamic_demod).
% 1.86/2.08     dependent: set(order_eq).
% 1.86/2.08     dependent: set(back_demod).
% 1.86/2.08     dependent: set(lrpo).
% 1.86/2.08     dependent: set(hyper_res).
% 1.86/2.08     dependent: set(unit_deletion).
% 1.86/2.08     dependent: set(factor).
% 1.86/2.08  
% 1.86/2.08  ------------> process usable:
% 1.86/2.08  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.86/2.08  ** KEPT (pick-wt=6): 2 [] -in(A,B)|element(A,B).
% 1.86/2.08  ** KEPT (pick-wt=10): 3 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.86/2.08  ** KEPT (pick-wt=9): 4 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.86/2.08  ** KEPT (pick-wt=4): 5 [] -empty(A)|function(A).
% 1.86/2.08  ** KEPT (pick-wt=8): 6 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.86/2.08  ** KEPT (pick-wt=3): 7 [] -empty(powerset(A)).
% 1.86/2.08  ** KEPT (pick-wt=4): 8 [] -empty(A)|relation(A).
% 1.86/2.08  ** KEPT (pick-wt=8): 9 [] -element(A,B)|empty(B)|in(A,B).
% 1.86/2.08  ** KEPT (pick-wt=5): 10 [] -empty(A)|A=empty_set.
% 1.86/2.08  ** KEPT (pick-wt=5): 11 [] -in(A,B)| -empty(B).
% 1.86/2.08  ** KEPT (pick-wt=7): 12 [] -empty(A)|A=B| -empty(B).
% 1.86/2.08  ** KEPT (pick-wt=6): 13 [] -relation(A)|relation(relation_rng_restriction(B,A)).
% 1.86/2.08    Following clause subsumed by 13 during input processing: 0 [] -relation(A)| -function(A)|relation(relation_rng_restriction(B,A)).
% 1.86/2.08  ** KEPT (pick-wt=8): 14 [] -relation(A)| -function(A)|function(relation_rng_restriction(B,A)).
% 1.86/2.08  ** KEPT (pick-wt=5): 15 [] empty(A)| -empty($f2(A)).
% 1.86/2.08  ** KEPT (pick-wt=2): 16 [] -empty($c5).
% 1.86/2.08  ** KEPT (pick-wt=2): 17 [] -empty($c8).
% 1.86/2.08  ** KEPT (pick-wt=7): 18 [] -element(A,powerset(B))|subset(A,B).
% 1.86/2.08  ** KEPT (pick-wt=7): 19 [] element(A,powerset(B))| -subset(A,B).
% 1.86/2.08  ** KEPT (pick-wt=18): 20 [] relation_rng_restriction($c10,relation_rng_restriction($c11,$c9))!=relation_rng_restriction($c11,$c9)|relation_rng_restriction($c11,relation_rng_restriction($c10,$c9))!=relation_rng_restriction($c11,$c9).
% 1.86/2.08  ** KEPT (pick-wt=14): 21 [] -relation(A)| -subset(B,C)|relation_rng_restriction(C,relation_rng_restriction(B,A))=relation_rng_restriction(B,A).
% 1.86/2.08  ** KEPT (pick-wt=14): 22 [] -relation(A)| -subset(B,C)|relation_rng_restriction(B,relation_rng_restriction(C,A))=relation_rng_restriction(B,A).
% 1.86/2.08  
% 1.86/2.08  ------------> process sos:
% 1.86/2.08  ** KEPT (pick-wt=3): 25 [] A=A.
% 1.86/2.08  ** KEPT (pick-wt=2): 26 [] empty(empty_set).
% 1.86/2.08  ** KEPT (pick-wt=2): 27 [] relation(empty_set).
% 1.86/2.08    Following clause subsumed by 26 during input processing: 0 [] empty(empty_set).
% 1.86/2.08    Following clause subsumed by 27 during input processing: 0 [] relation(empty_set).
% 1.86/2.08  ** KEPT (pick-wt=2): 28 [] relation_empty_yielding(empty_set).
% 1.86/2.08    Following clause subsumed by 26 during input processing: 0 [] empty(empty_set).
% 1.86/2.08  ** KEPT (pick-wt=4): 29 [] element($f1(A),A).
% 1.86/2.08  ** KEPT (pick-wt=3): 30 [] subset(A,A).
% 1.86/2.08  ** KEPT (pick-wt=2): 31 [] relation($c1).
% 1.86/2.08  ** KEPT (pick-wt=2): 32 [] function($c1).
% 1.86/2.08  ** KEPT (pick-wt=2): 33 [] relation($c2).
% 1.86/2.08  ** KEPT (pick-wt=2): 34 [] empty($c2).
% 1.86/2.08  ** KEPT (pick-wt=2): 35 [] function($c2).
% 1.86/2.08  ** KEPT (pick-wt=2): 36 [] relation($c3).
% 1.86/2.08  ** KEPT (pick-wt=2): 37 [] function($c3).
% 1.86/2.08  ** KEPT (pick-wt=2): 38 [] one_to_one($c3).
% 1.86/2.08  ** KEPT (pick-wt=7): 39 [] empty(A)|element($f2(A),powerset(A)).
% 1.86/2.08  ** KEPT (pick-wt=5): 40 [] element($f3(A),powerset(A)).
% 1.86/2.08  ** KEPT (pick-wt=3): 41 [] empty($f3(A)).
% 1.86/2.08  ** KEPT (pick-wt=2): 42 [] empty($c4).
% 1.86/2.08  ** KEPT (pick-wt=2): 43 [] relation($c4).
% 1.86/2.08  ** KEPT (pick-wt=2): 44 [] relation($c5).
% 1.86/2.08  ** KEPT (pick-wt=2): 45 [] relation($c6).
% 1.86/2.08  ** KEPT (pick-wt=2): 46 [] relation_empty_yielding($c6).
% 1.86/2.08  ** KEPT (pick-wt=2): 47 [] empty($c7).
% 1.86/2.08  ** KEPT (pick-wt=2): 48 [] relation($c9).
% 1.86/2.08  ** KEPT (pick-wt=2): 49 [] function($c9).
% 1.86/2.08  ** KEPT (pick-wt=3): 50 [] subset($c11,$c10).
% 1.86/2.08    Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] A=A.
% 1.86/2.08  25 back subsumes 24.
% 1.86/2.08  
% 1.86/2.08  ======= end of input processing =======
% 1.86/2.08  
% 1.86/2.08  =========== start of search ===========
% 1.86/2.08  
% 1.86/2.08  -------- PROOF -------- 
% 1.86/2.08  
% 1.86/2.08  -----> EMPTY CLAUSE at   0.00 sec ----> 140 [back_demod,20,demod,128,116,unit_del,25,25] $F.
% 1.86/2.08  
% 1.86/2.08  Length of proof is 2.  Level of proof is 1.
% 1.86/2.08  
% 1.86/2.08  ---------------- PROOF ----------------
% 1.86/2.08  % SZS status Theorem
% 1.86/2.08  % SZS output start Refutation
% See solution above
% 1.86/2.08  ------------ end of proof -------------
% 1.86/2.08  
% 1.86/2.08  
% 1.86/2.08  Search stopped by max_proofs option.
% 1.86/2.08  
% 1.86/2.08  
% 1.86/2.08  Search stopped by max_proofs option.
% 1.86/2.08  
% 1.86/2.08  ============ end of search ============
% 1.86/2.08  
% 1.86/2.08  -------------- statistics -------------
% 1.86/2.08  clauses given                 27
% 1.86/2.08  clauses generated            125
% 1.86/2.08  clauses kept                 117
% 1.86/2.08  clauses forward subsumed      77
% 1.86/2.08  clauses back subsumed          3
% 1.86/2.08  Kbytes malloced              976
% 1.86/2.08  
% 1.86/2.08  ----------- times (seconds) -----------
% 1.86/2.08  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.86/2.08  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.86/2.08  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.86/2.08  
% 1.86/2.08  That finishes the proof of the theorem.
% 1.86/2.08  
% 1.86/2.08  Process 19984 finished Wed Jul 27 07:59:37 2022
% 1.86/2.08  Otter interrupted
% 1.86/2.08  PROOF FOUND
%------------------------------------------------------------------------------