TSTP Solution File: SET978+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n003.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 13:14:37 EDT 2022

% Result   : Theorem 1.70s 1.91s
% Output   : Refutation 1.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   2 unt;   3 nHn;   3 RR)
%            Number of literals    :   14 (   4 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ( ~ disjoint(A,B)
    | disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    file('SET978+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ disjoint(A,B)
    | disjoint(cartesian_product2(C,A),cartesian_product2(D,B)) ),
    file('SET978+1.p',unknown),
    [] ).

cnf(5,axiom,
    dollar_c6 != dollar_c5,
    file('SET978+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ disjoint(cartesian_product2(singleton(dollar_c6),dollar_c4),cartesian_product2(singleton(dollar_c5),dollar_c3))
    | ~ disjoint(cartesian_product2(dollar_c4,singleton(dollar_c6)),cartesian_product2(dollar_c3,singleton(dollar_c5))) ),
    file('SET978+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( A = B
    | disjoint(singleton(A),singleton(B)) ),
    file('SET978+1.p',unknown),
    [] ).

cnf(10,plain,
    ( A = B
    | disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ),
    inference(hyper,[status(thm)],[9,4]),
    [iquote('hyper,9,4')] ).

cnf(11,plain,
    ( A = B
    | disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ),
    inference(hyper,[status(thm)],[9,3]),
    [iquote('hyper,9,3')] ).

cnf(172,plain,
    $false,
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[11,6,10]),5,5]),
    [iquote('hyper,11,6,10,unit_del,5,5')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n003.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 10:26:26 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.70/1.91  ----- Otter 3.3f, August 2004 -----
% 1.70/1.91  The process was started by sandbox on n003.cluster.edu,
% 1.70/1.91  Wed Jul 27 10:26:26 2022
% 1.70/1.91  The command was "./otter".  The process ID is 1463.
% 1.70/1.91  
% 1.70/1.91  set(prolog_style_variables).
% 1.70/1.91  set(auto).
% 1.70/1.91     dependent: set(auto1).
% 1.70/1.91     dependent: set(process_input).
% 1.70/1.91     dependent: clear(print_kept).
% 1.70/1.91     dependent: clear(print_new_demod).
% 1.70/1.91     dependent: clear(print_back_demod).
% 1.70/1.91     dependent: clear(print_back_sub).
% 1.70/1.91     dependent: set(control_memory).
% 1.70/1.91     dependent: assign(max_mem, 12000).
% 1.70/1.91     dependent: assign(pick_given_ratio, 4).
% 1.70/1.91     dependent: assign(stats_level, 1).
% 1.70/1.91     dependent: assign(max_seconds, 10800).
% 1.70/1.91  clear(print_given).
% 1.70/1.91  
% 1.70/1.91  formula_list(usable).
% 1.70/1.91  all A (A=A).
% 1.70/1.91  exists A empty(A).
% 1.70/1.91  exists A (-empty(A)).
% 1.70/1.91  all A B (disjoint(A,B)->disjoint(B,A)).
% 1.70/1.91  all A B C D (disjoint(A,B)|disjoint(C,D)->disjoint(cartesian_product2(A,C),cartesian_product2(B,D))).
% 1.70/1.91  -(all A B C D (A!=B->disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))&disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))))).
% 1.70/1.91  all A B (A!=B->disjoint(singleton(A),singleton(B))).
% 1.70/1.91  end_of_list.
% 1.70/1.91  
% 1.70/1.91  -------> usable clausifies to:
% 1.70/1.91  
% 1.70/1.91  list(usable).
% 1.70/1.91  0 [] A=A.
% 1.70/1.91  0 [] empty($c1).
% 1.70/1.91  0 [] -empty($c2).
% 1.70/1.91  0 [] -disjoint(A,B)|disjoint(B,A).
% 1.70/1.91  0 [] -disjoint(A,B)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.91  0 [] -disjoint(C,D)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.91  0 [] $c6!=$c5.
% 1.70/1.91  0 [] -disjoint(cartesian_product2(singleton($c6),$c4),cartesian_product2(singleton($c5),$c3))| -disjoint(cartesian_product2($c4,singleton($c6)),cartesian_product2($c3,singleton($c5))).
% 1.70/1.91  0 [] A=B|disjoint(singleton(A),singleton(B)).
% 1.70/1.91  end_of_list.
% 1.70/1.91  
% 1.70/1.91  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.70/1.91  
% 1.70/1.91  This ia a non-Horn set with equality.  The strategy will be
% 1.70/1.91  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.91  deletion, with positive clauses in sos and nonpositive
% 1.70/1.91  clauses in usable.
% 1.70/1.91  
% 1.70/1.91     dependent: set(knuth_bendix).
% 1.70/1.91     dependent: set(anl_eq).
% 1.70/1.91     dependent: set(para_from).
% 1.70/1.91     dependent: set(para_into).
% 1.70/1.91     dependent: clear(para_from_right).
% 1.70/1.91     dependent: clear(para_into_right).
% 1.70/1.91     dependent: set(para_from_vars).
% 1.70/1.91     dependent: set(eq_units_both_ways).
% 1.70/1.91     dependent: set(dynamic_demod_all).
% 1.70/1.91     dependent: set(dynamic_demod).
% 1.70/1.91     dependent: set(order_eq).
% 1.70/1.91     dependent: set(back_demod).
% 1.70/1.91     dependent: set(lrpo).
% 1.70/1.91     dependent: set(hyper_res).
% 1.70/1.91     dependent: set(unit_deletion).
% 1.70/1.91     dependent: set(factor).
% 1.70/1.91  
% 1.70/1.91  ------------> process usable:
% 1.70/1.91  ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.70/1.91  ** KEPT (pick-wt=6): 2 [] -disjoint(A,B)|disjoint(B,A).
% 1.70/1.91  ** KEPT (pick-wt=10): 3 [] -disjoint(A,B)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.91  ** KEPT (pick-wt=10): 4 [] -disjoint(A,B)|disjoint(cartesian_product2(C,A),cartesian_product2(D,B)).
% 1.70/1.91  ** KEPT (pick-wt=3): 5 [] $c6!=$c5.
% 1.70/1.91  ** KEPT (pick-wt=18): 6 [] -disjoint(cartesian_product2(singleton($c6),$c4),cartesian_product2(singleton($c5),$c3))| -disjoint(cartesian_product2($c4,singleton($c6)),cartesian_product2($c3,singleton($c5))).
% 1.70/1.91  
% 1.70/1.91  ------------> process sos:
% 1.70/1.91  ** KEPT (pick-wt=3): 7 [] A=A.
% 1.70/1.91  ** KEPT (pick-wt=2): 8 [] empty($c1).
% 1.70/1.91  ** KEPT (pick-wt=8): 9 [] A=B|disjoint(singleton(A),singleton(B)).
% 1.70/1.91    Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.70/1.91  
% 1.70/1.91  ======= end of input processing =======
% 1.70/1.91  
% 1.70/1.91  =========== start of search ===========
% 1.70/1.91  
% 1.70/1.91  -------- PROOF -------- 
% 1.70/1.91  
% 1.70/1.91  -----> EMPTY CLAUSE at   0.01 sec ----> 172 [hyper,11,6,10,unit_del,5,5] $F.
% 1.70/1.91  
% 1.70/1.91  Length of proof is 2.  Level of proof is 1.
% 1.70/1.91  
% 1.70/1.91  ---------------- PROOF ----------------
% 1.70/1.91  % SZS status Theorem
% 1.70/1.91  % SZS output start Refutation
% See solution above
% 1.70/1.91  ------------ end of proof -------------
% 1.70/1.91  
% 1.70/1.91  
% 1.70/1.91  Search stopped by max_proofs option.
% 1.70/1.91  
% 1.70/1.91  
% 1.70/1.91  Search stopped by max_proofs option.
% 1.70/1.91  
% 1.70/1.91  ============ end of search ============
% 1.70/1.91  
% 1.70/1.91  -------------- statistics -------------
% 1.70/1.91  clauses given                 11
% 1.70/1.91  clauses generated            190
% 1.70/1.91  clauses kept                 171
% 1.70/1.91  clauses forward subsumed      28
% 1.70/1.91  clauses back subsumed          0
% 1.70/1.91  Kbytes malloced              976
% 1.70/1.91  
% 1.70/1.91  ----------- times (seconds) -----------
% 1.70/1.91  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.70/1.91  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.70/1.91  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.70/1.91  
% 1.70/1.91  That finishes the proof of the theorem.
% 1.70/1.91  
% 1.70/1.91  Process 1463 finished Wed Jul 27 10:26:28 2022
% 1.70/1.91  Otter interrupted
% 1.70/1.91  PROOF FOUND
%------------------------------------------------------------------------------