TSTP Solution File: SET604+3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET604+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n022.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 13:13:49 EDT 2022

% Result   : Theorem 1.73s 1.94s
% Output   : Refutation 1.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   4 unt;   0 nHn;   3 RR)
%            Number of literals    :    6 (   3 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    4 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( difference(A,B) = empty_set
    | ~ subset(A,B) ),
    file('SET604+3.p',unknown),
    [] ).

cnf(13,axiom,
    difference(empty_set,dollar_c1) != empty_set,
    file('SET604+3.p',unknown),
    [] ).

cnf(16,axiom,
    subset(empty_set,A),
    file('SET604+3.p',unknown),
    [] ).

cnf(20,plain,
    difference(empty_set,A) = empty_set,
    inference(hyper,[status(thm)],[16,2]),
    [iquote('hyper,16,2')] ).

cnf(22,plain,
    $false,
    inference(binary,[status(thm)],[20,13]),
    [iquote('binary,20.1,13.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET604+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Jul 27 10:42:35 EDT 2022
% 0.19/0.33  % CPUTime  : 
% 1.73/1.94  ----- Otter 3.3f, August 2004 -----
% 1.73/1.94  The process was started by sandbox2 on n022.cluster.edu,
% 1.73/1.94  Wed Jul 27 10:42:35 2022
% 1.73/1.94  The command was "./otter".  The process ID is 26464.
% 1.73/1.94  
% 1.73/1.94  set(prolog_style_variables).
% 1.73/1.94  set(auto).
% 1.73/1.94     dependent: set(auto1).
% 1.73/1.94     dependent: set(process_input).
% 1.73/1.94     dependent: clear(print_kept).
% 1.73/1.94     dependent: clear(print_new_demod).
% 1.73/1.94     dependent: clear(print_back_demod).
% 1.73/1.94     dependent: clear(print_back_sub).
% 1.73/1.94     dependent: set(control_memory).
% 1.73/1.94     dependent: assign(max_mem, 12000).
% 1.73/1.94     dependent: assign(pick_given_ratio, 4).
% 1.73/1.94     dependent: assign(stats_level, 1).
% 1.73/1.94     dependent: assign(max_seconds, 10800).
% 1.73/1.94  clear(print_given).
% 1.73/1.94  
% 1.73/1.94  formula_list(usable).
% 1.73/1.94  all A (A=A).
% 1.73/1.94  all B subset(empty_set,B).
% 1.73/1.94  all B C (difference(B,C)=empty_set<->subset(B,C)).
% 1.73/1.94  all B (-member(B,empty_set)).
% 1.73/1.94  all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.73/1.94  all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.73/1.94  all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.73/1.94  all B subset(B,B).
% 1.73/1.94  all B (empty(B)<-> (all C (-member(C,B)))).
% 1.73/1.94  -(all B (difference(empty_set,B)=empty_set)).
% 1.73/1.94  end_of_list.
% 1.73/1.94  
% 1.73/1.94  -------> usable clausifies to:
% 1.73/1.94  
% 1.73/1.94  list(usable).
% 1.73/1.94  0 [] A=A.
% 1.73/1.94  0 [] subset(empty_set,B).
% 1.73/1.94  0 [] difference(B,C)!=empty_set|subset(B,C).
% 1.73/1.94  0 [] difference(B,C)=empty_set| -subset(B,C).
% 1.73/1.94  0 [] -member(B,empty_set).
% 1.73/1.94  0 [] -member(D,difference(B,C))|member(D,B).
% 1.73/1.94  0 [] -member(D,difference(B,C))| -member(D,C).
% 1.73/1.94  0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.73/1.94  0 [] B!=C|subset(B,C).
% 1.73/1.94  0 [] B!=C|subset(C,B).
% 1.73/1.94  0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.73/1.94  0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.73/1.94  0 [] subset(B,C)|member($f1(B,C),B).
% 1.73/1.94  0 [] subset(B,C)| -member($f1(B,C),C).
% 1.73/1.94  0 [] subset(B,B).
% 1.73/1.94  0 [] -empty(B)| -member(C,B).
% 1.73/1.94  0 [] empty(B)|member($f2(B),B).
% 1.73/1.94  0 [] difference(empty_set,$c1)!=empty_set.
% 1.73/1.94  end_of_list.
% 1.73/1.94  
% 1.73/1.94  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.73/1.94  
% 1.73/1.94  This ia a non-Horn set with equality.  The strategy will be
% 1.73/1.94  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.94  deletion, with positive clauses in sos and nonpositive
% 1.73/1.94  clauses in usable.
% 1.73/1.94  
% 1.73/1.94     dependent: set(knuth_bendix).
% 1.73/1.94     dependent: set(anl_eq).
% 1.73/1.94     dependent: set(para_from).
% 1.73/1.94     dependent: set(para_into).
% 1.73/1.94     dependent: clear(para_from_right).
% 1.73/1.94     dependent: clear(para_into_right).
% 1.73/1.94     dependent: set(para_from_vars).
% 1.73/1.94     dependent: set(eq_units_both_ways).
% 1.73/1.94     dependent: set(dynamic_demod_all).
% 1.73/1.94     dependent: set(dynamic_demod).
% 1.73/1.94     dependent: set(order_eq).
% 1.73/1.94     dependent: set(back_demod).
% 1.73/1.94     dependent: set(lrpo).
% 1.73/1.94     dependent: set(hyper_res).
% 1.73/1.94     dependent: set(unit_deletion).
% 1.73/1.94     dependent: set(factor).
% 1.73/1.94  
% 1.73/1.94  ------------> process usable:
% 1.73/1.94  ** KEPT (pick-wt=8): 1 [] difference(A,B)!=empty_set|subset(A,B).
% 1.73/1.94  ** KEPT (pick-wt=8): 2 [] difference(A,B)=empty_set| -subset(A,B).
% 1.73/1.94  ** KEPT (pick-wt=3): 3 [] -member(A,empty_set).
% 1.73/1.94  ** KEPT (pick-wt=8): 4 [] -member(A,difference(B,C))|member(A,B).
% 1.73/1.94  ** KEPT (pick-wt=8): 5 [] -member(A,difference(B,C))| -member(A,C).
% 1.73/1.94  ** KEPT (pick-wt=11): 6 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.73/1.94  ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.73/1.94  ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.73/1.94  ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.73/1.94  ** KEPT (pick-wt=9): 10 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.73/1.94  ** KEPT (pick-wt=8): 11 [] subset(A,B)| -member($f1(A,B),B).
% 1.73/1.94  ** KEPT (pick-wt=5): 12 [] -empty(A)| -member(B,A).
% 1.73/1.94  ** KEPT (pick-wt=5): 13 [] difference(empty_set,$c1)!=empty_set.
% 1.73/1.94  
% 1.73/1.94  ------------> process sos:
% 1.73/1.94  ** KEPT (pick-wt=3): 15 [] A=A.
% 1.73/1.94  ** KEPT (pick-wt=3): 16 [] subset(empty_set,A).
% 1.73/1.94  ** KEPT (pick-wt=8): 17 [] subset(A,B)|member($f1(A,B),A).
% 1.73/1.94  ** KEPT (pick-wt=3): 18 [] subset(A,A).
% 1.73/1.94  ** KEPT (pick-wt=6): 19 [] empty(A)|member($f2(A),A).
% 1.73/1.94    Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.73/1.94  15 back subsumes 14.
% 1.73/1.94  
% 1.73/1.94  ======= end of input processing =======
% 1.73/1.94  
% 1.73/1.94  =========== start of search ===========
% 1.73/1.94  
% 1.73/1.94  -------- PROOF -------- 
% 1.73/1.94  
% 1.73/1.94  ----> UNIT CONFLICT at   0.00 sec ----> 22 [binary,20.1,13.1] $F.
% 1.73/1.94  
% 1.73/1.94  Length of proof is 1.  Level of proof is 1.
% 1.73/1.94  
% 1.73/1.94  ---------------- PROOF ----------------
% 1.73/1.94  % SZS status Theorem
% 1.73/1.94  % SZS output start Refutation
% See solution above
% 1.73/1.94  ------------ end of proof -------------
% 1.73/1.94  
% 1.73/1.94  
% 1.73/1.94  Search stopped by max_proofs option.
% 1.73/1.94  
% 1.73/1.94  
% 1.73/1.94  Search stopped by max_proofs option.
% 1.73/1.94  
% 1.73/1.94  ============ end of search ============
% 1.73/1.94  
% 1.73/1.94  -------------- statistics -------------
% 1.73/1.94  clauses given                  2
% 1.73/1.94  clauses generated              6
% 1.73/1.94  clauses kept                  20
% 1.73/1.94  clauses forward subsumed       5
% 1.73/1.94  clauses back subsumed          1
% 1.73/1.94  Kbytes malloced              976
% 1.73/1.94  
% 1.73/1.94  ----------- times (seconds) -----------
% 1.73/1.94  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.73/1.94  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.73/1.94  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.73/1.94  
% 1.73/1.94  That finishes the proof of the theorem.
% 1.73/1.94  
% 1.73/1.94  Process 26464 finished Wed Jul 27 10:42:37 2022
% 1.73/1.94  Otter interrupted
% 1.73/1.94  PROOF FOUND
%------------------------------------------------------------------------------