TSTP Solution File: SET012-4 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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 13:12:47 EDT 2022

% Result   : Unsatisfiable 3.44s 3.66s
% Output   : Refutation 3.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   17 (   7 unt;   5 nHn;  12 RR)
%            Number of literals    :   33 (  10 equ;  13 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   17 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ member(f1(A,B),A)
    | ~ member(f1(A,B),B)
    | A = B ),
    file('SET012-4.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ member(A,complement(B))
    | ~ member(A,B) ),
    file('SET012-4.p',unknown),
    [] ).

cnf(4,axiom,
    ( member(A,complement(B))
    | ~ little_set(A)
    | member(A,B) ),
    file('SET012-4.p',unknown),
    [] ).

cnf(7,axiom,
    as != cs,
    file('SET012-4.p',unknown),
    [] ).

cnf(8,plain,
    cs != as,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
    [iquote('copy,7,flip.1')] ).

cnf(11,axiom,
    ( little_set(f1(A,B))
    | A = B ),
    file('SET012-4.p',unknown),
    [] ).

cnf(12,axiom,
    ( member(f1(A,B),A)
    | member(f1(A,B),B)
    | A = B ),
    file('SET012-4.p',unknown),
    [] ).

cnf(14,axiom,
    complement(as) = bs,
    file('SET012-4.p',unknown),
    [] ).

cnf(16,axiom,
    complement(bs) = cs,
    file('SET012-4.p',unknown),
    [] ).

cnf(20,plain,
    ( ~ member(A,bs)
    | ~ member(A,as) ),
    inference(para_from,[status(thm),theory(equality)],[14,3]),
    [iquote('para_from,13.1.1,3.1.2')] ).

cnf(22,plain,
    ( A = cs
    | ~ member(f1(cs,A),cs)
    | ~ member(f1(cs,A),A) ),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,2]),16,16,16]),
    [iquote('para_into,15.1.1,2.3.1,demod,16,16,16')] ).

cnf(24,plain,
    ( ~ member(A,cs)
    | ~ member(A,bs) ),
    inference(para_from,[status(thm),theory(equality)],[16,3]),
    [iquote('para_from,15.1.1,3.1.2')] ).

cnf(30,plain,
    ( A = B
    | member(f1(A,B),complement(C))
    | member(f1(A,B),C) ),
    inference(hyper,[status(thm)],[11,4]),
    [iquote('hyper,11,4')] ).

cnf(2094,plain,
    ( A = as
    | member(f1(A,as),cs)
    | member(f1(A,as),A) ),
    inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[30,20,12]),16])]),
    [iquote('hyper,30,20,12,demod,16,factor_simp')] ).

cnf(2173,plain,
    member(f1(cs,as),cs),
    inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[2094]),8]),
    [iquote('factor,2094.2.3,unit_del,8')] ).

cnf(2482,plain,
    member(f1(cs,as),bs),
    inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2173,22,30]),14]),8,8]),
    [iquote('hyper,2173,22,30,demod,14,unit_del,8,8')] ).

cnf(3677,plain,
    $false,
    inference(hyper,[status(thm)],[2482,24,2173]),
    [iquote('hyper,2482,24,2173')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.09/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n023.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 11:05:48 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 3.44/3.66  ----- Otter 3.3f, August 2004 -----
% 3.44/3.66  The process was started by sandbox on n023.cluster.edu,
% 3.44/3.66  Wed Jul 27 11:05:48 2022
% 3.44/3.66  The command was "./otter".  The process ID is 31734.
% 3.44/3.66  
% 3.44/3.66  set(prolog_style_variables).
% 3.44/3.66  set(auto).
% 3.44/3.66     dependent: set(auto1).
% 3.44/3.66     dependent: set(process_input).
% 3.44/3.66     dependent: clear(print_kept).
% 3.44/3.66     dependent: clear(print_new_demod).
% 3.44/3.66     dependent: clear(print_back_demod).
% 3.44/3.66     dependent: clear(print_back_sub).
% 3.44/3.66     dependent: set(control_memory).
% 3.44/3.66     dependent: assign(max_mem, 12000).
% 3.44/3.66     dependent: assign(pick_given_ratio, 4).
% 3.44/3.66     dependent: assign(stats_level, 1).
% 3.44/3.66     dependent: assign(max_seconds, 10800).
% 3.44/3.66  clear(print_given).
% 3.44/3.66  
% 3.44/3.66  list(usable).
% 3.44/3.66  0 [] A=A.
% 3.44/3.66  0 [] -member(X,Y)|little_set(X).
% 3.44/3.66  0 [] little_set(f1(X,Y))|X=Y.
% 3.44/3.66  0 [] member(f1(X,Y),X)|member(f1(X,Y),Y)|X=Y.
% 3.44/3.66  0 [] -member(f1(X,Y),X)| -member(f1(X,Y),Y)|X=Y.
% 3.44/3.66  0 [] -member(Z,complement(X))| -member(Z,X).
% 3.44/3.66  0 [] member(Z,complement(X))| -little_set(Z)|member(Z,X).
% 3.44/3.66  0 [] -member(Z,empty_set).
% 3.44/3.66  0 [] member(Z,universal_set)| -little_set(Z).
% 3.44/3.66  0 [] complement(as)=bs.
% 3.44/3.66  0 [] complement(bs)=cs.
% 3.44/3.66  0 [] as!=cs.
% 3.44/3.66  end_of_list.
% 3.44/3.66  
% 3.44/3.66  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 3.44/3.66  
% 3.44/3.66  This ia a non-Horn set with equality.  The strategy will be
% 3.44/3.66  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.44/3.66  deletion, with positive clauses in sos and nonpositive
% 3.44/3.66  clauses in usable.
% 3.44/3.66  
% 3.44/3.66     dependent: set(knuth_bendix).
% 3.44/3.66     dependent: set(anl_eq).
% 3.44/3.66     dependent: set(para_from).
% 3.44/3.66     dependent: set(para_into).
% 3.44/3.66     dependent: clear(para_from_right).
% 3.44/3.66     dependent: clear(para_into_right).
% 3.44/3.66     dependent: set(para_from_vars).
% 3.44/3.66     dependent: set(eq_units_both_ways).
% 3.44/3.66     dependent: set(dynamic_demod_all).
% 3.44/3.66     dependent: set(dynamic_demod).
% 3.44/3.66     dependent: set(order_eq).
% 3.44/3.66     dependent: set(back_demod).
% 3.44/3.66     dependent: set(lrpo).
% 3.44/3.66     dependent: set(hyper_res).
% 3.44/3.66     dependent: set(unit_deletion).
% 3.44/3.66     dependent: set(factor).
% 3.44/3.66  
% 3.44/3.66  ------------> process usable:
% 3.44/3.66  ** KEPT (pick-wt=5): 1 [] -member(A,B)|little_set(A).
% 3.44/3.66  ** KEPT (pick-wt=13): 2 [] -member(f1(A,B),A)| -member(f1(A,B),B)|A=B.
% 3.44/3.66  ** KEPT (pick-wt=7): 3 [] -member(A,complement(B))| -member(A,B).
% 3.44/3.66  ** KEPT (pick-wt=9): 4 [] member(A,complement(B))| -little_set(A)|member(A,B).
% 3.44/3.66  ** KEPT (pick-wt=3): 5 [] -member(A,empty_set).
% 3.44/3.66  ** KEPT (pick-wt=5): 6 [] member(A,universal_set)| -little_set(A).
% 3.44/3.66  ** KEPT (pick-wt=3): 8 [copy,7,flip.1] cs!=as.
% 3.44/3.66  
% 3.44/3.66  ------------> process sos:
% 3.44/3.66  ** KEPT (pick-wt=3): 10 [] A=A.
% 3.44/3.66  ** KEPT (pick-wt=7): 11 [] little_set(f1(A,B))|A=B.
% 3.44/3.66  ** KEPT (pick-wt=13): 12 [] member(f1(A,B),A)|member(f1(A,B),B)|A=B.
% 3.44/3.66  ** KEPT (pick-wt=4): 13 [] complement(as)=bs.
% 3.44/3.66  ---> New Demodulator: 14 [new_demod,13] complement(as)=bs.
% 3.44/3.66  ** KEPT (pick-wt=4): 15 [] complement(bs)=cs.
% 3.44/3.66  ---> New Demodulator: 16 [new_demod,15] complement(bs)=cs.
% 3.44/3.66    Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 3.44/3.66  10 back subsumes 9.
% 3.44/3.66  >>>> Starting back demodulation with 14.
% 3.44/3.66  >>>> Starting back demodulation with 16.
% 3.44/3.66  
% 3.44/3.66  ======= end of input processing =======
% 3.44/3.66  
% 3.44/3.66  =========== start of search ===========
% 3.44/3.66  
% 3.44/3.66  -------- PROOF -------- 
% 3.44/3.66  
% 3.44/3.66  -----> EMPTY CLAUSE at   1.57 sec ----> 3677 [hyper,2482,24,2173] $F.
% 3.44/3.66  
% 3.44/3.66  Length of proof is 8.  Level of proof is 4.
% 3.44/3.66  
% 3.44/3.66  ---------------- PROOF ----------------
% 3.44/3.66  % SZS status Unsatisfiable
% 3.44/3.66  % SZS output start Refutation
% See solution above
% 3.44/3.66  ------------ end of proof -------------
% 3.44/3.66  
% 3.44/3.66  
% 3.44/3.66  Search stopped by max_proofs option.
% 3.44/3.66  
% 3.44/3.66  
% 3.44/3.66  Search stopped by max_proofs option.
% 3.44/3.66  
% 3.44/3.66  ============ end of search ============
% 3.44/3.66  
% 3.44/3.66  -------------- statistics -------------
% 3.44/3.66  clauses given                 74
% 3.44/3.66  clauses generated          10060
% 3.44/3.66  clauses kept                3672
% 3.44/3.66  clauses forward subsumed    6423
% 3.44/3.66  clauses back subsumed        721
% 3.44/3.66  Kbytes malloced             3906
% 3.44/3.66  
% 3.44/3.66  ----------- times (seconds) -----------
% 3.44/3.66  user CPU time          1.57          (0 hr, 0 min, 1 sec)
% 3.44/3.66  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 3.44/3.66  wall-clock time        3             (0 hr, 0 min, 3 sec)
% 3.44/3.66  
% 3.44/3.66  That finishes the proof of the theorem.
% 3.44/3.66  
% 3.44/3.66  Process 31734 finished Wed Jul 27 11:05:51 2022
% 3.44/3.66  Otter interrupted
% 3.44/3.66  PROOF FOUND
%------------------------------------------------------------------------------