TSTP Solution File: SET591+3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n004.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 13:13:46 EDT 2022

% Result   : Theorem 1.72s 1.90s
% Output   : Refutation 1.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   16 (   7 unt;   5 nHn;  11 RR)
%            Number of literals    :   28 (   7 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   18 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ subset(A,B)
    | ~ member(C,A)
    | member(C,B) ),
    file('SET591+3.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(A,difference(B,C))
    | ~ member(A,C) ),
    file('SET591+3.p',unknown),
    [] ).

cnf(6,axiom,
    ~ member(A,empty_set),
    file('SET591+3.p',unknown),
    [] ).

cnf(9,axiom,
    ( A = B
    | ~ subset(A,B)
    | ~ subset(B,A) ),
    file('SET591+3.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ empty(A)
    | ~ member(B,A) ),
    file('SET591+3.p',unknown),
    [] ).

cnf(11,axiom,
    dollar_c2 != empty_set,
    file('SET591+3.p',unknown),
    [] ).

cnf(12,plain,
    empty_set != dollar_c2,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
    [iquote('copy,11,flip.1')] ).

cnf(15,axiom,
    ( subset(A,B)
    | member(dollar_f1(A,B),A) ),
    file('SET591+3.p',unknown),
    [] ).

cnf(17,axiom,
    ( empty(A)
    | member(dollar_f2(A),A) ),
    file('SET591+3.p',unknown),
    [] ).

cnf(18,axiom,
    subset(dollar_c2,difference(dollar_c1,dollar_c2)),
    file('SET591+3.p',unknown),
    [] ).

cnf(25,plain,
    ( member(dollar_f1(A,B),A)
    | B = A
    | member(dollar_f1(B,A),B) ),
    inference(hyper,[status(thm)],[15,9,15]),
    [iquote('hyper,15,9,15')] ).

cnf(91,plain,
    ( A = empty_set
    | member(dollar_f1(A,empty_set),A) ),
    inference(hyper,[status(thm)],[25,6]),
    [iquote('hyper,25,6')] ).

cnf(200,plain,
    ( A = empty_set
    | member(dollar_f2(A),A) ),
    inference(hyper,[status(thm)],[91,10,17]),
    [iquote('hyper,91,10,17')] ).

cnf(283,plain,
    member(dollar_f2(dollar_c2),difference(dollar_c1,dollar_c2)),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[200,1,18]),12]),
    [iquote('hyper,200,1,18,unit_del,12')] ).

cnf(362,plain,
    empty_set = dollar_c2,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[283,4,200])]),
    [iquote('hyper,283,4,200,flip.1')] ).

cnf(364,plain,
    $false,
    inference(binary,[status(thm)],[362,12]),
    [iquote('binary,362.1,12.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n004.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 10:36:21 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.72/1.90  ----- Otter 3.3f, August 2004 -----
% 1.72/1.90  The process was started by sandbox2 on n004.cluster.edu,
% 1.72/1.90  Wed Jul 27 10:36:21 2022
% 1.72/1.90  The command was "./otter".  The process ID is 17681.
% 1.72/1.90  
% 1.72/1.90  set(prolog_style_variables).
% 1.72/1.90  set(auto).
% 1.72/1.90     dependent: set(auto1).
% 1.72/1.90     dependent: set(process_input).
% 1.72/1.90     dependent: clear(print_kept).
% 1.72/1.90     dependent: clear(print_new_demod).
% 1.72/1.90     dependent: clear(print_back_demod).
% 1.72/1.90     dependent: clear(print_back_sub).
% 1.72/1.90     dependent: set(control_memory).
% 1.72/1.90     dependent: assign(max_mem, 12000).
% 1.72/1.90     dependent: assign(pick_given_ratio, 4).
% 1.72/1.90     dependent: assign(stats_level, 1).
% 1.72/1.90     dependent: assign(max_seconds, 10800).
% 1.72/1.90  clear(print_given).
% 1.72/1.90  
% 1.72/1.90  formula_list(usable).
% 1.72/1.90  all A (A=A).
% 1.72/1.90  all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.72/1.90  all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.72/1.90  all B (-member(B,empty_set)).
% 1.72/1.90  all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.72/1.90  all B subset(B,B).
% 1.72/1.90  all B (empty(B)<-> (all C (-member(C,B)))).
% 1.72/1.90  -(all B C (subset(B,difference(C,B))->B=empty_set)).
% 1.72/1.90  end_of_list.
% 1.72/1.90  
% 1.72/1.90  -------> usable clausifies to:
% 1.72/1.90  
% 1.72/1.90  list(usable).
% 1.72/1.90  0 [] A=A.
% 1.72/1.90  0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.72/1.90  0 [] subset(B,C)|member($f1(B,C),B).
% 1.72/1.90  0 [] subset(B,C)| -member($f1(B,C),C).
% 1.72/1.90  0 [] -member(D,difference(B,C))|member(D,B).
% 1.72/1.90  0 [] -member(D,difference(B,C))| -member(D,C).
% 1.72/1.90  0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.72/1.90  0 [] -member(B,empty_set).
% 1.72/1.90  0 [] B!=C|subset(B,C).
% 1.72/1.90  0 [] B!=C|subset(C,B).
% 1.72/1.90  0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.72/1.90  0 [] subset(B,B).
% 1.72/1.90  0 [] -empty(B)| -member(C,B).
% 1.72/1.90  0 [] empty(B)|member($f2(B),B).
% 1.72/1.90  0 [] subset($c2,difference($c1,$c2)).
% 1.72/1.90  0 [] $c2!=empty_set.
% 1.72/1.90  end_of_list.
% 1.72/1.90  
% 1.72/1.90  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.72/1.90  
% 1.72/1.90  This ia a non-Horn set with equality.  The strategy will be
% 1.72/1.90  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.90  deletion, with positive clauses in sos and nonpositive
% 1.72/1.90  clauses in usable.
% 1.72/1.90  
% 1.72/1.90     dependent: set(knuth_bendix).
% 1.72/1.90     dependent: set(anl_eq).
% 1.72/1.90     dependent: set(para_from).
% 1.72/1.90     dependent: set(para_into).
% 1.72/1.90     dependent: clear(para_from_right).
% 1.72/1.90     dependent: clear(para_into_right).
% 1.72/1.90     dependent: set(para_from_vars).
% 1.72/1.90     dependent: set(eq_units_both_ways).
% 1.72/1.90     dependent: set(dynamic_demod_all).
% 1.72/1.90     dependent: set(dynamic_demod).
% 1.72/1.90     dependent: set(order_eq).
% 1.72/1.90     dependent: set(back_demod).
% 1.72/1.90     dependent: set(lrpo).
% 1.72/1.90     dependent: set(hyper_res).
% 1.72/1.90     dependent: set(unit_deletion).
% 1.72/1.90     dependent: set(factor).
% 1.72/1.90  
% 1.72/1.90  ------------> process usable:
% 1.72/1.90  ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.72/1.90  ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 1.72/1.90  ** KEPT (pick-wt=8): 3 [] -member(A,difference(B,C))|member(A,B).
% 1.72/1.90  ** KEPT (pick-wt=8): 4 [] -member(A,difference(B,C))| -member(A,C).
% 1.72/1.90  ** KEPT (pick-wt=11): 5 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.72/1.90  ** KEPT (pick-wt=3): 6 [] -member(A,empty_set).
% 1.72/1.90  ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.72/1.90  ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.72/1.90  ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.72/1.90  ** KEPT (pick-wt=5): 10 [] -empty(A)| -member(B,A).
% 1.72/1.90  ** KEPT (pick-wt=3): 12 [copy,11,flip.1] empty_set!=$c2.
% 1.72/1.90  
% 1.72/1.90  ------------> process sos:
% 1.72/1.90  ** KEPT (pick-wt=3): 14 [] A=A.
% 1.72/1.90  ** KEPT (pick-wt=8): 15 [] subset(A,B)|member($f1(A,B),A).
% 1.72/1.90  ** KEPT (pick-wt=3): 16 [] subset(A,A).
% 1.72/1.90  ** KEPT (pick-wt=6): 17 [] empty(A)|member($f2(A),A).
% 1.72/1.90  ** KEPT (pick-wt=5): 18 [] subset($c2,difference($c1,$c2)).
% 1.72/1.90    Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.72/1.90  14 back subsumes 13.
% 1.72/1.90  
% 1.72/1.90  ======= end of input processing =======
% 1.72/1.90  
% 1.72/1.90  =========== start of search ===========
% 1.72/1.90  
% 1.72/1.90  -------- PROOF -------- 
% 1.72/1.90  
% 1.72/1.90  ----> UNIT CONFLICT at   0.03 sec ----> 364 [binary,362.1,12.1] $F.
% 1.72/1.90  
% 1.72/1.90  Length of proof is 6.  Level of proof is 5.
% 1.72/1.90  
% 1.72/1.90  ---------------- PROOF ----------------
% 1.72/1.90  % SZS status Theorem
% 1.72/1.90  % SZS output start Refutation
% See solution above
% 1.72/1.90  ------------ end of proof -------------
% 1.72/1.90  
% 1.72/1.90  
% 1.72/1.90  Search stopped by max_proofs option.
% 1.72/1.90  
% 1.72/1.90  
% 1.72/1.90  Search stopped by max_proofs option.
% 1.72/1.90  
% 1.72/1.90  ============ end of search ============
% 1.72/1.90  
% 1.72/1.90  -------------- statistics -------------
% 1.72/1.90  clauses given                 19
% 1.72/1.90  clauses generated            762
% 1.72/1.90  clauses kept                 361
% 1.72/1.90  clauses forward subsumed     413
% 1.72/1.90  clauses back subsumed          1
% 1.72/1.90  Kbytes malloced              976
% 1.72/1.90  
% 1.72/1.90  ----------- times (seconds) -----------
% 1.72/1.90  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 1.72/1.90  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.72/1.90  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.72/1.90  
% 1.72/1.90  That finishes the proof of the theorem.
% 1.72/1.90  
% 1.72/1.90  Process 17681 finished Wed Jul 27 10:36:22 2022
% 1.72/1.90  Otter interrupted
% 1.72/1.90  PROOF FOUND
%------------------------------------------------------------------------------