TSTP Solution File: SET014-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n014.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 2.91s 3.07s
% Output   : Refutation 2.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   19 (   9 unt;   7 nHn;  14 RR)
%            Number of literals    :   31 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ member(A,B)
    | ~ subset(B,C)
    | member(A,C) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ member(member_of_1_not_of_2(A,B),B)
    | subset(A,B) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(A,B)
    | ~ member(A,complement(B)) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ member(A,union(B,C))
    | member(A,B)
    | member(A,C) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(18,axiom,
    ~ subset(union(as,bs),cs),
    file('SET014-2.p',unknown),
    [] ).

cnf(22,axiom,
    ( subset(A,B)
    | member(member_of_1_not_of_2(A,B),A) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(23,axiom,
    ( member(A,B)
    | member(A,complement(B)) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(26,axiom,
    subset(as,cs),
    file('SET014-2.p',unknown),
    [] ).

cnf(27,axiom,
    subset(bs,cs),
    file('SET014-2.p',unknown),
    [] ).

cnf(28,plain,
    member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)),
    inference(hyper,[status(thm)],[22,18]),
    [iquote('hyper,22,18')] ).

cnf(46,plain,
    ( member(member_of_1_not_of_2(A,B),complement(B))
    | subset(A,B) ),
    inference(hyper,[status(thm)],[23,3]),
    [iquote('hyper,23,3')] ).

cnf(47,plain,
    ( member(A,complement(bs))
    | member(A,cs) ),
    inference(hyper,[status(thm)],[23,2,27]),
    [iquote('hyper,23,2,27')] ).

cnf(48,plain,
    ( member(A,complement(as))
    | member(A,cs) ),
    inference(hyper,[status(thm)],[23,2,26]),
    [iquote('hyper,23,2,26')] ).

cnf(91,plain,
    ( member(member_of_1_not_of_2(union(as,bs),cs),as)
    | member(member_of_1_not_of_2(union(as,bs),cs),bs) ),
    inference(hyper,[status(thm)],[28,7]),
    [iquote('hyper,28,7')] ).

cnf(2914,plain,
    member(member_of_1_not_of_2(union(as,bs),cs),complement(cs)),
    inference(hyper,[status(thm)],[46,18]),
    [iquote('hyper,46,18')] ).

cnf(3212,plain,
    member(member_of_1_not_of_2(union(as,bs),cs),complement(as)),
    inference(hyper,[status(thm)],[2914,4,48]),
    [iquote('hyper,2914,4,48')] ).

cnf(3291,plain,
    member(member_of_1_not_of_2(union(as,bs),cs),bs),
    inference(hyper,[status(thm)],[3212,4,91]),
    [iquote('hyper,3212,4,91')] ).

cnf(3296,plain,
    member(member_of_1_not_of_2(union(as,bs),cs),cs),
    inference(hyper,[status(thm)],[3291,4,47]),
    [iquote('hyper,3291,4,47')] ).

cnf(3325,plain,
    $false,
    inference(hyper,[status(thm)],[3296,4,2914]),
    [iquote('hyper,3296,4,2914')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13  % Command  : otter-tptp-script %s
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Jul 27 10:56:09 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 2.91/3.07  ----- Otter 3.3f, August 2004 -----
% 2.91/3.07  The process was started by sandbox on n014.cluster.edu,
% 2.91/3.07  Wed Jul 27 10:56:09 2022
% 2.91/3.07  The command was "./otter".  The process ID is 32297.
% 2.91/3.07  
% 2.91/3.07  set(prolog_style_variables).
% 2.91/3.07  set(auto).
% 2.91/3.07     dependent: set(auto1).
% 2.91/3.07     dependent: set(process_input).
% 2.91/3.07     dependent: clear(print_kept).
% 2.91/3.07     dependent: clear(print_new_demod).
% 2.91/3.07     dependent: clear(print_back_demod).
% 2.91/3.07     dependent: clear(print_back_sub).
% 2.91/3.07     dependent: set(control_memory).
% 2.91/3.07     dependent: assign(max_mem, 12000).
% 2.91/3.07     dependent: assign(pick_given_ratio, 4).
% 2.91/3.07     dependent: assign(stats_level, 1).
% 2.91/3.07     dependent: assign(max_seconds, 10800).
% 2.91/3.07  clear(print_given).
% 2.91/3.07  
% 2.91/3.07  list(usable).
% 2.91/3.07  0 [] -member(X,empty_set).
% 2.91/3.07  0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 2.91/3.07  0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 2.91/3.07  0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 2.91/3.07  0 [] member(X,Xs)|member(X,complement(Xs)).
% 2.91/3.07  0 [] -member(X,Xs)| -member(X,complement(Xs)).
% 2.91/3.07  0 [] -member(X,Xs)|member(X,union(Xs,Ys)).
% 2.91/3.07  0 [] -member(X,Ys)|member(X,union(Xs,Ys)).
% 2.91/3.07  0 [] -member(X,union(Xs,Ys))|member(X,Xs)|member(X,Ys).
% 2.91/3.07  0 [] -member(X,Xs)| -member(X,Ys)|member(X,intersection(Xs,Ys)).
% 2.91/3.07  0 [] -member(X,intersection(Xs,Ys))|member(X,Xs).
% 2.91/3.07  0 [] -member(X,intersection(Xs,Ys))|member(X,Ys).
% 2.91/3.07  0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 2.91/3.07  0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 2.91/3.07  0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 2.91/3.07  0 [] e_qual_sets(Xs,Xs).
% 2.91/3.07  0 [] -e_qual_sets(Xs,Ys)|e_qual_sets(Ys,Xs).
% 2.91/3.07  0 [] -e_qual_sets(Xs,Ys)| -e_qual_sets(Ys,Zs)|e_qual_sets(Xs,Zs).
% 2.91/3.07  0 [] e_qual_elements(X,X).
% 2.91/3.07  0 [] -e_qual_elements(X,Y)|e_qual_elements(Y,X).
% 2.91/3.07  0 [] -e_qual_elements(X,Y)| -e_qual_elements(Y,Z)|e_qual_elements(X,Z).
% 2.91/3.07  0 [] subset(as,cs).
% 2.91/3.07  0 [] subset(bs,cs).
% 2.91/3.07  0 [] -subset(union(as,bs),cs).
% 2.91/3.07  end_of_list.
% 2.91/3.07  
% 2.91/3.07  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 2.91/3.07  
% 2.91/3.07  This is a non-Horn set without equality.  The strategy will
% 2.91/3.07  be ordered hyper_res, unit deletion, and factoring, with
% 2.91/3.07  satellites in sos and with nuclei in usable.
% 2.91/3.07  
% 2.91/3.07     dependent: set(hyper_res).
% 2.91/3.07     dependent: set(factor).
% 2.91/3.07     dependent: set(unit_deletion).
% 2.91/3.07  
% 2.91/3.07  ------------> process usable:
% 2.91/3.07  ** KEPT (pick-wt=3): 1 [] -member(A,empty_set).
% 2.91/3.07  ** KEPT (pick-wt=9): 2 [] -member(A,B)| -subset(B,C)|member(A,C).
% 2.91/3.07  ** KEPT (pick-wt=8): 3 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 2.91/3.07  ** KEPT (pick-wt=7): 4 [] -member(A,B)| -member(A,complement(B)).
% 2.91/3.07  ** KEPT (pick-wt=8): 5 [] -member(A,B)|member(A,union(B,C)).
% 2.91/3.07  ** KEPT (pick-wt=8): 6 [] -member(A,B)|member(A,union(C,B)).
% 2.91/3.07  ** KEPT (pick-wt=11): 7 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 2.91/3.07  ** KEPT (pick-wt=11): 8 [] -member(A,B)| -member(A,C)|member(A,intersection(B,C)).
% 2.91/3.07  ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,B).
% 2.91/3.07  ** KEPT (pick-wt=8): 10 [] -member(A,intersection(B,C))|member(A,C).
% 2.91/3.07  ** KEPT (pick-wt=6): 11 [] -e_qual_sets(A,B)|subset(A,B).
% 2.91/3.07  ** KEPT (pick-wt=6): 12 [] -e_qual_sets(A,B)|subset(B,A).
% 2.91/3.07  ** KEPT (pick-wt=9): 13 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 2.91/3.07  ** KEPT (pick-wt=6): 14 [] -e_qual_sets(A,B)|e_qual_sets(B,A).
% 2.91/3.07  ** KEPT (pick-wt=9): 15 [] -e_qual_sets(A,B)| -e_qual_sets(B,C)|e_qual_sets(A,C).
% 2.91/3.07  ** KEPT (pick-wt=6): 16 [] -e_qual_elements(A,B)|e_qual_elements(B,A).
% 2.91/3.07  ** KEPT (pick-wt=9): 17 [] -e_qual_elements(A,B)| -e_qual_elements(B,C)|e_qual_elements(A,C).
% 2.91/3.07  ** KEPT (pick-wt=5): 18 [] -subset(union(as,bs),cs).
% 2.91/3.07  
% 2.91/3.07  ------------> process sos:
% 2.91/3.07  ** KEPT (pick-wt=8): 22 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 2.91/3.07  ** KEPT (pick-wt=7): 23 [] member(A,B)|member(A,complement(B)).
% 2.91/3.07  ** KEPT (pick-wt=3): 24 [] e_qual_sets(A,A).
% 2.91/3.07  ** KEPT (pick-wt=3): 25 [] e_qual_elements(A,A).
% 2.91/3.07  ** KEPT (pick-wt=3): 26 [] subset(as,cs).
% 2.91/3.07  ** KEPT (pick-wt=3): 27 [] subset(bs,cs).
% 2.91/3.07  24 back subsumes 21.
% 2.91/3.07  
% 2.91/3.07  ======= end of input processing =======
% 2.91/3.07  
% 2.91/3.07  =========== start of search ===========
% 2.91/3.07  
% 2.91/3.07  
% 2.91/3.07  Resetting weight limit to 10.
% 2.91/3.07  
% 2.91/3.07  
% 2.91/3.07  Resetting weight limit to 10.
% 2.91/3.07  
% 2.91/3.07  sos_size=2703
% 2.91/3.07  
% 2.91/3.07  
% 2.91/3.07  Resetting weight limit to 9.
% 2.91/3.07  
% 2.91/3.07  
% 2.91/3.07  Resetting weight limit to 9.
% 2.91/3.07  
% 2.91/3.07  sos_size=2766
% 2.91/3.07  
% 2.91/3.07  -------- PROOF -------- 
% 2.91/3.07  
% 2.91/3.07  -----> EMPTY CLAUSE at   1.13 sec ----> 3325 [hyper,3296,4,2914] $F.
% 2.91/3.07  
% 2.91/3.07  Length of proof is 9.  Level of proof is 5.
% 2.91/3.07  
% 2.91/3.07  ---------------- PROOF ----------------
% 2.91/3.07  % SZS status Unsatisfiable
% 2.91/3.07  % SZS output start Refutation
% See solution above
% 2.91/3.07  ------------ end of proof -------------
% 2.91/3.07  
% 2.91/3.07  
% 2.91/3.07  Search stopped by max_proofs option.
% 2.91/3.07  
% 2.91/3.07  
% 2.91/3.07  Search stopped by max_proofs option.
% 2.91/3.07  
% 2.91/3.07  ============ end of search ============
% 2.91/3.07  
% 2.91/3.07  -------------- statistics -------------
% 2.91/3.07  clauses given                335
% 2.91/3.07  clauses generated          54598
% 2.91/3.07  clauses kept                3324
% 2.91/3.07  clauses forward subsumed    6550
% 2.91/3.07  clauses back subsumed         35
% 2.91/3.07  Kbytes malloced             5859
% 2.91/3.07  
% 2.91/3.07  ----------- times (seconds) -----------
% 2.91/3.07  user CPU time          1.13          (0 hr, 0 min, 1 sec)
% 2.91/3.07  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.91/3.07  wall-clock time        3             (0 hr, 0 min, 3 sec)
% 2.91/3.07  
% 2.91/3.07  That finishes the proof of the theorem.
% 2.91/3.07  
% 2.91/3.07  Process 32297 finished Wed Jul 27 10:56:12 2022
% 2.91/3.07  Otter interrupted
% 2.91/3.07  PROOF FOUND
%------------------------------------------------------------------------------