TSTP Solution File: TOP005-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n006.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 13:26:48 EDT 2022

% Result   : Unsatisfiable 1.81s 2.02s
% Output   : Refutation 1.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   21 (  10 unt;   3 nHn;  18 RR)
%            Number of literals    :   39 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   28 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ element_of_set(A,union_of_members(B))
    | element_of_set(A,f1(B,A)) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ element_of_set(A,union_of_members(B))
    | element_of_collection(f1(B,A),B) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ element_of_collection(A,top_of_basis(B))
    | ~ element_of_set(C,A)
    | element_of_set(C,f10(B,A,C)) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ element_of_collection(A,top_of_basis(B))
    | ~ element_of_set(C,A)
    | element_of_collection(f10(B,A,C),B) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ element_of_collection(A,top_of_basis(B))
    | ~ element_of_set(C,A)
    | subset_sets(f10(B,A,C),A) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( element_of_collection(A,top_of_basis(B))
    | ~ element_of_set(f11(B,A),C)
    | ~ element_of_collection(C,B)
    | ~ subset_sets(C,A) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ subset_sets(A,B)
    | ~ element_of_collection(B,C)
    | subset_sets(A,union_of_members(C)) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ subset_collections(A,B)
    | ~ element_of_collection(C,A)
    | element_of_collection(C,B) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(10,axiom,
    ~ element_of_collection(union_of_members(g),top_of_basis(f)),
    file('TOP005-2.p',unknown),
    [] ).

cnf(11,axiom,
    ( element_of_collection(A,top_of_basis(B))
    | element_of_set(f11(B,A),A) ),
    file('TOP005-2.p',unknown),
    [] ).

cnf(12,axiom,
    subset_collections(g,top_of_basis(f)),
    file('TOP005-2.p',unknown),
    [] ).

cnf(14,plain,
    ( element_of_collection(union_of_members(A),top_of_basis(B))
    | element_of_collection(f1(A,f11(B,union_of_members(A))),A) ),
    inference(hyper,[status(thm)],[11,2]),
    [iquote('hyper,11,2')] ).

cnf(15,plain,
    ( element_of_collection(union_of_members(A),top_of_basis(B))
    | element_of_set(f11(B,union_of_members(A)),f1(A,f11(B,union_of_members(A)))) ),
    inference(hyper,[status(thm)],[11,1]),
    [iquote('hyper,11,1')] ).

cnf(16,plain,
    element_of_collection(f1(g,f11(f,union_of_members(g))),g),
    inference(hyper,[status(thm)],[14,10]),
    [iquote('hyper,14,10')] ).

cnf(27,plain,
    element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)),
    inference(hyper,[status(thm)],[16,9,12]),
    [iquote('hyper,16,9,12')] ).

cnf(35,plain,
    subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[27,5,15]),10]),
    [iquote('hyper,27,5,15,unit_del,10')] ).

cnf(37,plain,
    element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[27,4,15]),10]),
    [iquote('hyper,27,4,15,unit_del,10')] ).

cnf(39,plain,
    element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[27,3,15]),10]),
    [iquote('hyper,27,3,15,unit_del,10')] ).

cnf(88,plain,
    subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)),
    inference(hyper,[status(thm)],[35,8,16]),
    [iquote('hyper,35,8,16')] ).

cnf(94,plain,
    element_of_collection(union_of_members(g),top_of_basis(f)),
    inference(hyper,[status(thm)],[88,6,39,37]),
    [iquote('hyper,88,6,39,37')] ).

cnf(95,plain,
    $false,
    inference(binary,[status(thm)],[94,10]),
    [iquote('binary,94.1,10.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n006.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 01:58:02 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.81/2.02  ----- Otter 3.3f, August 2004 -----
% 1.81/2.02  The process was started by sandbox2 on n006.cluster.edu,
% 1.81/2.02  Wed Jul 27 01:58:02 2022
% 1.81/2.02  The command was "./otter".  The process ID is 27594.
% 1.81/2.02  
% 1.81/2.02  set(prolog_style_variables).
% 1.81/2.02  set(auto).
% 1.81/2.02     dependent: set(auto1).
% 1.81/2.02     dependent: set(process_input).
% 1.81/2.02     dependent: clear(print_kept).
% 1.81/2.02     dependent: clear(print_new_demod).
% 1.81/2.02     dependent: clear(print_back_demod).
% 1.81/2.02     dependent: clear(print_back_sub).
% 1.81/2.02     dependent: set(control_memory).
% 1.81/2.02     dependent: assign(max_mem, 12000).
% 1.81/2.02     dependent: assign(pick_given_ratio, 4).
% 1.81/2.02     dependent: assign(stats_level, 1).
% 1.81/2.02     dependent: assign(max_seconds, 10800).
% 1.81/2.02  clear(print_given).
% 1.81/2.02  
% 1.81/2.02  list(usable).
% 1.81/2.02  0 [] -element_of_set(U,union_of_members(Vf))|element_of_set(U,f1(Vf,U)).
% 1.81/2.02  0 [] -element_of_set(U,union_of_members(Vf))|element_of_collection(f1(Vf,U),Vf).
% 1.81/2.02  0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_set(X,f10(Vf,U,X)).
% 1.81/2.02  0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_collection(f10(Vf,U,X),Vf).
% 1.81/2.02  0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|subset_sets(f10(Vf,U,X),U).
% 1.81/2.02  0 [] element_of_collection(U,top_of_basis(Vf))|element_of_set(f11(Vf,U),U).
% 1.81/2.02  0 [] element_of_collection(U,top_of_basis(Vf))| -element_of_set(f11(Vf,U),Uu11)| -element_of_collection(Uu11,Vf)| -subset_sets(Uu11,U).
% 1.81/2.02  0 [] subset_sets(X,Y)| -element_of_set(U,X)|element_of_set(U,Y).
% 1.81/2.02  0 [] -subset_sets(X,Y)| -element_of_collection(Y,Z)|subset_sets(X,union_of_members(Z)).
% 1.81/2.02  0 [] -subset_collections(X,Y)| -element_of_collection(U,X)|element_of_collection(U,Y).
% 1.81/2.02  0 [] subset_collections(g,top_of_basis(f)).
% 1.81/2.02  0 [] -element_of_collection(union_of_members(g),top_of_basis(f)).
% 1.81/2.02  end_of_list.
% 1.81/2.02  
% 1.81/2.02  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.81/2.02  
% 1.81/2.02  This is a non-Horn set without equality.  The strategy will
% 1.81/2.02  be ordered hyper_res, unit deletion, and factoring, with
% 1.81/2.02  satellites in sos and with nuclei in usable.
% 1.81/2.02  
% 1.81/2.02     dependent: set(hyper_res).
% 1.81/2.02     dependent: set(factor).
% 1.81/2.02     dependent: set(unit_deletion).
% 1.81/2.02  
% 1.81/2.02  ------------> process usable:
% 1.81/2.02  ** KEPT (pick-wt=9): 1 [] -element_of_set(A,union_of_members(B))|element_of_set(A,f1(B,A)).
% 1.81/2.02  ** KEPT (pick-wt=9): 2 [] -element_of_set(A,union_of_members(B))|element_of_collection(f1(B,A),B).
% 1.81/2.02  ** KEPT (pick-wt=13): 3 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_set(C,f10(B,A,C)).
% 1.81/2.02  ** KEPT (pick-wt=13): 4 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_collection(f10(B,A,C),B).
% 1.81/2.02  ** KEPT (pick-wt=13): 5 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|subset_sets(f10(B,A,C),A).
% 1.81/2.02  ** KEPT (pick-wt=15): 6 [] element_of_collection(A,top_of_basis(B))| -element_of_set(f11(B,A),C)| -element_of_collection(C,B)| -subset_sets(C,A).
% 1.81/2.02  ** KEPT (pick-wt=9): 7 [] subset_sets(A,B)| -element_of_set(C,A)|element_of_set(C,B).
% 1.81/2.02  ** KEPT (pick-wt=10): 8 [] -subset_sets(A,B)| -element_of_collection(B,C)|subset_sets(A,union_of_members(C)).
% 1.81/2.02  ** KEPT (pick-wt=9): 9 [] -subset_collections(A,B)| -element_of_collection(C,A)|element_of_collection(C,B).
% 1.81/2.02  ** KEPT (pick-wt=5): 10 [] -element_of_collection(union_of_members(g),top_of_basis(f)).
% 1.81/2.02  
% 1.81/2.02  ------------> process sos:
% 1.81/2.02  ** KEPT (pick-wt=9): 11 [] element_of_collection(A,top_of_basis(B))|element_of_set(f11(B,A),A).
% 1.81/2.02  ** KEPT (pick-wt=4): 12 [] subset_collections(g,top_of_basis(f)).
% 1.81/2.02  
% 1.81/2.02  ======= end of input processing =======
% 1.81/2.02  
% 1.81/2.02  =========== start of search ===========
% 1.81/2.02  
% 1.81/2.02  -------- PROOF -------- 
% 1.81/2.02  
% 1.81/2.02  ----> UNIT CONFLICT at   0.01 sec ----> 95 [binary,94.1,10.1] $F.
% 1.81/2.02  
% 1.81/2.02  Length of proof is 9.  Level of proof is 6.
% 1.81/2.02  
% 1.81/2.02  ---------------- PROOF ----------------
% 1.81/2.02  % SZS status Unsatisfiable
% 1.81/2.02  % SZS output start Refutation
% See solution above
% 1.81/2.02  ------------ end of proof -------------
% 1.81/2.02  
% 1.81/2.02  
% 1.81/2.02  Search stopped by max_proofs option.
% 1.81/2.02  
% 1.81/2.02  
% 1.81/2.02  Search stopped by max_proofs option.
% 1.81/2.02  
% 1.81/2.02  ============ end of search ============
% 1.81/2.02  
% 1.81/2.02  -------------- statistics -------------
% 1.81/2.02  clauses given                 17
% 1.81/2.02  clauses generated            105
% 1.81/2.02  clauses kept                  94
% 1.81/2.02  clauses forward subsumed      23
% 1.81/2.02  clauses back subsumed          0
% 1.81/2.02  Kbytes malloced              976
% 1.81/2.02  
% 1.81/2.02  ----------- times (seconds) -----------
% 1.81/2.02  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.81/2.02  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.81/2.02  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.81/2.02  
% 1.81/2.02  That finishes the proof of the theorem.
% 1.81/2.02  
% 1.81/2.02  Process 27594 finished Wed Jul 27 01:58:03 2022
% 1.81/2.02  Otter interrupted
% 1.81/2.02  PROOF FOUND
%------------------------------------------------------------------------------