TSTP Solution File: GRP123-4.003 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 12:56:07 EDT 2022

% Result   : Unsatisfiable 1.94s 2.10s
% Output   : Refutation 1.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   19 (  10 unt;   5 nHn;  18 RR)
%            Number of literals    :   40 (   0 equ;  16 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   21 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product(A,e_1,B)
    | product(A,e_2,B)
    | product(A,e_3,B) ),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(3,axiom,
    ~ e_qualish(e_1,e_2),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(5,axiom,
    ~ e_qualish(e_2,e_1),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(8,axiom,
    ~ e_qualish(e_3,e_2),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | e_qualish(C,D) ),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,B,C)
    | e_qualish(A,D) ),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,E,C)
    | ~ product(F,B,A)
    | ~ product(F,E,D)
    | e_qualish(B,E) ),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(24,plain,
    ( ~ product(A,B,C)
    | ~ product(C,D,C)
    | ~ product(C,B,A)
    | e_qualish(B,D) ),
    inference(factor,[status(thm)],[14]),
    [iquote('factor,14.2.4')] ).

cnf(25,axiom,
    group_element(e_1),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(26,axiom,
    group_element(e_2),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(28,axiom,
    product(A,A,A),
    file('GRP123-4.003.p',unknown),
    [] ).

cnf(31,plain,
    ( product(e_1,e_1,e_2)
    | product(e_1,e_2,e_2)
    | product(e_1,e_3,e_2) ),
    inference(hyper,[status(thm)],[26,2,25]),
    [iquote('hyper,26,2,25')] ).

cnf(32,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_2,e_1)
    | product(e_2,e_3,e_1) ),
    inference(hyper,[status(thm)],[26,2,25]),
    [iquote('hyper,26,2,25')] ).

cnf(54,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_3,e_2) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[31,10,28]),3]),
    [iquote('hyper,31,10,28,unit_del,3')] ).

cnf(56,plain,
    product(e_1,e_3,e_2),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[54,12,28]),5]),
    [iquote('hyper,54,12,28,unit_del,5')] ).

cnf(57,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_3,e_1) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[32,12,28]),3]),
    [iquote('hyper,32,12,28,unit_del,3')] ).

cnf(63,plain,
    product(e_2,e_3,e_1),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[57,10,28]),5]),
    [iquote('hyper,57,10,28,unit_del,5')] ).

cnf(65,plain,
    e_qualish(e_3,e_2),
    inference(hyper,[status(thm)],[63,24,56,28]),
    [iquote('hyper,63,24,56,28')] ).

cnf(66,plain,
    $false,
    inference(binary,[status(thm)],[65,8]),
    [iquote('binary,65.1,8.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.12  % 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 05:11:46 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.94/2.10  ----- Otter 3.3f, August 2004 -----
% 1.94/2.10  The process was started by sandbox on n006.cluster.edu,
% 1.94/2.10  Wed Jul 27 05:11:47 2022
% 1.94/2.10  The command was "./otter".  The process ID is 8822.
% 1.94/2.10  
% 1.94/2.10  set(prolog_style_variables).
% 1.94/2.10  set(auto).
% 1.94/2.10     dependent: set(auto1).
% 1.94/2.10     dependent: set(process_input).
% 1.94/2.10     dependent: clear(print_kept).
% 1.94/2.10     dependent: clear(print_new_demod).
% 1.94/2.10     dependent: clear(print_back_demod).
% 1.94/2.10     dependent: clear(print_back_sub).
% 1.94/2.10     dependent: set(control_memory).
% 1.94/2.10     dependent: assign(max_mem, 12000).
% 1.94/2.10     dependent: assign(pick_given_ratio, 4).
% 1.94/2.10     dependent: assign(stats_level, 1).
% 1.94/2.10     dependent: assign(max_seconds, 10800).
% 1.94/2.10  clear(print_given).
% 1.94/2.10  
% 1.94/2.10  list(usable).
% 1.94/2.10  0 [] -group_element(X)| -group_element(Y)|product(e_1,X,Y)|product(e_2,X,Y)|product(e_3,X,Y).
% 1.94/2.10  0 [] -group_element(X)| -group_element(Y)|product(X,e_1,Y)|product(X,e_2,Y)|product(X,e_3,Y).
% 1.94/2.10  0 [] group_element(e_1).
% 1.94/2.10  0 [] group_element(e_2).
% 1.94/2.10  0 [] group_element(e_3).
% 1.94/2.10  0 [] -e_qualish(e_1,e_2).
% 1.94/2.10  0 [] -e_qualish(e_1,e_3).
% 1.94/2.10  0 [] -e_qualish(e_2,e_1).
% 1.94/2.10  0 [] -e_qualish(e_2,e_3).
% 1.94/2.10  0 [] -e_qualish(e_3,e_1).
% 1.94/2.10  0 [] -e_qualish(e_3,e_2).
% 1.94/2.10  0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 1.94/2.10  0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.94/2.10  0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.94/2.10  0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.94/2.10  0 [] product(X,X,X).
% 1.94/2.10  0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,Y1,X1)| -product(Z2,Y2,X2)|e_qualish(X1,X2).
% 1.94/2.10  0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,Y1,X1)| -product(Z2,Y2,X2)|e_qualish(Y1,Y2).
% 1.94/2.10  end_of_list.
% 1.94/2.10  
% 1.94/2.10  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.94/2.10  
% 1.94/2.10  This is a non-Horn set without equality.  The strategy will
% 1.94/2.10  be ordered hyper_res, unit deletion, and factoring, with
% 1.94/2.10  satellites in sos and with nuclei in usable.
% 1.94/2.10  
% 1.94/2.10     dependent: set(hyper_res).
% 1.94/2.10     dependent: set(factor).
% 1.94/2.10     dependent: set(unit_deletion).
% 1.94/2.10  
% 1.94/2.10  ------------> process usable:
% 1.94/2.10  ** KEPT (pick-wt=16): 1 [] -group_element(A)| -group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_3,A,B).
% 1.94/2.10  ** KEPT (pick-wt=16): 2 [] -group_element(A)| -group_element(B)|product(A,e_1,B)|product(A,e_2,B)|product(A,e_3,B).
% 1.94/2.10  ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_2).
% 1.94/2.10  ** KEPT (pick-wt=3): 4 [] -e_qualish(e_1,e_3).
% 1.94/2.10  ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_1).
% 1.94/2.10  ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_3).
% 1.94/2.10  ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_1).
% 1.94/2.10  ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_2).
% 1.94/2.10  ** KEPT (pick-wt=16): 9 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3).
% 1.94/2.10  ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.94/2.10  ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.94/2.10  ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.94/2.10  ** KEPT (pick-wt=19): 13 [] -product(A,B,C)| -product(D,E,C)| -product(F,B,A)| -product(F,E,D)|e_qualish(A,D).
% 1.94/2.10  ** KEPT (pick-wt=19): 14 [] -product(A,B,C)| -product(D,E,C)| -product(F,B,A)| -product(F,E,D)|e_qualish(B,E).
% 1.94/2.10  
% 1.94/2.10  ------------> process sos:
% 1.94/2.10  ** KEPT (pick-wt=2): 25 [] group_element(e_1).
% 1.94/2.10  ** KEPT (pick-wt=2): 26 [] group_element(e_2).
% 1.94/2.10  ** KEPT (pick-wt=2): 27 [] group_element(e_3).
% 1.94/2.10  ** KEPT (pick-wt=4): 28 [] product(A,A,A).
% 1.94/2.10  
% 1.94/2.10  ======= end of input processing =======
% 1.94/2.10  
% 1.94/2.10  =========== start of search ===========
% 1.94/2.10  
% 1.94/2.10  -------- PROOF -------- 
% 1.94/2.10  
% 1.94/2.10  ----> UNIT CONFLICT at   0.02 sec ----> 66 [binary,65.1,8.1] $F.
% 1.94/2.10  
% 1.94/2.10  Length of proof is 8.  Level of proof is 4.
% 1.94/2.10  
% 1.94/2.10  ---------------- PROOF ----------------
% 1.94/2.10  % SZS status Unsatisfiable
% 1.94/2.10  % SZS output start Refutation
% See solution above
% 1.94/2.10  ------------ end of proof -------------
% 1.94/2.10  
% 1.94/2.10  
% 1.94/2.10  Search stopped by max_proofs option.
% 1.94/2.10  
% 1.94/2.10  
% 1.94/2.10  Search stopped by max_proofs option.
% 1.94/2.10  
% 1.94/2.10  ============ end of search ============
% 1.94/2.10  
% 1.94/2.10  -------------- statistics -------------
% 1.94/2.10  clauses given                 18
% 1.94/2.10  clauses generated            791
% 1.94/2.10  clauses kept                  65
% 1.94/2.10  clauses forward subsumed     744
% 1.94/2.10  clauses back subsumed         26
% 1.94/2.10  Kbytes malloced              976
% 1.94/2.10  
% 1.94/2.10  ----------- times (seconds) -----------
% 1.94/2.10  user CPU time          0.02          (0 hr, 0 min, 0 sec)
% 1.94/2.10  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.94/2.10  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.94/2.10  
% 1.94/2.10  That finishes the proof of the theorem.
% 1.94/2.10  
% 1.94/2.10  Process 8822 finished Wed Jul 27 05:11:48 2022
% 1.94/2.10  Otter interrupted
% 1.94/2.10  PROOF FOUND
%------------------------------------------------------------------------------