TSTP Solution File: GRP123-9.003 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP123-9.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n027.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 12:56:08 EDT 2022

% Result   : Unsatisfiable 1.67s 1.88s
% Output   : Refutation 1.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   29 (  16 unt;   8 nHn;  27 RR)
%            Number of literals    :   56 (   0 equ;  19 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   26 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ e_qualish(e_1,e_2),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(5,axiom,
    ~ e_qualish(e_2,e_1),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(6,axiom,
    ~ e_qualish(e_2,e_3),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(7,axiom,
    ~ e_qualish(e_3,e_1),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(8,axiom,
    ~ e_qualish(e_3,e_2),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product1(A,B,e_1)
    | product1(A,B,e_2)
    | product1(A,B,e_3) ),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(A,D,C)
    | e_qualish(B,D) ),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(D,B,C)
    | e_qualish(A,D) ),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product2(A,B,e_1)
    | product2(A,B,e_2)
    | product2(A,B,e_3) ),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ product2(A,B,C)
    | ~ product2(A,D,C)
    | e_qualish(B,D) ),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ product2(A,B,C)
    | ~ product2(D,B,C)
    | e_qualish(A,D) ),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(C,B,D)
    | product2(D,A,B) ),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(29,axiom,
    group_element(e_1),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(30,axiom,
    group_element(e_2),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(31,axiom,
    group_element(e_3),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(32,axiom,
    product1(A,A,A),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(33,axiom,
    product2(A,A,A),
    file('GRP123-9.003.p',unknown),
    [] ).

cnf(38,plain,
    ( product2(e_1,e_2,e_1)
    | product2(e_1,e_2,e_2)
    | product2(e_1,e_2,e_3) ),
    inference(hyper,[status(thm)],[30,13,29]),
    [iquote('hyper,30,13,29')] ).

cnf(52,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_3,e_2)
    | product1(e_2,e_3,e_3) ),
    inference(hyper,[status(thm)],[31,9,30]),
    [iquote('hyper,31,9,30')] ).

cnf(53,plain,
    ( product1(e_1,e_3,e_1)
    | product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3) ),
    inference(hyper,[status(thm)],[31,9,29]),
    [iquote('hyper,31,9,29')] ).

cnf(65,plain,
    ( product2(e_1,e_2,e_2)
    | product2(e_1,e_2,e_3) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[38,15,33]),3]),
    [iquote('hyper,38,15,33,unit_del,3')] ).

cnf(67,plain,
    product2(e_1,e_2,e_3),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[65,16,33]),5]),
    [iquote('hyper,65,16,33,unit_del,5')] ).

cnf(96,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_3,e_3) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[52,11,32]),6]),
    [iquote('hyper,52,11,32,unit_del,6')] ).

cnf(100,plain,
    product1(e_2,e_3,e_1),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[96,12,32]),8]),
    [iquote('hyper,96,12,32,unit_del,8')] ).

cnf(102,plain,
    ( product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[53,12,100]),5]),
    [iquote('hyper,53,12,100,unit_del,5')] ).

cnf(112,plain,
    product1(e_1,e_3,e_2),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[102,12,32]),7]),
    [iquote('hyper,102,12,32,unit_del,7')] ).

cnf(120,plain,
    product2(e_2,e_2,e_3),
    inference(hyper,[status(thm)],[112,17,100]),
    [iquote('hyper,112,17,100')] ).

cnf(122,plain,
    e_qualish(e_1,e_2),
    inference(hyper,[status(thm)],[120,16,67]),
    [iquote('hyper,120,16,67')] ).

cnf(123,plain,
    $false,
    inference(binary,[status(thm)],[122,3]),
    [iquote('binary,122.1,3.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP123-9.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n027.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 05:13:21 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.67/1.88  ----- Otter 3.3f, August 2004 -----
% 1.67/1.88  The process was started by sandbox on n027.cluster.edu,
% 1.67/1.88  Wed Jul 27 05:13:21 2022
% 1.67/1.88  The command was "./otter".  The process ID is 11027.
% 1.67/1.88  
% 1.67/1.88  set(prolog_style_variables).
% 1.67/1.88  set(auto).
% 1.67/1.88     dependent: set(auto1).
% 1.67/1.88     dependent: set(process_input).
% 1.67/1.88     dependent: clear(print_kept).
% 1.67/1.88     dependent: clear(print_new_demod).
% 1.67/1.88     dependent: clear(print_back_demod).
% 1.67/1.88     dependent: clear(print_back_sub).
% 1.67/1.88     dependent: set(control_memory).
% 1.67/1.88     dependent: assign(max_mem, 12000).
% 1.67/1.88     dependent: assign(pick_given_ratio, 4).
% 1.67/1.88     dependent: assign(stats_level, 1).
% 1.67/1.88     dependent: assign(max_seconds, 10800).
% 1.67/1.88  clear(print_given).
% 1.67/1.88  
% 1.67/1.88  list(usable).
% 1.67/1.88  0 [] -group_element(X)| -group_element(Y)|product(e_1,X,Y)|product(e_2,X,Y)|product(e_3,X,Y).
% 1.67/1.88  0 [] -group_element(X)| -group_element(Y)|product(X,e_1,Y)|product(X,e_2,Y)|product(X,e_3,Y).
% 1.67/1.88  0 [] group_element(e_1).
% 1.67/1.88  0 [] group_element(e_2).
% 1.67/1.88  0 [] group_element(e_3).
% 1.67/1.88  0 [] -e_qualish(e_1,e_2).
% 1.67/1.88  0 [] -e_qualish(e_1,e_3).
% 1.67/1.88  0 [] -e_qualish(e_2,e_1).
% 1.67/1.88  0 [] -e_qualish(e_2,e_3).
% 1.67/1.88  0 [] -e_qualish(e_3,e_1).
% 1.67/1.88  0 [] -e_qualish(e_3,e_2).
% 1.67/1.88  0 [] -group_element(X)| -group_element(Y)|product1(X,Y,e_1)|product1(X,Y,e_2)|product1(X,Y,e_3).
% 1.67/1.88  0 [] -product1(X,Y,W)| -product1(X,Y,Z)|e_qualish(W,Z).
% 1.67/1.88  0 [] -product1(X,W,Y)| -product1(X,Z,Y)|e_qualish(W,Z).
% 1.67/1.88  0 [] -product1(W,Y,X)| -product1(Z,Y,X)|e_qualish(W,Z).
% 1.67/1.88  0 [] product1(X,X,X).
% 1.67/1.88  0 [] -group_element(X)| -group_element(Y)|product2(X,Y,e_1)|product2(X,Y,e_2)|product2(X,Y,e_3).
% 1.67/1.88  0 [] -product2(X,Y,W)| -product2(X,Y,Z)|e_qualish(W,Z).
% 1.67/1.88  0 [] -product2(X,W,Y)| -product2(X,Z,Y)|e_qualish(W,Z).
% 1.67/1.88  0 [] -product2(W,Y,X)| -product2(Z,Y,X)|e_qualish(W,Z).
% 1.67/1.88  0 [] product2(X,X,X).
% 1.67/1.88  0 [] -product1(X,Y,Z1)| -product1(Z1,Y,Z2)|product2(Z2,X,Y).
% 1.67/1.88  end_of_list.
% 1.67/1.88  
% 1.67/1.88  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.67/1.88  
% 1.67/1.88  This is a non-Horn set without equality.  The strategy will
% 1.67/1.88  be ordered hyper_res, unit deletion, and factoring, with
% 1.67/1.88  satellites in sos and with nuclei in usable.
% 1.67/1.88  
% 1.67/1.88     dependent: set(hyper_res).
% 1.67/1.88     dependent: set(factor).
% 1.67/1.88     dependent: set(unit_deletion).
% 1.67/1.88  
% 1.67/1.88  ------------> process usable:
% 1.67/1.88  ** 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).
% 1.67/1.88  ** 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).
% 1.67/1.88  ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_2).
% 1.67/1.88  ** KEPT (pick-wt=3): 4 [] -e_qualish(e_1,e_3).
% 1.67/1.88  ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_1).
% 1.67/1.88  ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_3).
% 1.67/1.88  ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_1).
% 1.67/1.88  ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_2).
% 1.67/1.88  ** KEPT (pick-wt=16): 9 [] -group_element(A)| -group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3).
% 1.67/1.88  ** KEPT (pick-wt=11): 10 [] -product1(A,B,C)| -product1(A,B,D)|e_qualish(C,D).
% 1.67/1.88  ** KEPT (pick-wt=11): 11 [] -product1(A,B,C)| -product1(A,D,C)|e_qualish(B,D).
% 1.67/1.88  ** KEPT (pick-wt=11): 12 [] -product1(A,B,C)| -product1(D,B,C)|e_qualish(A,D).
% 1.67/1.88  ** KEPT (pick-wt=16): 13 [] -group_element(A)| -group_element(B)|product2(A,B,e_1)|product2(A,B,e_2)|product2(A,B,e_3).
% 1.67/1.88  ** KEPT (pick-wt=11): 14 [] -product2(A,B,C)| -product2(A,B,D)|e_qualish(C,D).
% 1.67/1.88  ** KEPT (pick-wt=11): 15 [] -product2(A,B,C)| -product2(A,D,C)|e_qualish(B,D).
% 1.67/1.88  ** KEPT (pick-wt=11): 16 [] -product2(A,B,C)| -product2(D,B,C)|e_qualish(A,D).
% 1.67/1.88  ** KEPT (pick-wt=12): 17 [] -product1(A,B,C)| -product1(C,B,D)|product2(D,A,B).
% 1.67/1.88  
% 1.67/1.88  ------------> process sos:
% 1.67/1.88  ** KEPT (pick-wt=2): 29 [] group_element(e_1).
% 1.67/1.88  ** KEPT (pick-wt=2): 30 [] group_element(e_2).
% 1.67/1.88  ** KEPT (pick-wt=2): 31 [] group_element(e_3).
% 1.67/1.88  ** KEPT (pick-wt=4): 32 [] product1(A,A,A).
% 1.67/1.88  ** KEPT (pick-wt=4): 33 [] product2(A,A,A).
% 1.67/1.88  
% 1.67/1.88  ======= end of input processing =======
% 1.67/1.88  
% 1.67/1.88  =========== start of search ===========
% 1.67/1.88  
% 1.67/1.88  -------- PROOF -------- 
% 1.67/1.88  
% 1.67/1.88  ----> UNIT CONFLICT at   0.01 sec ----> 123 [binary,122.1,3.1] $F.
% 1.67/1.88  
% 1.67/1.88  Length of proof is 11.  Level of proof is 7.
% 1.67/1.88  
% 1.67/1.88  ---------------- PROOF ----------------
% 1.67/1.88  % SZS status Unsatisfiable
% 1.67/1.88  % SZS output start Refutation
% See solution above
% 1.67/1.88  ------------ end of proof -------------
% 1.67/1.88  
% 1.67/1.88  
% 1.67/1.88  Search stopped by max_proofs option.
% 1.67/1.88  
% 1.67/1.88  
% 1.67/1.88  Search stopped by max_proofs option.
% 1.67/1.88  
% 1.67/1.88  ============ end of search ============
% 1.67/1.88  
% 1.67/1.88  -------------- statistics -------------
% 1.67/1.88  clauses given                 48
% 1.67/1.88  clauses generated            794
% 1.67/1.88  clauses kept                 122
% 1.67/1.88  clauses forward subsumed     694
% 1.67/1.88  clauses back subsumed         58
% 1.67/1.88  Kbytes malloced              976
% 1.67/1.88  
% 1.67/1.88  ----------- times (seconds) -----------
% 1.67/1.88  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.67/1.88  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.67/1.88  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.67/1.88  
% 1.67/1.88  That finishes the proof of the theorem.
% 1.67/1.88  
% 1.67/1.88  Process 11027 finished Wed Jul 27 05:13:23 2022
% 1.67/1.88  Otter interrupted
% 1.67/1.88  PROOF FOUND
%------------------------------------------------------------------------------