TSTP Solution File: GRP123-7.003 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP123-7.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n017.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 1.61s 1.78s
% Output   : Refutation 1.61s
% 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(2,axiom,
    ~ e_qualish(e_1,e_2),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(4,axiom,
    ~ e_qualish(e_2,e_1),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(5,axiom,
    ~ e_qualish(e_2,e_3),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(6,axiom,
    ~ e_qualish(e_3,e_1),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(7,axiom,
    ~ e_qualish(e_3,e_2),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product1(A,B,e_1)
    | product1(A,B,e_2)
    | product1(A,B,e_3) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(A,D,C)
    | e_qualish(B,D) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(D,B,C)
    | e_qualish(A,D) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product2(A,B,e_1)
    | product2(A,B,e_2)
    | product2(A,B,e_3) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ product2(A,B,C)
    | ~ product2(A,D,C)
    | e_qualish(B,D) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ product2(A,B,C)
    | ~ product2(D,B,C)
    | e_qualish(A,D) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(C,B,D)
    | product2(D,A,B) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(31,axiom,
    group_element(e_1),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(32,axiom,
    group_element(e_2),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(33,axiom,
    group_element(e_3),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(34,axiom,
    product1(A,A,A),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(35,axiom,
    product2(A,A,A),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(36,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)],[32,12,31]),
    [iquote('hyper,32,12,31')] ).

cnf(44,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)],[33,8,32]),
    [iquote('hyper,33,8,32')] ).

cnf(45,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)],[33,8,31]),
    [iquote('hyper,33,8,31')] ).

cnf(49,plain,
    ( product2(e_1,e_2,e_2)
    | product2(e_1,e_2,e_3) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[36,14,35]),2]),
    [iquote('hyper,36,14,35,unit_del,2')] ).

cnf(51,plain,
    product2(e_1,e_2,e_3),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[49,15,35]),4]),
    [iquote('hyper,49,15,35,unit_del,4')] ).

cnf(80,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_3,e_3) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[44,10,34]),5]),
    [iquote('hyper,44,10,34,unit_del,5')] ).

cnf(84,plain,
    product1(e_2,e_3,e_1),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[80,11,34]),7]),
    [iquote('hyper,80,11,34,unit_del,7')] ).

cnf(86,plain,
    ( product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[45,11,84]),4]),
    [iquote('hyper,45,11,84,unit_del,4')] ).

cnf(96,plain,
    product1(e_1,e_3,e_2),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[86,11,34]),6]),
    [iquote('hyper,86,11,34,unit_del,6')] ).

cnf(104,plain,
    product2(e_2,e_2,e_3),
    inference(hyper,[status(thm)],[96,16,84]),
    [iquote('hyper,96,16,84')] ).

cnf(106,plain,
    e_qualish(e_1,e_2),
    inference(hyper,[status(thm)],[104,15,51]),
    [iquote('hyper,104,15,51')] ).

cnf(107,plain,
    $false,
    inference(binary,[status(thm)],[106,2]),
    [iquote('binary,106.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GRP123-7.003 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n017.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 04:30:33 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.61/1.78  ----- Otter 3.3f, August 2004 -----
% 1.61/1.78  The process was started by sandbox on n017.cluster.edu,
% 1.61/1.78  Wed Jul 27 04:30:33 2022
% 1.61/1.78  The command was "./otter".  The process ID is 16461.
% 1.61/1.78  
% 1.61/1.78  set(prolog_style_variables).
% 1.61/1.78  set(auto).
% 1.61/1.78     dependent: set(auto1).
% 1.61/1.78     dependent: set(process_input).
% 1.61/1.78     dependent: clear(print_kept).
% 1.61/1.78     dependent: clear(print_new_demod).
% 1.61/1.78     dependent: clear(print_back_demod).
% 1.61/1.78     dependent: clear(print_back_sub).
% 1.61/1.78     dependent: set(control_memory).
% 1.61/1.78     dependent: assign(max_mem, 12000).
% 1.61/1.78     dependent: assign(pick_given_ratio, 4).
% 1.61/1.78     dependent: assign(stats_level, 1).
% 1.61/1.78     dependent: assign(max_seconds, 10800).
% 1.61/1.78  clear(print_given).
% 1.61/1.78  
% 1.61/1.78  list(usable).
% 1.61/1.78  0 [] next(e_1,e_2).
% 1.61/1.78  0 [] next(e_2,e_3).
% 1.61/1.78  0 [] greater(e_2,e_1).
% 1.61/1.78  0 [] greater(e_3,e_1).
% 1.61/1.78  0 [] greater(e_3,e_2).
% 1.61/1.78  0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.61/1.78  0 [] group_element(e_1).
% 1.61/1.78  0 [] group_element(e_2).
% 1.61/1.78  0 [] group_element(e_3).
% 1.61/1.78  0 [] -e_qualish(e_1,e_2).
% 1.61/1.78  0 [] -e_qualish(e_1,e_3).
% 1.61/1.78  0 [] -e_qualish(e_2,e_1).
% 1.61/1.78  0 [] -e_qualish(e_2,e_3).
% 1.61/1.78  0 [] -e_qualish(e_3,e_1).
% 1.61/1.78  0 [] -e_qualish(e_3,e_2).
% 1.61/1.78  0 [] -group_element(X)| -group_element(Y)|product1(X,Y,e_1)|product1(X,Y,e_2)|product1(X,Y,e_3).
% 1.61/1.78  0 [] -product1(X,Y,W)| -product1(X,Y,Z)|e_qualish(W,Z).
% 1.61/1.78  0 [] -product1(X,W,Y)| -product1(X,Z,Y)|e_qualish(W,Z).
% 1.61/1.78  0 [] -product1(W,Y,X)| -product1(Z,Y,X)|e_qualish(W,Z).
% 1.61/1.78  0 [] product1(X,X,X).
% 1.61/1.78  0 [] -group_element(X)| -group_element(Y)|product2(X,Y,e_1)|product2(X,Y,e_2)|product2(X,Y,e_3).
% 1.61/1.78  0 [] -product2(X,Y,W)| -product2(X,Y,Z)|e_qualish(W,Z).
% 1.61/1.78  0 [] -product2(X,W,Y)| -product2(X,Z,Y)|e_qualish(W,Z).
% 1.61/1.78  0 [] -product2(W,Y,X)| -product2(Z,Y,X)|e_qualish(W,Z).
% 1.61/1.78  0 [] product2(X,X,X).
% 1.61/1.78  0 [] -product1(X,Y,Z1)| -product1(Z1,Y,Z2)|product2(Z2,X,Y).
% 1.61/1.78  end_of_list.
% 1.61/1.78  
% 1.61/1.78  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.61/1.78  
% 1.61/1.78  This is a non-Horn set without equality.  The strategy will
% 1.61/1.78  be ordered hyper_res, unit deletion, and factoring, with
% 1.61/1.78  satellites in sos and with nuclei in usable.
% 1.61/1.78  
% 1.61/1.78     dependent: set(hyper_res).
% 1.61/1.78     dependent: set(factor).
% 1.61/1.78     dependent: set(unit_deletion).
% 1.61/1.78  
% 1.61/1.78  ------------> process usable:
% 1.61/1.78  ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.61/1.78  ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.61/1.78  ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_3).
% 1.61/1.78  ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_1).
% 1.61/1.78  ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_3).
% 1.61/1.78  ** KEPT (pick-wt=3): 6 [] -e_qualish(e_3,e_1).
% 1.61/1.78  ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_2).
% 1.61/1.78  ** KEPT (pick-wt=16): 8 [] -group_element(A)| -group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3).
% 1.61/1.78  ** KEPT (pick-wt=11): 9 [] -product1(A,B,C)| -product1(A,B,D)|e_qualish(C,D).
% 1.61/1.78  ** KEPT (pick-wt=11): 10 [] -product1(A,B,C)| -product1(A,D,C)|e_qualish(B,D).
% 1.61/1.78  ** KEPT (pick-wt=11): 11 [] -product1(A,B,C)| -product1(D,B,C)|e_qualish(A,D).
% 1.61/1.78  ** KEPT (pick-wt=16): 12 [] -group_element(A)| -group_element(B)|product2(A,B,e_1)|product2(A,B,e_2)|product2(A,B,e_3).
% 1.61/1.78  ** KEPT (pick-wt=11): 13 [] -product2(A,B,C)| -product2(A,B,D)|e_qualish(C,D).
% 1.61/1.78  ** KEPT (pick-wt=11): 14 [] -product2(A,B,C)| -product2(A,D,C)|e_qualish(B,D).
% 1.61/1.78  ** KEPT (pick-wt=11): 15 [] -product2(A,B,C)| -product2(D,B,C)|e_qualish(A,D).
% 1.61/1.78  ** KEPT (pick-wt=12): 16 [] -product1(A,B,C)| -product1(C,B,D)|product2(D,A,B).
% 1.61/1.78  
% 1.61/1.78  ------------> process sos:
% 1.61/1.78  ** KEPT (pick-wt=3): 26 [] next(e_1,e_2).
% 1.61/1.78  ** KEPT (pick-wt=3): 27 [] next(e_2,e_3).
% 1.61/1.78  ** KEPT (pick-wt=3): 28 [] greater(e_2,e_1).
% 1.61/1.78  ** KEPT (pick-wt=3): 29 [] greater(e_3,e_1).
% 1.61/1.78  ** KEPT (pick-wt=3): 30 [] greater(e_3,e_2).
% 1.61/1.78  ** KEPT (pick-wt=2): 31 [] group_element(e_1).
% 1.61/1.78  ** KEPT (pick-wt=2): 32 [] group_element(e_2).
% 1.61/1.78  ** KEPT (pick-wt=2): 33 [] group_element(e_3).
% 1.61/1.78  ** KEPT (pick-wt=4): 34 [] product1(A,A,A).
% 1.61/1.78  ** KEPT (pick-wt=4): 35 [] product2(A,A,A).
% 1.61/1.78  
% 1.61/1.78  ======= end of input processing =======
% 1.61/1.78  
% 1.61/1.78  =========== start of search ===========
% 1.61/1.78  
% 1.61/1.78  -------- PROOF -------- 
% 1.61/1.78  
% 1.61/1.78  ----> UNIT CONFLICT at   0.01 sec ----> 107 [binary,106.1,2.1] $F.
% 1.61/1.78  
% 1.61/1.78  Length of proof is 11.  Level of proof is 7.
% 1.61/1.78  
% 1.61/1.78  ---------------- PROOF ----------------
% 1.61/1.78  % SZS status Unsatisfiable
% 1.61/1.78  % SZS output start Refutation
% See solution above
% 1.61/1.78  ------------ end of proof -------------
% 1.61/1.78  
% 1.61/1.78  
% 1.61/1.78  Search stopped by max_proofs option.
% 1.61/1.78  
% 1.61/1.78  
% 1.61/1.78  Search stopped by max_proofs option.
% 1.61/1.78  
% 1.61/1.78  ============ end of search ============
% 1.61/1.78  
% 1.61/1.78  -------------- statistics -------------
% 1.61/1.78  clauses given                 43
% 1.61/1.78  clauses generated            762
% 1.61/1.78  clauses kept                 106
% 1.61/1.78  clauses forward subsumed     682
% 1.61/1.78  clauses back subsumed         58
% 1.61/1.78  Kbytes malloced              976
% 1.61/1.78  
% 1.61/1.78  ----------- times (seconds) -----------
% 1.61/1.78  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.61/1.78  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.61/1.78  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.61/1.78  
% 1.61/1.78  That finishes the proof of the theorem.
% 1.61/1.78  
% 1.61/1.78  Process 16461 finished Wed Jul 27 04:30:34 2022
% 1.61/1.78  Otter interrupted
% 1.61/1.78  PROOF FOUND
%------------------------------------------------------------------------------