TSTP Solution File: GRP132-2.002 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP132-2.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n003.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 12:56:30 EDT 2022

% Result   : Unsatisfiable 1.83s 2.03s
% Output   : Refutation 1.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   23 (  10 unt;   9 nHn;  23 RR)
%            Number of literals    :   46 (   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    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   20 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ~ e_qualish(e_1,e_2),
    file('GRP132-2.002.p',unknown),
    [] ).

cnf(3,axiom,
    ~ e_qualish(e_2,e_1),
    file('GRP132-2.002.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product(A,B,e_1)
    | product(A,B,e_2) ),
    file('GRP132-2.002.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ product(A,B,C)
    | ~ product(A,D,C)
    | e_qualish(B,D) ),
    file('GRP132-2.002.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,B,C)
    | e_qualish(A,D) ),
    file('GRP132-2.002.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,E,C)
    | ~ product(F,A,B)
    | ~ product(F,D,E)
    | e_qualish(B,E) ),
    file('GRP132-2.002.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ group_element(A)
    | product(A,A,e_1)
    | product(A,A,e_2) ),
    inference(factor,[status(thm)],[4]),
    [iquote('factor,4.1.2')] ).

cnf(21,plain,
    ( ~ product(A,B,C)
    | ~ product(C,C,C)
    | ~ product(C,A,B)
    | e_qualish(B,C) ),
    inference(factor,[status(thm)],[9]),
    [iquote('factor,9.2.4')] ).

cnf(24,axiom,
    group_element(e_1),
    file('GRP132-2.002.p',unknown),
    [] ).

cnf(25,axiom,
    group_element(e_2),
    file('GRP132-2.002.p',unknown),
    [] ).

cnf(26,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference(hyper,[status(thm)],[24,10]),
    [iquote('hyper,24,10')] ).

cnf(27,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2) ),
    inference(hyper,[status(thm)],[25,10]),
    [iquote('hyper,25,10')] ).

cnf(28,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2) ),
    inference(hyper,[status(thm)],[25,4,24]),
    [iquote('hyper,25,4,24')] ).

cnf(29,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2) ),
    inference(hyper,[status(thm)],[25,4,24]),
    [iquote('hyper,25,4,24')] ).

cnf(44,plain,
    ( product(e_1,e_2,e_1)
    | product(e_2,e_2,e_1) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[28,7,27]),3]),
    [iquote('hyper,28,7,27,unit_del,3')] ).

cnf(45,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_1,e_1) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[28,6,26]),2]),
    [iquote('hyper,28,6,26,unit_del,2')] ).

cnf(56,plain,
    ( product(e_2,e_1,e_1)
    | product(e_1,e_1,e_1) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[29,7,26]),2]),
    [iquote('hyper,29,7,26,unit_del,2')] ).

cnf(71,plain,
    product(e_1,e_2,e_1),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[45,21,44,28]),3])])]),
    [iquote('hyper,45,21,44,28,unit_del,3,factor_simp,factor_simp')] ).

cnf(74,plain,
    product(e_2,e_2,e_2),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[71,7,27]),3]),
    [iquote('hyper,71,7,27,unit_del,3')] ).

cnf(75,plain,
    product(e_1,e_1,e_2),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[71,6,26]),2]),
    [iquote('hyper,71,6,26,unit_del,2')] ).

cnf(76,plain,
    product(e_2,e_1,e_1),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[56,6,71]),3]),
    [iquote('hyper,56,6,71,unit_del,3')] ).

cnf(77,plain,
    e_qualish(e_1,e_2),
    inference(hyper,[status(thm)],[76,21,75,74]),
    [iquote('hyper,76,21,75,74')] ).

cnf(78,plain,
    $false,
    inference(binary,[status(thm)],[77,2]),
    [iquote('binary,77.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GRP132-2.002 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 05:13:56 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.83/2.03  ----- Otter 3.3f, August 2004 -----
% 1.83/2.03  The process was started by sandbox2 on n003.cluster.edu,
% 1.83/2.03  Wed Jul 27 05:13:56 2022
% 1.83/2.03  The command was "./otter".  The process ID is 1359.
% 1.83/2.03  
% 1.83/2.03  set(prolog_style_variables).
% 1.83/2.03  set(auto).
% 1.83/2.03     dependent: set(auto1).
% 1.83/2.03     dependent: set(process_input).
% 1.83/2.03     dependent: clear(print_kept).
% 1.83/2.03     dependent: clear(print_new_demod).
% 1.83/2.03     dependent: clear(print_back_demod).
% 1.83/2.03     dependent: clear(print_back_sub).
% 1.83/2.03     dependent: set(control_memory).
% 1.83/2.03     dependent: assign(max_mem, 12000).
% 1.83/2.03     dependent: assign(pick_given_ratio, 4).
% 1.83/2.03     dependent: assign(stats_level, 1).
% 1.83/2.03     dependent: assign(max_seconds, 10800).
% 1.83/2.03  clear(print_given).
% 1.83/2.03  
% 1.83/2.03  list(usable).
% 1.83/2.03  0 [] next(e_1,e_2).
% 1.83/2.03  0 [] greater(e_2,e_1).
% 1.83/2.03  0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.83/2.03  0 [] group_element(e_1).
% 1.83/2.03  0 [] group_element(e_2).
% 1.83/2.03  0 [] -e_qualish(e_1,e_2).
% 1.83/2.03  0 [] -e_qualish(e_2,e_1).
% 1.83/2.03  0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2).
% 1.83/2.03  0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.83/2.03  0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.83/2.03  0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.83/2.03  0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(X1,X2).
% 1.83/2.03  0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(Y1,Y2).
% 1.83/2.03  end_of_list.
% 1.83/2.03  
% 1.83/2.03  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.83/2.03  
% 1.83/2.03  This is a non-Horn set without equality.  The strategy will
% 1.83/2.03  be ordered hyper_res, unit deletion, and factoring, with
% 1.83/2.03  satellites in sos and with nuclei in usable.
% 1.83/2.03  
% 1.83/2.03     dependent: set(hyper_res).
% 1.83/2.03     dependent: set(factor).
% 1.83/2.03     dependent: set(unit_deletion).
% 1.83/2.03  
% 1.83/2.03  ------------> process usable:
% 1.83/2.03  ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.83/2.03  ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.83/2.03  ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 1.83/2.03  ** KEPT (pick-wt=12): 4 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2).
% 1.83/2.03  ** KEPT (pick-wt=11): 5 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.83/2.03  ** KEPT (pick-wt=11): 6 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.83/2.03  ** KEPT (pick-wt=11): 7 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.83/2.03  ** KEPT (pick-wt=19): 8 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(A,D).
% 1.83/2.03  ** KEPT (pick-wt=19): 9 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(B,E).
% 1.83/2.03  
% 1.83/2.03  ------------> process sos:
% 1.83/2.03  ** KEPT (pick-wt=3): 22 [] next(e_1,e_2).
% 1.83/2.03  ** KEPT (pick-wt=3): 23 [] greater(e_2,e_1).
% 1.83/2.03  ** KEPT (pick-wt=2): 24 [] group_element(e_1).
% 1.83/2.03  ** KEPT (pick-wt=2): 25 [] group_element(e_2).
% 1.83/2.03  
% 1.83/2.03  ======= end of input processing =======
% 1.83/2.03  
% 1.83/2.03  =========== start of search ===========
% 1.83/2.03  
% 1.83/2.03  -------- PROOF -------- 
% 1.83/2.03  
% 1.83/2.03  ----> UNIT CONFLICT at   0.08 sec ----> 78 [binary,77.1,2.1] $F.
% 1.83/2.03  
% 1.83/2.03  Length of proof is 14.  Level of proof is 6.
% 1.83/2.03  
% 1.83/2.03  ---------------- PROOF ----------------
% 1.83/2.03  % SZS status Unsatisfiable
% 1.83/2.03  % SZS output start Refutation
% See solution above
% 1.83/2.03  ------------ end of proof -------------
% 1.83/2.03  
% 1.83/2.03  
% 1.83/2.03  Search stopped by max_proofs option.
% 1.83/2.03  
% 1.83/2.03  
% 1.83/2.03  Search stopped by max_proofs option.
% 1.83/2.03  
% 1.83/2.03  ============ end of search ============
% 1.83/2.03  
% 1.83/2.03  -------------- statistics -------------
% 1.83/2.03  clauses given                 35
% 1.83/2.03  clauses generated           3958
% 1.83/2.03  clauses kept                  77
% 1.83/2.03  clauses forward subsumed    3894
% 1.83/2.03  clauses back subsumed         43
% 1.83/2.03  Kbytes malloced              976
% 1.83/2.03  
% 1.83/2.03  ----------- times (seconds) -----------
% 1.83/2.03  user CPU time          0.08          (0 hr, 0 min, 0 sec)
% 1.83/2.03  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.83/2.03  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.83/2.03  
% 1.83/2.03  That finishes the proof of the theorem.
% 1.83/2.03  
% 1.83/2.03  Process 1359 finished Wed Jul 27 05:13:58 2022
% 1.83/2.03  Otter interrupted
% 1.83/2.03  PROOF FOUND
%------------------------------------------------------------------------------