TSTP Solution File: GRP131-2.002 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP131-2.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n021.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 1.73s 1.97s
% Output   : Refutation 1.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   26 (  10 unt;  10 nHn;  26 RR)
%            Number of literals    :   57 (   0 equ;  23 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   :   31 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ~ e_qualish(e_1,e_2),
    file('GRP131-2.002.p',unknown),
    [] ).

cnf(3,axiom,
    ~ e_qualish(e_2,e_1),
    file('GRP131-2.002.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product(A,B,e_1)
    | product(A,B,e_2) ),
    file('GRP131-2.002.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ product(A,B,C)
    | ~ product(A,D,C)
    | e_qualish(B,D) ),
    file('GRP131-2.002.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,B,C)
    | e_qualish(A,D) ),
    file('GRP131-2.002.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,E,C)
    | ~ product(F,B,A)
    | ~ product(F,E,D)
    | e_qualish(A,D) ),
    file('GRP131-2.002.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,E,C)
    | ~ product(F,B,A)
    | ~ product(F,E,D)
    | e_qualish(B,E) ),
    file('GRP131-2.002.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(15,plain,
    ( ~ product(A,B,C)
    | ~ product(C,D,C)
    | ~ product(C,B,A)
    | e_qualish(A,C) ),
    inference(factor,[status(thm)],[8]),
    [iquote('factor,8.2.4')] ).

cnf(17,plain,
    ( ~ product(A,B,C)
    | ~ product(C,D,C)
    | ~ product(C,B,A)
    | e_qualish(B,D) ),
    inference(factor,[status(thm)],[9]),
    [iquote('factor,9.2.4')] ).

cnf(20,axiom,
    group_element(e_1),
    file('GRP131-2.002.p',unknown),
    [] ).

cnf(21,axiom,
    group_element(e_2),
    file('GRP131-2.002.p',unknown),
    [] ).

cnf(22,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference(hyper,[status(thm)],[20,10]),
    [iquote('hyper,20,10')] ).

cnf(23,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2) ),
    inference(hyper,[status(thm)],[21,10]),
    [iquote('hyper,21,10')] ).

cnf(24,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2) ),
    inference(hyper,[status(thm)],[21,4,20]),
    [iquote('hyper,21,4,20')] ).

cnf(25,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2) ),
    inference(hyper,[status(thm)],[21,4,20]),
    [iquote('hyper,21,4,20')] ).

cnf(35,plain,
    ( product(e_1,e_2,e_2)
    | product(e_2,e_2,e_2) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[24,7,23]),3]),
    [iquote('hyper,24,7,23,unit_del,3')] ).

cnf(39,plain,
    ( product(e_1,e_2,e_1)
    | product(e_2,e_2,e_1) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[24,7,23]),3]),
    [iquote('hyper,24,7,23,unit_del,3')] ).

cnf(40,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_1,e_1) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[24,6,22]),2]),
    [iquote('hyper,24,6,22,unit_del,2')] ).

cnf(48,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_2,e_1) ),
    inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[25,17,25,23]),2])]),
    [iquote('hyper,25,17,25,23,unit_del,2,factor_simp')] ).

cnf(66,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)],[40,17,39,24]),3])])]),
    [iquote('hyper,40,17,39,24,unit_del,3,factor_simp,factor_simp')] ).

cnf(68,plain,
    product(e_1,e_1,e_2),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[66,17,66,22]),3]),
    [iquote('hyper,66,17,66,22,unit_del,3')] ).

cnf(70,plain,
    product(e_2,e_2,e_2),
    inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[66,15,23,35]),3])]),
    [iquote('hyper,66,15,23,35,unit_del,3,factor_simp')] ).

cnf(71,plain,
    product(e_2,e_1,e_1),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[48,7,66]),2]),
    [iquote('hyper,48,7,66,unit_del,2')] ).

cnf(72,plain,
    e_qualish(e_1,e_2),
    inference(hyper,[status(thm)],[71,17,68,70]),
    [iquote('hyper,71,17,68,70')] ).

cnf(73,plain,
    $false,
    inference(binary,[status(thm)],[72,2]),
    [iquote('binary,72.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP131-2.002 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n021.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 04:58:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.73/1.97  ----- Otter 3.3f, August 2004 -----
% 1.73/1.97  The process was started by sandbox on n021.cluster.edu,
% 1.73/1.97  Wed Jul 27 04:58:53 2022
% 1.73/1.97  The command was "./otter".  The process ID is 22021.
% 1.73/1.97  
% 1.73/1.97  set(prolog_style_variables).
% 1.73/1.97  set(auto).
% 1.73/1.97     dependent: set(auto1).
% 1.73/1.97     dependent: set(process_input).
% 1.73/1.97     dependent: clear(print_kept).
% 1.73/1.97     dependent: clear(print_new_demod).
% 1.73/1.97     dependent: clear(print_back_demod).
% 1.73/1.97     dependent: clear(print_back_sub).
% 1.73/1.97     dependent: set(control_memory).
% 1.73/1.97     dependent: assign(max_mem, 12000).
% 1.73/1.97     dependent: assign(pick_given_ratio, 4).
% 1.73/1.97     dependent: assign(stats_level, 1).
% 1.73/1.97     dependent: assign(max_seconds, 10800).
% 1.73/1.97  clear(print_given).
% 1.73/1.97  
% 1.73/1.97  list(usable).
% 1.73/1.97  0 [] next(e_1,e_2).
% 1.73/1.97  0 [] greater(e_2,e_1).
% 1.73/1.97  0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.73/1.97  0 [] group_element(e_1).
% 1.73/1.97  0 [] group_element(e_2).
% 1.73/1.97  0 [] -e_qualish(e_1,e_2).
% 1.73/1.97  0 [] -e_qualish(e_2,e_1).
% 1.73/1.97  0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2).
% 1.73/1.97  0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.73/1.97  0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.73/1.97  0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.73/1.97  0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,Y1,X1)| -product(Z2,Y2,X2)|e_qualish(X1,X2).
% 1.73/1.97  0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,Y1,X1)| -product(Z2,Y2,X2)|e_qualish(Y1,Y2).
% 1.73/1.97  end_of_list.
% 1.73/1.97  
% 1.73/1.97  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.73/1.97  
% 1.73/1.97  This is a non-Horn set without equality.  The strategy will
% 1.73/1.97  be ordered hyper_res, unit deletion, and factoring, with
% 1.73/1.97  satellites in sos and with nuclei in usable.
% 1.73/1.97  
% 1.73/1.97     dependent: set(hyper_res).
% 1.73/1.97     dependent: set(factor).
% 1.73/1.97     dependent: set(unit_deletion).
% 1.73/1.97  
% 1.73/1.97  ------------> process usable:
% 1.73/1.97  ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.73/1.97  ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.73/1.97  ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 1.73/1.97  ** KEPT (pick-wt=12): 4 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2).
% 1.73/1.97  ** KEPT (pick-wt=11): 5 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.73/1.97  ** KEPT (pick-wt=11): 6 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.73/1.97  ** KEPT (pick-wt=11): 7 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.73/1.97  ** KEPT (pick-wt=19): 8 [] -product(A,B,C)| -product(D,E,C)| -product(F,B,A)| -product(F,E,D)|e_qualish(A,D).
% 1.73/1.97  ** KEPT (pick-wt=19): 9 [] -product(A,B,C)| -product(D,E,C)| -product(F,B,A)| -product(F,E,D)|e_qualish(B,E).
% 1.73/1.97  
% 1.73/1.97  ------------> process sos:
% 1.73/1.97  ** KEPT (pick-wt=3): 18 [] next(e_1,e_2).
% 1.73/1.97  ** KEPT (pick-wt=3): 19 [] greater(e_2,e_1).
% 1.73/1.97  ** KEPT (pick-wt=2): 20 [] group_element(e_1).
% 1.73/1.97  ** KEPT (pick-wt=2): 21 [] group_element(e_2).
% 1.73/1.97  
% 1.73/1.97  ======= end of input processing =======
% 1.73/1.97  
% 1.73/1.97  =========== start of search ===========
% 1.73/1.97  
% 1.73/1.97  -------- PROOF -------- 
% 1.73/1.97  
% 1.73/1.97  ----> UNIT CONFLICT at   0.08 sec ----> 73 [binary,72.1,2.1] $F.
% 1.73/1.97  
% 1.73/1.97  Length of proof is 16.  Level of proof is 6.
% 1.73/1.97  
% 1.73/1.97  ---------------- PROOF ----------------
% 1.73/1.97  % SZS status Unsatisfiable
% 1.73/1.97  % SZS output start Refutation
% See solution above
% 1.73/1.97  ------------ end of proof -------------
% 1.73/1.97  
% 1.73/1.97  
% 1.73/1.97  Search stopped by max_proofs option.
% 1.73/1.97  
% 1.73/1.97  
% 1.73/1.97  Search stopped by max_proofs option.
% 1.73/1.97  
% 1.73/1.97  ============ end of search ============
% 1.73/1.97  
% 1.73/1.97  -------------- statistics -------------
% 1.73/1.97  clauses given                 35
% 1.73/1.97  clauses generated           4850
% 1.73/1.97  clauses kept                  72
% 1.73/1.97  clauses forward subsumed    4791
% 1.73/1.97  clauses back subsumed         42
% 1.73/1.97  Kbytes malloced              976
% 1.73/1.97  
% 1.73/1.97  ----------- times (seconds) -----------
% 1.73/1.97  user CPU time          0.08          (0 hr, 0 min, 0 sec)
% 1.73/1.97  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.73/1.97  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.73/1.97  
% 1.73/1.97  That finishes the proof of the theorem.
% 1.73/1.97  
% 1.73/1.97  Process 22021 finished Wed Jul 27 04:58:54 2022
% 1.73/1.97  Otter interrupted
% 1.73/1.97  PROOF FOUND
%------------------------------------------------------------------------------