TSTP Solution File: GRP124-7.004 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP124-7.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n029.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 12:56:09 EDT 2022

% Result   : Unsatisfiable 1.75s 1.94s
% Output   : Refutation 1.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   21
% Syntax   : Number of clauses     :   57 (  22 unt;  29 nHn;  55 RR)
%            Number of literals    :  125 (   0 equ;  24 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   30 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ~ e_qualish(e_1,e_2),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(3,axiom,
    ~ e_qualish(e_1,e_3),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(4,axiom,
    ~ e_qualish(e_1,e_4),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(5,axiom,
    ~ e_qualish(e_2,e_1),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(6,axiom,
    ~ e_qualish(e_2,e_3),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(7,axiom,
    ~ e_qualish(e_2,e_4),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(8,axiom,
    ~ e_qualish(e_3,e_1),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(9,axiom,
    ~ e_qualish(e_3,e_2),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product1(A,B,e_1)
    | product1(A,B,e_2)
    | product1(A,B,e_3)
    | product1(A,B,e_4) ),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(A,D,C)
    | e_qualish(B,D) ),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(D,B,C)
    | e_qualish(A,D) ),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product2(A,B,e_1)
    | product2(A,B,e_2)
    | product2(A,B,e_3)
    | product2(A,B,e_4) ),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ product2(A,B,C)
    | ~ product2(A,B,D)
    | e_qualish(C,D) ),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ product2(A,B,C)
    | ~ product2(A,D,C)
    | e_qualish(B,D) ),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ product2(A,B,C)
    | ~ product2(D,B,C)
    | e_qualish(A,D) ),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ product1(A,B,C)
    | ~ product1(C,A,D)
    | product2(D,B,A) ),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(41,axiom,
    group_element(e_1),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(42,axiom,
    group_element(e_2),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(43,axiom,
    group_element(e_3),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(45,axiom,
    product1(A,A,A),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(46,axiom,
    product2(A,A,A),
    file('GRP124-7.004.p',unknown),
    [] ).

cnf(49,plain,
    ( product1(e_1,e_2,e_1)
    | product1(e_1,e_2,e_2)
    | product1(e_1,e_2,e_3)
    | product1(e_1,e_2,e_4) ),
    inference(hyper,[status(thm)],[42,14,41]),
    [iquote('hyper,42,14,41')] ).

cnf(50,plain,
    ( product1(e_2,e_1,e_1)
    | product1(e_2,e_1,e_2)
    | product1(e_2,e_1,e_3)
    | product1(e_2,e_1,e_4) ),
    inference(hyper,[status(thm)],[42,14,41]),
    [iquote('hyper,42,14,41')] ).

cnf(51,plain,
    ( product2(e_2,e_3,e_1)
    | product2(e_2,e_3,e_2)
    | product2(e_2,e_3,e_3)
    | product2(e_2,e_3,e_4) ),
    inference(hyper,[status(thm)],[43,18,42]),
    [iquote('hyper,43,18,42')] ).

cnf(52,plain,
    ( product2(e_1,e_3,e_1)
    | product2(e_1,e_3,e_2)
    | product2(e_1,e_3,e_3)
    | product2(e_1,e_3,e_4) ),
    inference(hyper,[status(thm)],[43,18,41]),
    [iquote('hyper,43,18,41')] ).

cnf(55,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_3,e_2)
    | product1(e_2,e_3,e_3)
    | product1(e_2,e_3,e_4) ),
    inference(hyper,[status(thm)],[43,14,42]),
    [iquote('hyper,43,14,42')] ).

cnf(56,plain,
    ( product1(e_1,e_3,e_1)
    | product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3)
    | product1(e_1,e_3,e_4) ),
    inference(hyper,[status(thm)],[43,14,41]),
    [iquote('hyper,43,14,41')] ).

cnf(78,plain,
    ( product1(e_1,e_2,e_2)
    | product1(e_1,e_2,e_3)
    | product1(e_1,e_2,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[49,16,45]),2]),
    [iquote('hyper,49,16,45,unit_del,2')] ).

cnf(81,plain,
    ( product1(e_1,e_2,e_3)
    | product1(e_1,e_2,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[78,17,45]),5]),
    [iquote('hyper,78,17,45,unit_del,5')] ).

cnf(84,plain,
    ( product1(e_2,e_1,e_2)
    | product1(e_2,e_1,e_3)
    | product1(e_2,e_1,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[50,17,45]),2]),
    [iquote('hyper,50,17,45,unit_del,2')] ).

cnf(88,plain,
    ( product1(e_2,e_1,e_3)
    | product1(e_2,e_1,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[84,16,45]),5]),
    [iquote('hyper,84,16,45,unit_del,5')] ).

cnf(89,plain,
    ( product2(e_2,e_3,e_1)
    | product2(e_2,e_3,e_3)
    | product2(e_2,e_3,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[51,20,46]),6]),
    [iquote('hyper,51,20,46,unit_del,6')] ).

cnf(92,plain,
    ( product2(e_2,e_3,e_1)
    | product2(e_2,e_3,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[89,21,46]),9]),
    [iquote('hyper,89,21,46,unit_del,9')] ).

cnf(94,plain,
    ( product2(e_1,e_3,e_2)
    | product2(e_1,e_3,e_3)
    | product2(e_1,e_3,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[52,20,46]),3]),
    [iquote('hyper,52,20,46,unit_del,3')] ).

cnf(98,plain,
    ( product2(e_1,e_3,e_2)
    | product2(e_1,e_3,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[94,21,46]),8]),
    [iquote('hyper,94,21,46,unit_del,8')] ).

cnf(101,plain,
    ( product2(e_1,e_3,e_2)
    | product2(e_2,e_3,e_1) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[98,21,92]),5]),
    [iquote('hyper,98,21,92,unit_del,5')] ).

cnf(128,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_3,e_3)
    | product1(e_2,e_3,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[55,16,45]),6]),
    [iquote('hyper,55,16,45,unit_del,6')] ).

cnf(133,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_3,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[128,17,45]),9]),
    [iquote('hyper,128,17,45,unit_del,9')] ).

cnf(136,plain,
    ( product1(e_2,e_3,e_4)
    | product2(e_3,e_3,e_2)
    | product1(e_1,e_2,e_4) ),
    inference(hyper,[status(thm)],[133,22,81]),
    [iquote('hyper,133,22,81')] ).

cnf(137,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_1,e_3) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[133,16,88]),3]),
    [iquote('hyper,133,16,88,unit_del,3')] ).

cnf(143,plain,
    ( product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3)
    | product1(e_1,e_3,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[56,16,45]),3]),
    [iquote('hyper,56,16,45,unit_del,3')] ).

cnf(159,plain,
    ( product1(e_2,e_3,e_4)
    | product1(e_1,e_2,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[136,19,46]),9]),
    [iquote('hyper,136,19,46,unit_del,9')] ).

cnf(160,plain,
    ( product1(e_1,e_2,e_4)
    | product1(e_2,e_1,e_3) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[159,16,88]),3]),
    [iquote('hyper,159,16,88,unit_del,3')] ).

cnf(220,plain,
    ( product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[143,17,45]),8]),
    [iquote('hyper,143,17,45,unit_del,8')] ).

cnf(230,plain,
    ( product1(e_1,e_3,e_2)
    | product1(e_1,e_2,e_4) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[220,17,159]),5]),
    [iquote('hyper,220,17,159,unit_del,5')] ).

cnf(235,plain,
    ( product1(e_1,e_2,e_4)
    | product2(e_3,e_3,e_1) ),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[230,22,160])]),
    [iquote('hyper,230,22,160,factor_simp')] ).

cnf(236,plain,
    product1(e_1,e_3,e_2),
    inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[230,16,220]),9])]),
    [iquote('hyper,230,16,220,unit_del,9,factor_simp')] ).

cnf(237,plain,
    ( product2(e_3,e_3,e_1)
    | product1(e_2,e_3,e_1) ),
    inference(hyper,[status(thm)],[236,22,137]),
    [iquote('hyper,236,22,137')] ).

cnf(238,plain,
    ( product2(e_4,e_3,e_1)
    | product1(e_2,e_1,e_3) ),
    inference(hyper,[status(thm)],[236,22,88]),
    [iquote('hyper,236,22,88')] ).

cnf(256,plain,
    product1(e_1,e_2,e_4),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[235,19,46]),8]),
    [iquote('hyper,235,19,46,unit_del,8')] ).

cnf(263,plain,
    product1(e_2,e_3,e_1),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[237,19,46]),8]),
    [iquote('hyper,237,19,46,unit_del,8')] ).

cnf(264,plain,
    product2(e_4,e_3,e_2),
    inference(hyper,[status(thm)],[263,22,256]),
    [iquote('hyper,263,22,256')] ).

cnf(276,plain,
    product2(e_2,e_3,e_1),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[264,21,101]),4]),
    [iquote('hyper,264,21,101,unit_del,4')] ).

cnf(284,plain,
    product1(e_2,e_1,e_3),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[238,21,276]),7]),
    [iquote('hyper,238,21,276,unit_del,7')] ).

cnf(285,plain,
    product2(e_3,e_3,e_1),
    inference(hyper,[status(thm)],[284,22,236]),
    [iquote('hyper,284,22,236')] ).

cnf(286,plain,
    e_qualish(e_2,e_3),
    inference(hyper,[status(thm)],[285,21,276]),
    [iquote('hyper,285,21,276')] ).

cnf(287,plain,
    $false,
    inference(binary,[status(thm)],[286,6]),
    [iquote('binary,286.1,6.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP124-7.004 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n029.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 05:25:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.69/1.90  ----- Otter 3.3f, August 2004 -----
% 1.69/1.90  The process was started by sandbox on n029.cluster.edu,
% 1.69/1.90  Wed Jul 27 05:25:59 2022
% 1.69/1.90  The command was "./otter".  The process ID is 22094.
% 1.69/1.90  
% 1.69/1.90  set(prolog_style_variables).
% 1.69/1.90  set(auto).
% 1.69/1.90     dependent: set(auto1).
% 1.69/1.90     dependent: set(process_input).
% 1.69/1.90     dependent: clear(print_kept).
% 1.69/1.90     dependent: clear(print_new_demod).
% 1.69/1.90     dependent: clear(print_back_demod).
% 1.69/1.90     dependent: clear(print_back_sub).
% 1.69/1.90     dependent: set(control_memory).
% 1.69/1.90     dependent: assign(max_mem, 12000).
% 1.69/1.90     dependent: assign(pick_given_ratio, 4).
% 1.69/1.90     dependent: assign(stats_level, 1).
% 1.69/1.90     dependent: assign(max_seconds, 10800).
% 1.69/1.90  clear(print_given).
% 1.69/1.90  
% 1.69/1.90  list(usable).
% 1.69/1.90  0 [] next(e_1,e_2).
% 1.69/1.90  0 [] next(e_2,e_3).
% 1.69/1.90  0 [] next(e_3,e_4).
% 1.69/1.90  0 [] greater(e_2,e_1).
% 1.69/1.90  0 [] greater(e_3,e_1).
% 1.69/1.90  0 [] greater(e_4,e_1).
% 1.69/1.90  0 [] greater(e_3,e_2).
% 1.69/1.90  0 [] greater(e_4,e_2).
% 1.69/1.90  0 [] greater(e_4,e_3).
% 1.69/1.90  0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.69/1.90  0 [] group_element(e_1).
% 1.69/1.90  0 [] group_element(e_2).
% 1.69/1.90  0 [] group_element(e_3).
% 1.69/1.90  0 [] group_element(e_4).
% 1.69/1.90  0 [] -e_qualish(e_1,e_2).
% 1.69/1.90  0 [] -e_qualish(e_1,e_3).
% 1.69/1.90  0 [] -e_qualish(e_1,e_4).
% 1.69/1.90  0 [] -e_qualish(e_2,e_1).
% 1.69/1.90  0 [] -e_qualish(e_2,e_3).
% 1.69/1.90  0 [] -e_qualish(e_2,e_4).
% 1.69/1.90  0 [] -e_qualish(e_3,e_1).
% 1.69/1.90  0 [] -e_qualish(e_3,e_2).
% 1.69/1.90  0 [] -e_qualish(e_3,e_4).
% 1.69/1.90  0 [] -e_qualish(e_4,e_1).
% 1.69/1.90  0 [] -e_qualish(e_4,e_2).
% 1.69/1.90  0 [] -e_qualish(e_4,e_3).
% 1.69/1.90  0 [] -group_element(X)| -group_element(Y)|product1(X,Y,e_1)|product1(X,Y,e_2)|product1(X,Y,e_3)|product1(X,Y,e_4).
% 1.69/1.90  0 [] -product1(X,Y,W)| -product1(X,Y,Z)|e_qualish(W,Z).
% 1.69/1.90  0 [] -product1(X,W,Y)| -product1(X,Z,Y)|e_qualish(W,Z).
% 1.69/1.90  0 [] -product1(W,Y,X)| -product1(Z,Y,X)|e_qualish(W,Z).
% 1.69/1.90  0 [] product1(X,X,X).
% 1.69/1.90  0 [] -group_element(X)| -group_element(Y)|product2(X,Y,e_1)|product2(X,Y,e_2)|product2(X,Y,e_3)|product2(X,Y,e_4).
% 1.69/1.90  0 [] -product2(X,Y,W)| -product2(X,Y,Z)|e_qualish(W,Z).
% 1.69/1.90  0 [] -product2(X,W,Y)| -product2(X,Z,Y)|e_qualish(W,Z).
% 1.69/1.90  0 [] -product2(W,Y,X)| -product2(Z,Y,X)|e_qualish(W,Z).
% 1.69/1.90  0 [] product2(X,X,X).
% 1.69/1.90  0 [] -product1(X,Y,Z1)| -product1(Z1,X,Z2)|product2(Z2,Y,X).
% 1.69/1.90  end_of_list.
% 1.69/1.90  
% 1.69/1.90  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.69/1.90  
% 1.69/1.90  This is a non-Horn set without equality.  The strategy will
% 1.69/1.90  be ordered hyper_res, unit deletion, and factoring, with
% 1.69/1.90  satellites in sos and with nuclei in usable.
% 1.69/1.90  
% 1.69/1.90     dependent: set(hyper_res).
% 1.69/1.90     dependent: set(factor).
% 1.69/1.90     dependent: set(unit_deletion).
% 1.69/1.90  
% 1.69/1.90  ------------> process usable:
% 1.69/1.90  ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.69/1.90  ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.69/1.90  ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_3).
% 1.69/1.90  ** KEPT (pick-wt=3): 4 [] -e_qualish(e_1,e_4).
% 1.69/1.90  ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_1).
% 1.69/1.90  ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_3).
% 1.69/1.90  ** KEPT (pick-wt=3): 7 [] -e_qualish(e_2,e_4).
% 1.69/1.90  ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_1).
% 1.69/1.90  ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_2).
% 1.69/1.90  ** KEPT (pick-wt=3): 10 [] -e_qualish(e_3,e_4).
% 1.69/1.90  ** KEPT (pick-wt=3): 11 [] -e_qualish(e_4,e_1).
% 1.69/1.90  ** KEPT (pick-wt=3): 12 [] -e_qualish(e_4,e_2).
% 1.69/1.90  ** KEPT (pick-wt=3): 13 [] -e_qualish(e_4,e_3).
% 1.69/1.90  ** KEPT (pick-wt=20): 14 [] -group_element(A)| -group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)|product1(A,B,e_4).
% 1.69/1.90  ** KEPT (pick-wt=11): 15 [] -product1(A,B,C)| -product1(A,B,D)|e_qualish(C,D).
% 1.69/1.90  ** KEPT (pick-wt=11): 16 [] -product1(A,B,C)| -product1(A,D,C)|e_qualish(B,D).
% 1.69/1.90  ** KEPT (pick-wt=11): 17 [] -product1(A,B,C)| -product1(D,B,C)|e_qualish(A,D).
% 1.69/1.90  ** KEPT (pick-wt=20): 18 [] -group_element(A)| -group_element(B)|product2(A,B,e_1)|product2(A,B,e_2)|product2(A,B,e_3)|product2(A,B,e_4).
% 1.69/1.90  ** KEPT (pick-wt=11): 19 [] -product2(A,B,C)| -product2(A,B,D)|e_qualish(C,D).
% 1.69/1.90  ** KEPT (pick-wt=11): 20 [] -product2(A,B,C)| -product2(A,D,C)|e_qualish(B,D).
% 1.69/1.90  ** KEPT (pick-wt=11): 21 [] -product2(A,B,C)| -product2(D,B,C)|e_qualish(A,D).
% 1.69/1.90  ** KEPT (pick-wt=12): 22 [] -product1(A,B,C)| -product1(C,A,D)|product2(D,B,A).
% 1.69/1.90  
% 1.69/1.90  ------------> process sos:
% 1.69/1.90  ** KEPT (pick-wt=3): 32 [] next(e_1,e_2).
% 1.69/1.90  ** KEPT (pick-wt=3): 33 [] next(e_2,e_3).
% 1.69/1.90  ** KEPT (pick-wt=3): 34 [] next(e_3,e_4).
% 1.69/1.90  ** KEPT (pick-wt=3): 35 [] greater(e_2,e_1).
% 1.69/1.90  ** KEPT (pick-wt=3): 36 [] greater(e_3,e_1).
% 1.69/1.90  ** KEPT (pick-wt=3): 37 [] greater(e_4,e_1).
% 1.75/1.94  ** KEPT (pick-wt=3): 38 [] greater(e_3,e_2).
% 1.75/1.94  ** KEPT (pick-wt=3): 39 [] greater(e_4,e_2).
% 1.75/1.94  ** KEPT (pick-wt=3): 40 [] greater(e_4,e_3).
% 1.75/1.94  ** KEPT (pick-wt=2): 41 [] group_element(e_1).
% 1.75/1.94  ** KEPT (pick-wt=2): 42 [] group_element(e_2).
% 1.75/1.94  ** KEPT (pick-wt=2): 43 [] group_element(e_3).
% 1.75/1.94  ** KEPT (pick-wt=2): 44 [] group_element(e_4).
% 1.75/1.94  ** KEPT (pick-wt=4): 45 [] product1(A,A,A).
% 1.75/1.94  ** KEPT (pick-wt=4): 46 [] product2(A,A,A).
% 1.75/1.94  46 back subsumes 31.
% 1.75/1.94  
% 1.75/1.94  ======= end of input processing =======
% 1.75/1.94  
% 1.75/1.94  =========== start of search ===========
% 1.75/1.94  
% 1.75/1.94  -------- PROOF -------- 
% 1.75/1.94  
% 1.75/1.94  ----> UNIT CONFLICT at   0.04 sec ----> 287 [binary,286.1,6.1] $F.
% 1.75/1.94  
% 1.75/1.94  Length of proof is 35.  Level of proof is 14.
% 1.75/1.94  
% 1.75/1.94  ---------------- PROOF ----------------
% 1.75/1.94  % SZS status Unsatisfiable
% 1.75/1.94  % SZS output start Refutation
% See solution above
% 1.75/1.94  ------------ end of proof -------------
% 1.75/1.94  
% 1.75/1.94  
% 1.75/1.94  Search stopped by max_proofs option.
% 1.75/1.94  
% 1.75/1.94  
% 1.75/1.94  Search stopped by max_proofs option.
% 1.75/1.94  
% 1.75/1.94  ============ end of search ============
% 1.75/1.94  
% 1.75/1.94  -------------- statistics -------------
% 1.75/1.94  clauses given                 84
% 1.75/1.94  clauses generated           2332
% 1.75/1.94  clauses kept                 286
% 1.75/1.94  clauses forward subsumed    2083
% 1.75/1.94  clauses back subsumed        189
% 1.75/1.94  Kbytes malloced              976
% 1.75/1.94  
% 1.75/1.94  ----------- times (seconds) -----------
% 1.75/1.94  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.75/1.94  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.75/1.94  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.75/1.94  
% 1.75/1.94  That finishes the proof of the theorem.
% 1.75/1.94  
% 1.75/1.94  Process 22094 finished Wed Jul 27 05:26:01 2022
% 1.75/1.94  Otter interrupted
% 1.75/1.94  PROOF FOUND
%------------------------------------------------------------------------------