TSTP Solution File: GRP608-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP608-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n012.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 12:57:21 EDT 2022

% Result   : Unsatisfiable 1.71s 1.92s
% Output   : Refutation 1.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   36 (  36 unt;   0 nHn;   3 RR)
%            Number of literals    :   36 (  35 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   83 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(a,b) != multiply(b,a),
    file('GRP608-1.p',unknown),
    [] ).

cnf(2,plain,
    multiply(b,a) != multiply(a,b),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
    [iquote('copy,1,flip.1')] ).

cnf(4,axiom,
    double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B,
    file('GRP608-1.p',unknown),
    [] ).

cnf(6,axiom,
    multiply(A,B) = inverse(double_divide(B,A)),
    file('GRP608-1.p',unknown),
    [] ).

cnf(8,plain,
    inverse(double_divide(A,B)) = multiply(B,A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
    [iquote('copy,6,flip.1')] ).

cnf(9,plain,
    double_divide(multiply(multiply(double_divide(A,B),inverse(C)),A),B) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8]),
    [iquote('back_demod,4,demod,8,8')] ).

cnf(11,plain,
    double_divide(multiply(multiply(A,inverse(B)),multiply(multiply(double_divide(C,D),inverse(A)),C)),D) = B,
    inference(para_into,[status(thm),theory(equality)],[9,9]),
    [iquote('para_into,9.1.1.1.1.1,9.1.1')] ).

cnf(13,plain,
    double_divide(multiply(multiply(double_divide(A,B),multiply(C,D)),A),B) = double_divide(D,C),
    inference(para_into,[status(thm),theory(equality)],[9,8]),
    [iquote('para_into,9.1.1.1.1.2,7.1.1')] ).

cnf(15,plain,
    multiply(A,multiply(multiply(double_divide(B,A),inverse(C)),B)) = inverse(C),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,8])]),
    [iquote('para_from,9.1.1,7.1.1.1,flip.1')] ).

cnf(37,plain,
    double_divide(inverse(A),multiply(A,inverse(B))) = B,
    inference(para_into,[status(thm),theory(equality)],[11,15]),
    [iquote('para_into,11.1.1.1,15.1.1')] ).

cnf(53,plain,
    multiply(multiply(A,inverse(B)),inverse(A)) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[37,8])]),
    [iquote('para_from,37.1.1,7.1.1.1,flip.1')] ).

cnf(59,plain,
    multiply(inverse(A),inverse(multiply(B,inverse(A)))) = inverse(B),
    inference(para_into,[status(thm),theory(equality)],[53,53]),
    [iquote('para_into,53.1.1.1,53.1.1')] ).

cnf(63,plain,
    double_divide(inverse(multiply(A,inverse(B))),inverse(B)) = A,
    inference(para_from,[status(thm),theory(equality)],[53,37]),
    [iquote('para_from,53.1.1,37.1.1.2')] ).

cnf(69,plain,
    double_divide(inverse(inverse(A)),inverse(B)) = multiply(B,inverse(A)),
    inference(para_into,[status(thm),theory(equality)],[63,53]),
    [iquote('para_into,63.1.1.1.1,53.1.1')] ).

cnf(70,plain,
    multiply(A,inverse(B)) = double_divide(inverse(inverse(B)),inverse(A)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[69])]),
    [iquote('copy,69,flip.1')] ).

cnf(84,plain,
    inverse(multiply(A,inverse(B))) = multiply(inverse(A),inverse(inverse(B))),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[59,53])]),
    [iquote('para_into,59.1.1.2.1,53.1.1,flip.1')] ).

cnf(95,plain,
    double_divide(multiply(inverse(A),inverse(inverse(B))),inverse(B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[63]),84]),
    [iquote('back_demod,63,demod,84')] ).

cnf(135,plain,
    double_divide(double_divide(inverse(inverse(A)),inverse(multiply(double_divide(inverse(A),B),multiply(C,D)))),B) = double_divide(D,C),
    inference(para_from,[status(thm),theory(equality)],[70,13]),
    [iquote('para_from,70.1.1,13.1.1.1')] ).

cnf(143,plain,
    multiply(double_divide(inverse(inverse(A)),inverse(B)),inverse(B)) = inverse(A),
    inference(para_from,[status(thm),theory(equality)],[70,53]),
    [iquote('para_from,70.1.1,53.1.1.1')] ).

cnf(149,plain,
    double_divide(double_divide(inverse(inverse(A)),multiply(multiply(B,inverse(A)),inverse(inverse(C)))),B) = C,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[70,9]),84,8]),
    [iquote('para_from,70.1.1,9.1.1.1,demod,84,8')] ).

cnf(333,plain,
    inverse(multiply(A,multiply(B,C))) = multiply(inverse(A),inverse(multiply(B,C))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[84,8]),8]),
    [iquote('para_into,83.1.1.1.2,7.1.1,demod,8')] ).

cnf(358,plain,
    double_divide(double_divide(inverse(inverse(A)),multiply(multiply(B,inverse(A)),inverse(multiply(C,D)))),B) = double_divide(D,C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[135]),333,8]),
    [iquote('back_demod,135,demod,333,8')] ).

cnf(398,plain,
    multiply(inverse(A),multiply(inverse(B),inverse(inverse(B)))) = inverse(A),
    inference(para_from,[status(thm),theory(equality)],[143,15]),
    [iquote('para_from,143.1.1,15.1.1.2.1')] ).

cnf(400,plain,
    double_divide(multiply(multiply(A,inverse(B)),multiply(inverse(C),inverse(inverse(C)))),inverse(A)) = B,
    inference(para_from,[status(thm),theory(equality)],[143,11]),
    [iquote('para_from,143.1.1,11.1.1.1.2.1')] ).

cnf(475,plain,
    multiply(multiply(A,B),multiply(inverse(C),inverse(inverse(C)))) = multiply(A,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[398,8]),8]),
    [iquote('para_into,398.1.1.1,7.1.1,demod,8')] ).

cnf(494,plain,
    double_divide(multiply(A,inverse(B)),inverse(A)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[400]),475]),
    [iquote('back_demod,400,demod,475')] ).

cnf(511,plain,
    inverse(inverse(A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[494,95])]),
    [iquote('para_into,494.1.1,95.1.1,flip.1')] ).

cnf(574,plain,
    double_divide(double_divide(A,multiply(multiply(B,inverse(A)),inverse(multiply(C,D)))),B) = double_divide(D,C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[358]),511]),
    [iquote('back_demod,358,demod,511')] ).

cnf(633,plain,
    double_divide(double_divide(A,multiply(multiply(B,inverse(A)),C)),B) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[149]),511,511]),
    [iquote('back_demod,149,demod,511,511')] ).

cnf(698,plain,
    inverse(multiply(A,B)) = double_divide(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[574]),633]),
    [iquote('back_demod,574,demod,633')] ).

cnf(875,plain,
    multiply(multiply(A,B),inverse(A)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[511,53]),511]),
    [iquote('para_from,510.1.1,53.1.1.1.2,demod,511')] ).

cnf(935,plain,
    double_divide(A,double_divide(A,B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[875,494]),698]),
    [iquote('para_from,875.1.1,494.1.1.1,demod,698')] ).

cnf(939,plain,
    double_divide(double_divide(A,B),A) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[875,37]),698]),
    [iquote('para_from,875.1.1,37.1.1.2,demod,698')] ).

cnf(965,plain,
    double_divide(A,B) = double_divide(B,A),
    inference(para_into,[status(thm),theory(equality)],[939,935]),
    [iquote('para_into,939.1.1.1,935.1.1')] ).

cnf(1226,plain,
    multiply(A,B) = multiply(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[965,8]),8]),
    [iquote('para_from,965.1.1,7.1.1.1,demod,8')] ).

cnf(1227,plain,
    $false,
    inference(binary,[status(thm)],[1226,2]),
    [iquote('binary,1226.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : GRP608-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n012.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 05:02:50 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.71/1.92  ----- Otter 3.3f, August 2004 -----
% 1.71/1.92  The process was started by sandbox on n012.cluster.edu,
% 1.71/1.92  Wed Jul 27 05:02:50 2022
% 1.71/1.92  The command was "./otter".  The process ID is 29122.
% 1.71/1.92  
% 1.71/1.92  set(prolog_style_variables).
% 1.71/1.92  set(auto).
% 1.71/1.92     dependent: set(auto1).
% 1.71/1.92     dependent: set(process_input).
% 1.71/1.92     dependent: clear(print_kept).
% 1.71/1.92     dependent: clear(print_new_demod).
% 1.71/1.92     dependent: clear(print_back_demod).
% 1.71/1.92     dependent: clear(print_back_sub).
% 1.71/1.92     dependent: set(control_memory).
% 1.71/1.92     dependent: assign(max_mem, 12000).
% 1.71/1.92     dependent: assign(pick_given_ratio, 4).
% 1.71/1.92     dependent: assign(stats_level, 1).
% 1.71/1.92     dependent: assign(max_seconds, 10800).
% 1.71/1.92  clear(print_given).
% 1.71/1.92  
% 1.71/1.92  list(usable).
% 1.71/1.92  0 [] A=A.
% 1.71/1.92  0 [] double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)=B.
% 1.71/1.92  0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.71/1.92  0 [] multiply(a,b)!=multiply(b,a).
% 1.71/1.92  end_of_list.
% 1.71/1.92  
% 1.71/1.92  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.92  
% 1.71/1.92  All clauses are units, and equality is present; the
% 1.71/1.92  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.92  
% 1.71/1.92     dependent: set(knuth_bendix).
% 1.71/1.92     dependent: set(anl_eq).
% 1.71/1.92     dependent: set(para_from).
% 1.71/1.92     dependent: set(para_into).
% 1.71/1.92     dependent: clear(para_from_right).
% 1.71/1.92     dependent: clear(para_into_right).
% 1.71/1.92     dependent: set(para_from_vars).
% 1.71/1.92     dependent: set(eq_units_both_ways).
% 1.71/1.92     dependent: set(dynamic_demod_all).
% 1.71/1.92     dependent: set(dynamic_demod).
% 1.71/1.92     dependent: set(order_eq).
% 1.71/1.92     dependent: set(back_demod).
% 1.71/1.92     dependent: set(lrpo).
% 1.71/1.92  
% 1.71/1.92  ------------> process usable:
% 1.71/1.92  ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.71/1.92  
% 1.71/1.92  ------------> process sos:
% 1.71/1.92  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.71/1.92  ** KEPT (pick-wt=14): 4 [] double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)=B.
% 1.71/1.92  ---> New Demodulator: 5 [new_demod,4] double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)=B.
% 1.71/1.92  ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.71/1.92  ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.71/1.92    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.71/1.92  >>>> Starting back demodulation with 5.
% 1.71/1.92  >>>> Starting back demodulation with 8.
% 1.71/1.92      >> back demodulating 4 with 8.
% 1.71/1.92  >>>> Starting back demodulation with 10.
% 1.71/1.92  
% 1.71/1.92  ======= end of input processing =======
% 1.71/1.92  
% 1.71/1.92  =========== start of search ===========
% 1.71/1.92  
% 1.71/1.92  
% 1.71/1.92  Resetting weight limit to 9.
% 1.71/1.92  
% 1.71/1.92  
% 1.71/1.92  Resetting weight limit to 9.
% 1.71/1.92  
% 1.71/1.92  sos_size=269
% 1.71/1.92  
% 1.71/1.92  -------- PROOF -------- 
% 1.71/1.92  
% 1.71/1.92  ----> UNIT CONFLICT at   0.04 sec ----> 1227 [binary,1226.1,2.1] $F.
% 1.71/1.92  
% 1.71/1.92  Length of proof is 32.  Level of proof is 18.
% 1.71/1.92  
% 1.71/1.92  ---------------- PROOF ----------------
% 1.71/1.92  % SZS status Unsatisfiable
% 1.71/1.92  % SZS output start Refutation
% See solution above
% 1.71/1.93  ------------ end of proof -------------
% 1.71/1.93  
% 1.71/1.93  
% 1.71/1.93  Search stopped by max_proofs option.
% 1.71/1.93  
% 1.71/1.93  
% 1.71/1.93  Search stopped by max_proofs option.
% 1.71/1.93  
% 1.71/1.93  ============ end of search ============
% 1.71/1.93  
% 1.71/1.93  -------------- statistics -------------
% 1.71/1.93  clauses given                 37
% 1.71/1.93  clauses generated            613
% 1.71/1.93  clauses kept                 717
% 1.71/1.93  clauses forward subsumed     535
% 1.71/1.93  clauses back subsumed          8
% 1.71/1.93  Kbytes malloced             4882
% 1.71/1.93  
% 1.71/1.93  ----------- times (seconds) -----------
% 1.71/1.93  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.71/1.93  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.71/1.93  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.71/1.93  
% 1.71/1.93  That finishes the proof of the theorem.
% 1.71/1.93  
% 1.71/1.93  Process 29122 finished Wed Jul 27 05:02:52 2022
% 1.71/1.93  Otter interrupted
% 1.71/1.93  PROOF FOUND
%------------------------------------------------------------------------------