TSTP Solution File: GRP576-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 12:57:17 EDT 2022

% Result   : Unsatisfiable 1.66s 1.87s
% Output   : Refutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   39 (  39 unt;   0 nHn;   6 RR)
%            Number of literals    :   39 (  38 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   50 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(a,b) != multiply(b,a),
    file('GRP576-1.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(3,axiom,
    A = A,
    file('GRP576-1.p',unknown),
    [] ).

cnf(4,axiom,
    double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B,
    file('GRP576-1.p',unknown),
    [] ).

cnf(7,axiom,
    multiply(A,B) = double_divide(double_divide(B,A),identity),
    file('GRP576-1.p',unknown),
    [] ).

cnf(9,axiom,
    inverse(A) = double_divide(A,identity),
    file('GRP576-1.p',unknown),
    [] ).

cnf(10,axiom,
    identity = double_divide(A,inverse(A)),
    file('GRP576-1.p',unknown),
    [] ).

cnf(11,plain,
    double_divide(A,double_divide(A,identity)) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10]),9])]),
    [iquote('copy,10,demod,9,flip.1')] ).

cnf(13,plain,
    double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),7,7])]),
    [iquote('back_demod,2,demod,7,7,flip.1')] ).

cnf(14,plain,
    double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))),double_divide(identity,identity)) = B,
    inference(para_into,[status(thm),theory(equality)],[4,11]),
    [iquote('para_into,4.1.1.1.2.1.2,11.1.1')] ).

cnf(18,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A,
    inference(para_into,[status(thm),theory(equality)],[4,11]),
    [iquote('para_into,4.1.1.1.2.1,11.1.1')] ).

cnf(20,plain,
    double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
    inference(para_into,[status(thm),theory(equality)],[4,4]),
    [iquote('para_into,4.1.1.1.2.1,4.1.1')] ).

cnf(21,plain,
    double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
    [iquote('copy,20,flip.1')] ).

cnf(25,plain,
    double_divide(double_divide(double_divide(A,identity),A),double_divide(identity,identity)) = identity,
    inference(para_from,[status(thm),theory(equality)],[18,4]),
    [iquote('para_from,18.1.1,4.1.1.1.2')] ).

cnf(27,plain,
    double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
    inference(para_from,[status(thm),theory(equality)],[18,4]),
    [iquote('para_from,18.1.1,4.1.1.1.2.1')] ).

cnf(30,plain,
    double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),27]),
    [iquote('back_demod,21,demod,27')] ).

cnf(33,plain,
    double_divide(identity,identity) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,25]),25])]),
    [iquote('para_into,14.1.1.1.2,24.1.1,demod,25,flip.1')] ).

cnf(35,plain,
    double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),identity) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,11]),33]),
    [iquote('para_into,14.1.1.1.2,11.1.1,demod,33')] ).

cnf(38,plain,
    double_divide(double_divide(identity,double_divide(A,identity)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),33,33]),
    [iquote('back_demod,26,demod,33,33')] ).

cnf(40,plain,
    double_divide(double_divide(double_divide(A,identity),A),identity) = identity,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),33]),
    [iquote('back_demod,24,demod,33')] ).

cnf(42,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),33]),
    [iquote('back_demod,18,demod,33')] ).

cnf(62,plain,
    double_divide(double_divide(A,identity),A) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,40]),33,33,33])]),
    [iquote('para_into,34.1.1.1.1.1,40.1.1,demod,33,33,33,flip.1')] ).

cnf(64,plain,
    double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),A) = identity,
    inference(para_from,[status(thm),theory(equality)],[35,11]),
    [iquote('para_from,34.1.1,11.1.1.2')] ).

cnf(69,plain,
    double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[35,30]),35]),
    [iquote('para_from,34.1.1,30.1.1.2.1.2,demod,35')] ).

cnf(70,plain,
    double_divide(A,double_divide(double_divide(double_divide(A,identity),identity),identity)) = identity,
    inference(para_into,[status(thm),theory(equality)],[62,35]),
    [iquote('para_into,62.1.1.1,34.1.1')] ).

cnf(72,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,B),identity)))) = double_divide(B,double_divide(identity,double_divide(A,identity))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[62,30]),69])]),
    [iquote('para_from,62.1.1,30.1.1.2.1,demod,69,flip.1')] ).

cnf(79,plain,
    double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(identity,A)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[38,35]),35]),
    [iquote('para_into,38.1.1.1.2,34.1.1,demod,35')] ).

cnf(81,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[42]),79]),
    [iquote('back_demod,42,demod,79')] ).

cnf(82,plain,
    double_divide(A,B) = double_divide(B,double_divide(identity,double_divide(A,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[72]),81]),
    [iquote('back_demod,72,demod,81')] ).

cnf(83,plain,
    double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(B,A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[82])]),
    [iquote('copy,82,flip.1')] ).

cnf(86,plain,
    double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,30]),35]),
    [iquote('para_from,64.1.1,30.1.1.2.1.2,demod,35')] ).

cnf(89,plain,
    double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(identity,A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[70,30]),86,86,81])]),
    [iquote('para_from,70.1.1,30.1.1.2.1,demod,86,86,81,flip.1')] ).

cnf(93,plain,
    double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[86]),89]),
    [iquote('back_demod,85,demod,89')] ).

cnf(95,plain,
    double_divide(identity,double_divide(identity,A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[81]),89]),
    [iquote('back_demod,80,demod,89')] ).

cnf(110,plain,
    double_divide(A,identity) = double_divide(identity,A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[89]),95]),
    [iquote('back_demod,88,demod,95')] ).

cnf(115,plain,
    double_divide(identity,double_divide(A,identity)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[110,35]),93])]),
    [iquote('para_into,110.1.1,34.1.1,demod,93,flip.1')] ).

cnf(116,plain,
    double_divide(A,B) = double_divide(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[83]),115]),
    [iquote('back_demod,83,demod,115')] ).

cnf(136,plain,
    double_divide(double_divide(a,b),identity) != double_divide(double_divide(a,b),identity),
    inference(para_from,[status(thm),theory(equality)],[116,13]),
    [iquote('para_from,116.1.1,13.1.1.1')] ).

cnf(137,plain,
    $false,
    inference(binary,[status(thm)],[136,3]),
    [iquote('binary,136.1,3.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n003.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 05:06:26 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.66/1.87  ----- Otter 3.3f, August 2004 -----
% 1.66/1.87  The process was started by sandbox on n003.cluster.edu,
% 1.66/1.87  Wed Jul 27 05:06:26 2022
% 1.66/1.87  The command was "./otter".  The process ID is 19005.
% 1.66/1.87  
% 1.66/1.87  set(prolog_style_variables).
% 1.66/1.87  set(auto).
% 1.66/1.87     dependent: set(auto1).
% 1.66/1.87     dependent: set(process_input).
% 1.66/1.87     dependent: clear(print_kept).
% 1.66/1.87     dependent: clear(print_new_demod).
% 1.66/1.87     dependent: clear(print_back_demod).
% 1.66/1.87     dependent: clear(print_back_sub).
% 1.66/1.87     dependent: set(control_memory).
% 1.66/1.87     dependent: assign(max_mem, 12000).
% 1.66/1.87     dependent: assign(pick_given_ratio, 4).
% 1.66/1.87     dependent: assign(stats_level, 1).
% 1.66/1.87     dependent: assign(max_seconds, 10800).
% 1.66/1.87  clear(print_given).
% 1.66/1.87  
% 1.66/1.87  list(usable).
% 1.66/1.87  0 [] A=A.
% 1.66/1.87  0 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.66/1.87  0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.66/1.87  0 [] inverse(A)=double_divide(A,identity).
% 1.66/1.87  0 [] identity=double_divide(A,inverse(A)).
% 1.66/1.87  0 [] multiply(a,b)!=multiply(b,a).
% 1.66/1.87  end_of_list.
% 1.66/1.87  
% 1.66/1.87  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.87  
% 1.66/1.87  All clauses are units, and equality is present; the
% 1.66/1.87  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.87  
% 1.66/1.87     dependent: set(knuth_bendix).
% 1.66/1.87     dependent: set(anl_eq).
% 1.66/1.87     dependent: set(para_from).
% 1.66/1.87     dependent: set(para_into).
% 1.66/1.87     dependent: clear(para_from_right).
% 1.66/1.87     dependent: clear(para_into_right).
% 1.66/1.87     dependent: set(para_from_vars).
% 1.66/1.87     dependent: set(eq_units_both_ways).
% 1.66/1.87     dependent: set(dynamic_demod_all).
% 1.66/1.87     dependent: set(dynamic_demod).
% 1.66/1.87     dependent: set(order_eq).
% 1.66/1.87     dependent: set(back_demod).
% 1.66/1.87     dependent: set(lrpo).
% 1.66/1.87  
% 1.66/1.87  ------------> process usable:
% 1.66/1.87  ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.66/1.87  
% 1.66/1.87  ------------> process sos:
% 1.66/1.87  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.66/1.87  ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.66/1.87  ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.66/1.87  ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.66/1.87  ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.66/1.87  ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 1.66/1.87  ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 1.66/1.87  ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.66/1.87  ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 1.66/1.87    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.66/1.87  >>>> Starting back demodulation with 5.
% 1.66/1.87  >>>> Starting back demodulation with 7.
% 1.66/1.87      >> back demodulating 2 with 7.
% 1.66/1.87  >>>> Starting back demodulation with 9.
% 1.66/1.87  >>>> Starting back demodulation with 12.
% 1.66/1.87  
% 1.66/1.87  ======= end of input processing =======
% 1.66/1.87  
% 1.66/1.87  =========== start of search ===========
% 1.66/1.87  
% 1.66/1.87  -------- PROOF -------- 
% 1.66/1.87  
% 1.66/1.87  ----> UNIT CONFLICT at   0.00 sec ----> 137 [binary,136.1,3.1] $F.
% 1.66/1.87  
% 1.66/1.87  Length of proof is 32.  Level of proof is 13.
% 1.66/1.87  
% 1.66/1.87  ---------------- PROOF ----------------
% 1.66/1.87  % SZS status Unsatisfiable
% 1.66/1.87  % SZS output start Refutation
% See solution above
% 1.66/1.87  ------------ end of proof -------------
% 1.66/1.87  
% 1.66/1.87  
% 1.66/1.87  Search stopped by max_proofs option.
% 1.66/1.87  
% 1.66/1.87  
% 1.66/1.87  Search stopped by max_proofs option.
% 1.66/1.87  
% 1.66/1.87  ============ end of search ============
% 1.66/1.87  
% 1.66/1.87  -------------- statistics -------------
% 1.66/1.87  clauses given                 24
% 1.66/1.87  clauses generated            194
% 1.66/1.87  clauses kept                  74
% 1.66/1.87  clauses forward subsumed     184
% 1.66/1.87  clauses back subsumed          2
% 1.66/1.87  Kbytes malloced              976
% 1.66/1.87  
% 1.66/1.87  ----------- times (seconds) -----------
% 1.66/1.87  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.87  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.87  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.66/1.87  
% 1.66/1.87  That finishes the proof of the theorem.
% 1.66/1.87  
% 1.66/1.87  Process 19005 finished Wed Jul 27 05:06:28 2022
% 1.66/1.87  Otter interrupted
% 1.66/1.87  PROOF FOUND
%------------------------------------------------------------------------------