TSTP Solution File: GRP584-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n013.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 12:57:18 EDT 2022

% Result   : Unsatisfiable 1.79s 2.03s
% Output   : Refutation 1.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   47 (  47 unt;   0 nHn;   6 RR)
%            Number of literals    :   47 (  46 equ;   4 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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   64 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(a,b) != multiply(b,a),
    file('GRP584-1.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('GRP584-1.p',unknown),
    [] ).

cnf(4,axiom,
    double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C,
    file('GRP584-1.p',unknown),
    [] ).

cnf(7,axiom,
    multiply(A,B) = double_divide(double_divide(B,A),identity),
    file('GRP584-1.p',unknown),
    [] ).

cnf(9,axiom,
    inverse(A) = double_divide(A,identity),
    file('GRP584-1.p',unknown),
    [] ).

cnf(10,axiom,
    identity = double_divide(A,inverse(A)),
    file('GRP584-1.p',unknown),
    [] ).

cnf(12,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(A,double_divide(identity,double_divide(B,double_divide(double_divide(identity,identity),A)))),double_divide(identity,identity)) = B,
    inference(para_into,[status(thm),theory(equality)],[4,12]),
    [iquote('para_into,4.1.1.1.2.1,11.1.1')] ).

cnf(16,plain,
    double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,identity)) = B,
    inference(para_into,[status(thm),theory(equality)],[4,12]),
    [iquote('para_into,4.1.1.1.2.2.2,11.1.1')] ).

cnf(20,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(identity,identity)) = A,
    inference(para_into,[status(thm),theory(equality)],[4,12]),
    [iquote('para_into,4.1.1.1.2.2,11.1.1')] ).

cnf(22,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
    inference(para_into,[status(thm),theory(equality)],[4,4]),
    [iquote('para_into,4.1.1.1.2.2,4.1.1')] ).

cnf(23,plain,
    double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),C)),double_divide(identity,identity)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
    [iquote('copy,22,flip.1')] ).

cnf(25,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)],[20,12]),12,12])]),
    [iquote('para_into,20.1.1.1.2.1,11.1.1,demod,12,12,flip.1')] ).

cnf(26,plain,
    double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(identity,C)),identity),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),25,25]),
    [iquote('back_demod,23,demod,25,25')] ).

cnf(29,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),25]),
    [iquote('back_demod,20,demod,25')] ).

cnf(32,plain,
    double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),identity) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),25]),
    [iquote('back_demod,16,demod,25')] ).

cnf(34,plain,
    double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),identity) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),25,25]),
    [iquote('back_demod,14,demod,25,25')] ).

cnf(38,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),A) = identity,
    inference(para_from,[status(thm),theory(equality)],[29,12]),
    [iquote('para_from,28.1.1,11.1.1.2')] ).

cnf(42,plain,
    double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,identity))) = double_divide(double_divide(identity,double_divide(identity,B)),identity),
    inference(para_into,[status(thm),theory(equality)],[26,38]),
    [iquote('para_into,26.1.1.2.2.2,38.1.1')] ).

cnf(46,plain,
    double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,25]),25])]),
    [iquote('para_into,26.1.1.2.2.2,24.1.1,demod,25,flip.1')] ).

cnf(48,plain,
    double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,12]),46]),
    [iquote('para_into,26.1.1.2.2.2,11.1.1,demod,46')] ).

cnf(49,plain,
    double_divide(A,double_divide(double_divide(identity,B),identity)) = double_divide(identity,double_divide(identity,double_divide(B,A))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,38]),46,29]),
    [iquote('para_into,26.1.1.2.2,38.1.1,demod,46,29')] ).

cnf(56,plain,
    double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[42])]),46])]),
    [iquote('copy,42,flip.1,demod,46,flip.1')] ).

cnf(65,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),48,46]),
    [iquote('back_demod,32,demod,48,46')] ).

cnf(84,plain,
    double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,38]),25,46]),
    [iquote('para_into,34.1.1.1.2.2,38.1.1,demod,25,46')] ).

cnf(96,plain,
    double_divide(identity,double_divide(identity,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)],[65]),84]),
    [iquote('back_demod,65,demod,84')] ).

cnf(99,plain,
    double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),B) = identity,
    inference(para_from,[status(thm),theory(equality)],[34,12]),
    [iquote('para_from,34.1.1,11.1.1.2')] ).

cnf(109,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
    inference(para_into,[status(thm),theory(equality)],[99,25]),
    [iquote('para_into,99.1.1.1.2.2.2,24.1.1')] ).

cnf(128,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))) = double_divide(identity,double_divide(identity,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)],[109,34]),25,84])]),
    [iquote('para_from,109.1.1,34.1.1.1.2.2,demod,25,84,flip.1')] ).

cnf(133,plain,
    double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),128]),
    [iquote('back_demod,56,demod,128')] ).

cnf(141,plain,
    double_divide(A,identity) = double_divide(identity,double_divide(identity,double_divide(identity,A))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,25]),25]),
    [iquote('para_into,49.1.1.2.1,24.1.1,demod,25')] ).

cnf(144,plain,
    double_divide(identity,double_divide(identity,double_divide(A,double_divide(identity,A)))) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,109]),84,128,96])]),
    [iquote('para_into,49.1.1,109.1.1,demod,84,128,96,flip.1')] ).

cnf(150,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,A))) = double_divide(A,identity),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[141])]),
    [iquote('copy,141,flip.1')] ).

cnf(201,plain,
    double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[150,150])]),
    [iquote('para_into,150.1.1.2,150.1.1,flip.1')] ).

cnf(202,plain,
    double_divide(double_divide(A,double_divide(identity,A)),identity) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[150,144]),25])]),
    [iquote('para_into,150.1.1.2,144.1.1,demod,25,flip.1')] ).

cnf(207,plain,
    double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,A))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),201]),
    [iquote('back_demod,49,demod,201')] ).

cnf(216,plain,
    double_divide(identity,double_divide(A,double_divide(identity,A))) = identity,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[202,109]),25,25]),
    [iquote('para_from,202.1.1,109.1.1.1.2.2,demod,25,25')] ).

cnf(259,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[216,34]),84]),
    [iquote('para_from,216.1.1,34.1.1.1.2,demod,84')] ).

cnf(276,plain,
    double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[133]),259]),
    [iquote('back_demod,133,demod,259')] ).

cnf(290,plain,
    double_divide(identity,double_divide(identity,A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),259]),
    [iquote('back_demod,95,demod,259')] ).

cnf(294,plain,
    double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(B,identity),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[276])]),290])]),
    [iquote('copy,276,flip.1,demod,290,flip.1')] ).

cnf(312,plain,
    double_divide(identity,double_divide(A,identity)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[259]),294]),
    [iquote('back_demod,258,demod,294')] ).

cnf(337,plain,
    double_divide(A,B) = double_divide(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[207]),312,290]),
    [iquote('back_demod,207,demod,312,290')] ).

cnf(365,plain,
    double_divide(double_divide(a,b),identity) != double_divide(double_divide(a,b),identity),
    inference(para_from,[status(thm),theory(equality)],[337,13]),
    [iquote('para_from,337.1.1,13.1.1.1')] ).

cnf(366,plain,
    $false,
    inference(binary,[status(thm)],[365,3]),
    [iquote('binary,365.1,3.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n013.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 05:08:00 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.79/2.03  ----- Otter 3.3f, August 2004 -----
% 1.79/2.03  The process was started by sandbox on n013.cluster.edu,
% 1.79/2.03  Wed Jul 27 05:08:00 2022
% 1.79/2.03  The command was "./otter".  The process ID is 23357.
% 1.79/2.03  
% 1.79/2.03  set(prolog_style_variables).
% 1.79/2.03  set(auto).
% 1.79/2.03     dependent: set(auto1).
% 1.79/2.03     dependent: set(process_input).
% 1.79/2.03     dependent: clear(print_kept).
% 1.79/2.03     dependent: clear(print_new_demod).
% 1.79/2.03     dependent: clear(print_back_demod).
% 1.79/2.03     dependent: clear(print_back_sub).
% 1.79/2.03     dependent: set(control_memory).
% 1.79/2.03     dependent: assign(max_mem, 12000).
% 1.79/2.03     dependent: assign(pick_given_ratio, 4).
% 1.79/2.03     dependent: assign(stats_level, 1).
% 1.79/2.03     dependent: assign(max_seconds, 10800).
% 1.79/2.03  clear(print_given).
% 1.79/2.03  
% 1.79/2.03  list(usable).
% 1.79/2.03  0 [] A=A.
% 1.79/2.03  0 [] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.79/2.03  0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.79/2.03  0 [] inverse(A)=double_divide(A,identity).
% 1.79/2.03  0 [] identity=double_divide(A,inverse(A)).
% 1.79/2.03  0 [] multiply(a,b)!=multiply(b,a).
% 1.79/2.03  end_of_list.
% 1.79/2.03  
% 1.79/2.03  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.79/2.03  
% 1.79/2.03  All clauses are units, and equality is present; the
% 1.79/2.03  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.79/2.03  
% 1.79/2.03     dependent: set(knuth_bendix).
% 1.79/2.03     dependent: set(anl_eq).
% 1.79/2.03     dependent: set(para_from).
% 1.79/2.03     dependent: set(para_into).
% 1.79/2.03     dependent: clear(para_from_right).
% 1.79/2.03     dependent: clear(para_into_right).
% 1.79/2.03     dependent: set(para_from_vars).
% 1.79/2.03     dependent: set(eq_units_both_ways).
% 1.79/2.03     dependent: set(dynamic_demod_all).
% 1.79/2.03     dependent: set(dynamic_demod).
% 1.79/2.03     dependent: set(order_eq).
% 1.79/2.03     dependent: set(back_demod).
% 1.79/2.03     dependent: set(lrpo).
% 1.79/2.03  
% 1.79/2.03  ------------> process usable:
% 1.79/2.03  ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.79/2.03  
% 1.79/2.03  ------------> process sos:
% 1.79/2.03  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.79/2.03  ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.79/2.03  ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.79/2.03  ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.79/2.03  ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.79/2.03  ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 1.79/2.03  ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 1.79/2.03  ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.79/2.03  ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 1.79/2.03    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.79/2.03  >>>> Starting back demodulation with 5.
% 1.79/2.03  >>>> Starting back demodulation with 7.
% 1.79/2.03      >> back demodulating 2 with 7.
% 1.79/2.03  >>>> Starting back demodulation with 9.
% 1.79/2.03  >>>> Starting back demodulation with 12.
% 1.79/2.03  
% 1.79/2.03  ======= end of input processing =======
% 1.79/2.03  
% 1.79/2.03  =========== start of search ===========
% 1.79/2.03  
% 1.79/2.03  -------- PROOF -------- 
% 1.79/2.03  
% 1.79/2.03  ----> UNIT CONFLICT at   0.02 sec ----> 366 [binary,365.1,3.1] $F.
% 1.79/2.03  
% 1.79/2.03  Length of proof is 40.  Level of proof is 17.
% 1.79/2.03  
% 1.79/2.03  ---------------- PROOF ----------------
% 1.79/2.03  % SZS status Unsatisfiable
% 1.79/2.03  % SZS output start Refutation
% See solution above
% 1.79/2.03  ------------ end of proof -------------
% 1.79/2.03  
% 1.79/2.03  
% 1.79/2.03  Search stopped by max_proofs option.
% 1.79/2.03  
% 1.79/2.03  
% 1.79/2.03  Search stopped by max_proofs option.
% 1.79/2.03  
% 1.79/2.03  ============ end of search ============
% 1.79/2.03  
% 1.79/2.03  -------------- statistics -------------
% 1.79/2.03  clauses given                 33
% 1.79/2.03  clauses generated            426
% 1.79/2.03  clauses kept                 208
% 1.79/2.03  clauses forward subsumed     437
% 1.79/2.03  clauses back subsumed          5
% 1.79/2.03  Kbytes malloced             1953
% 1.79/2.03  
% 1.79/2.03  ----------- times (seconds) -----------
% 1.79/2.03  user CPU time          0.02          (0 hr, 0 min, 0 sec)
% 1.79/2.03  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.79/2.03  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.79/2.03  
% 1.79/2.03  That finishes the proof of the theorem.
% 1.79/2.03  
% 1.79/2.03  Process 23357 finished Wed Jul 27 05:08:01 2022
% 1.79/2.03  Otter interrupted
% 1.79/2.03  PROOF FOUND
%------------------------------------------------------------------------------