TSTP Solution File: GRP578-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP578-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n014.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 1.73s 1.92s
% Output   : Refutation 1.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   31 (  31 unt;   0 nHn;   8 RR)
%            Number of literals    :   31 (  30 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   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   :   38 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(identity,a2) != a2,
    file('GRP578-1.p',unknown),
    [] ).

cnf(3,axiom,
    double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
    file('GRP578-1.p',unknown),
    [] ).

cnf(6,axiom,
    multiply(A,B) = double_divide(double_divide(B,A),identity),
    file('GRP578-1.p',unknown),
    [] ).

cnf(8,axiom,
    inverse(A) = double_divide(A,identity),
    file('GRP578-1.p',unknown),
    [] ).

cnf(9,axiom,
    identity = double_divide(A,inverse(A)),
    file('GRP578-1.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)],[9]),8])]),
    [iquote('copy,9,demod,8,flip.1')] ).

cnf(12,plain,
    double_divide(double_divide(a2,identity),identity) != a2,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6]),
    [iquote('back_demod,1,demod,6')] ).

cnf(13,plain,
    double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B,
    inference(para_into,[status(thm),theory(equality)],[3,11]),
    [iquote('para_into,3.1.1.1.2.1.1,10.1.1')] ).

cnf(25,plain,
    double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A,
    inference(para_into,[status(thm),theory(equality)],[13,11]),
    [iquote('para_into,13.1.1.1.2,10.1.1')] ).

cnf(33,plain,
    double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
    inference(para_into,[status(thm),theory(equality)],[25,11]),
    [iquote('para_into,25.1.1.1.1.1,10.1.1')] ).

cnf(37,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),double_divide(identity,identity)) = B,
    inference(para_from,[status(thm),theory(equality)],[25,3]),
    [iquote('para_from,25.1.1,3.1.1.1.2.1.1')] ).

cnf(40,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,3]),11]),
    [iquote('para_from,33.1.1,3.1.1.1.2.1,demod,11')] ).

cnf(44,plain,
    double_divide(identity,identity) = identity,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[40,13]),40,40]),
    [iquote('para_from,39.1.1,13.1.1.1.2,demod,40,40')] ).

cnf(47,plain,
    double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),identity) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),44,44]),
    [iquote('back_demod,37,demod,44,44')] ).

cnf(58,plain,
    double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),44]),
    [iquote('back_demod,25,demod,44')] ).

cnf(73,plain,
    double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),identity) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),58]),
    [iquote('back_demod,47,demod,58')] ).

cnf(79,plain,
    double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(A,identity),
    inference(para_into,[status(thm),theory(equality)],[73,11]),
    [iquote('para_into,73.1.1.1.2.1,10.1.1')] ).

cnf(81,plain,
    double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),B),
    inference(para_into,[status(thm),theory(equality)],[73,73]),
    [iquote('para_into,73.1.1.1.2,73.1.1')] ).

cnf(83,plain,
    double_divide(double_divide(A,identity),identity) = double_divide(double_divide(B,A),B),
    inference(para_from,[status(thm),theory(equality)],[73,58]),
    [iquote('para_from,73.1.1,57.1.1.1.1')] ).

cnf(84,plain,
    double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),B) = identity,
    inference(para_from,[status(thm),theory(equality)],[73,11]),
    [iquote('para_from,73.1.1,10.1.1.2')] ).

cnf(86,plain,
    double_divide(double_divide(A,B),A) = double_divide(double_divide(B,identity),identity),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[83])]),
    [iquote('copy,83,flip.1')] ).

cnf(94,plain,
    double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A),
    inference(para_from,[status(thm),theory(equality)],[79,58]),
    [iquote('para_from,79.1.1,57.1.1.1.1')] ).

cnf(100,plain,
    double_divide(identity,double_divide(identity,A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),94]),
    [iquote('back_demod,57,demod,94')] ).

cnf(107,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)],[81,44]),44])]),
    [iquote('para_into,81.1.1.1,43.1.1,demod,44,flip.1')] ).

cnf(110,plain,
    double_divide(double_divide(A,double_divide(double_divide(B,C),B)),A) = C,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[81,73])]),
    [iquote('para_into,81.1.1,73.1.1,flip.1')] ).

cnf(114,plain,
    double_divide(double_divide(A,a2),A) != a2,
    inference(para_from,[status(thm),theory(equality)],[83,12]),
    [iquote('para_from,83.1.1,12.1.1')] ).

cnf(133,plain,
    double_divide(identity,double_divide(a2,identity)) != a2,
    inference(para_into,[status(thm),theory(equality)],[114,107]),
    [iquote('para_into,114.1.1.1,107.1.1')] ).

cnf(140,plain,
    double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,107])]),
    [iquote('para_into,86.1.1.1,107.1.1,flip.1')] ).

cnf(145,plain,
    double_divide(double_divide(A,B),A) = double_divide(identity,double_divide(B,identity)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,84]),100,140]),
    [iquote('para_into,86.1.1.1,84.1.1,demod,100,140')] ).

cnf(163,plain,
    double_divide(identity,double_divide(A,identity)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[110]),145,145,145,140,100]),
    [iquote('back_demod,110,demod,145,145,145,140,100')] ).

cnf(165,plain,
    $false,
    inference(binary,[status(thm)],[163,133]),
    [iquote('binary,163.1,133.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP578-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n014.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 05:19:54 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.73/1.92  ----- Otter 3.3f, August 2004 -----
% 1.73/1.92  The process was started by sandbox on n014.cluster.edu,
% 1.73/1.92  Wed Jul 27 05:19:54 2022
% 1.73/1.92  The command was "./otter".  The process ID is 1386.
% 1.73/1.92  
% 1.73/1.92  set(prolog_style_variables).
% 1.73/1.92  set(auto).
% 1.73/1.92     dependent: set(auto1).
% 1.73/1.92     dependent: set(process_input).
% 1.73/1.92     dependent: clear(print_kept).
% 1.73/1.92     dependent: clear(print_new_demod).
% 1.73/1.92     dependent: clear(print_back_demod).
% 1.73/1.92     dependent: clear(print_back_sub).
% 1.73/1.92     dependent: set(control_memory).
% 1.73/1.92     dependent: assign(max_mem, 12000).
% 1.73/1.92     dependent: assign(pick_given_ratio, 4).
% 1.73/1.92     dependent: assign(stats_level, 1).
% 1.73/1.92     dependent: assign(max_seconds, 10800).
% 1.73/1.92  clear(print_given).
% 1.73/1.92  
% 1.73/1.92  list(usable).
% 1.73/1.92  0 [] A=A.
% 1.73/1.92  0 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.73/1.92  0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.73/1.92  0 [] inverse(A)=double_divide(A,identity).
% 1.73/1.92  0 [] identity=double_divide(A,inverse(A)).
% 1.73/1.92  0 [] multiply(identity,a2)!=a2.
% 1.73/1.92  end_of_list.
% 1.73/1.92  
% 1.73/1.92  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.73/1.92  
% 1.73/1.92  All clauses are units, and equality is present; the
% 1.73/1.92  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.73/1.92  
% 1.73/1.92     dependent: set(knuth_bendix).
% 1.73/1.92     dependent: set(anl_eq).
% 1.73/1.92     dependent: set(para_from).
% 1.73/1.92     dependent: set(para_into).
% 1.73/1.92     dependent: clear(para_from_right).
% 1.73/1.92     dependent: clear(para_into_right).
% 1.73/1.92     dependent: set(para_from_vars).
% 1.73/1.92     dependent: set(eq_units_both_ways).
% 1.73/1.92     dependent: set(dynamic_demod_all).
% 1.73/1.92     dependent: set(dynamic_demod).
% 1.73/1.92     dependent: set(order_eq).
% 1.73/1.92     dependent: set(back_demod).
% 1.73/1.92     dependent: set(lrpo).
% 1.73/1.92  
% 1.73/1.92  ------------> process usable:
% 1.73/1.92  ** KEPT (pick-wt=5): 1 [] multiply(identity,a2)!=a2.
% 1.73/1.92  
% 1.73/1.92  ------------> process sos:
% 1.73/1.92  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.73/1.92  ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.73/1.92  ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.73/1.92  ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.73/1.92  ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.73/1.92  ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.73/1.92  ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.73/1.92  ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.73/1.92  ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.73/1.92    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.73/1.92  >>>> Starting back demodulation with 4.
% 1.73/1.92  >>>> Starting back demodulation with 6.
% 1.73/1.92      >> back demodulating 1 with 6.
% 1.73/1.92  >>>> Starting back demodulation with 8.
% 1.73/1.92  >>>> Starting back demodulation with 11.
% 1.73/1.92  
% 1.73/1.92  ======= end of input processing =======
% 1.73/1.92  
% 1.73/1.92  =========== start of search ===========
% 1.73/1.92  
% 1.73/1.92  -------- PROOF -------- 
% 1.73/1.92  
% 1.73/1.92  ----> UNIT CONFLICT at   0.00 sec ----> 165 [binary,163.1,133.1] $F.
% 1.73/1.92  
% 1.73/1.92  Length of proof is 25.  Level of proof is 13.
% 1.73/1.92  
% 1.73/1.92  ---------------- PROOF ----------------
% 1.73/1.92  % SZS status Unsatisfiable
% 1.73/1.92  % SZS output start Refutation
% See solution above
% 1.73/1.92  ------------ end of proof -------------
% 1.73/1.92  
% 1.73/1.92  
% 1.73/1.92  Search stopped by max_proofs option.
% 1.73/1.92  
% 1.73/1.92  
% 1.73/1.92  Search stopped by max_proofs option.
% 1.73/1.92  
% 1.73/1.92  ============ end of search ============
% 1.73/1.92  
% 1.73/1.92  -------------- statistics -------------
% 1.73/1.92  clauses given                 25
% 1.73/1.92  clauses generated            187
% 1.73/1.92  clauses kept                  93
% 1.73/1.92  clauses forward subsumed     169
% 1.73/1.92  clauses back subsumed          3
% 1.73/1.92  Kbytes malloced             1953
% 1.73/1.92  
% 1.73/1.92  ----------- times (seconds) -----------
% 1.73/1.92  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.73/1.92  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.73/1.92  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.73/1.92  
% 1.73/1.92  That finishes the proof of the theorem.
% 1.73/1.92  
% 1.73/1.92  Process 1386 finished Wed Jul 27 05:19:55 2022
% 1.73/1.92  Otter interrupted
% 1.73/1.92  PROOF FOUND
%------------------------------------------------------------------------------