TSTP Solution File: GRP604-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n021.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 12:57:20 EDT 2022

% Result   : Unsatisfiable 1.72s 1.92s
% Output   : Refutation 1.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   52 (  52 unt;   0 nHn;   3 RR)
%            Number of literals    :   52 (  51 equ;   2 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   :  149 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(a,b) != multiply(b,a),
    file('GRP604-1.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,
    inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
    file('GRP604-1.p',unknown),
    [] ).

cnf(6,axiom,
    multiply(A,B) = inverse(double_divide(B,A)),
    file('GRP604-1.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,
    multiply(A,multiply(multiply(double_divide(B,A),C),B)) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8,8]),
    [iquote('back_demod,4,demod,8,8,8')] ).

cnf(11,plain,
    multiply(multiply(double_divide(A,double_divide(B,C)),D),A) = multiply(C,multiply(D,B)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,9])]),
    [iquote('para_into,9.1.1.2.1,9.1.1,flip.1')] ).

cnf(13,plain,
    multiply(double_divide(A,B),multiply(B,multiply(C,A))) = C,
    inference(para_from,[status(thm),theory(equality)],[11,9]),
    [iquote('para_from,11.1.1,9.1.1.2')] ).

cnf(15,plain,
    multiply(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
    inference(para_into,[status(thm),theory(equality)],[13,13]),
    [iquote('para_into,13.1.1.2.2,13.1.1')] ).

cnf(21,plain,
    multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
    inference(para_into,[status(thm),theory(equality)],[13,13]),
    [iquote('para_into,13.1.1.2,13.1.1')] ).

cnf(57,plain,
    double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
    inference(para_into,[status(thm),theory(equality)],[21,15]),
    [iquote('para_into,20.1.1,15.1.1')] ).

cnf(78,plain,
    multiply(double_divide(multiply(A,multiply(B,C)),D),A) = double_divide(C,multiply(D,B)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,57])]),
    [iquote('para_into,57.1.1.2.1,57.1.1,flip.1')] ).

cnf(79,plain,
    double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
    inference(para_into,[status(thm),theory(equality)],[57,15]),
    [iquote('para_into,57.1.1.2,15.1.1')] ).

cnf(87,plain,
    inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
    inference(para_from,[status(thm),theory(equality)],[57,8]),
    [iquote('para_from,57.1.1,7.1.1.1')] ).

cnf(91,plain,
    multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[87])]),
    [iquote('copy,87,flip.1')] ).

cnf(104,plain,
    double_divide(multiply(multiply(A,multiply(B,C)),D),double_divide(D,B)) = double_divide(C,A),
    inference(para_into,[status(thm),theory(equality)],[79,13]),
    [iquote('para_into,79.1.1.2.2,13.1.1')] ).

cnf(115,plain,
    inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
    inference(para_from,[status(thm),theory(equality)],[79,8]),
    [iquote('para_from,79.1.1,7.1.1.1')] ).

cnf(119,plain,
    multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[115])]),
    [iquote('copy,115,flip.1')] ).

cnf(179,plain,
    multiply(multiply(double_divide(A,B),double_divide(multiply(C,D),double_divide(D,A))),C) = inverse(B),
    inference(para_into,[status(thm),theory(equality)],[91,21]),
    [iquote('para_into,91.1.1.1.1.1,20.1.1')] ).

cnf(187,plain,
    inverse(A) = multiply(multiply(double_divide(B,A),double_divide(multiply(C,D),double_divide(D,B))),C),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[179])]),
    [iquote('copy,179,flip.1')] ).

cnf(207,plain,
    multiply(double_divide(A,double_divide(A,multiply(B,C))),inverse(B)) = C,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[91,13]),78]),
    [iquote('para_from,91.1.1,13.1.1.2,demod,78')] ).

cnf(223,plain,
    multiply(double_divide(A,inverse(B)),multiply(multiply(C,D),A)) = multiply(multiply(B,C),D),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[119,119]),8]),
    [iquote('para_into,119.1.1.1.2,119.1.1,demod,8')] ).

cnf(224,plain,
    multiply(double_divide(A,inverse(B)),multiply(C,A)) = inverse(multiply(double_divide(multiply(D,C),B),D)),
    inference(para_into,[status(thm),theory(equality)],[119,91]),
    [iquote('para_into,119.1.1.1.2,91.1.1')] ).

cnf(240,plain,
    multiply(multiply(A,B),C) = multiply(double_divide(D,inverse(A)),multiply(multiply(B,C),D)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[223])]),
    [iquote('copy,223,flip.1')] ).

cnf(241,plain,
    inverse(multiply(double_divide(multiply(A,B),C),A)) = multiply(double_divide(D,inverse(C)),multiply(B,D)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[224])]),
    [iquote('copy,224,flip.1')] ).

cnf(267,plain,
    multiply(multiply(A,B),multiply(inverse(A),C)) = multiply(B,C),
    inference(para_from,[status(thm),theory(equality)],[119,9]),
    [iquote('para_from,119.1.1,9.1.1.2.1')] ).

cnf(277,plain,
    multiply(double_divide(A,double_divide(A,inverse(B))),inverse(multiply(double_divide(multiply(C,D),B),C))) = D,
    inference(para_into,[status(thm),theory(equality)],[207,91]),
    [iquote('para_into,207.1.1.1.2.2,91.1.1')] ).

cnf(298,plain,
    double_divide(multiply(inverse(A),B),multiply(A,C)) = double_divide(B,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[207,57])]),
    [iquote('para_from,207.1.1,57.1.1.2,flip.1')] ).

cnf(388,plain,
    multiply(multiply(A,multiply(B,C)),D) = multiply(B,multiply(multiply(A,C),D)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[267,13]),8])]),
    [iquote('para_into,267.1.1.1,13.1.1,demod,8,flip.1')] ).

cnf(438,plain,
    double_divide(multiply(A,multiply(multiply(B,C),D)),double_divide(D,A)) = double_divide(C,B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[104]),388]),
    [iquote('back_demod,104,demod,388')] ).

cnf(477,plain,
    double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
    inference(para_from,[status(thm),theory(equality)],[298,79]),
    [iquote('para_from,298.1.1,79.1.1.2')] ).

cnf(479,plain,
    double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
    inference(para_from,[status(thm),theory(equality)],[298,57]),
    [iquote('para_from,298.1.1,57.1.1.2.1')] ).

cnf(480,plain,
    multiply(multiply(double_divide(A,B),inverse(C)),A) = inverse(multiply(C,B)),
    inference(para_from,[status(thm),theory(equality)],[298,91]),
    [iquote('para_from,298.1.1,91.1.1.1.1')] ).

cnf(490,plain,
    multiply(A,double_divide(B,multiply(A,C))) = double_divide(B,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[479,207])]),
    [iquote('para_into,479.1.1.2,207.1.1,flip.1')] ).

cnf(498,plain,
    multiply(A,double_divide(B,double_divide(C,D))) = double_divide(B,double_divide(C,multiply(A,D))),
    inference(para_into,[status(thm),theory(equality)],[490,490]),
    [iquote('para_into,490.1.1.2.2,490.1.1')] ).

cnf(514,plain,
    inverse(A) = multiply(double_divide(B,A),B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[187]),498,21]),
    [iquote('back_demod,187,demod,498,21')] ).

cnf(515,plain,
    multiply(double_divide(A,B),A) = inverse(B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[179]),498,21]),
    [iquote('back_demod,179,demod,498,21')] ).

cnf(548,plain,
    double_divide(A,double_divide(A,B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[514,477]),438]),
    [iquote('para_from,514.1.1,477.1.1.1.2.1,demod,438')] ).

cnf(576,plain,
    multiply(inverse(A),inverse(multiply(double_divide(multiply(B,C),A),B))) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[277]),548]),
    [iquote('back_demod,277,demod,548')] ).

cnf(590,plain,
    multiply(double_divide(multiply(A,B),C),A) = double_divide(B,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[548,57])]),
    [iquote('para_into,547.1.1.2,57.1.1,flip.1')] ).

cnf(593,plain,
    multiply(inverse(A),multiply(A,B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[576]),590,8]),
    [iquote('back_demod,576,demod,590,8')] ).

cnf(601,plain,
    multiply(double_divide(A,inverse(B)),multiply(C,A)) = multiply(B,C),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[241]),590,8])]),
    [iquote('back_demod,241,demod,590,8,flip.1')] ).

cnf(618,plain,
    multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[240]),601]),
    [iquote('back_demod,240,demod,601')] ).

cnf(638,plain,
    multiply(double_divide(A,B),multiply(inverse(C),A)) = inverse(multiply(C,B)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[480]),618]),
    [iquote('back_demod,480,demod,618')] ).

cnf(666,plain,
    double_divide(multiply(double_divide(A,B),multiply(inverse(C),A)),B) = C,
    inference(para_from,[status(thm),theory(equality)],[548,477]),
    [iquote('para_from,547.1.1,477.1.1.2')] ).

cnf(711,plain,
    inverse(inverse(A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[593,477]),548]),
    [iquote('para_from,593.1.1,477.1.1.1,demod,548')] ).

cnf(735,plain,
    inverse(multiply(A,B)) = double_divide(B,A),
    inference(para_into,[status(thm),theory(equality)],[711,8]),
    [iquote('para_into,711.1.1.1,7.1.1')] ).

cnf(740,plain,
    multiply(double_divide(A,B),multiply(inverse(C),A)) = double_divide(B,C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[638]),735]),
    [iquote('back_demod,638,demod,735')] ).

cnf(744,plain,
    double_divide(double_divide(A,B),A) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[666]),740]),
    [iquote('back_demod,666,demod,740')] ).

cnf(758,plain,
    double_divide(A,double_divide(B,A)) = B,
    inference(para_into,[status(thm),theory(equality)],[744,744]),
    [iquote('para_into,744.1.1.1,744.1.1')] ).

cnf(800,plain,
    multiply(A,B) = multiply(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[758,515]),8]),
    [iquote('para_from,758.1.1,515.1.1.1,demod,8')] ).

cnf(801,plain,
    $false,
    inference(binary,[status(thm)],[800,2]),
    [iquote('binary,800.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n021.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 05:25:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.72/1.92  ----- Otter 3.3f, August 2004 -----
% 1.72/1.92  The process was started by sandbox on n021.cluster.edu,
% 1.72/1.92  Wed Jul 27 05:25:38 2022
% 1.72/1.92  The command was "./otter".  The process ID is 17394.
% 1.72/1.92  
% 1.72/1.92  set(prolog_style_variables).
% 1.72/1.92  set(auto).
% 1.72/1.92     dependent: set(auto1).
% 1.72/1.92     dependent: set(process_input).
% 1.72/1.92     dependent: clear(print_kept).
% 1.72/1.92     dependent: clear(print_new_demod).
% 1.72/1.92     dependent: clear(print_back_demod).
% 1.72/1.92     dependent: clear(print_back_sub).
% 1.72/1.92     dependent: set(control_memory).
% 1.72/1.92     dependent: assign(max_mem, 12000).
% 1.72/1.92     dependent: assign(pick_given_ratio, 4).
% 1.72/1.92     dependent: assign(stats_level, 1).
% 1.72/1.92     dependent: assign(max_seconds, 10800).
% 1.72/1.92  clear(print_given).
% 1.72/1.92  
% 1.72/1.92  list(usable).
% 1.72/1.92  0 [] A=A.
% 1.72/1.92  0 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.72/1.92  0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.72/1.92  0 [] multiply(a,b)!=multiply(b,a).
% 1.72/1.92  end_of_list.
% 1.72/1.92  
% 1.72/1.92  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.72/1.92  
% 1.72/1.92  All clauses are units, and equality is present; the
% 1.72/1.92  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.72/1.92  
% 1.72/1.92     dependent: set(knuth_bendix).
% 1.72/1.92     dependent: set(anl_eq).
% 1.72/1.92     dependent: set(para_from).
% 1.72/1.92     dependent: set(para_into).
% 1.72/1.92     dependent: clear(para_from_right).
% 1.72/1.92     dependent: clear(para_into_right).
% 1.72/1.92     dependent: set(para_from_vars).
% 1.72/1.92     dependent: set(eq_units_both_ways).
% 1.72/1.92     dependent: set(dynamic_demod_all).
% 1.72/1.92     dependent: set(dynamic_demod).
% 1.72/1.92     dependent: set(order_eq).
% 1.72/1.92     dependent: set(back_demod).
% 1.72/1.92     dependent: set(lrpo).
% 1.72/1.92  
% 1.72/1.92  ------------> process usable:
% 1.72/1.92  ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.72/1.92  
% 1.72/1.92  ------------> process sos:
% 1.72/1.92  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.72/1.92  ** KEPT (pick-wt=14): 4 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.72/1.92  ---> New Demodulator: 5 [new_demod,4] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.72/1.92  ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.72/1.92  ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.72/1.92    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.72/1.92  >>>> Starting back demodulation with 5.
% 1.72/1.92  >>>> Starting back demodulation with 8.
% 1.72/1.92      >> back demodulating 4 with 8.
% 1.72/1.92  >>>> Starting back demodulation with 10.
% 1.72/1.92  
% 1.72/1.92  ======= end of input processing =======
% 1.72/1.92  
% 1.72/1.92  =========== start of search ===========
% 1.72/1.92  
% 1.72/1.92  
% 1.72/1.92  Resetting weight limit to 15.
% 1.72/1.92  
% 1.72/1.92  
% 1.72/1.92  Resetting weight limit to 15.
% 1.72/1.92  
% 1.72/1.92  sos_size=294
% 1.72/1.92  
% 1.72/1.92  -------- PROOF -------- 
% 1.72/1.92  
% 1.72/1.92  ----> UNIT CONFLICT at   0.03 sec ----> 801 [binary,800.1,2.1] $F.
% 1.72/1.92  
% 1.72/1.92  Length of proof is 48.  Level of proof is 23.
% 1.72/1.92  
% 1.72/1.92  ---------------- PROOF ----------------
% 1.72/1.92  % SZS status Unsatisfiable
% 1.72/1.92  % SZS output start Refutation
% See solution above
% 1.72/1.92  ------------ end of proof -------------
% 1.72/1.92  
% 1.72/1.92  
% 1.72/1.92  Search stopped by max_proofs option.
% 1.72/1.92  
% 1.72/1.92  
% 1.72/1.92  Search stopped by max_proofs option.
% 1.72/1.92  
% 1.72/1.92  ============ end of search ============
% 1.72/1.92  
% 1.72/1.92  -------------- statistics -------------
% 1.72/1.92  clauses given                 30
% 1.72/1.92  clauses generated            741
% 1.72/1.92  clauses kept                 563
% 1.72/1.92  clauses forward subsumed     483
% 1.72/1.92  clauses back subsumed          0
% 1.72/1.92  Kbytes malloced             4882
% 1.72/1.92  
% 1.72/1.92  ----------- times (seconds) -----------
% 1.72/1.92  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 1.72/1.92  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.72/1.92  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.72/1.92  
% 1.72/1.92  That finishes the proof of the theorem.
% 1.72/1.92  
% 1.72/1.92  Process 17394 finished Wed Jul 27 05:25:39 2022
% 1.72/1.92  Otter interrupted
% 1.72/1.92  PROOF FOUND
%------------------------------------------------------------------------------