TSTP Solution File: GRP602-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP602-1 : 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 12:57:20 EDT 2022

% Result   : Unsatisfiable 1.64s 1.86s
% Output   : Refutation 1.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   35 (  35 unt;   0 nHn;   4 RR)
%            Number of literals    :   35 (  34 equ;   3 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   :  103 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    file('GRP602-1.p',unknown),
    [] ).

cnf(3,axiom,
    inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
    file('GRP602-1.p',unknown),
    [] ).

cnf(5,axiom,
    multiply(A,B) = inverse(double_divide(B,A)),
    file('GRP602-1.p',unknown),
    [] ).

cnf(7,plain,
    inverse(double_divide(A,B)) = multiply(B,A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
    [iquote('copy,5,flip.1')] ).

cnf(8,plain,
    multiply(A,multiply(multiply(double_divide(B,A),C),B)) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),7,7,7]),
    [iquote('back_demod,3,demod,7,7,7')] ).

cnf(10,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)],[8,8])]),
    [iquote('para_into,8.1.1.2.1,8.1.1,flip.1')] ).

cnf(12,plain,
    multiply(double_divide(A,B),multiply(B,multiply(C,A))) = C,
    inference(para_from,[status(thm),theory(equality)],[10,8]),
    [iquote('para_from,10.1.1,8.1.1.2')] ).

cnf(14,plain,
    multiply(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
    inference(para_into,[status(thm),theory(equality)],[12,12]),
    [iquote('para_into,12.1.1.2.2,12.1.1')] ).

cnf(20,plain,
    multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
    inference(para_into,[status(thm),theory(equality)],[12,12]),
    [iquote('para_into,12.1.1.2,12.1.1')] ).

cnf(56,plain,
    double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
    inference(para_into,[status(thm),theory(equality)],[20,14]),
    [iquote('para_into,19.1.1,14.1.1')] ).

cnf(77,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)],[56,56])]),
    [iquote('para_into,56.1.1.2.1,56.1.1,flip.1')] ).

cnf(78,plain,
    double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
    inference(para_into,[status(thm),theory(equality)],[56,14]),
    [iquote('para_into,56.1.1.2,14.1.1')] ).

cnf(86,plain,
    inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
    inference(para_from,[status(thm),theory(equality)],[56,7]),
    [iquote('para_from,56.1.1,6.1.1.1')] ).

cnf(90,plain,
    multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[86])]),
    [iquote('copy,86,flip.1')] ).

cnf(103,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)],[78,12]),
    [iquote('para_into,78.1.1.2.2,12.1.1')] ).

cnf(114,plain,
    inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
    inference(para_from,[status(thm),theory(equality)],[78,7]),
    [iquote('para_from,78.1.1,6.1.1.1')] ).

cnf(118,plain,
    multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[114])]),
    [iquote('copy,114,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)],[90,20]),
    [iquote('para_into,90.1.1.1.1.1,19.1.1')] ).

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)],[90,12]),77]),
    [iquote('para_from,90.1.1,12.1.1.2,demod,77')] ).

cnf(223,plain,
    multiply(multiply(multiply(double_divide(A,multiply(b2,B)),multiply(B,A)),b2),a2) != a2,
    inference(para_from,[status(thm),theory(equality)],[114,1]),
    [iquote('para_from,114.1.1,1.1.1.1.1')] ).

cnf(268,plain,
    multiply(multiply(A,B),multiply(inverse(A),C)) = multiply(B,C),
    inference(para_from,[status(thm),theory(equality)],[118,8]),
    [iquote('para_from,118.1.1,8.1.1.2.1')] ).

cnf(293,plain,
    multiply(double_divide(A,double_divide(A,multiply(double_divide(B,C),D))),multiply(C,B)) = D,
    inference(para_into,[status(thm),theory(equality)],[207,7]),
    [iquote('para_into,207.1.1.2,6.1.1')] ).

cnf(299,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)],[207,56])]),
    [iquote('para_from,207.1.1,56.1.1.2,flip.1')] ).

cnf(389,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)],[268,12]),7])]),
    [iquote('para_into,268.1.1.1,12.1.1,demod,7,flip.1')] ).

cnf(422,plain,
    multiply(multiply(double_divide(A,multiply(b2,B)),A),multiply(multiply(B,b2),a2)) != a2,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[223]),389,389]),
    [iquote('back_demod,223,demod,389,389')] ).

cnf(440,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)],[103]),389]),
    [iquote('back_demod,103,demod,389')] ).

cnf(479,plain,
    double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
    inference(para_from,[status(thm),theory(equality)],[299,78]),
    [iquote('para_from,299.1.1,78.1.1.2')] ).

cnf(481,plain,
    double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
    inference(para_from,[status(thm),theory(equality)],[299,56]),
    [iquote('para_from,299.1.1,56.1.1.2.1')] ).

cnf(492,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)],[481,207])]),
    [iquote('para_into,481.1.1.2,207.1.1,flip.1')] ).

cnf(500,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)],[492,492]),
    [iquote('para_into,492.1.1.2.2,492.1.1')] ).

cnf(516,plain,
    inverse(A) = multiply(double_divide(B,A),B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[187]),500,20]),
    [iquote('back_demod,187,demod,500,20')] ).

cnf(550,plain,
    double_divide(A,double_divide(A,B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[516,479]),440]),
    [iquote('para_from,516.1.1,479.1.1.1.2.1,demod,440')] ).

cnf(568,plain,
    multiply(multiply(double_divide(A,B),C),multiply(B,A)) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[293]),550]),
    [iquote('back_demod,293,demod,550')] ).

cnf(570,plain,
    $false,
    inference(binary,[status(thm)],[568,422]),
    [iquote('binary,568.1,422.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP602-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12  % 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 05:17:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.64/1.86  ----- Otter 3.3f, August 2004 -----
% 1.64/1.86  The process was started by sandbox on n014.cluster.edu,
% 1.64/1.86  Wed Jul 27 05:17:09 2022
% 1.64/1.86  The command was "./otter".  The process ID is 23918.
% 1.64/1.86  
% 1.64/1.86  set(prolog_style_variables).
% 1.64/1.86  set(auto).
% 1.64/1.86     dependent: set(auto1).
% 1.64/1.86     dependent: set(process_input).
% 1.64/1.86     dependent: clear(print_kept).
% 1.64/1.86     dependent: clear(print_new_demod).
% 1.64/1.86     dependent: clear(print_back_demod).
% 1.64/1.86     dependent: clear(print_back_sub).
% 1.64/1.86     dependent: set(control_memory).
% 1.64/1.86     dependent: assign(max_mem, 12000).
% 1.64/1.86     dependent: assign(pick_given_ratio, 4).
% 1.64/1.86     dependent: assign(stats_level, 1).
% 1.64/1.86     dependent: assign(max_seconds, 10800).
% 1.64/1.86  clear(print_given).
% 1.64/1.86  
% 1.64/1.86  list(usable).
% 1.64/1.86  0 [] A=A.
% 1.64/1.86  0 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.64/1.86  0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.64/1.86  0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.64/1.86  end_of_list.
% 1.64/1.86  
% 1.64/1.86  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.64/1.86  
% 1.64/1.86  All clauses are units, and equality is present; the
% 1.64/1.86  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.64/1.86  
% 1.64/1.86     dependent: set(knuth_bendix).
% 1.64/1.86     dependent: set(anl_eq).
% 1.64/1.86     dependent: set(para_from).
% 1.64/1.86     dependent: set(para_into).
% 1.64/1.86     dependent: clear(para_from_right).
% 1.64/1.86     dependent: clear(para_into_right).
% 1.64/1.86     dependent: set(para_from_vars).
% 1.64/1.86     dependent: set(eq_units_both_ways).
% 1.64/1.86     dependent: set(dynamic_demod_all).
% 1.64/1.86     dependent: set(dynamic_demod).
% 1.64/1.86     dependent: set(order_eq).
% 1.64/1.86     dependent: set(back_demod).
% 1.64/1.86     dependent: set(lrpo).
% 1.64/1.86  
% 1.64/1.86  ------------> process usable:
% 1.64/1.86  ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.64/1.86  
% 1.64/1.86  ------------> process sos:
% 1.64/1.86  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.64/1.86  ** KEPT (pick-wt=14): 3 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.64/1.86  ---> New Demodulator: 4 [new_demod,3] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.64/1.86  ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.64/1.86  ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.64/1.86    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.64/1.86  >>>> Starting back demodulation with 4.
% 1.64/1.86  >>>> Starting back demodulation with 7.
% 1.64/1.86      >> back demodulating 3 with 7.
% 1.64/1.86  >>>> Starting back demodulation with 9.
% 1.64/1.86  
% 1.64/1.86  ======= end of input processing =======
% 1.64/1.86  
% 1.64/1.86  =========== start of search ===========
% 1.64/1.86  
% 1.64/1.86  
% 1.64/1.86  Resetting weight limit to 15.
% 1.64/1.86  
% 1.64/1.86  
% 1.64/1.86  Resetting weight limit to 15.
% 1.64/1.86  
% 1.64/1.86  sos_size=296
% 1.64/1.86  
% 1.64/1.86  -------- PROOF -------- 
% 1.64/1.86  
% 1.64/1.86  ----> UNIT CONFLICT at   0.01 sec ----> 570 [binary,568.1,422.1] $F.
% 1.64/1.86  
% 1.64/1.86  Length of proof is 31.  Level of proof is 16.
% 1.64/1.86  
% 1.64/1.86  ---------------- PROOF ----------------
% 1.64/1.86  % SZS status Unsatisfiable
% 1.64/1.86  % SZS output start Refutation
% See solution above
% 1.64/1.86  ------------ end of proof -------------
% 1.64/1.86  
% 1.64/1.86  
% 1.64/1.86  Search stopped by max_proofs option.
% 1.64/1.86  
% 1.64/1.86  
% 1.64/1.86  Search stopped by max_proofs option.
% 1.64/1.86  
% 1.64/1.86  ============ end of search ============
% 1.64/1.86  
% 1.64/1.86  -------------- statistics -------------
% 1.64/1.86  clauses given                 23
% 1.64/1.86  clauses generated            563
% 1.64/1.86  clauses kept                 412
% 1.64/1.86  clauses forward subsumed     310
% 1.64/1.86  clauses back subsumed          0
% 1.64/1.86  Kbytes malloced             4882
% 1.64/1.86  
% 1.64/1.86  ----------- times (seconds) -----------
% 1.64/1.86  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.64/1.86  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.64/1.86  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.64/1.86  
% 1.64/1.86  That finishes the proof of the theorem.
% 1.64/1.86  
% 1.64/1.86  Process 23918 finished Wed Jul 27 05:17:10 2022
% 1.64/1.86  Otter interrupted
% 1.64/1.86  PROOF FOUND
%------------------------------------------------------------------------------