TSTP Solution File: GRP609-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP609-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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 12:57:21 EDT 2022

% Result   : Unsatisfiable 1.86s 2.06s
% Output   : Refutation 1.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   40 (  40 unt;   0 nHn;   5 RR)
%            Number of literals    :   40 (  39 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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   93 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
    file('GRP609-1.p',unknown),
    [] ).

cnf(2,plain,
    multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
    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(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
    file('GRP609-1.p',unknown),
    [] ).

cnf(6,axiom,
    multiply(A,B) = inverse(double_divide(B,A)),
    file('GRP609-1.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(double_divide(A,B),multiply(B,multiply(C,A))) = 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(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
    inference(para_into,[status(thm),theory(equality)],[9,9]),
    [iquote('para_into,9.1.1.2.2,9.1.1')] ).

cnf(13,plain,
    multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
    inference(para_into,[status(thm),theory(equality)],[9,9]),
    [iquote('para_into,9.1.1.2,9.1.1')] ).

cnf(35,plain,
    double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,13])]),
    [iquote('para_into,11.1.1,13.1.1,flip.1')] ).

cnf(66,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)],[35,35])]),
    [iquote('para_into,35.1.1.2.1,35.1.1,flip.1')] ).

cnf(67,plain,
    double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
    inference(para_into,[status(thm),theory(equality)],[35,11]),
    [iquote('para_into,35.1.1.2,11.1.1')] ).

cnf(77,plain,
    inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
    inference(para_from,[status(thm),theory(equality)],[35,8]),
    [iquote('para_from,35.1.1,7.1.1.1')] ).

cnf(79,plain,
    multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[77])]),
    [iquote('copy,77,flip.1')] ).

cnf(101,plain,
    inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
    inference(para_from,[status(thm),theory(equality)],[67,8]),
    [iquote('para_from,67.1.1,7.1.1.1')] ).

cnf(102,plain,
    multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[101])]),
    [iquote('copy,101,flip.1')] ).

cnf(131,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)],[79,9]),66]),
    [iquote('para_from,79.1.1,9.1.1.2,demod,66')] ).

cnf(236,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)],[131,35])]),
    [iquote('para_from,131.1.1,35.1.1.2,flip.1')] ).

cnf(360,plain,
    double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
    inference(para_from,[status(thm),theory(equality)],[236,67]),
    [iquote('para_from,236.1.1,67.1.1.2')] ).

cnf(362,plain,
    double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
    inference(para_from,[status(thm),theory(equality)],[236,35]),
    [iquote('para_from,236.1.1,35.1.1.2.1')] ).

cnf(374,plain,
    double_divide(inverse(A),double_divide(B,double_divide(B,multiply(A,inverse(C))))) = C,
    inference(para_into,[status(thm),theory(equality)],[360,102]),
    [iquote('para_into,360.1.1.1,102.1.1')] ).

cnf(406,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)],[362,131])]),
    [iquote('para_into,362.1.1.2,131.1.1,flip.1')] ).

cnf(435,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)],[406,406]),
    [iquote('para_into,406.1.1.2.2,406.1.1')] ).

cnf(446,plain,
    double_divide(A,double_divide(B,double_divide(B,multiply(C,D)))) = double_divide(A,multiply(C,D)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[406,11]),435,66]),
    [iquote('para_into,406.1.1.2.2,11.1.1,demod,435,66')] ).

cnf(478,plain,
    double_divide(inverse(A),multiply(A,inverse(B))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[374]),446]),
    [iquote('back_demod,374,demod,446')] ).

cnf(528,plain,
    multiply(A,B) = double_divide(inverse(A),inverse(B)),
    inference(para_from,[status(thm),theory(equality)],[478,406]),
    [iquote('para_from,478.1.1,406.1.1.2')] ).

cnf(532,plain,
    double_divide(multiply(inverse(A),inverse(B)),A) = B,
    inference(para_from,[status(thm),theory(equality)],[478,67]),
    [iquote('para_from,478.1.1,67.1.1.2')] ).

cnf(553,plain,
    double_divide(inverse(A),double_divide(inverse(A),inverse(inverse(B)))) = B,
    inference(para_from,[status(thm),theory(equality)],[528,478]),
    [iquote('para_from,528.1.1,478.1.1.2')] ).

cnf(570,plain,
    double_divide(inverse(inverse(b1)),inverse(b1)) != multiply(inverse(a1),a1),
    inference(para_from,[status(thm),theory(equality)],[528,2]),
    [iquote('para_from,528.1.1,2.1.1')] ).

cnf(583,plain,
    multiply(A,multiply(B,inverse(A))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[532,13]),8]),
    [iquote('para_from,532.1.1,13.1.1.1,demod,8')] ).

cnf(592,plain,
    double_divide(A,double_divide(A,multiply(B,C))) = multiply(B,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[583,131])]),
    [iquote('para_into,583.1.1.2,131.1.1,flip.1')] ).

cnf(626,plain,
    multiply(double_divide(inverse(A),A),B) = B,
    inference(para_from,[status(thm),theory(equality)],[583,9]),
    [iquote('para_from,583.1.1,9.1.1.2')] ).

cnf(690,plain,
    multiply(A,double_divide(inverse(B),B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[626,67]),592]),
    [iquote('para_from,626.1.1,67.1.1.1,demod,592')] ).

cnf(692,plain,
    double_divide(A,double_divide(A,B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[626,13]),690]),
    [iquote('para_from,626.1.1,13.1.1.1.1,demod,690')] ).

cnf(701,plain,
    inverse(inverse(A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[553]),692]),
    [iquote('back_demod,553,demod,692')] ).

cnf(719,plain,
    double_divide(b1,inverse(b1)) != multiply(inverse(a1),a1),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[570]),701]),
    [iquote('back_demod,570,demod,701')] ).

cnf(763,plain,
    multiply(double_divide(A,inverse(A)),B) = B,
    inference(para_from,[status(thm),theory(equality)],[701,626]),
    [iquote('para_from,700.1.1,626.1.1.1.1')] ).

cnf(767,plain,
    multiply(inverse(A),multiply(B,A)) = B,
    inference(para_from,[status(thm),theory(equality)],[701,583]),
    [iquote('para_from,700.1.1,583.1.1.2.2')] ).

cnf(1026,plain,
    multiply(inverse(A),A) = double_divide(B,inverse(B)),
    inference(para_into,[status(thm),theory(equality)],[767,763]),
    [iquote('para_into,767.1.1.2,763.1.1')] ).

cnf(1028,plain,
    double_divide(A,inverse(A)) = multiply(inverse(B),B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1026])]),
    [iquote('copy,1026,flip.1')] ).

cnf(1029,plain,
    $false,
    inference(binary,[status(thm)],[1028,719]),
    [iquote('binary,1028.1,719.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : GRP609-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n023.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 05:53:48 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.86/2.06  ----- Otter 3.3f, August 2004 -----
% 1.86/2.06  The process was started by sandbox on n023.cluster.edu,
% 1.86/2.06  Wed Jul 27 05:53:48 2022
% 1.86/2.06  The command was "./otter".  The process ID is 2883.
% 1.86/2.06  
% 1.86/2.06  set(prolog_style_variables).
% 1.86/2.06  set(auto).
% 1.86/2.06     dependent: set(auto1).
% 1.86/2.06     dependent: set(process_input).
% 1.86/2.06     dependent: clear(print_kept).
% 1.86/2.06     dependent: clear(print_new_demod).
% 1.86/2.06     dependent: clear(print_back_demod).
% 1.86/2.06     dependent: clear(print_back_sub).
% 1.86/2.06     dependent: set(control_memory).
% 1.86/2.06     dependent: assign(max_mem, 12000).
% 1.86/2.06     dependent: assign(pick_given_ratio, 4).
% 1.86/2.06     dependent: assign(stats_level, 1).
% 1.86/2.06     dependent: assign(max_seconds, 10800).
% 1.86/2.06  clear(print_given).
% 1.86/2.06  
% 1.86/2.06  list(usable).
% 1.86/2.06  0 [] A=A.
% 1.86/2.06  0 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.86/2.06  0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.86/2.06  0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.86/2.06  end_of_list.
% 1.86/2.06  
% 1.86/2.06  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.86/2.06  
% 1.86/2.06  All clauses are units, and equality is present; the
% 1.86/2.06  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.86/2.06  
% 1.86/2.06     dependent: set(knuth_bendix).
% 1.86/2.06     dependent: set(anl_eq).
% 1.86/2.06     dependent: set(para_from).
% 1.86/2.06     dependent: set(para_into).
% 1.86/2.06     dependent: clear(para_from_right).
% 1.86/2.06     dependent: clear(para_into_right).
% 1.86/2.06     dependent: set(para_from_vars).
% 1.86/2.06     dependent: set(eq_units_both_ways).
% 1.86/2.06     dependent: set(dynamic_demod_all).
% 1.86/2.06     dependent: set(dynamic_demod).
% 1.86/2.06     dependent: set(order_eq).
% 1.86/2.06     dependent: set(back_demod).
% 1.86/2.06     dependent: set(lrpo).
% 1.86/2.06  
% 1.86/2.06  ------------> process usable:
% 1.86/2.06  ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.86/2.06  
% 1.86/2.06  ------------> process sos:
% 1.86/2.06  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.86/2.06  ** KEPT (pick-wt=14): 4 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.86/2.06  ---> New Demodulator: 5 [new_demod,4] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.86/2.06  ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.86/2.06  ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.86/2.06    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.86/2.06  >>>> Starting back demodulation with 5.
% 1.86/2.06  >>>> Starting back demodulation with 8.
% 1.86/2.06      >> back demodulating 4 with 8.
% 1.86/2.06  >>>> Starting back demodulation with 10.
% 1.86/2.06  
% 1.86/2.06  ======= end of input processing =======
% 1.86/2.06  
% 1.86/2.06  =========== start of search ===========
% 1.86/2.06  
% 1.86/2.06  
% 1.86/2.06  Resetting weight limit to 13.
% 1.86/2.06  
% 1.86/2.06  
% 1.86/2.06  Resetting weight limit to 13.
% 1.86/2.06  
% 1.86/2.06  sos_size=277
% 1.86/2.06  
% 1.86/2.06  
% 1.86/2.06  Resetting weight limit to 9.
% 1.86/2.06  
% 1.86/2.06  
% 1.86/2.06  Resetting weight limit to 9.
% 1.86/2.06  
% 1.86/2.06  sos_size=301
% 1.86/2.06  
% 1.86/2.06  -------- PROOF -------- 
% 1.86/2.06  
% 1.86/2.06  ----> UNIT CONFLICT at   0.04 sec ----> 1029 [binary,1028.1,719.1] $F.
% 1.86/2.06  
% 1.86/2.06  Length of proof is 36.  Level of proof is 22.
% 1.86/2.06  
% 1.86/2.06  ---------------- PROOF ----------------
% 1.86/2.06  % SZS status Unsatisfiable
% 1.86/2.06  % SZS output start Refutation
% See solution above
% 1.86/2.06  ------------ end of proof -------------
% 1.86/2.06  
% 1.86/2.06  
% 1.86/2.06  Search stopped by max_proofs option.
% 1.86/2.06  
% 1.86/2.06  
% 1.86/2.06  Search stopped by max_proofs option.
% 1.86/2.06  
% 1.86/2.06  ============ end of search ============
% 1.86/2.06  
% 1.86/2.06  -------------- statistics -------------
% 1.86/2.06  clauses given                 50
% 1.86/2.06  clauses generated           1585
% 1.86/2.06  clauses kept                 712
% 1.86/2.06  clauses forward subsumed     872
% 1.86/2.06  clauses back subsumed          2
% 1.86/2.06  Kbytes malloced             4882
% 1.86/2.06  
% 1.86/2.06  ----------- times (seconds) -----------
% 1.86/2.06  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.86/2.06  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.86/2.06  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.86/2.06  
% 1.86/2.06  That finishes the proof of the theorem.
% 1.86/2.06  
% 1.86/2.06  Process 2883 finished Wed Jul 27 05:53:50 2022
% 1.86/2.06  Otter interrupted
% 1.86/2.06  PROOF FOUND
%------------------------------------------------------------------------------