TSTP Solution File: GRP590-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP590-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n025.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 12:57:19 EDT 2022

% Result   : Unsatisfiable 1.94s 2.09s
% Output   : Refutation 1.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   30 (  30 unt;   0 nHn;   3 RR)
%            Number of literals    :   30 (  29 equ;   2 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   :   64 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    file('GRP590-1.p',unknown),
    [] ).

cnf(3,axiom,
    double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C,
    file('GRP590-1.p',unknown),
    [] ).

cnf(5,axiom,
    multiply(A,B) = inverse(double_divide(B,A)),
    file('GRP590-1.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,
    double_divide(multiply(multiply(inverse(A),B),double_divide(B,C)),C) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),7,7]),
    [iquote('back_demod,3,demod,7,7')] ).

cnf(11,plain,
    double_divide(multiply(multiply(multiply(A,B),C),double_divide(C,D)),D) = double_divide(B,A),
    inference(para_into,[status(thm),theory(equality)],[8,7]),
    [iquote('para_into,8.1.1.1.1.1,6.1.1')] ).

cnf(12,plain,
    double_divide(multiply(multiply(inverse(A),multiply(multiply(inverse(B),C),double_divide(C,D))),B),D) = A,
    inference(para_into,[status(thm),theory(equality)],[8,8]),
    [iquote('para_into,8.1.1.1.2,8.1.1')] ).

cnf(14,plain,
    multiply(A,multiply(multiply(inverse(B),C),double_divide(C,A))) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,7])]),
    [iquote('para_from,8.1.1,6.1.1.1,flip.1')] ).

cnf(42,plain,
    double_divide(multiply(inverse(A),A),inverse(B)) = B,
    inference(para_into,[status(thm),theory(equality)],[12,14]),
    [iquote('para_into,12.1.1.1.1,14.1.1')] ).

cnf(51,plain,
    double_divide(multiply(inverse(A),A),multiply(B,C)) = double_divide(C,B),
    inference(para_into,[status(thm),theory(equality)],[42,7]),
    [iquote('para_into,42.1.1.2,6.1.1')] ).

cnf(58,plain,
    double_divide(multiply(multiply(inverse(A),multiply(inverse(B),B)),C),inverse(C)) = A,
    inference(para_from,[status(thm),theory(equality)],[42,8]),
    [iquote('para_from,42.1.1,8.1.1.1.2')] ).

cnf(61,plain,
    multiply(inverse(A),multiply(inverse(B),B)) = inverse(A),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[42,7])]),
    [iquote('para_from,42.1.1,6.1.1.1,flip.1')] ).

cnf(62,plain,
    double_divide(multiply(inverse(A),B),inverse(B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),61]),
    [iquote('back_demod,58,demod,61')] ).

cnf(86,plain,
    double_divide(inverse(multiply(inverse(A),A)),inverse(B)) = B,
    inference(para_from,[status(thm),theory(equality)],[61,42]),
    [iquote('para_from,60.1.1,42.1.1.1')] ).

cnf(92,plain,
    double_divide(inverse(A),inverse(multiply(inverse(B),B))) = A,
    inference(para_from,[status(thm),theory(equality)],[61,62]),
    [iquote('para_from,60.1.1,62.1.1.1')] ).

cnf(147,plain,
    double_divide(multiply(A,B),inverse(multiply(inverse(C),C))) = double_divide(B,A),
    inference(para_into,[status(thm),theory(equality)],[92,7]),
    [iquote('para_into,92.1.1.1,6.1.1')] ).

cnf(152,plain,
    multiply(inverse(A),A) = multiply(inverse(B),B),
    inference(para_into,[status(thm),theory(equality)],[92,86]),
    [iquote('para_into,92.1.1,86.1.1')] ).

cnf(161,plain,
    double_divide(A,multiply(inverse(B),inverse(A))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[92,8]),147]),
    [iquote('para_from,92.1.1,8.1.1.1.2,demod,147')] ).

cnf(171,plain,
    double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[152,11]),11]),
    [iquote('para_from,152.1.1,10.1.1.1.1.1,demod,11')] ).

cnf(174,plain,
    multiply(multiply(inverse(A),A),a2) != a2,
    inference(para_from,[status(thm),theory(equality)],[152,1]),
    [iquote('para_from,152.1.1,1.1.1.1')] ).

cnf(213,plain,
    double_divide(A,multiply(inverse(B),B)) = inverse(A),
    inference(para_into,[status(thm),theory(equality)],[161,152]),
    [iquote('para_into,161.1.1.2,152.1.1')] ).

cnf(214,plain,
    inverse(A) = double_divide(A,multiply(inverse(B),B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[213])]),
    [iquote('copy,213,flip.1')] ).

cnf(233,plain,
    multiply(inverse(A),A) = double_divide(B,inverse(B)),
    inference(para_into,[status(thm),theory(equality)],[171,42]),
    [iquote('para_into,171.1.1,42.1.1')] ).

cnf(275,plain,
    inverse(inverse(A)) = multiply(multiply(inverse(B),B),A),
    inference(para_from,[status(thm),theory(equality)],[213,7]),
    [iquote('para_from,213.1.1,6.1.1.1')] ).

cnf(276,plain,
    multiply(multiply(inverse(A),A),B) = inverse(inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[275])]),
    [iquote('copy,275,flip.1')] ).

cnf(325,plain,
    double_divide(inverse(A),double_divide(B,inverse(B))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[214,92]),51]),
    [iquote('para_from,214.1.1,92.1.1.2,demod,51')] ).

cnf(387,plain,
    double_divide(A,double_divide(B,inverse(B))) = inverse(A),
    inference(para_from,[status(thm),theory(equality)],[233,161]),
    [iquote('para_from,233.1.1,161.1.1.2')] ).

cnf(486,plain,
    inverse(inverse(A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[387,325])]),
    [iquote('para_into,387.1.1,325.1.1,flip.1')] ).

cnf(497,plain,
    multiply(multiply(inverse(A),A),B) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[276]),486]),
    [iquote('back_demod,276,demod,486')] ).

cnf(499,plain,
    $false,
    inference(binary,[status(thm)],[497,174]),
    [iquote('binary,497.1,174.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GRP590-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n025.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 05:19:15 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.94/2.09  ----- Otter 3.3f, August 2004 -----
% 1.94/2.09  The process was started by sandbox on n025.cluster.edu,
% 1.94/2.09  Wed Jul 27 05:19:15 2022
% 1.94/2.09  The command was "./otter".  The process ID is 19029.
% 1.94/2.09  
% 1.94/2.09  set(prolog_style_variables).
% 1.94/2.09  set(auto).
% 1.94/2.09     dependent: set(auto1).
% 1.94/2.09     dependent: set(process_input).
% 1.94/2.09     dependent: clear(print_kept).
% 1.94/2.09     dependent: clear(print_new_demod).
% 1.94/2.09     dependent: clear(print_back_demod).
% 1.94/2.09     dependent: clear(print_back_sub).
% 1.94/2.09     dependent: set(control_memory).
% 1.94/2.09     dependent: assign(max_mem, 12000).
% 1.94/2.09     dependent: assign(pick_given_ratio, 4).
% 1.94/2.09     dependent: assign(stats_level, 1).
% 1.94/2.09     dependent: assign(max_seconds, 10800).
% 1.94/2.09  clear(print_given).
% 1.94/2.09  
% 1.94/2.09  list(usable).
% 1.94/2.09  0 [] A=A.
% 1.94/2.09  0 [] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.94/2.09  0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.94/2.09  0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.94/2.09  end_of_list.
% 1.94/2.09  
% 1.94/2.09  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.94/2.09  
% 1.94/2.09  All clauses are units, and equality is present; the
% 1.94/2.09  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.94/2.09  
% 1.94/2.09     dependent: set(knuth_bendix).
% 1.94/2.09     dependent: set(anl_eq).
% 1.94/2.09     dependent: set(para_from).
% 1.94/2.09     dependent: set(para_into).
% 1.94/2.09     dependent: clear(para_from_right).
% 1.94/2.09     dependent: clear(para_into_right).
% 1.94/2.09     dependent: set(para_from_vars).
% 1.94/2.09     dependent: set(eq_units_both_ways).
% 1.94/2.09     dependent: set(dynamic_demod_all).
% 1.94/2.09     dependent: set(dynamic_demod).
% 1.94/2.09     dependent: set(order_eq).
% 1.94/2.09     dependent: set(back_demod).
% 1.94/2.09     dependent: set(lrpo).
% 1.94/2.09  
% 1.94/2.09  ------------> process usable:
% 1.94/2.09  ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.94/2.09  
% 1.94/2.09  ------------> process sos:
% 1.94/2.09  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.94/2.09  ** KEPT (pick-wt=14): 3 [] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.94/2.09  ---> New Demodulator: 4 [new_demod,3] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.94/2.09  ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.94/2.09  ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.94/2.09    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.94/2.09  >>>> Starting back demodulation with 4.
% 1.94/2.09  >>>> Starting back demodulation with 7.
% 1.94/2.09      >> back demodulating 3 with 7.
% 1.94/2.09  >>>> Starting back demodulation with 9.
% 1.94/2.09  
% 1.94/2.09  ======= end of input processing =======
% 1.94/2.09  
% 1.94/2.09  =========== start of search ===========
% 1.94/2.09  
% 1.94/2.09  -------- PROOF -------- 
% 1.94/2.09  
% 1.94/2.09  ----> UNIT CONFLICT at   0.01 sec ----> 499 [binary,497.1,174.1] $F.
% 1.94/2.09  
% 1.94/2.09  Length of proof is 26.  Level of proof is 14.
% 1.94/2.09  
% 1.94/2.09  ---------------- PROOF ----------------
% 1.94/2.09  % SZS status Unsatisfiable
% 1.94/2.09  % SZS output start Refutation
% See solution above
% 1.94/2.09  ------------ end of proof -------------
% 1.94/2.09  
% 1.94/2.09  
% 1.94/2.09  Search stopped by max_proofs option.
% 1.94/2.09  
% 1.94/2.09  
% 1.94/2.09  Search stopped by max_proofs option.
% 1.94/2.09  
% 1.94/2.09  ============ end of search ============
% 1.94/2.09  
% 1.94/2.09  -------------- statistics -------------
% 1.94/2.09  clauses given                 29
% 1.94/2.09  clauses generated            453
% 1.94/2.09  clauses kept                 295
% 1.94/2.09  clauses forward subsumed     262
% 1.94/2.09  clauses back subsumed          1
% 1.94/2.09  Kbytes malloced             4882
% 1.94/2.09  
% 1.94/2.09  ----------- times (seconds) -----------
% 1.94/2.09  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.94/2.09  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.94/2.09  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.94/2.09  
% 1.94/2.09  That finishes the proof of the theorem.
% 1.94/2.09  
% 1.94/2.09  Process 19029 finished Wed Jul 27 05:19:17 2022
% 1.94/2.09  Otter interrupted
% 1.94/2.09  PROOF FOUND
%------------------------------------------------------------------------------