TSTP Solution File: GRP604-1 by EQP---0.9e

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n027.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  : 600s
% DateTime : Sat Jul 16 08:48:10 EDT 2022

% Result   : Unsatisfiable 0.70s 1.09s
% Output   : Refutation 0.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    1
% Syntax   : Number of clauses     :   40 (  40 unt;   0 nHn;   4 RR)
%            Number of literals    :   40 (   0 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  114 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)),B),
    file('GRP604-1.p',unknown),
    [] ).

cnf(2,plain,
    equal(inverse(double_divide(A,B)),multiply(B,A)),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(3,plain,
    equal(multiply(A,multiply(multiply(double_divide(B,A),C),B)),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1]),2,2,2]),
    [iquote('back_demod(1),demod([2,2,2])')] ).

cnf(4,plain,
    ~ equal(multiply(b,a),multiply(a,b)),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(5,plain,
    equal(multiply(multiply(double_divide(A,double_divide(B,C)),D),A),multiply(C,multiply(D,B))),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,3]),1]),
    [iquote('para(3,3),flip(1)')] ).

cnf(6,plain,
    equal(multiply(double_divide(A,B),multiply(B,multiply(C,A))),C),
    inference(para,[status(thm),theory(equality)],[5,3]),
    [iquote('para(5,3)')] ).

cnf(9,plain,
    equal(multiply(double_divide(multiply(A,B),double_divide(B,C)),A),C),
    inference(para,[status(thm),theory(equality)],[6,6]),
    [iquote('para(6,6)')] ).

cnf(13,plain,
    equal(multiply(double_divide(A,B),multiply(B,C)),double_divide(multiply(A,D),double_divide(D,C))),
    inference(para,[status(thm),theory(equality)],[9,6]),
    [iquote('para(9,6)')] ).

cnf(72,plain,
    equal(double_divide(multiply(A,B),double_divide(B,multiply(C,A))),C),
    inference(para,[status(thm),theory(equality)],[13,6]),
    [iquote('para(13,6)')] ).

cnf(81,plain,
    equal(inverse(A),multiply(double_divide(B,multiply(A,C)),multiply(C,B))),
    inference(para,[status(thm),theory(equality)],[72,2]),
    [iquote('para(72,2)')] ).

cnf(82,plain,
    equal(multiply(double_divide(A,multiply(B,C)),multiply(C,A)),inverse(B)),
    inference(flip,[status(thm),theory(equality)],[81]),
    [iquote('flip(81)')] ).

cnf(97,plain,
    equal(multiply(multiply(A,B),multiply(inverse(A),C)),multiply(B,C)),
    inference(para,[status(thm),theory(equality)],[82,3]),
    [iquote('para(82,3)')] ).

cnf(98,plain,
    equal(multiply(multiply(double_divide(A,B),C),multiply(multiply(B,A),D)),multiply(C,D)),
    inference(para,[status(thm),theory(equality)],[2,97]),
    [iquote('para(2,97)')] ).

cnf(101,plain,
    equal(multiply(double_divide(A,double_divide(A,multiply(B,C))),inverse(B)),C),
    inference(para,[status(thm),theory(equality)],[82,6]),
    [iquote('para(82,6)')] ).

cnf(102,plain,
    equal(multiply(double_divide(A,double_divide(A,multiply(double_divide(B,C),D))),multiply(C,B)),D),
    inference(para,[status(thm),theory(equality)],[2,101]),
    [iquote('para(2,101)')] ).

cnf(110,plain,
    equal(multiply(double_divide(inverse(A),B),multiply(B,C)),double_divide(D,double_divide(D,multiply(A,C)))),
    inference(para,[status(thm),theory(equality)],[101,6]),
    [iquote('para(101,6)')] ).

cnf(111,plain,
    equal(double_divide(A,double_divide(A,multiply(B,C))),multiply(double_divide(inverse(B),D),multiply(D,C))),
    inference(flip,[status(thm),theory(equality)],[110]),
    [iquote('flip(110)')] ).

cnf(150,plain,
    equal(double_divide(multiply(multiply(multiply(double_divide(A,B),C),A),D),double_divide(D,C)),B),
    inference(para,[status(thm),theory(equality)],[13,9]),
    [iquote('para(13,9)')] ).

cnf(153,plain,
    equal(inverse(A),multiply(double_divide(B,C),multiply(multiply(multiply(double_divide(D,A),C),D),B))),
    inference(para,[status(thm),theory(equality)],[150,2]),
    [iquote('para(150,2)')] ).

cnf(157,plain,
    equal(multiply(double_divide(A,B),multiply(multiply(C,multiply(B,D)),A)),multiply(C,D)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[153,2]),5]),
    [iquote('para(153,2),demod([5])')] ).

cnf(214,plain,
    equal(multiply(double_divide(multiply(multiply(A,B),C),D),multiply(D,multiply(E,C))),multiply(double_divide(B,A),E)),
    inference(para,[status(thm),theory(equality)],[98,6]),
    [iquote('para(98,6)')] ).

cnf(219,plain,
    equal(multiply(double_divide(multiply(A,B),C),multiply(C,D)),double_divide(E,double_divide(E,multiply(double_divide(B,A),D)))),
    inference(para,[status(thm),theory(equality)],[102,6]),
    [iquote('para(102,6)')] ).

cnf(220,plain,
    equal(double_divide(A,double_divide(A,multiply(double_divide(B,C),D))),multiply(double_divide(multiply(C,B),E),multiply(E,D))),
    inference(flip,[status(thm),theory(equality)],[219]),
    [iquote('flip(219)')] ).

cnf(248,plain,
    equal(multiply(double_divide(A,double_divide(A,B)),C),multiply(B,C)),
    inference(para,[status(thm),theory(equality)],[157,3]),
    [iquote('para(157,3)')] ).

cnf(255,plain,
    equal(multiply(multiply(A,B),inverse(A)),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[101]),248]),
    [iquote('back_demod(101),demod([248])')] ).

cnf(260,plain,
    equal(multiply(A,inverse(multiply(B,A))),inverse(B)),
    inference(para,[status(thm),theory(equality)],[255,255]),
    [iquote('para(255,255)')] ).

cnf(263,plain,
    equal(inverse(multiply(A,B)),multiply(inverse(A),inverse(B))),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[260,255]),1]),
    [iquote('para(260,255),flip(1)')] ).

cnf(278,plain,
    equal(multiply(double_divide(inverse(A),B),multiply(B,C)),multiply(A,C)),
    inference(para,[status(thm),theory(equality)],[255,6]),
    [iquote('para(255,6)')] ).

cnf(279,plain,
    equal(double_divide(A,double_divide(A,multiply(B,C))),multiply(B,C)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[111]),278]),
    [iquote('back_demod(111),demod([278])')] ).

cnf(281,plain,
    equal(multiply(double_divide(multiply(A,B),C),multiply(C,D)),multiply(double_divide(B,A),D)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[220]),279]),1]),
    [iquote('back_demod(220),demod([279]),flip(1)')] ).

cnf(282,plain,
    equal(multiply(double_divide(A,multiply(B,C)),multiply(D,A)),multiply(double_divide(C,B),D)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[214]),281]),
    [iquote('back_demod(214),demod([281])')] ).

cnf(288,plain,
    equal(multiply(double_divide(A,B),A),inverse(B)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[82]),282]),
    [iquote('back_demod(82),demod([282])')] ).

cnf(466,plain,
    equal(multiply(inverse(A),multiply(A,B)),B),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[288,255]),2]),
    [iquote('para(288,255),demod([2])')] ).

cnf(470,plain,
    equal(multiply(A,inverse(inverse(B))),multiply(B,A)),
    inference(para,[status(thm),theory(equality)],[466,255]),
    [iquote('para(466,255)')] ).

cnf(471,plain,
    equal(multiply(A,B),multiply(B,inverse(inverse(A)))),
    inference(flip,[status(thm),theory(equality)],[470]),
    [iquote('flip(470)')] ).

cnf(474,plain,
    equal(multiply(inverse(inverse(A)),B),multiply(A,B)),
    inference(para,[status(thm),theory(equality)],[466,466]),
    [iquote('para(466,466)')] ).

cnf(475,plain,
    ~ equal(multiply(a,inverse(inverse(b))),multiply(a,b)),
    inference(para,[status(thm),theory(equality)],[471,4]),
    [iquote('para(471,4)')] ).

cnf(496,plain,
    equal(inverse(inverse(A)),A),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[471,255]),263,263,474,466]),
    [iquote('para(471,255),demod([263,263,474,466])')] ).

cnf(501,plain,
    ~ equal(multiply(a,b),multiply(a,b)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[475]),496]),
    [iquote('back_demod(475),demod([496])')] ).

cnf(502,plain,
    $false,
    inference(conflict,[status(thm)],[501]),
    [iquote('xx_conflict(501)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12  % Command  : tptp2X_and_run_eqp %s
% 0.12/0.33  % Computer : n027.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  : 600
% 0.12/0.33  % DateTime : Tue Jun 14 10:03:03 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.70/1.09  ----- EQP 0.9e, May 2009 -----
% 0.70/1.09  The job began on n027.cluster.edu, Tue Jun 14 10:03:04 2022
% 0.70/1.09  The command was "./eqp09e".
% 0.70/1.09  
% 0.70/1.09  set(prolog_style_variables).
% 0.70/1.09  set(lrpo).
% 0.70/1.09  set(basic_paramod).
% 0.70/1.09  set(functional_subsume).
% 0.70/1.09  set(ordered_paramod).
% 0.70/1.09  set(prime_paramod).
% 0.70/1.09  set(para_pairs).
% 0.70/1.09  assign(pick_given_ratio,4).
% 0.70/1.09  clear(print_kept).
% 0.70/1.09  clear(print_new_demod).
% 0.70/1.09  clear(print_back_demod).
% 0.70/1.09  clear(print_given).
% 0.70/1.09  assign(max_mem,64000).
% 0.70/1.09  end_of_commands.
% 0.70/1.09  
% 0.70/1.09  Usable:
% 0.70/1.09  end_of_list.
% 0.70/1.09  
% 0.70/1.09  Sos:
% 0.70/1.09  0 (wt=-1) [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B.
% 0.70/1.09  0 (wt=-1) [] multiply(A,B) = inverse(double_divide(B,A)).
% 0.70/1.09  0 (wt=-1) [] -(multiply(a,b) = multiply(b,a)).
% 0.70/1.09  end_of_list.
% 0.70/1.09  
% 0.70/1.09  Demodulators:
% 0.70/1.09  end_of_list.
% 0.70/1.09  
% 0.70/1.09  Passive:
% 0.70/1.09  end_of_list.
% 0.70/1.09  
% 0.70/1.09  Starting to process input.
% 0.70/1.09  
% 0.70/1.09  ** KEPT: 1 (wt=14) [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B.
% 0.70/1.09  1 is a new demodulator.
% 0.70/1.09  
% 0.70/1.09  ** KEPT: 2 (wt=8) [flip(1)] inverse(double_divide(A,B)) = multiply(B,A).
% 0.70/1.09  2 is a new demodulator.
% 0.70/1.09      -> 2 back demodulating 1.
% 0.70/1.09  
% 0.70/1.09  ** KEPT: 3 (wt=11) [back_demod(1),demod([2,2,2])] multiply(A,multiply(multiply(double_divide(B,A),C),B)) = C.
% 0.70/1.09  3 is a new demodulator.
% 0.70/1.09  
% 0.70/1.09  ** KEPT: 4 (wt=7) [flip(1)] -(multiply(b,a) = multiply(a,b)).
% 0.70/1.09  ---------------- PROOF FOUND ----------------
% 0.70/1.09  % SZS status Unsatisfiable
% 0.70/1.09  
% 0.70/1.09  
% 0.70/1.09  After processing input:
% 0.70/1.09  
% 0.70/1.09  Usable:
% 0.70/1.09  end_of_list.
% 0.70/1.09  
% 0.70/1.09  Sos:
% 0.70/1.09  4 (wt=7) [flip(1)] -(multiply(b,a) = multiply(a,b)).
% 0.70/1.09  2 (wt=8) [flip(1)] inverse(double_divide(A,B)) = multiply(B,A).
% 0.70/1.09  3 (wt=11) [back_demod(1),demod([2,2,2])] multiply(A,multiply(multiply(double_divide(B,A),C),B)) = C.
% 0.70/1.09  end_of_list.
% 0.70/1.09  
% 0.70/1.09  Demodulators:
% 0.70/1.09  2 (wt=8) [flip(1)] inverse(double_divide(A,B)) = multiply(B,A).
% 0.70/1.09  3 (wt=11) [back_demod(1),demod([2,2,2])] multiply(A,multiply(multiply(double_divide(B,A),C),B)) = C.
% 0.70/1.09  end_of_list.
% 0.70/1.09  
% 0.70/1.09  Passive:
% 0.70/1.09  end_of_list.
% 0.70/1.09  
% 0.70/1.09  UNIT CONFLICT from 501 and x=x at   0.03 seconds.
% 0.70/1.09  
% 0.70/1.09  ---------------- PROOF ----------------
% 0.70/1.09  % SZS output start Refutation
% See solution above
% 0.70/1.10  ------------ end of proof -------------
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  ------------- memory usage ------------
% 0.70/1.10  Memory dynamically allocated (tp_alloc): 976.
% 0.70/1.10    type (bytes each)        gets      frees     in use      avail      bytes
% 0.70/1.10  sym_ent (  96)               56          0         56          0      5.2 K
% 0.70/1.10  term (  16)               25287      15583       9704         22    188.0 K
% 0.70/1.10  gen_ptr (   8)            49872       9684      40188         39    314.3 K
% 0.70/1.10  context ( 808)            13911      13909          2          4      4.7 K
% 0.70/1.10  trail (  12)               4888       4888          0          8      0.1 K
% 0.70/1.10  bt_node (  68)             2498       2495          3         14      1.1 K
% 0.70/1.10  ac_position (285432)          0          0          0          0      0.0 K
% 0.70/1.10  ac_match_pos (14044)          0          0          0          0      0.0 K
% 0.70/1.10  ac_match_free_vars_pos (4020)
% 0.70/1.10                                0          0          0          0      0.0 K
% 0.70/1.10  discrim (  12)             7301       4108       3193        590     44.3 K
% 0.70/1.10  flat (  40)               60106      60106          0         31      1.2 K
% 0.70/1.10  discrim_pos (  12)          750        750          0          1      0.0 K
% 0.70/1.10  fpa_head (  12)            2434          0       2434          0     28.5 K
% 0.70/1.10  fpa_tree (  28)             929        929          0         13      0.4 K
% 0.70/1.10  fpa_pos (  36)              732        732          0          1      0.0 K
% 0.70/1.10  literal (  12)             1578       1077        501          1      5.9 K
% 0.70/1.10  clause (  24)              1578       1077        501          1     11.8 K
% 0.70/1.10  list (  12)                 291        234         57          8      0.8 K
% 0.70/1.10  list_pos (  20)            2326       1265       1061         13     21.0 K
% 0.70/1.10  pair_index (   40)              2          0          2          0      0.1 K
% 0.70/1.10  
% 0.70/1.10  -------------- statistics -------------
% 0.70/1.10  Clauses input                  3
% 0.70/1.10    Usable input                   0
% 0.70/1.10    Sos input                      3
% 0.70/1.10    Demodulators input             0
% 0.70/1.10    Passive input                  0
% 0.70/1.10  
% 0.70/1.10  Processed BS (before search)   4
% 0.70/1.10  Forward subsumed BS            0
% 0.70/1.10  Kept BS                        4
% 0.70/1.10  New demodulators BS            3
% 0.70/1.10  Back demodulated BS            1
% 0.70/1.10  
% 0.70/1.10  Clauses or pairs given       391
% 0.70/1.10  Clauses generated            832
% 0.70/1.10  Forward subsumed             335
% 0.70/1.10  Deleted by weight              0
% 0.70/1.10  Deleted by variable count      0
% 0.70/1.10  Kept                         497
% 0.70/1.10  New demodulators             229
% 0.70/1.10  Back demodulated             272
% 0.70/1.10  Ordered paramod prunes         0
% 0.70/1.10  Basic paramod prunes        1374
% 0.70/1.10  Prime paramod prunes           3
% 0.70/1.10  Semantic prunes                0
% 0.70/1.10  
% 0.70/1.10  Rewrite attmepts            8948
% 0.70/1.10  Rewrites                     535
% 0.70/1.10  
% 0.70/1.10  FPA overloads                  0
% 0.70/1.10  FPA underloads                 0
% 0.70/1.10  
% 0.70/1.10  Usable size                    0
% 0.70/1.10  Sos size                     227
% 0.70/1.10  Demodulators size            102
% 0.70/1.10  Passive size                   0
% 0.70/1.10  Disabled size                273
% 0.70/1.10  
% 0.70/1.10  Proofs found                   1
% 0.70/1.10  
% 0.70/1.10  ----------- times (seconds) ----------- Tue Jun 14 10:03:04 2022
% 0.70/1.10  
% 0.70/1.10  user CPU time             0.03   (0 hr, 0 min, 0 sec)
% 0.70/1.10  system CPU time           0.02   (0 hr, 0 min, 0 sec)
% 0.70/1.10  wall-clock time           0      (0 hr, 0 min, 0 sec)
% 0.70/1.10  input time                0.00
% 0.70/1.10  paramodulation time       0.01
% 0.70/1.10  demodulation time         0.01
% 0.70/1.10  orient time               0.00
% 0.70/1.10  weigh time                0.00
% 0.70/1.10  forward subsume time      0.00
% 0.70/1.10  back demod find time      0.00
% 0.70/1.10  conflict time             0.00
% 0.70/1.10  LRPO time                 0.00
% 0.70/1.10  store clause time         0.00
% 0.70/1.10  disable clause time       0.00
% 0.70/1.10  prime paramod time        0.00
% 0.70/1.10  semantics time            0.00
% 0.70/1.10  
% 0.70/1.10  EQP interrupted
%------------------------------------------------------------------------------