TSTP Solution File: GRP190-2 by EQP---0.9e

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n032.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 08:45:52 EDT 2022

% Result   : Unsatisfiable 0.54s 0.99s
% Output   : Refutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   21 (  21 unt;   0 nHn;   5 RR)
%            Number of literals    :   21 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   29 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(multiply(identity,A),A),
    file('GRP190-2.p',unknown),
    [] ).

cnf(2,plain,
    equal(multiply(inverse(A),A),identity),
    file('GRP190-2.p',unknown),
    [] ).

cnf(3,plain,
    equal(multiply(multiply(A,B),C),multiply(A,multiply(B,C))),
    file('GRP190-2.p',unknown),
    [] ).

cnf(5,plain,
    equal(least_upper_bound(A,B),least_upper_bound(B,A)),
    file('GRP190-2.p',unknown),
    [] ).

cnf(11,plain,
    equal(greatest_lower_bound(A,least_upper_bound(A,B)),A),
    file('GRP190-2.p',unknown),
    [] ).

cnf(12,plain,
    equal(multiply(A,least_upper_bound(B,C)),least_upper_bound(multiply(A,B),multiply(A,C))),
    file('GRP190-2.p',unknown),
    [] ).

cnf(14,plain,
    equal(multiply(least_upper_bound(A,B),C),least_upper_bound(multiply(A,C),multiply(B,C))),
    file('GRP190-2.p',unknown),
    [] ).

cnf(16,plain,
    equal(least_upper_bound(a,b),a),
    file('GRP190-2.p',unknown),
    [] ).

cnf(17,plain,
    ~ equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)),
    file('GRP190-2.p',unknown),
    [] ).

cnf(18,plain,
    equal(multiply(inverse(A),multiply(A,B)),B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,3]),1]),1]),
    [iquote('para(2,3),demod([1]),flip(1)')] ).

cnf(36,plain,
    equal(greatest_lower_bound(A,least_upper_bound(B,A)),A),
    inference(para,[status(thm),theory(equality)],[5,11]),
    [iquote('para(5,11)')] ).

cnf(48,plain,
    equal(multiply(inverse(inverse(A)),identity),A),
    inference(para,[status(thm),theory(equality)],[2,18]),
    [iquote('para(2,18)')] ).

cnf(56,plain,
    equal(multiply(inverse(inverse(A)),B),multiply(A,B)),
    inference(para,[status(thm),theory(equality)],[18,18]),
    [iquote('para(18,18)')] ).

cnf(57,plain,
    equal(multiply(A,identity),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[48]),56]),
    [iquote('back_demod(48),demod([56])')] ).

cnf(61,plain,
    equal(inverse(inverse(A)),A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[56,57]),57]),1]),
    [iquote('para(56,57),demod([57]),flip(1)')] ).

cnf(62,plain,
    equal(multiply(A,inverse(A)),identity),
    inference(para,[status(thm),theory(equality)],[61,2]),
    [iquote('para(61,2)')] ).

cnf(64,plain,
    equal(least_upper_bound(multiply(inverse(least_upper_bound(A,B)),multiply(A,C)),multiply(inverse(least_upper_bound(A,B)),multiply(B,C))),C),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,18]),12]),
    [iquote('para(14,18),demod([12])')] ).

cnf(418,plain,
    equal(least_upper_bound(A,multiply(inverse(a),multiply(b,A))),A),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[16,64]),18,16]),
    [iquote('para(16,64),demod([18,16])')] ).

cnf(421,plain,
    equal(least_upper_bound(inverse(b),inverse(a)),inverse(b)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[62,418]),57]),
    [iquote('para(62,418),demod([57])')] ).

cnf(429,plain,
    equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)),
    inference(para,[status(thm),theory(equality)],[421,36]),
    [iquote('para(421,36)')] ).

cnf(430,plain,
    $false,
    inference(conflict,[status(thm)],[429,17]),
    [iquote('conflict(429,17)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.11  % Command  : tptp2X_and_run_eqp %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Mon Jun 13 15:42:42 EDT 2022
% 0.10/0.31  % CPUTime  : 
% 0.54/0.99  ----- EQP 0.9e, May 2009 -----
% 0.54/0.99  The job began on n032.cluster.edu, Mon Jun 13 15:42:42 2022
% 0.54/0.99  The command was "./eqp09e".
% 0.54/0.99  
% 0.54/0.99  set(prolog_style_variables).
% 0.54/0.99  set(lrpo).
% 0.54/0.99  set(basic_paramod).
% 0.54/0.99  set(functional_subsume).
% 0.54/0.99  set(ordered_paramod).
% 0.54/0.99  set(prime_paramod).
% 0.54/0.99  set(para_pairs).
% 0.54/0.99  assign(pick_given_ratio,4).
% 0.54/0.99  clear(print_kept).
% 0.54/0.99  clear(print_new_demod).
% 0.54/0.99  clear(print_back_demod).
% 0.54/0.99  clear(print_given).
% 0.54/0.99  assign(max_mem,64000).
% 0.54/0.99  end_of_commands.
% 0.54/0.99  
% 0.54/0.99  Usable:
% 0.54/0.99  end_of_list.
% 0.54/0.99  
% 0.54/0.99  Sos:
% 0.54/0.99  0 (wt=-1) [] multiply(identity,A) = A.
% 0.54/0.99  0 (wt=-1) [] multiply(inverse(A),A) = identity.
% 0.54/0.99  0 (wt=-1) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 0.54/0.99  0 (wt=-1) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 0.54/0.99  0 (wt=-1) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 0.54/0.99  0 (wt=-1) [] greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C).
% 0.54/0.99  0 (wt=-1) [] least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C).
% 0.54/0.99  0 (wt=-1) [] least_upper_bound(A,A) = A.
% 0.54/0.99  0 (wt=-1) [] greatest_lower_bound(A,A) = A.
% 0.54/0.99  0 (wt=-1) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 0.54/0.99  0 (wt=-1) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 0.54/0.99  0 (wt=-1) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 0.54/0.99  0 (wt=-1) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 0.54/0.99  0 (wt=-1) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 0.54/0.99  0 (wt=-1) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 0.54/0.99  0 (wt=-1) [] least_upper_bound(a,b) = a.
% 0.54/0.99  0 (wt=-1) [] -(greatest_lower_bound(inverse(a),inverse(b)) = inverse(a)).
% 0.54/0.99  end_of_list.
% 0.54/0.99  
% 0.54/0.99  Demodulators:
% 0.54/0.99  end_of_list.
% 0.54/0.99  
% 0.54/0.99  Passive:
% 0.54/0.99  end_of_list.
% 0.54/0.99  
% 0.54/0.99  Starting to process input.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 1 (wt=5) [] multiply(identity,A) = A.
% 0.54/0.99  1 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 2 (wt=6) [] multiply(inverse(A),A) = identity.
% 0.54/0.99  2 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 0.54/0.99  3 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 4 (wt=7) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 0.54/0.99  clause forward subsumed: 0 (wt=7) [flip(4)] greatest_lower_bound(B,A) = greatest_lower_bound(A,B).
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 5 (wt=7) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 0.54/0.99  clause forward subsumed: 0 (wt=7) [flip(5)] least_upper_bound(B,A) = least_upper_bound(A,B).
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 0.54/0.99  6 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 0.54/0.99  7 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 8 (wt=5) [] least_upper_bound(A,A) = A.
% 0.54/0.99  8 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 0.54/0.99  9 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 0.54/0.99  10 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 0.54/0.99  11 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 0.54/0.99  12 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 0.54/0.99  13 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 0.54/0.99  14 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 0.54/0.99  15 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 16 (wt=5) [] least_upper_bound(a,b) = a.
% 0.54/0.99  16 is a new demodulator.
% 0.54/0.99  
% 0.54/0.99  ** KEPT: 17 (wt=8) [] -(greatest_lower_bound(inverse(a),inverse(b)) = inverse(a)).
% 0.54/0.99  ---------------- PROOF FOUND ----------------
% 0.54/0.99  % SZS status Unsatisfiable
% 0.54/0.99  
% 0.54/0.99  
% 0.54/0.99  After processing input:
% 0.54/0.99  
% 0.54/0.99  Usable:
% 0.54/0.99  end_of_list.
% 0.54/0.99  
% 0.54/0.99  Sos:
% 0.54/0.99  1 (wt=5) [] multiply(identity,A) = A.
% 0.54/0.99  8 (wt=5) [] least_upper_bound(A,A) = A.
% 0.54/0.99  9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 0.54/0.99  16 (wt=5) [] least_upper_bound(a,b) = a.
% 0.54/0.99  2 (wt=6) [] multiply(inverse(A),A) = identity.
% 0.54/0.99  4 (wt=7) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 0.54/0.99  5 (wt=7) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 0.54/0.99  10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 0.54/0.99  11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 0.54/0.99  17 (wt=8) [] -(greatest_lower_bound(inverse(a),inverse(b)) = inverse(a)).
% 0.54/0.99  3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 0.54/0.99  6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 0.54/0.99  7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 0.54/0.99  12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 0.54/0.99  13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 0.54/0.99  14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 0.54/0.99  15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 0.54/0.99  end_of_list.
% 0.54/0.99  
% 0.54/0.99  Demodulators:
% 0.54/0.99  1 (wt=5) [] multiply(identity,A) = A.
% 0.54/0.99  2 (wt=6) [] multiply(inverse(A),A) = identity.
% 0.54/0.99  3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 0.54/0.99  6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 0.54/0.99  7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 0.54/0.99  8 (wt=5) [] least_upper_bound(A,A) = A.
% 0.54/0.99  9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 0.54/0.99  10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 0.54/0.99  11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 0.54/0.99  12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 0.54/0.99  13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 0.54/0.99  14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 0.54/0.99  15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 0.54/0.99  16 (wt=5) [] least_upper_bound(a,b) = a.
% 0.54/0.99  end_of_list.
% 0.54/0.99  
% 0.54/0.99  Passive:
% 0.54/0.99  end_of_list.
% 0.54/0.99  
% 0.54/0.99  UNIT CONFLICT from 429 and 17 at   0.03 seconds.
% 0.54/0.99  
% 0.54/0.99  ---------------- PROOF ----------------
% 0.54/0.99  % SZS output start Refutation
% See solution above
% 0.54/0.99  ------------ end of proof -------------
% 0.54/0.99  
% 0.54/0.99  
% 0.54/0.99  ------------- memory usage ------------
% 0.54/0.99  Memory dynamically allocated (tp_alloc): 976.
% 0.54/0.99    type (bytes each)        gets      frees     in use      avail      bytes
% 0.54/0.99  sym_ent (  96)               58          0         58          0      5.4 K
% 0.54/0.99  term (  16)               43777      36506       7271         21    140.7 K
% 0.54/0.99  gen_ptr (   8)            37165       8554      28611         20    223.7 K
% 0.54/0.99  context ( 808)            48025      48023          2          4      4.7 K
% 0.54/0.99  trail (  12)               1966       1966          0          5      0.1 K
% 0.54/0.99  bt_node (  68)            21791      21788          3         12      1.0 K
% 0.54/0.99  ac_position (285432)          0          0          0          0      0.0 K
% 0.54/0.99  ac_match_pos (14044)          0          0          0          0      0.0 K
% 0.54/0.99  ac_match_free_vars_pos (4020)
% 0.54/0.99                                0          0          0          0      0.0 K
% 0.54/0.99  discrim (  12)             6623        259       6364          0     74.6 K
% 0.54/0.99  flat (  40)               69833      69833          0         35      1.4 K
% 0.54/0.99  discrim_pos (  12)         2496       2496          0          1      0.0 K
% 0.54/0.99  fpa_head (  12)            2069          0       2069          0     24.2 K
% 0.54/0.99  fpa_tree (  28)            1367       1367          0         15      0.4 K
% 0.54/0.99  fpa_pos (  36)              787        787          0          1      0.0 K
% 0.54/0.99  literal (  12)             2371       1942        429          1      5.0 K
% 0.54/0.99  clause (  24)              2371       1942        429          1     10.1 K
% 0.54/0.99  list (  12)                 417        361         56          3      0.7 K
% 0.54/0.99  list_pos (  20)            1723        161       1562          0     30.5 K
% 0.54/0.99  pair_index (   40)              2          0          2          0      0.1 K
% 0.54/0.99  
% 0.54/0.99  -------------- statistics -------------
% 0.54/0.99  Clauses input                 17
% 0.54/0.99    Usable input                   0
% 0.54/0.99    Sos input                     17
% 0.54/0.99    Demodulators input             0
% 0.54/0.99    Passive input                  0
% 0.54/0.99  
% 0.54/0.99  Processed BS (before search)  19
% 0.54/0.99  Forward subsumed BS            2
% 0.54/0.99  Kept BS                       17
% 0.54/0.99  New demodulators BS           14
% 0.54/0.99  Back demodulated BS            0
% 0.54/0.99  
% 0.54/0.99  Clauses or pairs given      5061
% 0.54/0.99  Clauses generated           1668
% 0.54/0.99  Forward subsumed            1256
% 0.54/0.99  Deleted by weight              0
% 0.54/0.99  Deleted by variable count      0
% 0.54/0.99  Kept                         412
% 0.54/0.99  New demodulators             344
% 0.54/0.99  Back demodulated              32
% 0.54/0.99  Ordered paramod prunes         0
% 0.54/0.99  Basic paramod prunes       15494
% 0.54/0.99  Prime paramod prunes          40
% 0.54/0.99  Semantic prunes                0
% 0.54/0.99  
% 0.54/0.99  Rewrite attmepts           15939
% 0.54/0.99  Rewrites                    2280
% 0.54/0.99  
% 0.54/0.99  FPA overloads                  0
% 0.54/0.99  FPA underloads                 0
% 0.54/0.99  
% 0.54/0.99  Usable size                    0
% 0.54/0.99  Sos size                     396
% 0.54/0.99  Demodulators size            342
% 0.54/0.99  Passive size                   0
% 0.54/0.99  Disabled size                 32
% 0.54/0.99  
% 0.54/0.99  Proofs found                   1
% 0.54/0.99  
% 0.54/0.99  ----------- times (seconds) ----------- Mon Jun 13 15:42:42 2022
% 0.54/0.99  
% 0.54/0.99  user CPU time             0.03   (0 hr, 0 min, 0 sec)
% 0.54/0.99  system CPU time           0.05   (0 hr, 0 min, 0 sec)
% 0.54/0.99  wall-clock time           0      (0 hr, 0 min, 0 sec)
% 0.54/0.99  input time                0.00
% 0.54/0.99  paramodulation time       0.01
% 0.54/0.99  demodulation time         0.01
% 0.54/0.99  orient time               0.01
% 0.54/0.99  weigh time                0.00
% 0.54/0.99  forward subsume time      0.00
% 0.54/0.99  back demod find time      0.00
% 0.54/0.99  conflict time             0.00
% 0.54/0.99  LRPO time                 0.00
% 0.54/0.99  store clause time         0.00
% 0.54/0.99  disable clause time       0.00
% 0.54/0.99  prime paramod time        0.00
% 0.54/0.99  semantics time            0.00
% 0.54/0.99  
% 0.54/0.99  EQP interrupted
%------------------------------------------------------------------------------