TSTP Solution File: GRP172-2 by EQP---0.9e

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n015.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 08:45:41 EDT 2022

% Result   : Unsatisfiable 0.81s 1.34s
% Output   : Refutation 0.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   16 (  16 unt;   0 nHn;   7 RR)
%            Number of literals    :   16 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   17 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(multiply(identity,A),A),
    file('GRP172-2.p',unknown),
    [] ).

cnf(4,plain,
    equal(greatest_lower_bound(A,B),greatest_lower_bound(B,A)),
    file('GRP172-2.p',unknown),
    [] ).

cnf(5,plain,
    equal(least_upper_bound(A,B),least_upper_bound(B,A)),
    file('GRP172-2.p',unknown),
    [] ).

cnf(6,plain,
    equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C))),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(10,plain,
    equal(least_upper_bound(A,greatest_lower_bound(A,B)),A),
    file('GRP172-2.p',unknown),
    [] ).

cnf(15,plain,
    equal(multiply(greatest_lower_bound(A,B),C),greatest_lower_bound(multiply(A,C),multiply(B,C))),
    file('GRP172-2.p',unknown),
    [] ).

cnf(16,plain,
    equal(greatest_lower_bound(identity,a),identity),
    file('GRP172-2.p',unknown),
    [] ).

cnf(17,plain,
    equal(greatest_lower_bound(identity,b),identity),
    file('GRP172-2.p',unknown),
    [] ).

cnf(18,plain,
    ~ equal(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),
    file('GRP172-2.p',unknown),
    [] ).

cnf(37,plain,
    equal(least_upper_bound(A,greatest_lower_bound(B,A)),A),
    inference(para,[status(thm),theory(equality)],[4,10]),
    [iquote('para(4,10)')] ).

cnf(61,plain,
    equal(greatest_lower_bound(A,multiply(a,A)),A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[16,15]),1,1]),1]),
    [iquote('para(16,15),demod([1,1]),flip(1)')] ).

cnf(62,plain,
    equal(greatest_lower_bound(identity,greatest_lower_bound(b,A)),greatest_lower_bound(identity,A)),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[17,6]),1]),
    [iquote('para(17,6),flip(1)')] ).

cnf(387,plain,
    equal(greatest_lower_bound(identity,multiply(a,b)),identity),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[61,62]),17]),1]),
    [iquote('para(61,62),demod([17]),flip(1)')] ).

cnf(399,plain,
    equal(least_upper_bound(multiply(a,b),identity),multiply(a,b)),
    inference(para,[status(thm),theory(equality)],[387,37]),
    [iquote('para(387,37)')] ).

cnf(974,plain,
    equal(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[399,5]),1]),
    [iquote('para(399,5),flip(1)')] ).

cnf(975,plain,
    $false,
    inference(conflict,[status(thm)],[974,18]),
    [iquote('conflict(974,18)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12  % Command  : tptp2X_and_run_eqp %s
% 0.12/0.33  % Computer : n015.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 : Mon Jun 13 19:39:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.81/1.34  ----- EQP 0.9e, May 2009 -----
% 0.81/1.34  The job began on n015.cluster.edu, Mon Jun 13 19:39:24 2022
% 0.81/1.34  The command was "./eqp09e".
% 0.81/1.34  
% 0.81/1.34  set(prolog_style_variables).
% 0.81/1.34  set(lrpo).
% 0.81/1.34  set(basic_paramod).
% 0.81/1.34  set(functional_subsume).
% 0.81/1.34  set(ordered_paramod).
% 0.81/1.34  set(prime_paramod).
% 0.81/1.34  set(para_pairs).
% 0.81/1.34  assign(pick_given_ratio,4).
% 0.81/1.34  clear(print_kept).
% 0.81/1.34  clear(print_new_demod).
% 0.81/1.34  clear(print_back_demod).
% 0.81/1.34  clear(print_given).
% 0.81/1.34  assign(max_mem,64000).
% 0.81/1.34  end_of_commands.
% 0.81/1.34  
% 0.81/1.34  Usable:
% 0.81/1.34  end_of_list.
% 0.81/1.34  
% 0.81/1.34  Sos:
% 0.81/1.34  0 (wt=-1) [] multiply(identity,A) = A.
% 0.81/1.34  0 (wt=-1) [] multiply(inverse(A),A) = identity.
% 0.81/1.34  0 (wt=-1) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 0.81/1.34  0 (wt=-1) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 0.81/1.34  0 (wt=-1) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 0.81/1.34  0 (wt=-1) [] greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C).
% 0.81/1.34  0 (wt=-1) [] least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C).
% 0.81/1.34  0 (wt=-1) [] least_upper_bound(A,A) = A.
% 0.81/1.34  0 (wt=-1) [] greatest_lower_bound(A,A) = A.
% 0.81/1.34  0 (wt=-1) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 0.81/1.34  0 (wt=-1) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 0.81/1.34  0 (wt=-1) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 0.81/1.34  0 (wt=-1) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 0.81/1.34  0 (wt=-1) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 0.81/1.34  0 (wt=-1) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 0.81/1.34  0 (wt=-1) [] greatest_lower_bound(identity,a) = identity.
% 0.81/1.34  0 (wt=-1) [] greatest_lower_bound(identity,b) = identity.
% 0.81/1.34  0 (wt=-1) [] -(least_upper_bound(identity,multiply(a,b)) = multiply(a,b)).
% 0.81/1.34  end_of_list.
% 0.81/1.34  
% 0.81/1.34  Demodulators:
% 0.81/1.34  end_of_list.
% 0.81/1.34  
% 0.81/1.34  Passive:
% 0.81/1.34  end_of_list.
% 0.81/1.34  
% 0.81/1.34  Starting to process input.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 1 (wt=5) [] multiply(identity,A) = A.
% 0.81/1.34  1 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 2 (wt=6) [] multiply(inverse(A),A) = identity.
% 0.81/1.34  2 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 0.81/1.34  3 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 4 (wt=7) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 0.81/1.34  clause forward subsumed: 0 (wt=7) [flip(4)] greatest_lower_bound(B,A) = greatest_lower_bound(A,B).
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 5 (wt=7) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 0.81/1.34  clause forward subsumed: 0 (wt=7) [flip(5)] least_upper_bound(B,A) = least_upper_bound(A,B).
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 0.81/1.34  6 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 0.81/1.34  7 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 8 (wt=5) [] least_upper_bound(A,A) = A.
% 0.81/1.34  8 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 0.81/1.34  9 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 0.81/1.34  10 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 0.81/1.34  11 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 0.81/1.34  12 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 0.81/1.34  13 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 0.81/1.34  14 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 0.81/1.34  15 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 16 (wt=5) [] greatest_lower_bound(identity,a) = identity.
% 0.81/1.34  16 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 17 (wt=5) [] greatest_lower_bound(identity,b) = identity.
% 0.81/1.34  17 is a new demodulator.
% 0.81/1.34  
% 0.81/1.34  ** KEPT: 18 (wt=9) [] -(least_upper_bound(identity,multiply(a,b)) = multiply(a,b)).
% 0.81/1.34  ---------------- PROOF FOUND ----------------
% 0.81/1.34  % SZS status Unsatisfiable
% 0.81/1.34  
% 0.81/1.34  
% 0.81/1.34  After processing input:
% 0.81/1.34  
% 0.81/1.34  Usable:
% 0.81/1.34  end_of_list.
% 0.81/1.34  
% 0.81/1.34  Sos:
% 0.81/1.34  1 (wt=5) [] multiply(identity,A) = A.
% 0.81/1.34  8 (wt=5) [] least_upper_bound(A,A) = A.
% 0.81/1.34  9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 0.81/1.34  16 (wt=5) [] greatest_lower_bound(identity,a) = identity.
% 0.81/1.34  17 (wt=5) [] greatest_lower_bound(identity,b) = identity.
% 0.81/1.34  2 (wt=6) [] multiply(inverse(A),A) = identity.
% 0.81/1.34  4 (wt=7) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 0.81/1.34  5 (wt=7) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 0.81/1.34  10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 0.81/1.34  11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 0.81/1.34  18 (wt=9) [] -(least_upper_bound(identity,multiply(a,b)) = multiply(a,b)).
% 0.81/1.34  3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 0.81/1.34  6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 0.81/1.34  7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 0.81/1.34  12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 0.81/1.34  13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 0.81/1.34  14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 0.81/1.34  15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 0.81/1.34  end_of_list.
% 0.81/1.34  
% 0.81/1.34  Demodulators:
% 0.81/1.34  1 (wt=5) [] multiply(identity,A) = A.
% 0.81/1.34  2 (wt=6) [] multiply(inverse(A),A) = identity.
% 0.81/1.34  3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 0.81/1.34  6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 0.81/1.34  7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 0.81/1.34  8 (wt=5) [] least_upper_bound(A,A) = A.
% 0.81/1.34  9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 0.81/1.34  10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 0.81/1.34  11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 0.81/1.34  12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 0.81/1.34  13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 0.81/1.34  14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 0.81/1.34  15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 0.81/1.34  16 (wt=5) [] greatest_lower_bound(identity,a) = identity.
% 0.81/1.34  17 (wt=5) [] greatest_lower_bound(identity,b) = identity.
% 0.81/1.34  end_of_list.
% 0.81/1.34  
% 0.81/1.34  Passive:
% 0.81/1.34  end_of_list.
% 0.81/1.34  
% 0.81/1.34  UNIT CONFLICT from 974 and 18 at   0.06 seconds.
% 0.81/1.34  
% 0.81/1.34  ---------------- PROOF ----------------
% 0.81/1.34  % SZS output start Refutation
% See solution above
% 0.81/1.34  ------------ end of proof -------------
% 0.81/1.34  
% 0.81/1.34  
% 0.81/1.34  ------------- memory usage ------------
% 0.81/1.34  Memory dynamically allocated (tp_alloc): 1464.
% 0.81/1.34    type (bytes each)        gets      frees     in use      avail      bytes
% 0.81/1.34  sym_ent (  96)               58          0         58          0      5.4 K
% 0.81/1.34  term (  16)               92468      75601      16867         23    326.1 K
% 0.81/1.34  gen_ptr (   8)            86046      17279      68767         15    537.4 K
% 0.81/1.34  context ( 808)           111523     111521          2          5      5.5 K
% 0.81/1.34  trail (  12)               4804       4804          0          5      0.1 K
% 0.81/1.34  bt_node (  68)            54850      54847          3         14      1.1 K
% 0.81/1.34  ac_position (285432)          0          0          0          0      0.0 K
% 0.81/1.34  ac_match_pos (14044)          0          0          0          0      0.0 K
% 0.81/1.34  ac_match_free_vars_pos (4020)
% 0.81/1.34                                0          0          0          0      0.0 K
% 0.81/1.34  discrim (  12)            13368        640      12728          0    149.2 K
% 0.81/1.34  flat (  40)              168305     168305          0         91      3.6 K
% 0.81/1.34  discrim_pos (  12)         5352       5352          0          1      0.0 K
% 0.81/1.34  fpa_head (  12)            3046          0       3046          0     35.7 K
% 0.81/1.34  fpa_tree (  28)            2764       2764          0         39      1.1 K
% 0.81/1.34  fpa_pos (  36)             1656       1656          0          1      0.0 K
% 0.81/1.34  literal (  12)             5446       4472        974          1     11.4 K
% 0.81/1.34  clause (  24)              5446       4472        974          1     22.9 K
% 0.81/1.34  list (  12)                 741        685         56          3      0.7 K
% 0.81/1.34  list_pos (  20)            3773        351       3422          0     66.8 K
% 0.81/1.34  pair_index (   40)              2          0          2          0      0.1 K
% 0.81/1.34  
% 0.81/1.34  -------------- statistics -------------
% 0.81/1.34  Clauses input                 18
% 0.81/1.34    Usable input                   0
% 0.81/1.34    Sos input                     18
% 0.81/1.34    Demodulators input             0
% 0.81/1.34    Passive input                  0
% 0.81/1.34  
% 0.81/1.34  Processed BS (before search)  20
% 0.81/1.34  Forward subsumed BS            2
% 0.81/1.34  Kept BS                       18
% 0.81/1.34  New demodulators BS           15
% 0.81/1.34  Back demodulated BS            0
% 0.81/1.34  
% 0.81/1.34  Clauses or pairs given     12993
% 0.81/1.34  Clauses generated           3568
% 0.81/1.34  Forward subsumed            2612
% 0.81/1.34  Deleted by weight              0
% 0.81/1.34  Deleted by variable count      0
% 0.81/1.34  Kept                         956
% 0.81/1.34  New demodulators             667
% 0.81/1.34  Back demodulated              77
% 0.81/1.34  Ordered paramod prunes         0
% 0.81/1.34  Basic paramod prunes       48881
% 0.81/1.34  Prime paramod prunes         191
% 0.81/1.34  Semantic prunes                0
% 0.81/1.34  
% 0.81/1.34  Rewrite attmepts           35223
% 0.81/1.34  Rewrites                    4460
% 0.81/1.34  
% 0.81/1.34  FPA overloads                  0
% 0.81/1.34  FPA underloads                 0
% 0.81/1.34  
% 0.81/1.34  Usable size                    0
% 0.81/1.34  Sos size                     896
% 0.81/1.34  Demodulators size            657
% 0.81/1.34  Passive size                   0
% 0.81/1.34  Disabled size                 77
% 0.81/1.34  
% 0.81/1.34  Proofs found                   1
% 0.81/1.34  
% 0.81/1.34  ----------- times (seconds) ----------- Mon Jun 13 19:39:24 2022
% 0.81/1.34  
% 0.81/1.34  user CPU time             0.06   (0 hr, 0 min, 0 sec)
% 0.81/1.34  system CPU time           0.14   (0 hr, 0 min, 0 sec)
% 0.81/1.34  wall-clock time           0      (0 hr, 0 min, 0 sec)
% 0.81/1.34  input time                0.00
% 0.81/1.34  paramodulation time       0.03
% 0.81/1.34  demodulation time         0.01
% 0.81/1.34  orient time               0.00
% 0.81/1.34  weigh time                0.00
% 0.81/1.34  forward subsume time      0.00
% 0.81/1.34  back demod find time      0.00
% 0.81/1.34  conflict time             0.00
% 0.81/1.34  LRPO time                 0.00
% 0.81/1.34  store clause time         0.00
% 0.81/1.34  disable clause time       0.00
% 0.81/1.34  prime paramod time        0.01
% 0.81/1.34  semantics time            0.00
% 0.81/1.34  
% 0.81/1.34  EQP interrupted
%------------------------------------------------------------------------------