TSTP Solution File: LDA001-1 by EQP---0.9e

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n022.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 : Sun Jul 17 16:43:18 EDT 2022

% Result   : Unsatisfiable 0.45s 1.07s
% Output   : Refutation 0.45s
% Verified : 
% SZS Type : ERROR: Analysing output (Cycle in a tree)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(f(f(A,B),f(A,C)),f(A,f(B,C))),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(2,plain,
    equal(f(n1,n1),n2),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(3,plain,
    equal(f(n2,n1),n3),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(4,plain,
    equal(f(n2,n2),u),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(5,plain,
    ~ equal(f(f(u,u),u),f(f(n3,n2),u)),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(8,plain,
    equal(f(n2,f(n1,A)),f(n1,f(n1,A))),
    inference(para,[status(thm),theory(equality)],[2,1]),
    [iquote('para(2,1)')] ).

cnf(9,plain,
    equal(f(f(n1,A),n2),f(n1,f(A,n1))),
    inference(para,[status(thm),theory(equality)],[2,1]),
    [iquote('para(2,1)')] ).

cnf(10,plain,
    equal(f(n1,n2),u),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,8]),4,2]),1]),
    [iquote('para(2,8),demod([4,2]),flip(1)')] ).

cnf(11,plain,
    equal(f(n3,f(n2,A)),f(n1,f(n1,A))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,1]),8]),
    [iquote('para(3,1),demod([8])')] ).

cnf(13,plain,
    equal(f(u,f(n2,A)),f(n2,f(n2,A))),
    inference(para,[status(thm),theory(equality)],[4,1]),
    [iquote('para(4,1)')] ).

cnf(14,plain,
    equal(f(f(n2,A),u),f(n2,f(A,n2))),
    inference(para,[status(thm),theory(equality)],[4,1]),
    [iquote('para(4,1)')] ).

cnf(15,plain,
    equal(f(n2,u),f(n1,u)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[10,8]),10]),
    [iquote('para(10,8),demod([10])')] ).

cnf(16,plain,
    equal(f(u,n2),f(n1,n3)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[10,9]),3]),
    [iquote('para(10,9),demod([3])')] ).

cnf(23,plain,
    equal(f(n3,n3),u),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,11]),2,10]),
    [iquote('para(3,11),demod([2,10])')] ).

cnf(41,plain,
    equal(f(u,u),f(n1,u)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,13]),4,15]),
    [iquote('para(4,13),demod([4,15])')] ).

cnf(42,plain,
    ~ equal(f(f(n3,n2),u),f(f(n1,u),u)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[5]),41]),1]),
    [iquote('back_demod(5),demod([41]),flip(1)')] ).

cnf(53,plain,
    equal(f(f(n1,u),u),f(n1,f(n1,n3))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[15,14]),16,8]),
    [iquote('para(15,14),demod([16,8])')] ).

cnf(54,plain,
    ~ equal(f(f(n3,n2),u),f(n1,f(n1,n3))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[42]),53]),
    [iquote('back_demod(42),demod([53])')] ).

cnf(69,plain,
    equal(f(f(n3,A),u),f(n3,f(A,n3))),
    inference(para,[status(thm),theory(equality)],[23,1]),
    [iquote('para(23,1)')] ).

cnf(70,plain,
    ~ equal(f(n1,f(n1,n3)),f(n1,f(n1,n3))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[54]),69,11]),
    [iquote('back_demod(54),demod([69,11])')] ).

cnf(71,plain,
    $false,
    inference(conflict,[status(thm)],[70]),
    [iquote('xx_conflict(70)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : tptp2X_and_run_eqp %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon May 30 02:08:37 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.45/1.07  ----- EQP 0.9e, May 2009 -----
% 0.45/1.07  The job began on n022.cluster.edu, Mon May 30 02:08:38 2022
% 0.45/1.07  The command was "./eqp09e".
% 0.45/1.07  
% 0.45/1.07  set(prolog_style_variables).
% 0.45/1.07  set(lrpo).
% 0.45/1.07  set(basic_paramod).
% 0.45/1.07  set(functional_subsume).
% 0.45/1.07  set(ordered_paramod).
% 0.45/1.07  set(prime_paramod).
% 0.45/1.07  set(para_pairs).
% 0.45/1.07  assign(pick_given_ratio,4).
% 0.45/1.07  clear(print_kept).
% 0.45/1.07  clear(print_new_demod).
% 0.45/1.07  clear(print_back_demod).
% 0.45/1.07  clear(print_given).
% 0.45/1.07  assign(max_mem,64000).
% 0.45/1.07  end_of_commands.
% 0.45/1.07  
% 0.45/1.07  Usable:
% 0.45/1.07  end_of_list.
% 0.45/1.07  
% 0.45/1.07  Sos:
% 0.45/1.07  0 (wt=-1) [] f(A,f(B,C)) = f(f(A,B),f(A,C)).
% 0.45/1.07  0 (wt=-1) [] n2 = f(n1,n1).
% 0.45/1.07  0 (wt=-1) [] n3 = f(n2,n1).
% 0.45/1.07  0 (wt=-1) [] u = f(n2,n2).
% 0.45/1.07  0 (wt=-1) [] -(f(f(n3,n2),u) = f(f(u,u),u)).
% 0.45/1.07  end_of_list.
% 0.45/1.07  
% 0.45/1.07  Demodulators:
% 0.45/1.07  end_of_list.
% 0.45/1.07  
% 0.45/1.07  Passive:
% 0.45/1.07  end_of_list.
% 0.45/1.07  
% 0.45/1.07  Starting to process input.
% 0.45/1.07  
% 0.45/1.07  ** KEPT: 1 (wt=13) [flip(1)] f(f(A,B),f(A,C)) = f(A,f(B,C)).
% 0.45/1.07  1 is a new demodulator.
% 0.45/1.07  
% 0.45/1.07  ** KEPT: 2 (wt=5) [flip(1)] f(n1,n1) = n2.
% 0.45/1.07  2 is a new demodulator.
% 0.45/1.07  
% 0.45/1.07  ** KEPT: 3 (wt=5) [flip(1)] f(n2,n1) = n3.
% 0.45/1.07  3 is a new demodulator.
% 0.45/1.07  
% 0.45/1.07  ** KEPT: 4 (wt=5) [flip(1)] f(n2,n2) = u.
% 0.45/1.07  4 is a new demodulator.
% 0.45/1.07  
% 0.45/1.07  ** KEPT: 5 (wt=11) [flip(1)] -(f(f(u,u),u) = f(f(n3,n2),u)).
% 0.45/1.07  ---------------- PROOF FOUND ----------------
% 0.45/1.07  % SZS status Unsatisfiable
% 0.45/1.07  
% 0.45/1.07  
% 0.45/1.07  After processing input:
% 0.45/1.07  
% 0.45/1.07  Usable:
% 0.45/1.07  end_of_list.
% 0.45/1.07  
% 0.45/1.07  Sos:
% 0.45/1.07  2 (wt=5) [flip(1)] f(n1,n1) = n2.
% 0.45/1.07  3 (wt=5) [flip(1)] f(n2,n1) = n3.
% 0.45/1.07  4 (wt=5) [flip(1)] f(n2,n2) = u.
% 0.45/1.07  5 (wt=11) [flip(1)] -(f(f(u,u),u) = f(f(n3,n2),u)).
% 0.45/1.07  1 (wt=13) [flip(1)] f(f(A,B),f(A,C)) = f(A,f(B,C)).
% 0.45/1.07  end_of_list.
% 0.45/1.07  
% 0.45/1.07  Demodulators:
% 0.45/1.07  1 (wt=13) [flip(1)] f(f(A,B),f(A,C)) = f(A,f(B,C)).
% 0.45/1.07  2 (wt=5) [flip(1)] f(n1,n1) = n2.
% 0.45/1.07  3 (wt=5) [flip(1)] f(n2,n1) = n3.
% 0.45/1.07  4 (wt=5) [flip(1)] f(n2,n2) = u.
% 0.45/1.07  end_of_list.
% 0.45/1.07  
% 0.45/1.07  Passive:
% 0.45/1.07  end_of_list.
% 0.45/1.07  
% 0.45/1.07  UNIT CONFLICT from 70 and x=x at   0.00 seconds.
% 0.45/1.07  
% 0.45/1.07  ---------------- PROOF ----------------
% 0.45/1.07  % SZS output start Refutation
% See solution above
% 0.45/1.07  ------------ end of proof -------------
% 0.45/1.07  
% 0.45/1.07  
% 0.45/1.07  ------------- memory usage ------------
% 0.45/1.07  Memory dynamically allocated (tp_alloc): 488.
% 0.45/1.07    type (bytes each)        gets      frees     in use      avail      bytes
% 0.45/1.07  sym_ent (  96)               56          0         56          0      5.2 K
% 0.45/1.07  term (  16)                4482       3182       1300         14     25.4 K
% 0.45/1.07  gen_ptr (   8)             5531        496       5035         20     39.5 K
% 0.45/1.07  context ( 808)             4737       4735          2          3      3.9 K
% 0.45/1.07  trail (  12)                129        129          0          6      0.1 K
% 0.45/1.07  bt_node (  68)             2192       2189          3          8      0.7 K
% 0.45/1.07  ac_position (285432)          0          0          0          0      0.0 K
% 0.45/1.07  ac_match_pos (14044)          0          0          0          0      0.0 K
% 0.45/1.07  ac_match_free_vars_pos (4020)
% 0.45/1.07                                0          0          0          0      0.0 K
% 0.45/1.07  discrim (  12)             1272         47       1225         11     14.5 K
% 0.45/1.07  flat (  40)                7926       7926          0         39      1.5 K
% 0.45/1.07  discrim_pos (  12)          129        129          0          1      0.0 K
% 0.45/1.07  fpa_head (  12)             346          0        346          0      4.1 K
% 0.45/1.07  fpa_tree (  28)             277        277          0         21      0.6 K
% 0.45/1.07  fpa_pos (  36)              129        129          0          1      0.0 K
% 0.45/1.07  literal (  12)              214        144         70          0      0.8 K
% 0.45/1.07  clause (  24)               214        144         70          0      1.6 K
% 0.45/1.07  list (  12)                 119         62         57          2      0.7 K
% 0.45/1.07  list_pos (  20)             282         27        255          3      5.0 K
% 0.45/1.07  pair_index (   40)              2          0          2          0      0.1 K
% 0.45/1.07  
% 0.45/1.07  -------------- statistics -------------
% 0.45/1.07  Clauses input                  5
% 0.45/1.07    Usable input                   0
% 0.45/1.07    Sos input                      5
% 0.45/1.07    Demodulators input             0
% 0.45/1.07    Passive input                  0
% 0.45/1.07  
% 0.45/1.07  Processed BS (before search)   5
% 0.45/1.07  Forward subsumed BS            0
% 0.45/1.07  Kept BS                        5
% 0.45/1.07  New demodulators BS            4
% 0.45/1.07  Back demodulated BS            0
% 0.45/1.07  
% 0.45/1.07  Clauses or pairs given       226
% 0.45/1.07  Clauses generated            126
% 0.45/1.07  Forward subsumed              61
% 0.45/1.07  Deleted by weight              0
% 0.45/1.07  Deleted by variable count      0
% 0.45/1.07  Kept                          65
% 0.45/1.07  New demodulators              56
% 0.45/1.07  Back demodulated               5
% 0.45/1.07  Ordered paramod prunes         0
% 0.45/1.07  Basic paramod prunes         187
% 0.45/1.07  Prime paramod prunes           0
% 0.45/1.07  Semantic prunes                0
% 0.45/1.07  
% 0.45/1.07  Rewrite attmepts            1962
% 0.45/1.07  Rewrites                     126
% 0.45/1.07  
% 0.45/1.07  FPA overloads                  0
% 0.45/1.07  FPA underloads                 0
% 0.45/1.07  
% 0.45/1.07  Usable size                    0
% 0.45/1.07  Sos size                      64
% 0.45/1.07  Demodulators size             58
% 0.45/1.07  Passive size                   0
% 0.45/1.07  Disabled size                  5
% 0.45/1.07  
% 0.45/1.07  Proofs found                   1
% 0.45/1.07  
% 0.45/1.07  ----------- times (seconds) ----------- Mon May 30 02:08:38 2022
% 0.45/1.07  
% 0.45/1.07  user CPU time             0.00   (0 hr, 0 min, 0 sec)
% 0.45/1.07  system CPU time           0.01   (0 hr, 0 min, 0 sec)
% 0.45/1.07  wall-clock time           0      (0 hr, 0 min, 0 sec)
% 0.45/1.07  input time                0.00
% 0.45/1.07  paramodulation time       0.00
% 0.45/1.07  demodulation time         0.00
% 0.45/1.07  orient time               0.00
% 0.45/1.07  weigh time                0.00
% 0.45/1.07  forward subsume time      0.00
% 0.45/1.07  back demod find time      0.00
% 0.45/1.07  conflict time             0.00
% 0.45/1.07  LRPO time                 0.00
% 0.45/1.07  store clause time         0.00
% 0.45/1.07  disable clause time       0.00
% 0.45/1.07  prime paramod time        0.00
% 0.45/1.07  semantics time            0.00
% 0.45/1.07  
% 0.45/1.07  EQP interrupted
%------------------------------------------------------------------------------