TSTP Solution File: COL006-6 by EQP---0.9e

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : COL006-6 : TPTP v8.1.0. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n017.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 : Fri Jul 15 00:23:10 EDT 2022

% Result   : Unsatisfiable 0.75s 1.52s
% Output   : Refutation 0.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   13 (  13 unt;   0 nHn;   3 RR)
%            Number of literals    :   13 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   23 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C))),
    file('COL006-6.p',unknown),
    [] ).

cnf(2,plain,
    equal(apply(apply(A,B),apply(C,B)),apply(apply(apply(s,A),C),B)),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(3,plain,
    equal(apply(apply(k,A),B),A),
    file('COL006-6.p',unknown),
    [] ).

cnf(4,plain,
    equal(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),strong_fixed_point),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(5,plain,
    ~ equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(6,plain,
    equal(apply(apply(apply(s,k),A),B),B),
    inference(para,[status(thm),theory(equality)],[2,3]),
    [iquote('para(2,3)')] ).

cnf(7,plain,
    equal(apply(apply(apply(s,apply(k,A)),B),C),apply(A,apply(B,C))),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,2]),1]),
    [iquote('para(3,2),flip(1)')] ).

cnf(28,plain,
    equal(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),A)),apply(strong_fixed_point,A)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,1]),3]),1]),
    [iquote('para(4,1),demod([3]),flip(1)')] ).

cnf(43,plain,
    equal(apply(apply(A,apply(B,C)),apply(D,C)),apply(apply(apply(s,apply(apply(s,apply(k,A)),B)),D),C)),
    inference(para,[status(thm),theory(equality)],[7,2]),
    [iquote('para(7,2)')] ).

cnf(1714,plain,
    equal(apply(apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),A),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),A)),apply(strong_fixed_point,A)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[28,1]),6,6]),1]),
    [iquote('para(28,1),demod([6,6]),flip(1)')] ).

cnf(3327,plain,
    equal(apply(apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),A),B),C),apply(B,apply(apply(A,B),C))),
    inference(para,[status(thm),theory(equality)],[43,7]),
    [iquote('para(43,7)')] ).

cnf(3330,plain,
    equal(apply(A,apply(strong_fixed_point,A)),apply(strong_fixed_point,A)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1714]),3327,3,28]),
    [iquote('back_demod(1714),demod([3327,3,28])')] ).

cnf(3331,plain,
    $false,
    inference(conflict,[status(thm)],[3330,5]),
    [iquote('conflict(3330,5)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : COL006-6 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.13  % Command  : tptp2X_and_run_eqp %s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue May 31 11:51:11 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.75/1.52  ----- EQP 0.9e, May 2009 -----
% 0.75/1.52  The job began on n017.cluster.edu, Tue May 31 11:51:11 2022
% 0.75/1.52  The command was "./eqp09e".
% 0.75/1.52  
% 0.75/1.52  set(prolog_style_variables).
% 0.75/1.52  set(lrpo).
% 0.75/1.52  set(basic_paramod).
% 0.75/1.52  set(functional_subsume).
% 0.75/1.52  set(ordered_paramod).
% 0.75/1.52  set(prime_paramod).
% 0.75/1.52  set(para_pairs).
% 0.75/1.52  assign(pick_given_ratio,4).
% 0.75/1.52  clear(print_kept).
% 0.75/1.52  clear(print_new_demod).
% 0.75/1.52  clear(print_back_demod).
% 0.75/1.52  clear(print_given).
% 0.75/1.52  assign(max_mem,64000).
% 0.75/1.52  end_of_commands.
% 0.75/1.52  
% 0.75/1.52  Usable:
% 0.75/1.52  end_of_list.
% 0.75/1.52  
% 0.75/1.52  Sos:
% 0.75/1.52  0 (wt=-1) [] apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)).
% 0.75/1.52  0 (wt=-1) [] apply(apply(k,A),B) = A.
% 0.75/1.52  0 (wt=-1) [] strong_fixed_point = apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))).
% 0.75/1.52  0 (wt=-1) [] -(apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt))).
% 0.75/1.52  end_of_list.
% 0.75/1.52  
% 0.75/1.52  Demodulators:
% 0.75/1.52  end_of_list.
% 0.75/1.52  
% 0.75/1.52  Passive:
% 0.75/1.52  end_of_list.
% 0.75/1.52  
% 0.75/1.52  Starting to process input.
% 0.75/1.52  
% 0.75/1.52  ** KEPT: 1 (wt=15) [] apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)).
% 0.75/1.52  
% 0.75/1.52  ** KEPT: 2 (wt=15) [flip(1)] apply(apply(A,B),apply(C,B)) = apply(apply(apply(s,A),C),B).
% 0.75/1.52  clause forward subsumed: 0 (wt=15) [flip(2)] apply(apply(apply(s,A),C),B) = apply(apply(A,B),apply(C,B)).
% 0.75/1.52  
% 0.75/1.52  ** KEPT: 3 (wt=7) [] apply(apply(k,A),B) = A.
% 0.75/1.52  3 is a new demodulator.
% 0.75/1.52  
% 0.75/1.52  ** KEPT: 4 (wt=45) [flip(1)] apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) = strong_fixed_point.
% 0.75/1.52  4 is a new demodulator.
% 0.75/1.52  
% 0.75/1.52  ** KEPT: 5 (wt=9) [flip(1)] -(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) = apply(strong_fixed_point,fixed_pt)).
% 0.75/1.52  ---------------- PROOF FOUND ----------------
% 0.75/1.52  % SZS status Unsatisfiable
% 0.75/1.52  
% 0.75/1.52  
% 0.75/1.52  After processing input:
% 0.75/1.52  
% 0.75/1.52  Usable:
% 0.75/1.52  end_of_list.
% 0.75/1.52  
% 0.75/1.52  Sos:
% 0.75/1.52  3 (wt=7) [] apply(apply(k,A),B) = A.
% 0.75/1.52  5 (wt=9) [flip(1)] -(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) = apply(strong_fixed_point,fixed_pt)).
% 0.75/1.52  1 (wt=15) [] apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)).
% 0.75/1.52  2 (wt=15) [flip(1)] apply(apply(A,B),apply(C,B)) = apply(apply(apply(s,A),C),B).
% 0.75/1.52  4 (wt=45) [flip(1)] apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) = strong_fixed_point.
% 0.75/1.52  end_of_list.
% 0.75/1.52  
% 0.75/1.52  Demodulators:
% 0.75/1.52  3 (wt=7) [] apply(apply(k,A),B) = A.
% 0.75/1.52  4 (wt=45) [flip(1)] apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) = strong_fixed_point.
% 0.75/1.52  end_of_list.
% 0.75/1.52  
% 0.75/1.52  Passive:
% 0.75/1.52  end_of_list.
% 0.75/1.52  
% 0.75/1.52  UNIT CONFLICT from 3330 and 5 at   0.32 seconds.
% 0.75/1.52  
% 0.75/1.52  ---------------- PROOF ----------------
% 0.75/1.52  % SZS output start Refutation
% See solution above
% 0.75/1.52  ------------ end of proof -------------
% 0.75/1.52  
% 0.75/1.52  
% 0.75/1.52  ------------- memory usage ------------
% 0.75/1.52  Memory dynamically allocated (tp_alloc): 8300.
% 0.75/1.52    type (bytes each)        gets      frees     in use      avail      bytes
% 0.75/1.52  sym_ent (  96)               56          0         56          0      5.2 K
% 0.75/1.52  term (  16)              245072     135932     109140         98   2120.5 K
% 0.75/1.52  gen_ptr (   8)           571649      19952     551697         55   4310.6 K
% 0.75/1.52  context ( 808)           230998     230996          2          4      4.7 K
% 0.75/1.52  trail (  12)               6786       6786          0          4      0.0 K
% 0.75/1.52  bt_node (  68)            84833      84826          7         40      3.1 K
% 0.75/1.52  ac_position (285432)          0          0          0          0      0.0 K
% 0.75/1.52  ac_match_pos (14044)          0          0          0          0      0.0 K
% 0.75/1.52  ac_match_free_vars_pos (4020)
% 0.75/1.52                                0          0          0          0      0.0 K
% 0.75/1.52  discrim (  12)            69612       4944      64668         89    758.9 K
% 0.75/1.52  flat (  40)              764528     764528          0        133      5.2 K
% 0.75/1.52  discrim_pos (  12)         3480       3480          0          1      0.0 K
% 0.75/1.52  fpa_head (  12)            2635          0       2635          0     30.9 K
% 0.75/1.52  fpa_tree (  28)           30710      30710          0         67      1.8 K
% 0.75/1.52  fpa_pos (  36)             3984       3984          0          1      0.0 K
% 0.75/1.52  literal (  12)            11552       8222       3330          1     39.0 K
% 0.75/1.52  clause (  24)             11552       8222       3330          1     78.1 K
% 0.75/1.52  list (  12)                 713        656         57          2      0.7 K
% 0.75/1.52  list_pos (  20)           11132       1078      10054          4    196.4 K
% 0.75/1.52  pair_index (   40)              2          0          2          0      0.1 K
% 0.75/1.52  
% 0.75/1.52  -------------- statistics -------------
% 0.75/1.52  Clauses input                  4
% 0.75/1.52    Usable input                   0
% 0.75/1.52    Sos input                      4
% 0.75/1.52    Demodulators input             0
% 0.75/1.52    Passive input                  0
% 0.75/1.52  
% 0.75/1.52  Processed BS (before search)   6
% 0.75/1.52  Forward subsumed BS            1
% 0.75/1.52  Kept BS                        5
% 0.75/1.52  New demodulators BS            2
% 0.75/1.52  Back demodulated BS            0
% 0.75/1.52  
% 0.75/1.52  Clauses or pairs given      3335
% 0.75/1.52  Clauses generated           5943
% 0.75/1.52  Forward subsumed            2618
% 0.75/1.52  Deleted by weight              0
% 0.75/1.52  Deleted by variable count      0
% 0.75/1.52  Kept                        3325
% 0.75/1.52  New demodulators             652
% 0.75/1.52  Back demodulated             241
% 0.75/1.52  Ordered paramod prunes         0
% 0.75/1.52  Basic paramod prunes       23560
% 0.75/1.52  Prime paramod prunes           8
% 0.75/1.52  Semantic prunes                0
% 0.75/1.52  
% 0.75/1.52  Rewrite attmepts          145962
% 0.75/1.52  Rewrites                    1712
% 0.75/1.52  
% 0.75/1.52  FPA overloads                  0
% 0.75/1.52  FPA underloads                 0
% 0.75/1.52  
% 0.75/1.52  Usable size                    0
% 0.75/1.52  Sos size                    3088
% 0.75/1.52  Demodulators size            549
% 0.75/1.52  Passive size                   0
% 0.75/1.52  Disabled size                241
% 0.75/1.52  
% 0.75/1.52  Proofs found                   1
% 0.75/1.52  
% 0.75/1.52  ----------- times (seconds) ----------- Tue May 31 11:51:12 2022
% 0.75/1.52  
% 0.75/1.52  user CPU time             0.32   (0 hr, 0 min, 0 sec)
% 0.75/1.52  system CPU time           0.10   (0 hr, 0 min, 0 sec)
% 0.75/1.52  wall-clock time           1      (0 hr, 0 min, 1 sec)
% 0.75/1.52  input time                0.00
% 0.75/1.52  paramodulation time       0.03
% 0.75/1.52  demodulation time         0.04
% 0.75/1.52  orient time               0.02
% 0.75/1.52  weigh time                0.01
% 0.75/1.52  forward subsume time      0.04
% 0.75/1.52  back demod find time      0.04
% 0.75/1.52  conflict time             0.02
% 0.75/1.52  LRPO time                 0.01
% 0.75/1.52  store clause time         0.08
% 0.75/1.52  disable clause time       0.01
% 0.75/1.52  prime paramod time        0.01
% 0.75/1.52  semantics time            0.00
% 0.75/1.52  
% 0.75/1.52  EQP interrupted
%------------------------------------------------------------------------------